scaling surface and subsurface flow processes in ... · on model resolution; and (iii) apply the...

SCALING SURFACE AND SUBSURFACE FLOW

PROCESSES IN HYDROLOGIC MODELS

A Dissertation Presented

By

Yuanhao Zhao

to

The Department of Civil and Environmental Engineering

in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

in the field of

Civil Engineering

Northeastern University

Boston, Massachusetts

May, 2019

ii

ABSTRACT

Hydrologic models have improved significantly over the past 50 years, transforming from

empirically-based and spatially-lumped to physically-based and distributed. In light of

these advances, new challenges such as scaling have emerged. Although challenges related

to scaling in hydrology have been investigated for decades, they still persists throughout

the measurement and modeling communities. This dissertation investigates hydraulic

scaling in hydrologic models with three specific objectives: (i) quantify how simulated

flowpath and runoff response timing characteristics varying with spatial model resolution;

(ii) develop an approach for estimating scale-dependent routing process parameters based

on model resolution; and (iii) apply the scaling approach in a multi-scale model calibration

application.

To overcome scaling effects on simulated streamflow dynamics, an upscaling

framework is developed to minimize the surface and subsurface travel time differences

between conceptual model representations and distributed topographic-based methods.

Surface roughness and hydraulic conductivity are modified to increase and/or decrease the

surface and subsurface flow velocities and associated travel times. Results show that the

scaling approach leads to streamflow responses from coarse model resolutions that are

consistent with responses from fine model resolutions. The scaling method is used in a

model calibration application. Surface and subsurface routing parameters are upscaled to a

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coarse model resolution and calibrated using runoff derived from USGS streamflow

measurements. The calibrated parameters are then downscaled to a fine model resolution

and the resulting fine scale model performance are verified.

The scaling approach accounts for changes in flowpath processes and adjusts model

parameters such that the magnitude and timing of hydrologic responses from coarse model

resolutions are consistent with fine scale models. An application of this scaling approach

is in using coarser scale models for calibration and uncertainty analyses to decrease

computational demands. The study reveals non-linear relationships between model

resolution, topographic and surface/subsurface routing characteristics in the Ohio River

Basin. The scaling approach and findings provide insights for improving the representation

of flowpath processes in Earth System Models or other large-scale modeling applications.

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DEDICATION

To My Family,

especially my daughter Mia.

v

ACKNOWLEDGEMENTS

So many people I need to appreciate for their support on this long journey of my Ph.D.

study. I would like to express my deep gratitude to my advisor, Professor R. Edward

Beighley, for his patient guidance and useful critiques of this research work. I really

appreciate he gave me the opportunity to pursue my doctor degree. His mentorship was

essential for me to complete this research.

I would also like to thank my committee members for their thoughtful feedback and

valuable advice: Professor Auroop Ganguly, Professor Amy Mueller and Professor Aron

Stubbins. This dissertation cannot be finished without their suggestions.

I would also like to extend my thanks to my current and previous colleagues:

Dongmei Feng, Roozbeh Raoufi, Yeosang Yoon, and Cassandra Nickles. It was a great joy

to work with them and I thank to them for their help on my research.

Finally, I would like to acknowledge with gratitude, the support and love of my

family: my parents, Caihua Ju and Baoshun Zhao, you are my backbone and you always

have faith in me; my lovely and beautiful wife, Jun Gu, for your accompany on my Ph.D.

journey and many delightful moments.

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TABLE OF CONTENTS

ABSTRACT ....................................................................................................................... ii

DEDICATION.................................................................................................................. iv

ACKNOWLEDGEMENTS ............................................................................................. v

TABLE OF CONTENTS ................................................................................................ vi

LIST OF TABLES ............................................................................................................ x

LIST OF FIGURES ........................................................................................................ xii

1. INTRODUCTION..................................................................................................... 1

1.1. Background ....................................................................................................... 1

1.2. Research Questions ........................................................................................... 4

2. UPSCALING SURFACE RUNOFF PROCESSES IN LARGE SCALE

HYDROLOGIC MODELS: APPLICATION TO THE OHIO RIVER BASIN ........ 6

Abstract .......................................................................................................................... 6

2.1. Introduction ....................................................................................................... 7

2.2. Methods ............................................................................................................ 10

2.2.1. Study Site .................................................................................................. 10

2.2.2. Hydrologic Model ..................................................................................... 11

2.2.3. Scaling of Catchments and Streams .......................................................... 14

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2.2.4. Runoff Flowpaths and Travel Times ........................................................ 18

2.2.5. Scaling of Surface Roughness .................................................................. 21

2.3. Results and Discussion .................................................................................... 25

2.3.1. Beta Distribution for Travel Time ............................................................ 25

2.3.2. Travel Time CDF Matching Approach ..................................................... 26

2.3.3. Synthetic Runoff Experiment without Parameter Scaling ........................ 29

2.3.4. Synthetic Runoff Experiment with Parameter Scaling ............................. 31

2.3.5. Effect of Pixel Scale Drainage Pattern...................................................... 34

2.3.6. Refined Parameter Scaling ........................................................................ 37

2.4. Conclusions ...................................................................................................... 41

3. UPSCALING SURFACE RUNOFF ROUGHNESS USING SPATIALLY

DISTRIBUTED VELOCITIES IN THE TRAVEL TIME MATCHING (TTM)

METHOD ........................................................................................................................ 44

Abstract ........................................................................................................................ 44

3.1. Introduction ..................................................................................................... 45

3.2. Methodology .................................................................................................... 47

3.2.1. Study Site .................................................................................................. 47

3.2.2. Hillslope River Routing (HRR) Model ..................................................... 49

3.2.3. Simulated Travel Time and Velocity from Fine Scale Model .................. 49

3.2.4. Travel Time Matching .............................................................................. 55

3.3. Results & Discussion ....................................................................................... 57

3.3.1. Travel Time Grids ..................................................................................... 58

3.3.2. Simulated Stream Flow without TTM Method ......................................... 59

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3.3.3. Simulated Streamflow after TTM Method ............................................... 60

3.3.4. Uniform Factor.......................................................................................... 66

3.3.5. Scaled Surface Roughness ........................................................................ 70

3.4. Conclusion ....................................................................................................... 74

4. SCALING SURFACE AND SUBSURFACE ROUTING PROCESSES IN

HYDROLOGIC MODELS ............................................................................................ 76

Abstract ........................................................................................................................ 76

4.1. Introduction ..................................................................................................... 78

4.2. Methodology .................................................................................................... 80

4.2.1. Travel Time Matching Framework ........................................................... 82

4.2.2. Travel Time Distributions for Subsurface Runoff .................................... 82

4.2.3. Matching Travel Times by Adjusting Hydraulic Conductivity ................ 84

4.2.4. Runoff Generation .................................................................................... 86

4.2.5. Model Calibration ..................................................................................... 87

4.3. Results and Discussion .................................................................................... 88

4.3.1. Travel Time Matching for Subsurface Runoff.......................................... 88

4.3.2. Ohio River Basin Runoff .......................................................................... 92

4.3.3. TTM Method for both Surface and Subsurface Flow ............................... 94

4.3.4. Calibration Using USGS Streamflow ....................................................... 98

4.4. Conclusion ..................................................................................................... 105

5. SUMMARY AND FUTURE WORK .................................................................. 107

5.1. Summary ........................................................................................................ 107

5.2. Limitations ..................................................................................................... 110

ix

5.3. Future Work .................................................................................................. 112

REFERENCE ................................................................................................................ 115

APPENDIX .................................................................................................................... 135

A.1 USGS Gages in Ohio River Basin ..................................................................... 135

A.2 Sample Code ....................................................................................................... 139

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LIST OF TABLES

Table 2.1: Catchment and flowpath summary statistics for each model scale. ................ 16

Table 2.2: Mean surface roughness adjustment factor (ks,i) for each ∆X segment along the

hillslope for each model scale. .......................................................................................... 28

Table 2.3. Mean percent change in the time-to-peak (∆Tp) and peak discharge (∆Qp) from

all gauge locations for each model scale compared to the 1 km2 model scale for the initial

setup, after CDF scaling and after the combination of both CDF scaling and uniform

correction coefficient (λ); values in parentheses represent the range in percent changes

between the different gauge locations. .............................................................................. 33

Table 3. 1. Difference in peak discharge from the outlet of Ohio River Basin and NSE for

all model resolution during the calibration process. ......................................................... 69

Table 4. 1. Average Nash–Sutcliffe efficiency coefficient (NSE), root mean square error

(RMSE), and peak error (Ep) for six U.S. Geological Survey gauges from the different

model resolutions with and without application of Travel Time Matching (TTM). ······· 96

Table 4.2. Combinations of surface (λs) and subsurface (λh) uniform scale factors at

different model resolutions with the optimal Nash–Sutcliffe efficiency coefficient (NSE)

and root mean square error (RMSE). ................................................................................ 98

Table 4.3. Comparison of average root mean square error (RMSE) and model run time for

selected U.S. Geological Survey gauges for the different model resolutions. .................. 99

xi

Table 4.4. Root mean square error (RMSE) for five selected gauges at 320 km2 model

resolution and a comparison of the same gauges at 1 km2 with and without the same

calibrated parameters. ..................................................................................................... 103

Table A. 1. Detailed information about the 6 USGS gages in Ohio River Basin used in

TTM method. ······················································································ 135

Table A. 2. Information for 90 USGS gauges used in the generation of runoff map for Ohio

River Basin...................................................................................................................... 136

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LIST OF FIGURES

Figure 1.1 Hydrologic processes and characteristics at varied temporal and spatial scales.

Adapted from Bloschl and Sivapalan (1995) ...................................................................... 2

Figure 2.1: Ohio River Basin with selected USGS stream gauge locations and stream

networks based on three different threshold areas (AT = 100, 1,000 and 10,000 km2). ... 11

Figure 2.2: Landscape partitioning in the Hillslope River Routing model: (a) basin-wide

river network, (b) individual river reach and catchment unit, (c) catchment split into two

planes, (d) conceptual model for plane and channel routing showing potential length

discretization, and (e) plane similarity assumption in HRR (i.e., only one representative

plane segment simulated for each model unit with lateral runoff applied uniformly along

both sides; note only one side shown here). ..................................................................... 13

Figure 2.3: Comparison between the longest flowpaths and river networks at each model

scale: (a) one 10,000 km2 scale catchment with individual 3,200; 1,000; and 320 km2 scale

catchment located along its longest flowpaths; (b) 320 km2 catchment with 100; 32; and 10

km2 catchments within; and (c) 10 km2 catchment with 3.2 and 1 km2 catchments within.

Note, see shaded area in Figure 1 for reference to the entire the Ohio River Basin ......... 15

xiii

Figure 2.4: Mean longest flowpath (Lm) and plane lengths (Lp) for all model units for

different model scales, and comparison between threshold area (AT) and mean model unit

area (Am). .......................................................................................................................... 16

Figure 2.5: Travel time Cumulative Distributions Function (CDFs) based on all individual

90-m grid cell travel times within a given catchment, and the Beta distribution

approximated using the mean and standard deviation of grid cell travel times in four

difference catchments for models scales of: (a) 10; (b) 100; (c) 1,000; (d). 10,000 km2. 19

Figure 2.6: Comparison between travel time CDFs based on the Beta distribution

approximated from individual 90-m grid cell travel times, uniform plane assumption in

HRR and CDF matching results in four difference catchments for models scales of: (a) 10;

(b) 100; (c) 1,000; (d) 10,000 km2. ................................................................................... 25

Figure 2.7: Simulated hydrographs at the outlet of the Ohio basin for 9 model scales based

on synthetic runoff experiment (i.e., uniformly distributed runoff, 1 cm in 24 hours) using

identical roughness values for all model scales. ............................................................... 31

Figure 2.8: Simulated hydrographs at the outlet of the Ohio basin for 8 model scales using

the: dynamic travel time estimation method: (a) without and (b) with the uniform roughness

coefficient correction. ....................................................................................................... 34

Figure 2.9: Area accumulation (a,c,e) for three catchments (b,d,f) for a 10 km2 model scale;

two headwater catchments (a-d) and one interbasin (e-f). ................................................ 36

Figure 2.10: Mean area accumulation ratios (γ) for each model scales (AT). ................... 39

Figure 2.11: Comparison between Correction coefficient (λ) and the average plane length

(Lp) for different model scales. ......................................................................................... 40

xiv

Figure 3.1. Illustration of model unit partitioning for Hillslope River Routing model for

model resolution of 1000 km2: (a) river network with USGS gauges represented in

triangular shape; (b) selected model unit; (c) catchment plane separation; (d) conceptual

model for hillslope and channel routing; (e) hillslope routing similarity. ........................ 48

Figure 3.2. Example of the relationship between average hillslope velocity and the length

of the plane from the sample unit at reference model resolution for: (a) constant (8.66%)

and (b) varied (10.59%) hillslope scenarios. .................................................................... 52

Figure 3.3. Approximation of channel width based on accumulated drainage area in Ohio

River Basin derived from (Allen and Pavelsky, 2015) ..................................................... 54

Figure 3.4. A zoom-in view of the travel time for a selected area in the Ohio River Basin

for four model resolutions and the varied slope scenario. ................................................ 59

Figure 3.5. Simulated discharge based on the 2-year 24 hour NRCS type II rainfall

synthetic experiment on Ohio River Basin for 2 scenarios: (a) constant and (b) varied

hillslope and channel slope without application of ITTM method ................................... 60

Figure 3.6. Simulated discharge after modification of surface roughness using ITTM

method for (a) uniform and (b) varied slope conditions at different model resolutions, and

the average surface roughness modification factor of (c) uniform and (d) varied slope for

different model resolutions. .............................................................................................. 62

Figure 3.7. Comparison of landscape-based and model based-travel time from 1 model unit

at 1km2 .............................................................................................................................. 63

xv

Figure 3.8. (a). Selected catchment at 3,200 km2 model resolution and the model units from

1km2 lay under the catchment and (b) the hydrographs for the same outlet of the catchment

from 3,200 and 1 km2 with varied situations of modified surface roughness................... 65

Figure 3.9. Hydrographs with the application of uniform scale factor for (a). uniform and

(b). varied slope scenarios for different model resolutions. .............................................. 67

Figure 3.10 Mean surface roughness from all model units at different model resolutions

after applying the TTM method for (a) uniform and (b) varied slope scenarios. ............. 71

Figure 3.11. Relationships for ratio of flowpath lengths (Rp) with the final surface

roughness (N’) and ratios of surface runoff velocity (RV) and surface roughness (RN). ... 72

Figure 3.12. Distribution and density of surface roughness and model flowpath length at

different model resolutions after applying the TTM method for the uniform (a,c,e) and

varied (b,d,f) slope scenario. Color indicates the density of the surface roughness. ........ 73

Figure 4.1. The Ohio River Basin and landscape partitioning in the hillslope river routing

model. (a) A river network of 1000 km2 with six selected U.S. Geological Survey gauges.

(b) One model unit (catchment). (c) A catchment split by a channel. (d) A conceptual

illustration of hillslope and channel routing. .................................................................... 81

Figure 4.2. Hydrographs from the outlet of the Ohio River Basin with synthetic subsurface

runoff at 1000 km2 for (a) before and (b) after apply the TTM framework. ..................... 89

Figure 4.3. The mean modified hydraulic conductivity (Kh) along the hillslope for each

model resolution................................................................................................................ 90

Figure 4.4. (a) uniform scale factors, (b) mean model unit scaled hydraulic conductivity,

and (c) simulated discharges for all model resolutions. .................................................... 91

xvi

Figure 4.5. U.S. Geological Survey (USGS) tributary gauges and their contributing land

area (90) selected to derive runoff throughout the Ohio River Basin. .............................. 92

Figure 4.6. Separation of surface and subsurface flow for the Ohio River Basin using

recursive digital filter. ....................................................................................................... 93

Figure 4.7. Simulated flow at the outlet of the Ohio River Basin at various model

resolutions using a U.S. Geological Survey Ohio River Basin runoff (a and c) without and

(b and d) with the travel time matching method. .............................................................. 95

Figure 4.8. Impacts of surface (λs) and subsurface (λh) uniform scale factors on peak

discharge error, Nash–Sutcliffe efficiency coefficient (NSE), and root mean square error

(RMSE) for the 3200 km2 model resolution. .................................................................... 97

Figure 4.9. Percent change in root mean square error (RMSE) and model run time from the

different model resolutions. .............................................................................................. 99

Figure 4.10 Calibration of the hillslope river routing model at 320 km2 for all five selected

U.S. Geological Survey gauges based on average root mean square error (RMSE) for three

parameters: (a) a uniform parameter for hydraulic conductivity (fh), (b) a uniform

parameter for surface roughness (fs), and (c) a uniform parameter for channel roughness

(fn). .................................................................................................................................. 101

Figure 4.11. (a) Four-dimensional and (b–d) three-dimensional plots of the root mean

square error from various ranges of three parameters during the HRR calibration process

after application of the travel time matching method. .................................................... 104

xvii

Figure 4.12. Estimated (a) surface roughness (N**) and (b) hydraulic conductivity (K**)

based on the TTM framework and calibration to USGS streamflow for different model

resolutions. ...................................................................................................................... 105

1

1. INTRODUCTION

1.1. Background

With advances in computational capability, hydrologic models have improved significantly

in the past 50 years (Bierkens, 2015; Farmer and Vogel, 2016; Yamazaki and Trigg, 2016),

transforming from lump and empirical solutions to physical based distributed models

(Sivapalan, 2018). Hydrologic modeling applications have also expanded in terms of

spatial extent from induvial catchments and basins to continental and global scale and

integrated with other disciplines such as atmospheric and oceanographic modeling. New

challenges are emerging in this process (Fatichi et al., 2016; Tan et al., 2015). One example

is “scaling” which represents how heterogeneous physical properties and processes

describing the hydrologic cycle vary based on the spatial resolution and/or temporal period

taken into account (Bergstrom and Graham, 1998; Beven, 1995; Bloschl and Sivapalan,

1995; Kitanidis, 2015; Merz et al., 2009; Skoien et al., 2003; Wood et al., 1990). Figure

1.1 shows numerous hydrologic processes across different temporal and spatial scales. For

example, surface and subsurface stormflow are shown to operate over similar length scales

ranging from roughly 10 m to 1 km, while channel flow length scales range from 1’s to

1000’s km. These processes also operate at different time scales ranging from min’s to

day’s. However, in many hydrologic models, the spatial and temporal model resolutions,

for which these processes are conceptualized, are not sufficient to differentiate these

dominant process components. This results in processes (e.g., overland flow) not being

included or forced to operate at much longer length scales (e.g., overland flow length in

2

model accounting for a combination of overland flow channel flow). In the case of

overland flow, surface roughness in the model would need to be altered (i.e., scaled) to

account for the aggregate flow processes.

Figure 1.1 Hydrologic processes and characteristics at varied temporal and spatial scales.

Adapted from Bloschl and Sivapalan (1995)

Common techniques to deal with scaling are downscaling and upscaling. The

purpose of downscaling (i.e., disaggregating) is to transfer the information from coarser to

finer scale. Upscaling (i.e., aggregating), in contrast, is to transfer the information from

finer to coarser scale. Numerous studies have leveraged advanced computational power

3

and downscaling techniques to parameterize and force hydrologic models operating at fine

scales (e.g., 1’s to 10’s meters). However, in applications using ensembles (i.e., multi:

models, parameters, forcings, initial conditions), including uncertainty, or requiring

calibration, it is debatable whether current computational resources are sufficient or will

be in the near future. Upscaling is an effective technique to increase computational

efficiency, which is especially useful for simulating large spatial scales: continental to

global (Kitanidis, 2015; Pau et al., 2016; Rakovec et al., 2016).

Progress has been made to understand and overcome scaling challenges in

hydrologic modeling. Many studies have focused on downscaling forcing data such as

precipitation or evapotranspiration (Charles et al., 2004; Stoll et al., 2011; Wang et al.,

2013). Advancements in satellite remote sensing have provided many new forcing data

sources for downscaling applications. For example, numerous studies present methods to

downscale Tropical Rainfall Measurement Mission (TRMM) precipitation for use in

hydrologic models (Bieniek et al., 2016; Chen et al., 2015). Land cover and soil properties,

which are vital in hydrologic modeling, can also be measured using remote sensing. Some

examples are the soil moisture from Soil Moisture Active/Passive Mission (SMAP) and

land cover characteristics from Moderate Resolution Imaging Spectroradiometer Mission

(MODIS) (De Jeu et al., 2014; Friedl et al., 2002; Liu et al., 2011; Pan et al., 2016).

However, few studies investigate the effect of model resolution (e.g., grid size) on scaling,

or overcome the scaling effects based on runoff generation or flowpath processes.

In general, model resolution (i.e., spatial scale) affects simulated hydrologic

response because the resolution imparts unique flowpath characteristics. For example,

Molnar and Julien (2000) show how calibrated parameters related to the surface runoff

4

vary with model grid cell size to match the peak discharge from the observed flow. They

found that the model requires overland and channel roughness to increase average 50% as

grid-cell size increases 100%. Casey et al. (2015) found that spatial model resolution

affects peak flow and time to peak significantly and propose guidelines for choosing

optimal subdivision spatial scale in the rainfall-runoff modeling. They suggested to

subdivide a catchment if mean subarea curve numbers differ by more than five (e.g.,

subareas with mean CN’s 65 and 71 should be subdivided). However, no methods have

been proposed to overcome spatial scaling when parameterizing semi-distributed

hydrologic models (i.e., sub-catchments or hydrologic response units used to define

computational units). This dissertation addresses that gap and provides a framework for

scaling surface and subsurface routing process model parameters applicable to any spatial

model resolution such that simulated hydrologic responses (i.e., streamflow) are scale

independent (i.e., consistent responses regardless of model scale). Moreover, the

dissertation will answer the following research questions.

1.2. Research Questions

The three primary Dissertation research questions are listed below:

1) How do simulated flowpath characteristics and runoff response timings change with

spatial model resolution?

2) Can representative travel time characteristics be used to estimate scale-dependent

process parameters in semi-distributed hydrologic models?

3) Can scaling be used to transfer calibrated model parameters across model resolutions?

5

Questions 1 and 2 are answered in Chapters 2 and 3. Question 3 is answered in

Chapter 4. Chapter 5 summarizes the answers to all questions and provides

recommendations for future research. Chapters 2-4 are adapted from independent journal

manuscripts.

6

2. UPSCALING SURFACE RUNOFF PROCESSES IN

LARGE SCALE HYDROLOGIC MODELS:

APPLICATION TO THE OHIO RIVER BASIN

Abstract

The objective of this research is to upscale surface runoff routing processes in larger scale

hydrologic models while maintaining event hydrograph peak discharge and timing

characteristics. A scaling method is developed and applied in the Ohio River Basin using

a synthetic 24-hr runoff experiment. The method combines statistical and physically-based

techniques. Cumulative Probability Distributions (CDFs) for surface flowpath travel times

based on 90-m topographic data and conceptualized model units representing individual

catchments in the Hillslope River Routing (HRR) model are equated by adjusting surface

roughness along HRR hillslopes. The CDF travel time for individual catchments based on

90-m topographic data are approximated using the beta distribution to facilitate

applications for large watersheds. Nine model scales are considered: 1, 3.2, 10, 32, 100,

320, 1000, 3200 and 10000 km2, where model scale represents the threshold area used to

define the underlying river network and catchment boundaries. In this study, the reference

model scale is 1 km2. Simulated hydrographs at the outlet of the Ohio River Basin for the

eight coarser model scales have peak discharge and time-to-peak discharge values that are

nearly identical to the reference scale model. To match hydrograph characteristics from

model scales ranging four orders of magnitude, surface roughness values along the

hillslope flowpaths are adjusted by, on average, -85% to +94%, where the positive values

are for the 3.2 km2 scale and the largest reductions are for the 10,000 km2 scale.

7

2.1. Introduction

Scaling is the transfer of information across space and time scales (Bloschl and Sivapalan,

1995). Although challenges related to scaling in hydrology have been investigated for

decades (Klemes, 1983; Sivapalan et al., 1987), scaling issues still persist throughout the

measurement and modeling communities (Wood et al., 2011). In general, more studies

have focused on space scale (Atkinson and Tate, 2000) as compared to temporal scale

(Koutsoyiannis, 2005), with even fewer investigating the coupled interactions of both space

and time scales (Ogden and Julien, 1993).

Scale can be categorized as: observation, process or model. Examples of

observation scale include point measurements of rainfall over hours or days, cross-

sectional measurements of streamflow (instantaneous or daily average), and topography in

the form of digital elevation models (DEMs) with different cell sizes (e.g., 30 or 90 m)

(Molnar and Julien, 2000). Process scale refers to the physical length and time over which

an individual hydrological process occurs. For example, overland flow travels meters to

kilometers in seconds to hours and is subjected to surface roughness features ranging from

millimeters to centimeters. Ideally, the process and observation scales should be similar

(Bloschl and Sivapalan, 1995). Model scale is the length and time steps used in a

hydrological model to discretize relevant processes, obtain input parameters/forcings, and

perform numerical solutions. Model scale can be somewhat arbitrary with the modeler

often determining the scale based on the balance between computational demands and

available input data. General techniques to deal with the scale challenges are upscaling and

downscaling (Sivapalan et al., 2003), which provide methods for transferring information

from one scale to a larger or smaller scale, respectively (Gupta et al., 2012).

8

Bloschl and Sivapalan (1995) proposed that the challenge in scaling is the

heterogeneity and variability of nature catchments over space and time. Numerous studies

have investigated strategies to overcome the scaling challenge. Schaake et al. (1996)

developed a lumped physically-based model using combined physical and statistical

methods to deal with spatial and temporal scales. Bachmair and Weiler (2014) investigated

interactions of runoff generation processes at different space scales and found that

hillslopes should not be considered as homogeneous units. Kim and Ivanov (2015)

developed a dynamic downscaling framework to apply climate forcings at the regional

scale for estimating surface and subsurface flow in ungauged basins. Examples of key

studies investigating the effect of grid cell size or spatial resolution include: (Horritt and

Bates, 2001; Molnar and Julien, 2000; Vazquez et al., 2002). The findings from these

studies suggest that the spatial resolution producing optimal performance (e.g., similarity

between simulated and observed streamflow hydrographs) varies for different models. For

example, Horritt and Bates (2001) found that the LISFLOOD-FP model (De Roo et al.,

2000) reaches the optimal performance at a resolution of 100m. (Molnar and Julien, 2000)

used the CASC2D model (Julien and Saghafian, 1991) and found that the model requires

overland and channel roughness to increase as grid-cell size increasing. Zhang and

Montgomery (1994) applied TOPMODEL (Beven et al., 1984) and proposed an optimal

grid size of 10m. McGlynn et al. (2004) investigated the role of catchment area and found

that event response lag times increased as catchment area increased. Sulis et al. (2011)

investigated the effects of different model resolutions and found that the discharge volume

increased as the grid cell size increased.

9

Rainfall is also an important input that varies significantly with different spatial and

temporal scales (Bell and Moore, 2000; Vieux and Imgarten, 2012). Depending on the

model scale, upscaling or downscaling methods are required to modify the rainfall data

(Ogden and Julien, 1993). Upscaling, which is the simpler of the two, tends to reduce

rainfall intensities, which can impact process models such as infiltration where runoff is

generated based on the difference between rainfall and infiltration rates (Jana and Mohanty,

2012). Although downscaling can produce local, higher intensities, there are many

challenges associated with building the spatial/temporal structure of rainfall events at finer

resolutions (Maraun et al., 2010).

Scaling of soil properties, such as soil moisture (Guo et al., 2015; Ojha and

Govindaraju, 2015) and hydraulic conductivity (Ojha et al., 2014), has received a lot of

focus given its importance in surface and subsurface runoff generation and

evapotranspiration (Rojas et al., 2008). Heuvelink and Pebesma (1999) presented a review

of methods for dealing with scaling and uncertainty in soil properties. Western and Bloschl

(1999) examined the change of soil moisture with varying measurement scale using

geostatistical techniques to define soil moisture patterns. Doubkova et al. (2014)

investigated spatial scale effects on soil moisture remote sensing products and found that a

spatial scale of 2 km lead to minimized noise and errors in the surface soil moisture

measurements. In general, statistical techniques have been widely used to deal with scaling:

temporal (Robinson and Sivapalan, 1997) and spatial (Skoien et al., 2003).

Although it is rational to assume that parameters may need to be change when

changing model scale (Bergstrom and Graham, 1998), the question is how to transfer the

information between scales, or can ‘effective’ parameters at small scales can be used at

10

large scales (Wood, 1994). For example, Bloschl (2001) supports identifying dominant

processes at a given scale and developing models to focus on those processes. In this study,

we focus on surface runoff, which we consider the dominant process in event streamflow

from the Ohio River Basin. We present a method that combines statistical techniques and

physically-based hydrological modeling. The method uses the information from hydrologic

flowpaths and surface runoff travel time distributions to modify surface roughness along

simulated hillslopes. Our approach captures information from the DEM scale and transfers

that information to coarser model scales while ensuring the simulated event runoff

hydrographs (peak and timing) match the response of finer model scales. One advantage

of this approach is a reduction in computational time with limited loss of hydrograph

accuracy.

2.2. Methods

2.2.1. Study Site

The Ohio River is the largest tributary of the Mississippi River based on discharge. The

Ohio River Basin drains an area of roughly 500,000 km2 (Figure 2.1) spanning fractions

of 14 states and integrates a population of nearly 25 million people. The main river flow

length is approximate 1,580 km (White et al., 2005). The mean annual discharge from the

Ohio River Basin is 7,900 m3/s, based on data from USGS gauge No. 03611500 for the

period 1929 - 2014. The land cover within the Ohio River Basin (ORB) is distributed

between developed, undeveloped (i.e., forests and grasses) and agriculture lands: 2, 36 and

62%, based on NASA’s moderate resolution imaging spectroradiometer (MODIS) type 1

11

land cover product: MCD12C1 (Friedl et al., 2002). In this study, the surface topography

is based on the DEM developed from NASA’s Shuttle Radar Topography Mission (SRTM)

(Farr et al., 2007), with a horizontal resolution of 3 arc-sec (∼90 m).

Figure 2.1: Ohio River Basin with selected USGS stream gauge locations and stream

networks based on three different threshold areas (AT = 100, 1,000 and 10,000 km2).

2.2.2. Hydrologic Model

For this study, we used the Hillslope River Routing (HRR) model (Beighley et al., 2009;

Beighley et al., 2011). The HRR model simulates: vertical water and energy balance to

estimate surface and subsurface runoff; lateral surface and subsurface runoff

12

transformation using kinematic waves; channel and floodplain discharge using diffusion

waves; and most recently, lake/reservoir storage and discharge routing (Beighley et al.,

2015; Yoon and Beighley, 2015). The HRR model operates on individual catchments using

an open book concept (Figure 2.2) to provide lateral surface and subsurface runoff to each

river reach and performs channel routing throughout the entire river network. Thus, the

key computational units are catchments and river reaches. Figure 2.2 shows how the

landscape is discretized in the HRR model. For a given catchment, the two planes are

separated into ∆Xp units from the drainage divide to the channel reach (i.e., hillslope

flowpath), and the river reach (i.e., stream segment) is separated into ∆Xc units from the

upstream to downstream ends (river flowpath). To reduce computational demands, HRR

typically assumes hillslope responses within a catchment are similar and only one

representative hillslope is simulated with the results applied to both sides of all ∆Xc

segment.

13

Figure 2.2: Landscape partitioning in the Hillslope River Routing model: (a) basin-wide river network, (b) individual river reach and

catchment unit, (c) catchment split into two planes, (d) conceptual model for plane and channel routing showing potential length

discretization, and (e) plane similarity assumption in HRR (i.e., only one representative plane segment simulated for each model unit

with lateral runoff applied uniformly along both sides; note only one side shown here).

14

2.2.3. Scaling of Catchments and Streams

In this study, the model scale is defined based on the source area (i.e., threshold area) used

to define the start of a stream reach and the resulting drainage network. For instance, a

model scale of 100 km2 implies that all streams drain an area of at least 100 km2. Figure

2.1 shows the Ohio River Basin with three different scales: 100; 1,000; and 10,000 km2.

Nine scales (incrementing by 0.5 log units) were investigated in this study: 1; 3.2; 10; 32;

100; 320; 1,000; 3,200 and 10,000 km2. Catchment (i.e., model unit) boundaries, land

areas and channel lengths were determined using python and ArcGIS. To define the model

unit dimensions (i.e., channel and hillslope/plane flowpath lengths), we use the channel

segment contained within the catchment. Currently, we assume each catchment is divided

equally, which means the left half plane (P1) is equal in area to the right half plane (P2),

see Figure 2.2. Note that, for headwater catchments, we extent the channel upstream along

its longest flowpath (Lm) until the channel’s drainage area is less than 1 km2. This

additional step is taken because the threshold area concept can provide very short channel

reaches in headwater catchments. Figure 3 illustrates how the catchments and channels

vary with scale (i.e., different threshold areas), and Table 1 provides summary statistics for

the nine model scales in the Ohio River Basin. For each catchment, the channel length (Lm)

(i.e., longest flowpath) is measured using ArcGIS. Then, the catchment plane length (Lp)

is calculated as (A/2)/Lm. The cumulative channel and plane length for each scale are the

sum of the channel and plane lengths from all model units.

15

Figure 2.3: Comparison between the longest flowpaths and river networks at each model

scale: (a) one 10,000 km2 scale catchment with individual 3,200; 1,000; and 320 km2

scale catchment located along its longest flowpaths; (b) 320 km2 catchment with 100; 32;

and 10 km2 catchments within; and (c) 10 km2 catchment with 3.2 and 1 km2 catchments

within. Note, see shaded area in Figure 1 for reference to the entire the Ohio River Basin

16

Table 2.1: Catchment and flowpath summary statistics for each model scale.

Scale,

km2 Unit

Mean

catchment

area, km2

Mean

plane

length,

km

Mean

channel

length

,km

Total

plane

length,

km

Total

channel

length, km

Model

compute

time, sec

10,000 37 14,200 21.2 348 784 12,900 1.6

3,200 109 4,820 12.8 192 2,790 20,900 1.7

1,000 347 1,510 7.41 102 5,140 35,400 1.7

320 1,085 484 4.45 52.1 9,660 56,500 1.7

100 3,517 149 2.74 25.9 19,300 91,400 2.3

32 10,788 48.7 1.75 12.9 37,800 140,000 4.1

10 34,613 15.2 1.12 6.34 77,200 219,000 29

3.2 107,565 4.88 0.76 3.03 163,000 326,000 289

1 342,283 1.53 0.73 1.25 496,000 671,000 4510

Figure 2.4: Mean longest flowpath (Lm) and plane lengths (Lp) for all model units for

different model scales, and comparison between threshold area (AT) and mean model unit

area (Am).

17

Given our focus on scale, we clarify our definition of model scale as the threshold

area used to develop the river network. Figure 2.4 shows a linear relationship between

average catchment (i.e., model unit) drainage area and threshold area, where the average

model unit area is roughly 1.43 times the corresponding threshold area. If we consider the

median area the relationship (not shown) is 1.15. Although the agreement is not one-to-

one, we use threshold area to represent model scale in this paper.

As noted above, we only consider variations in surface flowpath processes

(overland and channel flow hydraulics) at different model scales. Future efforts will

combine flowpath with hydrologic processes (i.e., averaging heterogeneous soil properties

and spatially distributed rainfall). To illustrate the impacts of model scale on flowpath

processes, Figure 2.4 shows how the average and cumulative plane length (Lp) vary non-

linearly with model scale. As the model scale increases, the plane lengths within a given

model unit increases. However, as model scale increases the number of model units

decreases (Table 2.1) and the cumulative plane length integrated throughout the entire

Ohio River Basin decreases. Similar relationships exist for channel length (Table 2.1).

Figure 2.4 highlights two important points: (i) the decrease in cumulative length with

increasing model scale implies that the model captures less flowpath processes as model

scale increases; and (ii) the increase in hillslope (i.e., plane) length with increasing model

scale indicates that within a given model unit, channel flowpaths are replaces with hillslope

or overland flowpaths, which are much slower (Di Lazzaro and Volpi, 2011; Grimaldi et

al., 2010) Thus, although larger model scales have less cumulative flowpaths, the hillslope

flowpaths within a given unit are much longer which significantly attenuates runoff

response.

18

2.2.4. Runoff Flowpaths and Travel Times

Here, we focus on the effect of model scale on surface runoff timing. Two travel times are

considered: model-based (TM) and landscape-based (TL). Model-based travel time is

defined by the spatial arrangement and open book assumption of the model units and their

approximated channel and plane lengths (Figure 2.2) as discussed above and in Beighley

et al. (2009; 2014). In HRR, surface runoff is generated on the hillslope, travels along the

hillslope as overland flow to a channel reach and is routed downstream to the watershed

outlet. Thus, TM for a given location within a model unit depends on the assumed flowpath

processes. For a given land area represented by different model scales (Figure 2.3), there

is a difference in flowpath processes (i.e., more or less overland or channel flow lengths).

To illustrate these differences, we define the model-based travel time (TM,k) for a given

location within a model unit as:

��,� = ��,�� + ��,�� 2.1

where Lp,k and Lc,k are the plane and channel flow lengths from a given location k within a

model unit to the unit’s outlet location, and Vp and Vc are the plane and channel flow

velocities. For this analysis, we assume that Vp is 0.01 m/s and Vc is 1 m/s; a velocity ratio

of channel and hillslope is 100. Grimaldi et al. (2010) proposed that for the manning’s

method the mean lower hillslope velocity is 0.02 m/s and the mean channel velocity is 2

m/s, which has the same velocity ratio. Note that, these assumed velocities are only used

to investigate the impacts of model scale on potential surface runoff timing.

In the HRR model, kinematic and diffusion wave methodologies are used to

simulate surface and channel routing, respectively. For each half catchment, the HRR

19

model typically uses 10 segments along the hillslope flow length and 10 segments along

the channel to solve the routing equations, which means there are 100 sub-catchment units

in each half plane (Figure 2.2d). The model travel time for each sub-catchment unit (TM,k)

is calculated using Eq. 1. If Lp,k is the total length of the plane and Lc,k is the total length

of the channel in a model unit, Eq. 1 represents the maximum travel time within a given

model unit. Thus, each model unit is characterized by 100 travel times. Figure 2.5 shows

the cumulative distribution function (CDF) of travel times (TM,k) for individual model units

at different model scales.

Figure 2.5: Travel time Cumulative Distributions Function (CDFs) based on all

individual 90-m grid cell travel times within a given catchment, and the Beta distribution

approximated using the mean and standard deviation of grid cell travel times in four

difference catchments for models scales of: (a) 10; (b) 100; (c) 1,000; (d). 10,000 km2.

20

The landscape-based travel time (TL,k) is also determined using Eq. 2.1 except that

channel and hillslope flow lengths are obtained from gridded D8 flow directions derived

from the SRTM elevation data using ArcGIS. For TL,k, we use a threshold area of 1 km2 to

separate hillslope and channel pathways and assign their associated flow velocities. Thus,

there are two differences between the two travel times: 1) the assumed flowpath

arrangement, and 2) the number of locations for which travel time is determined. For

example, TM,k is based on HRR model unit dimensions (see Figure 2.2), while TL,k is based

on pixel-to-pixel flow lengths and a dense river network (channel flow for all pixels

draining ≥ 1 km2; overland flow for all pixels draining < 1 km2). For TL,k, we use travels

times from each 90 by 90 meter pixel within the model unit (e.g., 1000’s of pixel per unit)

compared to the 100 sub-units in TM,k. Figure 2.5a-d shows the CDF of travel times (TL,k)

for 2,600; 32,000; 220,000; and 3.2M pixels, respectively, within one model unit at

different model scales.

Here, we use frequency distributions (cumulative distribution function, CDF) of

travel time to characterize catchment runoff response. Thus, for each model scale we

determine CDFs for both TM,k and TL,k for all catchments throughout the river network.

Although the process of determining TL,k is straightforward, if the size of a catchment (i.e.,

many pixels within) or number of catchments is large, characterizing the TL,k travel time

CDF for each catchment is time consuming. Here, we assume that TL,k can be approximated

with the beta distribution (Vose, 2008) as:

� ~ ��(�, �) 2.2

21

where X is the TL,k, and α and β are the shape parameters of the beta distribution. The

Momentum Matching Estimation (MME) (Vose, 2000) method is used to estimate shape

factors: α and β. The expected value (mean, µ) of the beta distribution is:

� = �(�) = �� + � 2.3

where E(X) is the first momentum and the second moment (variance, σ2) is:

�� = ��(� − �)�� = ��(� + �)�(� + � + 1) 2.4

For each catchment at each scale, the mean and standard deviation for TL,k are determined

using python and ArcGIS, and the shape factors α and β are found by solving Eqs 2.3 and

2.4.

2.2.5. Scaling of Surface Roughness

As discussed above, as model scale increases, the assumed hillslope flow length increases,

which slows the runoff response (see Figure 2.5). In order to maintain response timing

characteristics of the finest scale model, we propose to adjust the surface roughness

parameter to speed up surface runoff travel time in the coarser scale models (i.e., model

scales > 1 km2) to match the landscape-based travel time of finest scale mode (1 km2). In

other words, we modify the plane velocity in the HRR model to adjust the CDF of TM,k to

match the CDF of TL,k.

As discussed before, in the HRR model, both planes are assumed to be identical

and one plane is discretized into ∆Xp segments (e.g., 10) along the assumed hillslope

pathway and ∆Xc segments (e.g., 10) along the channel providing ∆Xp times ∆Xc space

22

steps (e.g., 10x10 =100) for each unit. However, in the current version of the HRR model,

the hillslope flowpaths to the channel are also assumed to be identical (excess water, length,

slope and roughness), and only one of the kinematic wave routing solution is performed

for the model unit (i.e., for each ∆Xc step along the channel, hillslope response is identical

from both sides). Thus, we only consider the number of ∆Xp steps (i.e., 10) in our procedure

for matching travel time distributions, and we evaluate the CDF’s at ten probably values:

5%, 15%, 25%, 35%, 45%, 55%, 65%, 75%, 85%, and 95%. We assume that the 5% is

controlled by the flowpath from the midpoint of the bottom hillslope segment (i.e., just

before runoff discharges into the channel), and the 95% is controlled by the flowpath from

the midpoint of the upper most hillslope segment.

Additionally, because the main channel within a model unit of any scale is also a

channel pathway in the fine scale model, we maintain the channel travel times (i.e., velocity)

for all scales. For example, as model scale increases, hillslope length increases to account

for both hillslope and channel flowpaths on either side of the main channel, but every main

channel in the coarse scale model is also a channel in the fine scale model. In other words,

there are less main channels (less cumulative channel length) in the coarser models, but for

those channels that are included, their pathways are identical to the fine scale model (i.e.,

channel pathways in the coarser models does not represent multiple flowpath processes).

In contrast, the hillslope pathways in the coarser scale models represent a combination of

both channel and hillslope flowpath processes from the fine scale model. Therefore, we

only consider hillslope roughness variations in order to maintain surface response timing

at the watershed outlet.

23

Starting from the bottom segment of the hillslope for each catchment, the difference

between the model- and landscape-based travel time CDF is:

∆�(5%) = CDF�(5%) − $%&'(5%) 2.5

where $%&� and $%&' are CDF values at 5% for a given catchment for HRR and

landscape. Figure 2.6 shows the initial CDFs for both. Next, to match CDF values, an

adjusted plane velocity for segment i (i.e., i = 1 for segment 1 for CDF values at 5%) is

assumed to be:

(,)∗ = '∆+,∆+-. /∆0(1%) 2.6

where L∆X is the plane segment length which is equal to the model unit plane length (LP)

divided by the number of hillslope ∆X steps (i.e., 10), ∆�(5%) is the travel time difference

calculated from Eq. 2.5, and Vp is the assumed plan velocity (see above). With the adjusted

plane velocity for the segment, the velocity modification ratio, 23,) , for the segment is

determined:

23,) = 45,6∗4� 2.7

Note that, the velocity ratio is not directly used in the HRR model to increase or

decrease the flow velocity on the plane, because the plane velocity in HRR is determined

based on a kinematic wave solution and Manning’s equation, which varies along the

flowpath and with flow depth. Rather, we determine a surface roughness adjustment factor:

78,) = 1/23,) 2.8

to increase/decrease roughness in the relationship between flow depth and discharge (y =

a qb) in the kinematic wave solution, where a = (ki*/1.49/Sp

0.5)b and b = 3/5 based on the

wide-rectangular channel assumption for Manning’s equation, Sp is the plane slope, and ki*

24

is the adjusted surface roughness factor for the first bottom segment, determined by N x

ks,i, where N is surface roughness value used in the fine scale model based on land cover

conditions. For each segment, the CDFM* is recalculated, and the procedure for determining

78,) is repeated for next uphill segment using Eqs. 5-8. For each segment, the representative

CDF probability (Pi) is determined by:

:) = 5 + 10 ∗ �< − 1� 2.9

Note that, the 78,) values above are the initial values for the 10 segments. To find the

optimum combination of the 78,) values, the procedure is repeated until the minimum

average difference of 78,) values (�=) is determined:

�= = ∑ 78,)?@A − ∑ 78,)? AB)C A AB)C A 10 2.10

where m is the iteration number and m > 1. Once, the minimum difference is determined,

considered the corresponding 78,) values are used as the optimal combination.

25

Figure 2.6: Comparison between travel time CDFs based on the Beta distribution

approximated from individual 90-m grid cell travel times, uniform plane assumption in

HRR and CDF matching results in four difference catchments for models scales of: (a)

10; (b) 100; (c) 1,000; (d) 10,000 km2.

2.3. Results and Discussion

2.3.1. Beta Distribution for Travel Time

Central to the travel time matching approach is our approximation of the landscape-based

travel time. As noted above, working with individual pixel-based distributions is a

significant challenge for large basins, and we assume the beta distribution to fit the data.

Figure 2.5 shows that the cumulative distribution function (CDF) of TL,k for sample

catchments from four model scales shown in Figure 2.3 (10; 100; 1000; 10,000 km2) based

on the individual pixel values and the approximated beta distribution. The figure shows

26

that the beta distribution matches the travel time distribution well. Based on the

Kolmogorov-Smirnov (KS) and Pearson correlation goodness-of-fit tests to tests and a 5%

level of significance, the CDFL’s for all sample catchments are shown to fit the beta

distributed.

2.3.2. Travel Time CDF Matching Approach

To illustrate our CDF matching approach, Figure 2.6 shows the initial (CFDM) and

adjusted (CFDM*) model-based travel time distributions compared to the landscape-based

(CDFL) distribution for 4 different model scales: 10; 100; 1000; and 10,000 km2. Two

points are highlighted. One, the initial CDFM is shifted to the right for model scales greater

than 10 km2 because of the increased hillslope flowpath length. At 10 km2, the model and

landscape-based CFDs are similar suggesting that for this particular model unit the “open

book” approximation for the resulting channel and hillslope flow lengths are consistent

with the fine scale model (1 km2). Two, Figure 2.6 shows that CDF matching procedure

works well, with essentially no difference between CDFM* and CDFL. Note that, here we

accomplish the task of capturing the detailed surface runoff response timing characteristics

(i.e., 1 km2) for coarser model scales. Table 2.2 lists the average ks,i of all model units

within each model scale. These results clearly show how the scaling works. For scales ≥

1,000 km2, all roughness values must be decreased (i.e., all ks,i values are less than 1.0) to

speed up runoff response. For scales 3.2 to 320 km2, a combination of increased and

decreased roughness is used to match travel times. For 3.2 km2, only 1 of the 10 segments

had a roughness value less than one. For the most part, roughness was increased to slow

the runoff response for 3.2 km2. In the above, results are based on assumed constant

27

channel and overland flow velocities. Next, we evaluate simulated hydrographs at the

outlet of the Ohio River Basin using the HRR model where channel and overland flow

velocities are varied with flow depth.

28

Table 2.2: Mean surface roughness adjustment factor (ks,i) for each ∆X segment along the hillslope for each model scale.

Scale,

Km2 1 2 3 4 5 6 7 8 9 10

10,000 0.0336 0.0987 0.0989 0.1123 0.1319 0.1202 0.1167 0.1416 0.1952 0.4666

3,200 0.0245 0.1112 0.1515 0.1613 0.1664 0.1738 0.1863 0.2197 0.2763 0.4423

1,000 0.0244 0.1727 0.2559 0.2676 0.2724 0.2820 0.2959 0.3411 0.4252 0.7049

320 0.0180 0.2673 0.3825 0.3876 0.3902 0.4065 0.4439 0.5195 0.6679 1.1473

100 0.0199 0.4057 0.5431 0.5481 0.5722 0.6213 0.7022 0.8299 1.0589 1.6472

32 0.0335 0.5925 0.7192 0.7690 0.8402 0.9369 1.0700 1.2626 1.5941 2.4427

10 0.0941 0.8092 0.9686 1.0864 1.2196 1.3800 1.5843 1.8664 2.3297 3.4441

3.2 0.1962 0.9986 1.2416 1.4407 1.6494 1.8836 2.1610 2.5181 3.0598 4.2296

29

Although our focus is on scaling, Table 2.1 lists the computational time required

to simulate each model scale. Here, we used a Dell Workstation with 2 CPUs each having

6 cores and hyper-threading providing a total to 24 compute cores. As the model scale

decreased, the number of compute cores used for simulation increased. For instance, the

simulation of 10,000 km2 scale used 4 compute cores, while 22 cores were utilized for the

100 km2 scale and finer. Still, the results show a large reduction in computational time for

the 32 km2 and larger scales; each taking less than 5 seconds. For the reference scale (1

km2), the computational time is 1.3 hours. Being able to represent the reference scale

flowpath characteristics and timing using even 10 or 32 km2 scale provides 2 to 3 orders

of magnitude decrease in computational time.

2.3.3. Synthetic Runoff Experiment without Parameter Scaling

To evaluate and compare simulated hydrographs, a synthetic runoff experiment was

performed (1 cm of effective surface runoff uniformly distributed over 24 hours).

Although the models were run for 30 days, we focus on the first 10 days to illustrate the

effect of model scale. Hydrographs from the different scales were exported from the model

at six USGS streamflow gauge locations (Fig. 2.1). Figure 7 shows hydrographs of the

outlet gauge for all 9 model scales without any scaling of roughness. As model scale

increases, peak flow magnitude decreases and time to peak increases. For example, the

peak and time to peak are 34,900 m3/s and 49 hours, respectively, for the 1 km2 model scale

and 21,700 m3/s and 61 hours for the 100 km2 model, which represents a decrease in Qp of

38% and an increase in Tp of 25%. For the 100 km2 model, as the drainage area decreases

from the outlet gauge to most upstream gauge (Fig. 2.1), the change in peak discharge

30

increases from 38% to 49% with a mean of 43% while the difference in Tp remains

relatively consistent with a mean of 21%. These results are consistent for all model scales.

Table 3 list the mean change of Tp and Qp as well as the range (max – min) from all gauge

locations.

The large change watershed response is because channel and hillslope flowpaths

are combined into longer hillslope flowpaths as model scale increases (i.e., hillslope flow

length increases with scale). For example, the 1 km2 scale model has a mean hillslope

length of 0.7 km compared to 2.7 km for the 100 km2 scale model. In general, the 2.7 km

hillslope in the 100 km2 scale model represents the 0.7 km hillslope plus 2 km of channel

flow length from the 1 km2 scale model. With our assumption of the plane velocity (0.01

m/s) and channel velocity (1 m/s), it takes much longer for the water to travel the 2.7 km

at the 100 km2 scale (3.1 days to travel 2.7 km at 0.01 m/s) as compared to the 1 km2 scale

(0.8 days to travel 0.7 km at 0.01 m/s and 2.0 km at 1 m/s). Although these results were

expected, understanding how flowpath processes are altered with increasing model scale

provides a basis for adjusting effective overland flow velocity (i.e., surface roughness) to

ensure flowpath response timing remains constant with scale.

31

Figure 2.7: Simulated hydrographs at the outlet of the Ohio basin for 9 model scales

based on synthetic runoff experiment (i.e., uniformly distributed runoff, 1 cm in 24

hours) using identical roughness values for all model scales.

2.3.4. Synthetic Runoff Experiment with Parameter Scaling

In this experiment, we use the same runoff event (i.e., 1 cm of effective rainfall) described

above with surface roughness scale factors determined to match travel time CDFs. Table

2 presents the mean surface roughness factor for the 10 hillslope flow segments at the

different model scales. It shows that the first segment (downhill-most) has the lowest ks,i

value relative to all 10 segments, which means the flow velocity is increased the most, and

the last (uphill-most) segment has the highest value. Starting with the scale 320 km2, ks,i

for one segment (i.e., uphill-most) is greater than 1, with the number of segments having

32

ks,i greater than 1 increasing as the scale is further reduced. This makes sense because we

match the response travel time CDF for the catchment. The response from the bottom

segments is speeded up to capture the quick response times and the upper segments are

slowed to capture the maximum travel time. Excluding the bottom segment, the mean ks,i

value increases as scale decreases in all cases. For the largest three scales, the mean ks,i

values for bottom segment begin to increase with scale, which is likely due to the overall

length of the segments getting large. For example, the mean segment length for 1,000 and

10,000 km2 scales are 2.1 and 1.3 km, respectively.

Figure 2.8a shows the hydrographs for all nine model scales at the outlet of the

Ohio River Basin based on the travel time matching method. Compared to the un-scaled

model results (Fig. 2.7), the scaled results show better agreement for the magnitude and

timing of the peak discharge from the 1 km2 model. For example, the difference in the

time to peak for the scaled models compared to the 1 km2 model ranges from 47 to 51

hours, and the difference in peak discharge ranges from 12 to 23%. In contrast, the

unscaled models resulted in timing differences of 49 to 71 hours and peak discharge

differences of 3.5 to 87%. Table 2.3 shows the improvement for Tp and Qp for all model

scales except Qp at 3.2 km2. The mean differences in Tp are less than 5.5% and the mean

differences in Qp are less than 20%. However, for model scale 3.2 km2, the mean difference

increased to 14% compared to un-scaled mean difference in Qp of 4.1%.

33

Table 2.3. Mean percent change in the time-to-peak (∆Tp) and peak discharge (∆Qp) from

all gauge locations for each model scale compared to the 1 km2 model scale for the initial

setup, after CDF scaling and after the combination of both CDF scaling and uniform

correction coefficient (λ); values in parentheses represent the range in percent changes

between the different gauge locations.

Scale,

Km2

Initial CDF Scaling CDF Scaling and λ

∆Tp ∆Qp ∆Tp ∆Qp ∆Tp ∆Qp

10000 39 (10) 90 (5.3) 5.4 (9.2) 17 (7.7) 16 (8.3) 6.4 (12)

3200 37 (23) 83 (5.3) 3.7 (2.1) 19 (3.9) 12 (6.5) 1.2 (3.6)

1000 30 (13) 72 (10) 2.4 (4.7) 15 (3.1) 8.1 (4.1) 0.9 (2.8)

320 25 (10) 59 (13) 1.0 (2.9) 16 (3.3) 6.3 (4.7) 0.7 (2.6)

100 21 (8.2) 43 (11) 2.7 (5.1) 17 (3.7) 4.9 (6.8) 0.7 (1.8)

32 14 (5.2) 29 (9.5) 3.2 (4.1) 16 (3.6) 2.8 (2.6) 0.3 (1.1)

10 5.7 (3.6) 15 (4.1) 2.8 (2.0) 15 (3.5) 2.8 (2.6) 0.4 (0.6)

3.2 1.0 (2.6) 4.1 (1.3) 2.8 (2.0) 14 (3.0) 2.0 (2.9) 0.2 (0.5)

The scaled surface roughness results show a dramatic improvement in the recession

limb of the hydrographs except for 3.2 km2, which results in less favorable results. This is

because our method only alters the plane surface roughness and not channel roughness.

From Table 1, we see that the average plane length increases by only 30 m (or 1.04 times

longer) as the scale increases from 1 and 3.2 km2, and the average channel length is roughly

2.4 times longer (1.8 km). In contrast, changes in hillslope and channel lengths tend to

increase by 1.6 and 2.0 times, respectively, from one scale to the next (e.g., from 10 to 32

km2). Additional research is needed to better understand why there is a disproportionately

large change in channel length and small change in hillslope length from the 1 and 3.2 km2

models scales.

34

Figure 2.8: Simulated hydrographs at the outlet of the Ohio basin for 8 model scales using

the: dynamic travel time estimation method: (a) without and (b) with the uniform roughness

coefficient correction.

2.3.5. Effect of Pixel Scale Drainage Pattern

Although the results show that the travel time CDF matching method improves the general

hydrograph shape, the peak discharges still do not match the peak from the 1 km2 scale.

We hypothesize that the difference in peak discharge is because of our “open book”

assumption, which is commonly used in numerous hydrological models, for estimating

idealized flowpaths and plane lengths. Using GIS, the accumulation of drainage area along

the channel flowpath from a sample catchment based on the integration of individual 90-

m pixels and their DEM-derived flow directions was determined. Similarly, the HRR

accumulation of drainage area along the channel was determined. Figure 2.9 compares the

35

two area accumulation patterns. Note that, in the HRR model, a uniform distribution of

area along the channel is assumed (Fig. 2.2d) and when accumulated, the result is a linear

relationship (Fig. 9c). For the sample catchments, we see that the pixel-based area

accumulation varies as compared than our assumed linear pattern. The vertical jumps in

area at roughly 90, 80 and 10% of the channel length in Fig. 9a,c,e, respectively, indicate

a tributary entered the main channel. However, the general patterns appear to agree

reasonably well and will likely improve as the drainage area of the upstream end of the

river reach increases.

To assess our uniform area assumption at all model scales, we determined the mean

difference in area accumulation between the two methods at the midpoint of each

catchment’s channel:

D = ∑ E̅(,)E̅',)?)CA

G 2.11

where E̅(,) is the mean pixel-based area accumulation along the main channel in model unit

i, E̅',) is mean of the linear area accumulation, and m is the total model units at a given

scale, If γ equals to 1, it means the HRR plane assumption agrees with the pixel-scale

drainage network at the midpoint along the main channel. If γ is less than 1, the pixel-scale

network has more land area draining to the main channel downstream of the midpoint.

36

Figure 2.9: Area accumulation (a,c,e) for three catchments (b,d,f) for a 10 km2 model

scale; two headwater catchments (a-d) and one interbasin (e-f).

If γ is greater than 1, the pixel-scale network has more area draining to the channel upstream

of the midpoint. Figure 2.10 shows the mean area differences for all model scales. We

see that γ approaches one for between the 10 and 32 km2 scales. For coarser scales, the

difference is slightly less than one but relatively stable until the coarsest scale. For the

finer scales, the difference rapidly increases suggesting that the pixel-scale drainage pattern

37

is not uniform and has more area entering the channel below the midpoint (i.e., small

tributaries draining parallel to the main channel then entering the channel just upstream of

the outlet).

Based on these results, river networks developed with threshold areas between 10

and 32 km2 provide drainage patterns that generally agree with the uniform plane

approximate used in HRR. The results also suggest that it may be possible to use the pixel-

based area patterns to develop additional idealized hillslope shapes for use in the HRR

model (e.g., triangular or trapezoid) that are better for select catchments/scales than our

assumed rectangle. Although future research is needed to investigate this possibility, it

could lead to better representation header water catchment response timing in hydrologic

models.

2.3.6. Refined Parameter Scaling

Although Figure 8a shows that the travel time matching approach improves model response

hydrograph shape and time as compared to no scaling (Fig. 2.7), the peak discharges are

still not the same as the finest scale model. As discussed above, there are three important

reasons for this discrepancy: (i) the uniform area contribution to HRR channels used to

determine reprehensive hillslope lengths, (ii) the uniform plane response along the channel

(i.e., only one hillslope response determined for each catchment and integrated along the

channel), (iii) the finite number of ∆X steps along the hillslope and channel (i.e., 10 steps),

and (iv) assumed uniform, constant channel and hillslope flow velocities. To clarify

reasons ii and iii, Figure 2.2 shows the assumed hillslope and channel arrangement used

in HRR. There are ten ∆XP steps along the hillslope and ten ∆Xc steps along the channel

38

for a total of 100 computational units. However, because of reason ii our approach to alter

the travel time distribution is limited to only 10 ks,i values along one hillslope, and the 10

ks,i values are assumed to be identical for all hillslope segments entering the channel along

each channel ∆Xc steps. Thus, in the current version of HRR, the 100 hillslope

computational units are approximated by the number of hillslope ∆Xp steps (i.e., 10).

Although future research on catchment shape approximations, representative flow

velocities, and HRR computational methods address the above, we investigate a uniform

scaling parameter to account for these issues and provide consistent peak discharges for all

model scales. To accomplish this, we use a uniform correction coefficient (λ) applied to

all model units. As discussed previously, the surface roughness in HRR’s hillslope

kinematic wave method (k*) is the adjusted surface roughness factor (k* = N x ks,i). Here,

we refine the adjusted roughness (k** = N x ks,i x λ) to improve peak discharge. Note that,

the correction coefficient is applied uniformly to all catchments. The criteria used to

optimize λ is to minimize the absolute value of the peak discharge error between the larger

and 1 km2 model scales at the outlet of the basin:

∆H = |HJ − HA| 2.12

where HJ is the peak discharge for scale x and HA is the peak discharge for scale 1 km2.

Figure 2.8b shows that the final hydrographs for the different model scales at the outlet of

Ohio River Basin match the 1 km2 scale. The comparison at other gauge locations are

similar to the results discussed for Figures 2.7 and 2.8a. Although the peak discharges are

identical at the outlet gauge, there are small differences at the other gauge locations with

the mean difference in Qp between gauges ranging from 0.2% for the 3.2 km2 scale to 6.4%

for the 10,000 km2 scale (Table 2.3). In terms of time, there is slight shift in the timing of

39

the peak discharge as compared the timing in Figure 8a with initial CDF matching results

(Table 2.3). For example, the coarsest model arrives 8 hours early with the finest scale

model (3.2 km2) arriving at roughly the same time. The reason for this is likely due to the

decrease in roughness along the bottom most hillslope segment which discharges directly

into the channel. As model scale increase, the length of this segment increases and when

combined with a uniform reduction in roughness, the response time tends to decrease more

than from finer scales.

Figure 2.10: Mean area accumulation ratios (γ) for each model scales (AT).

The optimized uniform correction coefficients are shown in Figure 2.11, which

suggests there is a relationship between the correction coefficient and the mean hillslope

length from each model scale. As hillslope length increases, roughness must be reduced

more (e.g., λ decreases from roughly 0.55 to 0.40). Using the equation for the correction

coefficient and average plane length at each scale, the HRR models were re-run for the

Ohio River Basin, see Fig. 2.12a. From the figure, we see that the difference for the time

40

of peak of each scale changed by 0.1 to 5 hours as compared to Fig. 2.8b, and the peak

flow of each scale changed by 0.3 to 1.9 % with a mean change of 0.9%. Given the relative

small change in hydrograph shape, the relationship in Fig. 2.11 can be directly used to

perform the surface roughness scaling correction. However, Figure 2.12b shows the

hydrographs from all model scales after using the relationship in Fig. 2.11 for each model

unit (i.e., no-uniform correction factors based on the length in each individual model unit).

Here, peak flows are higher than the peak flow of 1 km2 by 5 to 8.7% suggesting that the

uniform relationship shown in Figure 2.11 is less effective when applied to individual

model units. This is logical given that the relationship was developed using basin-wide

mean hillslope length values.

Figure 2.11: Comparison between Correction coefficient (λ) and the average plane length

(Lp) for different model scales.

41

2.4. Conclusions

Issues associated with hydrological scaling has been investigated for decades, and as

model scales continue to approach process scales, our hydrologic understanding gained

from model assessment and sensitivity analyses continues to grow. However, the data

and computational requirements to operate at relevant process scales still represent

significant challenges, especially in the context of regional and global modeling. Here,

we show that surface runoff processes related to flow hydraulics simulated in the HRR

model can be scaled for hillslopes representing catchments ranging from 1 to 10,000

km2, where “scaled” implies streamflow hydrographs simulated from all scales

maintain similar shape, peak and timing characteristics. One benefit of the presented

scaling approach is that it can be used to optimize model scale based on available data

and computational resources while maintaining hydrographs with peak and timing

properties associated with fine scale flowpath characteristics.

The presented method for surface runoff scaling is a two-step process. First,

travel time CDFs from flowpath characteristics derived from 90-m DEM pixels within

a given catchment and corresponding hillslope and channel flowpaths approximated in

the HRR model, which change with model scale, are matched. To approximate the

pixel scale travel time CDF, the beta distribution is used. For the model CDF, surface

roughness values are adjusted along the model’s hillslope flow length, and an

interactive approach is used to minimize the difference between the two CDFs.

Although the peak discharges from the coarser scale models scaled with only CDF

matching increase and agree more closely with the finest scale model (1 km2), the

“initial scaled model” results do not exactly match the peak or time-to-peak. For

42

example, the difference in peak discharge from the scaled model to the finest scale

model ranged from 12 to 23% at the basin outlet. Several possible reasons are: use of

representative, constant surface and channel flow velocities to determine pixel scale travel

time; catchment shape and similarity approximations in the HRR model; and the number

of computational ∆X steps along simulated hillslopes (i.e., 10).

To add count for these limitations, a second adjustment is performed using a

uniform correction coefficient. The correction coefficient was determined by minimizing

peak discharge error at the Ohio River Basin outlet gauge between a given model scale and

finest scale. The resulting hydrographs from each model scale match the finest scale

with a mean peak discharge error of 0.02%. A relationship between the correction

coefficient and average plane length for each scale was then determined. The resulting

relationship was used to re-simulate the hydrographs. Peak discharge errors only

increase slightly over the results for the optimized coefficients. Mean error increased

to only 0.04%. Similar, changes in model results were consistent at other gauge

locations.

The comparison of the accumulated drainage area along the river channels in

the HRR model and 90-m DEM derived drainage networks shows that the “open book”

catchment assumption in HRR does not always approximate the actual drainage pattern

which can impact surface runoff timing. Future research will investigate the use of

flexible model unit shapes based on accumulated drainage area and channel along

model channels, which can be broken into unique hillslopes along a model unit’s

channel. This will provide more flexibility for matching model unit and DEM-based

travel time CDFs. Note that, the present scaling is focused only on surface runoff.

43

Future efforts are planned for subsurface runoff routing and hydrologic (i.e., rainfall-

runoff processes) scaling to compliment the approach presented here.

44

3. UPSCALING SURFACE RUNOFF ROUGHNESS

USING SPATIALLY DISTRIBUTED VELOCITIES

IN THE TRAVEL TIME MATCHING (TTM)

METHOD

Abstract

This paper expands on the Travel Time Matching (TTM) method for scaling hillslope and

channel flow velocities within hydrologic models. Seven model resolutions are

investigated: 3.2, 10, 32, 100, 320, 1000, 3200 km2, where model resolution represents the

threshold area used to define the underlying river network and catchment boundaries (i.e.,

model units). The observational-scale model resolution is defined using a river network

with a threshold area of 1 km2. A case study in the Ohio River Basin (roughly 500,000 km2)

is presented using a synthetic 24-hr rainfall-runoff experiment and the Hillslope River

Routing (HRR) Model. Two scenarios are investigated: uniform and varied hillslope slopes.

For each model resolution, within each model unit, two travel time Cumulative Distribution

Functions (CDFs) derived from flowpaths and velocities at the pixel (90-m) and

conceptualized model scales are matched by adjusting surface roughness. The hillslope and

channel velocities are derived from kinematic wave overland flow routing and a

combination of Muskingum-Cunge channel routing and the Manning’s equation. Using the

scaled surface roughness, simulated hydrographs at the outlet of the Ohio River Basin for

seven model resolutions are shown to be nearly identical based on both correlation and

Nash-Sutcliffe efficiency. The proposed scaling framework can be used to transfer the

observational-scale hydrologic characteristics to selected model resolutions.

45

3.1. Introduction

Simulated hydrologic responses from models operating at different spatial scales (or model

resolution) have been investigated for decades (Bierkens, 2015; Bloschl, 2001; Bloschl and

Sivapalan, 1995; McDonnell et al., 2007; Western et al., 2001; Wood et al., 1988). Yet,

the issue of how to parameterize models operating at resolutions beyond the measurement

scale are not fully understood. Methods to overcome the challenges associated with spatial

scale are generally classified as upscaling or downscaling, with downscaling the most

common. Downscaling refers to the process of transferring information from coarse to

finer resolution (Charles et al., 2004; Kitanidis, 2015; Sivapalan et al., 2003). For example,

remote sensing data such as precipitation or evapotranspiration derived from the satellite

observations can be downscaled from grid cell dimensions of hundreds of kilometers to

hundreds of meters, which is quite useful especially for simulating of small, upland

catchments (Chen et al., 2015; Pau et al., 2016). In contrast, upscaling is the process of

transferring information from fine to coarser resolution (Soulsby et al., 2006; Wood, 2009).

Upscaling is especially useful for transferring field measurements to spatially averaged

model parameters representing individual hillslopes or even entire catchments (Crow et al.,

2012; Crow et al., 2005; Pau et al., 2016).

Travel time is an important characteristic describing the movement of water in a

catchment (Baiamonte and Singh, 2016; McGuire et al., 2005; Van der Velde et al., 2012).

Travel time is dependent on both surface and subsurface flowpath characteristics and has

broader implications than only rainfall-runoff response. For example, Benettin et al. (2013)

applied travel time distributions in several hydro-chemical models to estimate chemical

cycles in small catchments in the Netherlands. However, estimating travel time is

46

challenging and often achieved using empirical methods. For example, the Natural

Resources Conservation Service (NRCS, formally known as the Soil Conservation Service,

SCS) recommends estimating the time of concentration (i.e., longest surface water travel

time within a watershed) based on an empirical equation based on watershed response lag

time (NRCS, 1972), which is a function of watershed slope, longest flowpath and curve

number (CN). The method has been widely applied to catchments having varied land cover

and soil types. Recently, Botter et al. (2011) developed a stochastic framework to calculate

residence and travel time for a catchment. The framework is based on hydrologic forcings

such as precipitation and evapotranspiration, solved using analytical methods, and

considers soil-vegetation dynamics. With the advances in remotely sensed data such as

digital elevation model data and land cover, more physics-based methods have been

developed. Zuazo et al. (2014) investigated different analytical methods and numerical

modeling approaches for determining spatially distributed travel time based on DEMs.

They found that considering detailed information along the hillslope based on DEMs

characteristics improved model performance. They also suggested that the validity of

kinematic-wave approximation decreases as the length of the hillslope increases.

Central to estimating travel time, is the distribution of velocities along flowpaths,

which can vary significantly in space and time. Gad (2014) proposed a method derived

from DEM flowpaths and empirical relationships for channel velocity based on drainage

area. Zhao and Wu (2015) performed laboratory scale surface runoff experiments to

characterize travel times and developed a method to estimate dynamic velocities based on

a relationship with upstream drainage area. However, their mean velocity is based on

steady state conditions, which is difficult to estimate within large spatial scale systems.

47

Here, we expand upon the Travel Time Matching (TTM) method presented in

(Zhao and Beighley, 2017) for scaling surface roughness in hydrologic models to account

for variations in local slopes and velocities. A case study is presented for the Ohio River

Basin using the Hillslope River Routing model (HRR) (Beighley et al., 2009; Beighley et

al., 2015; Yoon and Beighley, 2015). Two scenarios are investigated: constant and varied

slope. The framework is applied to seven model resolutions (3.2, 10, 32, 100, 320, 1000,

3200 km2) using an observational-scale model resolution of 1 km2.

3.2. Methodology

3.2.1. Study Site

With a drainage area of roughly 500,000 km2 (14 US states), the Ohio River Basin is the

5th largest tributary to the Mississippi River Basin (Renfrew, 1991). According to the

National Aeronautics and Space Administration’s (NASA’s) moderate-resolution imaging

spectroradiometer (MODIS) Type I land-cover data product MCD12C1 (Friedl et al., 2002)

for year 2012, the basin is roughly 2% developed, 36% undeveloped (i.e., forests and

grasses), and 62% agricultural lands. In this research, the surface topography is derived

based on the DEM developed from NASA’s Shuttle Radar Topography Mission (SRTM)

with a horizontal resolution of 3 arc seconds (~90m) (Farr et al., 2007), which is widely

used in many large-scale hydrologic models. Figure 3.1a shows the river network on a

basis of a threshold area of 1,000 km2 and the 6 USGS gauges along the Ohio River used

in this study.

48

Figure 3.1. Illustration of model unit partitioning for Hillslope River Routing model for model resolution of 1000 km2: (a) river network

with USGS gauges represented in triangular shape; (b) selected model unit; (c) catchment plane separation; (d) conceptual model for

hillslope and channel routing; (e) hillslope routing similarity.

49

3.2.2. Hillslope River Routing (HRR) Model

The Hillslope River Routing (HRR) model (Beighley et al., 2009) is used in this study. The

model simulates vertical water and energy balance to estimate surface and subsurface

runoff; lateral surface and subsurface runoff transformation using kinematic wave routing;

and channel and floodplain discharge using a diffusion wave approximation. The key

computational units are hillslopes and channel reaches, where hillslope (i.e., planes) are

approximated as rectangular and draining laterally the unit’s river reach. Figure 3.1 shows

a discretized example of one catchment in HRR model. It illustrates the transformation

process for one catchment to one HRR model unit. The catchment is divided by the channel

into two planes, which are assumed identical (i.e. area, plane length, slope, etc.). The plane

and channel are divided into 10 sections, and to reduce the computational cost, lateral

overland and subsurface flows contributing to the channel are assumed uniformly

distributed along the channel. Plane and channel slopes are determined by averaging pixel

slopes, based on the SRTM DEM, within the catchment and along the channel segment,

respectively.

3.2.3. Simulated Travel Time and Velocity from Fine Scale Model

This study builds on the Travel Time Matching (TTM) method from (Zhao and Beighley,

2017) with spatially varied, average velocities instead of spatially uniform, prescribed

velocities (i.e., 0.01 m/s for hillslope flow and 1 m/s for channel flow). In general, the

TTM method matches the travel time distributions between two model resolutions (i.e.,

scales) by adjusting surface runoff roughness along the hillslope to account for differences

50

in flowpath processes between scales (i.e., typically, coarse scale model surface roughness

is reduced to match the faster response in the fine scale model due to its additional channel

density).

Given that surface flow velocities are not spatially uniform but rather influenced by

several factors such as slope, roughness and contributing area (i.e., runoff magnitude),

spatially varied velocities are used to match travel times. Travel time distributions are

generated for each model resolution and matched to a reference model resolution (i.e., 1

km2 in this study). The challenge in this process is estimating the reference scale travel

time distribution for a given coarse scale model unit. In general, velocities from the fine

scale model are extracted and transferred to pixel (i.e., DEM) scale velocities. Using the

DEM, flow directions and flowpaths are determined and combined with the pixel scale

velocities to calculate the downstream travel time for each pixel. With grid based travel

times and coarse resolution model unit boundaries, the fine scale travel time distribution

for the coarse scale model unit can be approximated using a Beta distribution with the mean

and standard deviation of pixel scale travel times within a the coarse scale model unit (Zhao

and Beighley, 2017). The following sections describe the generation of hillslope and

channel velocities, which are used to create the pixel scale travel times representing the

fine scale model.

Hillslope velocity from fine scale model

In order to generate spatially varied surface runoff velocities to implement the TTM

method, surface runoff velocities for a spatially uniform synthetic storm event (Zhao and

Beighley, 2017) are simulated using the fine resolution HRR model (i.e., 1 km2) on the

51

high performance computing cluster at Northeastern University. The synthetic runoff is

derived from a 2-year 24-hour rainfall event. The hourly runoff is determined using NRCS

runoff curve number (CN) method, the NRCS Type II rainfall distribution, a total rainfall

depth of 7.62 cm, and a CN value of 67 (i.e., typical to the watershed). After the 24-h period,

the simulation continued for 29 days for a total simulation duration of 30 days. Note that,

there are 10 model sections (∆X steps) along each HRR model unit’s hillslope. The

hillslope flow velocities from each section at each time step (i.e., 60 min) for each model

unit (i.e., 339,635 units) were exported and the maximum hillslope flow velocity for each

section was extracted. The average hillslope flow velocity (Va,i) for each model unit section

(i) is approximated as half of the maximum:

Va,i = 4K,6� 3.1

where Vm,i is maximum event hillslope flow velocity for section i, with i ranging from 1

to 10.

Next, for each model unit, a relationship between the hillslope velocity (Va,i) and

cumulative upslope flow length from section i to the top of the hillslope (i = 1) is developed:

�,) = ��8.)M 3.2

where Vp,i is the hillslope velocity at a location, i, along the plane, α and β are the fitted

parameters (i.e., unique values for each model unit), and Ls,i is the cumulative upslope flow

length along on the plane:

�8,) = <10 �� 3.3

where Lp is the length of the model unit plane and i is the section number in the model unit

number from 1 to 10, with 1 representing the most upslope section. Figure 3.2 shows the

52

velocity relations from a sample model unit ID 218,551. The goal of this step is to develop

a function (eq. 3.2) to transfer the velocities from the fine scale HRR model to the pixel

scale using cumulative upslope flow length for a given pixel within a model unit.

Figure 3.2. Example of the relationship between average hillslope velocity and the length

of the plane from the sample unit at reference model resolution for: (a) constant (8.66%)

and (b) varied (10.59%) hillslope scenarios.

Channel velocity from fine scale model

Unlike hillslope velocity, the channel velocity cannot be exported from HRR model

directly because HRR uses the Muskingum-Cunge routing method to estimates discharges

along the channel for each time step (i.e., does not determine velocities). Thus, river

discharges are exported, and the channel velocities are estimated based on Manning’s

equation with the wide rectangular channel assumption. In HRR, there are 10 sections

along the channel. The discharges for each channel section at each time step are exported

from fine scale model and the average channel discharge (Qa,i) is determined:

Qa,i = NK,6� 3.4

where Qm,i is the maximum channel discharge for each section i. Unlike hillslope velocities,

the channel discharges do not vary much from upstream to downstream in most cases. Thus,

53

the channel discharge for each section within a model unit is fit to linear function (Zhao

and Beighley, 2017):

Qa,i = � E) + O 3.5

where a and b are the parameters for linear function and Ai is the cumulated upstream

drainage area (km2) at each channel section i; i = 1 corresponds to the most upstream

section.

With the average channel discharge, the average channel velocity is determined

using the Manning’s equation assuming the channel a wide rectangular channel. The

estimated discharge Qa,i (m3/s) is used to solve the Manning’s equation for the average

water depth, Di, (m) at section i along the channel:

HP,) = 1Q %)1/RS)T)A/� 3.6

where n is the channel roughness, Si is the slope of the channel determined from the DEM,

and Wi is the average channel width (m) approximated using a relationship between channel

width (Allen and Pavelsky, 2015) and upstream drainage area; see Figure 3.3. Using the

derived width and depth, channel velocity is calculated as:

�,) = HP,)EJ,) 3.7

where Ax,i is cross-sectional area (DiWi) and both Di and Wi can be estimated at any location

along the channel based on upstream drainage area.

54

Figure 3.3. Approximation of channel width based on accumulated drainage area in Ohio

River Basin derived from (Allen and Pavelsky, 2015)

Travel time estimation

Two travel times are used in this study. One is the model-based travel time from HRR,

which is simply approximated based on rectangular shape assumption of the model unit.

The second is the landscape-based travel time derived using the average channel and

hillslope velocities, which are determined from the reference model resolution and re-

mapped to DEM pixel scale velocities within each fine scale model unit based on

downstream flow length and accumulated drainage area (Eqs. 3.2 & 3.5/3.7). The model-

based travel time is derived from HRR for each coarse model resolution. With the

assumption of a rectangular plane, the model-based travel time (��) for a given model unit

is determined as:

�� = U ∆��,)AB

)CA 3.8

55

where ∆X is plane flow length for one length step along the hillslope (∆X=Lp/10); and �,) is plane velocity for a given location i along the hillslope. Note that, �,) in this analysis is

spatially varied between model units based on their topography and drainage pattern

characteristics (i.e., slope and plane length) used in HRR to simulate surface runoff. Also,

the travel time allocated to channel flow is excluded because the main stream within a

model unit is also a channel in the reference model resolution. This concept is discussed in

more detail later for the landscape-based travel time.

The landscape-based travel time (�') for a model unit at the coarse model resolution

is generated using pixel scale travel times based on velocities from fine scale model. Note

that, the travel time associated with pixels along the main streams is excluded for

landscape-based travel time distributions generated for each coarser scale model. For

example, to generate the landscape-based travel time grid for 1,000 km2 model resolution,

the travel time along the channel pixels for the 1000 km2 model are removed. Thus, the

travel time grid for 1000 km2 model resolution is the travel time for only the hillslope

portion of the model unit. This is done because both the fine and coarse scale models

simulate channel flow along the exact same channel path. In addition, the model-based

travel time only considers the travel time on the plane. Thus, the flowpath process (i.e.,

channel flow) and computational methods are identical between models and no scaling of

surface roughness is required.

3.2.4. Travel Time Matching

The travel time distribution extracted from the travel time grid derived based on the fine

scale model simulation (�') using the coarse scale model boundary is considered as the

56

“true” travel time distribution. If the travel time distribution of the coarse scale model unit

based on HRR approximations (��) is different from the “true” distribution, the surface

roughness of the coarse model unit is adjusted to increase or decrease plane velocity and

the associated travel time.

As illustrated in Figure 3.1, for each model unit, only one of the kinematic wave

routing solution is implemented and the plane response to the channel is assumed to be

uniform along the channel. Ten quantiles of the travel time CDF are used: 10, 20, 30, 40,

50, 60, 70, 80, 90, and 99%. Several things should be noted here. First, unlike the quantiles

selected from the middle of the section in (Zhao and Beighley, 2017), this study uses

quantiles from the end of each the section to exactly match the location of average

velocities simulated for the hillslope. Secondly, the last CDF is 99% instead of 100% to

eliminate occasional large values in the last 1% of the travel time CDF due to the fitting

process. Using 99% instead of 100% of travel time CDF reduces computational time for

the matching process and ultimately yields less bias; see Results section. Lastly, as

discussed above, every section along the plane is divided into 10 sections. Since the

average hillslope velocity is determined at the end of each section, the average velocity for

a given section (Va,i) is estimated by:

�,) = ) + )/A 2 (< > 1) 3.9

where i is the section number. For the first section (i = 1; most upslope section), half of

the average velocity is used.

The travel time matching procedure starts from the bottom of the plane, and the

difference between the CDF of model- and landscape-based travel times is:

57

∆� (<%) = $%&�(<%) − $%&'(<%) 3.10

where M and L correspond to model-based and landscaped-based, respectively; and i is the

number of 10 quantiles of the CDFs: 10, 20, 30, 40, 50, 60, 70, 80, 90, and 99. The adjusted

model-based plane velocity (�,)∗ ) for segment i is determined by:

�,)∗ = �∆X�∆X?,) − ∆�(<%)

3.11

where �∆X is the model-based plane segment length and ?,) is the original plane velocity

exported from HRR, and the velocity modification ratio 2) is determined:

2) = �,)∗?,) 3.12

From this point, the matching process is identical to Zhao and Beighley (2017). The

surface roughness adjustment factor for the segment (7) ) is the inverse value of 2), and

surface roughness used for kinematic wave routing in HRR is multiplied by 7). Note that,

7) is adjusted for each hillslope section from the bottom to top, and the model-based travel

time CDF is recalculated with each newly generated 7). To obtain the optimal 7) values,

the procedure is repeated until the root mean square error (RMSE) between the CDF’s less

than the 1% of the initial RMSE between CDFL and CDFM.

3.3. Results & Discussion

Two slope scenarios are investigated: (1) spatially constant slopes for hillslopes (Sp =

8.66%) and channels (Sc = 2.57%) determined by averaging slopes for all model units in

the reference model resolution (1 km2); and (2) spatially varied slopes hillslopes and

58

channels representing the slopes derived from DEM. The purpose for the constant slope

condition is to compare with the results from Zhao and Beighley (2017), which used

constant velocities for hillslopes and channels. For the varied slope case, a minimum slope

was set to 0.01% to account to challenges associated with DEM accuracy.

3.3.1. Travel Time Grids

To develop the travel time grids, the velocities from reference model resolution (i.e., 1 km2)

are re-mapped to DEM pixel scale. For hillslope velocity, α and β in equation (3.2) are

determined for each model unit. The mean Pearson correlation coefficient for the power

functions for both uniform and varied slope scenarios from all model units (i.e., 339,635

units) at the reference model resolution is 0.99. The minimum correlation coefficient for

uniform slope case is 0.89 and 0.75 for varied slope case. Figure 3.2 shows an example

model unit for the uniform and varied slope scenarios, the correlations are both 0.99. Using

equation (3.2) and upstream flow lengths (Ls), a grid of hillslope velocities is generated. A

similar procedure is performed for channel velocity, where parameters a and b in equation

(3.5); channel widths derived based on (Allen and Pavelsky, 2015) in Figure 3.3; and

channel depths using equation (3.6) are determined. A combined velocity grid for both

hillslope and channel velocities was determined. As with surface runoff, the mean

correlation value for equation 3.5 from all model units was 0.99 ranging from 0.75 to 0.99.

The travel time grids for the varied slope scenario for 4 model resolutions are shown

in Figure 3.4. A rectangular area is selected to illustrate the effect of exclusion of the

shared common channel on travel time raster at different model resolutions. From 3200 to

59

100 km2, there are more channels in the finer spatial resolution. This results in shorter travel

times, especially for the pixels near the additional channels in the finer model resolution.

Figure 3.4. A zoom-in view of the travel time for a selected area in the Ohio River Basin

for four model resolutions and the varied slope scenario.

3.3.2. Simulated Stream Flow without TTM Method

As discussed above, a synthetic runoff experiment was applied to assess the hydrologic

response for uniform and varied slope conditions. Figure 3.5 shows the discharges from

the outlet of the Ohio River Basin for different model resolutions. Although the HRR model

runs for 30 days, the hydrograph only shows 10 days which tends to capture the key

hydrologic response and timing. For the uniform slope condition, the peak flow decreases

and the time to reach the peak increases as the model resolution increases. There are three

reasons for this pattern: (1) the plane and channel slopes are constant for all model units;

(2) more channels are represented in the finer scale models; and (3) planes are shorted in

60

the finer scale models. The hydrographs for the varied slope condition have the same

general trend. However, it should be noted that there are two peaks for the varied slope

condition, except for 3,200 km2 (i.e., the coarsest model). An explanation for this scenario

can be linked to the travel time grids for the varied slope condition in Figure 3.4, which

shows that the Ohio River Basin can be divided into two regions (i.e., northwest and

southeast). The travel time for northwestern region is longer as compared to southeastern

region.

Figure 3.5. Simulated discharge based on the 2-year 24 hour NRCS type II rainfall

synthetic experiment on Ohio River Basin for 2 scenarios: (a) constant and (b) varied

hillslope and channel slope without application of ITTM method

3.3.3. Simulated Streamflow after TTM Method

Figure 3.6a and 3.6b show the simulated hydrographs for uniform and varied slope cases

after applying the adjusted surface roughness from the TTM method. For the uniform slope

case, the method effectively improves the agreement of the coarser scale model

hydrographs to the fine scale model output in terms of both magnitude and timing. For the

61

varied slope case, the method improves the magnitude for both of the peaks with better

improvement in the second peak.

Figure 3.6c and 3.6d shows the mean values for the adjusted surface roughness

factors for each section of all model units at the difference spatial resolutions. For both

uniform and varied slope cases, the surface roughness factors follow a pattern where

correction factors increase from the bottom to top sections except for the first section (i.e.,

most downslope section). This indicates that surface roughness is often reduced at the

bottom of the hillslope and increased at the top (i.e., a larger correction factor at the top

increases travel time). Recall that in HRR, all sections on a given plane have the same

length (i.e., rectangular plane), which is not the same as in the landscape-based travel time.

For the bottom sections of the plane in HRR, the travel time CDF is often longer and

velocity needs to be decreased to match the landscape-based travel time. After the surface

roughness are reduced and velocities are increased for the bottom sections, the uppermost

sections of the plane need to be slower to match the landscape-based travel time. This

scenario suggests that the rectangular shape of planes in the HRR model needs to be re-

evaluated. For example, a triangular plane that has wider upslope area or multiple irregular

length planes along the channel could provide a better agreement with the landscape-based

travel time CDF.

Figure 3.6. Simulated discharge after modification of surface roughness using TTM method for (a) uniform and (b) varied slope

conditions at different model resolutions, and the average surface roughness modification factor of (c) uniform and (d) varied slope for

different model resolutions.

Another factor that leads to the mismatch of the hydrographs between coarse and

fine model resolutions is the travel time difference at 1 km2. Recall that a key assumption

in the TTM method is that the landscape travel time represents the model travel time at the

reference model resolution. A sample model unit from the 1km2 model resolution is

randomly selected to assess this assumption. The CDFs for the model-based and

landscape-based travel times (Figure 3.7) show that the model travel time at 1 km2 is

shorter than the landscape-based travel time. Although the TTM procedure matches the

travel time distributions from the coarser model resolutions to the landscape-based travel

time (i.e., not the 1km2 model-based travel time), the coarser scale models are compared

to the 1km2 model response (Figure 3.6). The mismatch highlighted in Figures 3.6 – 3.7

suggest that surface roughness from coarser models should be further reduced to match the

model-based travel time at 1km2.

Figure 3.7. Comparison of landscape-based and model based-travel time from 1 model

unit at 1km2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20000 40000 60000 80000 100000

CD

F

Travel time, sec

GIS Travel Time

HRR Travel Time

64

The example discussed above is a single model unit at 1km2, which can be one of

the many units within a catchment at a coarser resolution. For instance, Figure 3.8a shows

a catchment for the 3,200 km2 model resolution, which contains 2,412 units from 1km2

model. As a test, the TTM method is applied on the 1km2 model units. The results show

that the surface roughness on the hillslope needs to be increased roughly 1.3 times for

model-based travel time to match the landscape-based travel time. Note that, the TTM was

not applied to the 1 km2 model scale in this study. It was initially assumed that this would

not be needed because the hillslope and channel velocities used to determine the landscape-

based travel time are derived from the 1 km2 model resolution. However, further analysis

suggests that even at the fine scale, there can be relatively large difference in travel time

due to differences in landscape and model flowpaths and velocity dynamics (i.e., mean

velocities, eqs. 3.1 and 3.9, used in TTM as compared to dynamic velocities simulated in

HRR to produce the hydrographs).

65

Figure 3.8. (a). Selected catchment at 3,200 km2 model resolution and the model units

from 1km2 lay under the catchment and (b) the hydrographs for the same outlet of the

catchment from 3,200 and 1 km2 with varied situations of modified surface roughness.

In this example, the 1km2 model surface roughness values should be increased by

1.3 time to decrease the velocities and increase the travel times. However, since the 1km2

model hydrographs serve as the benchmark in this study, the velocities used in the

landscape-based travel time should be increased 1.3 times to match the model-based travel

time at 1km2. Given that the coarse scale model travel time is matched to the landscape-

based travel time, the coarse scale model velocities should be increased 1.3 times as well

(i.e., reduced surface roughness by a factor of 1/1.3 or 0.8). However, the results (Figure

3.8b) indicate that 0.8 is not a sufficient decrease in the surface roughness for the coarser

0

0.2

0.4

0.6

0.8

1

1.2

8 20 32 44

Dis

cha

rge

, cm

sT

ho

usa

nd

s

Time, hour

1 km2

ITTM

Uniform factor ~0.8

Uniform factor ~ 0.4

Orig

(a)

(b)

66

model resolutions to match the 1km2 hydrographs. The 0.8 accounts for the hillslope travel

time differences at 1km2 but not channel travel times. Recall that velocities from both the

hillslopes and channels in the 1km2 model were used to derive the landscape-based travel

time grid. If the hillslope velocities are faster, the resulting channel velocities are also faster.

Thus, hillslope velocities in the coarser scale models, which integrate both hillslopes and

channels from the 1km2 model scale, should be increased more than 1.3 time to account

for the faster channel velocities from the 1km2 model. Assuming that the channel velocities

also needs to increase by a factor of 1.3 and that each 1km2 model unit within a coarser

scale model contributes one hillslope and channel segment to the landscape-based travel

time, the hillslope velocities for the catchment at 3200 km2 need to be increased by a factor

of 2x1.3 or 2.6 times (i.e., reduce surface roughness by a factor or 1/2.6 or 0.4). Figure

3.8b shows that the peak discharge and shape of the resulting hydrograph for a factor of

0.4 is nearly identical to the 1km2 model output. The factor ∼0.4 is specific to the selected

3200 km2 catchment but not exact because there are additional influences such as relative

importance of channel vs. hillslope travel time, model vs. landscape flowpaths, model unit

shape, etc. Given these additional factors, a uniform factor is determined manually for each

model resolution based on matching the coarser scale model hydrographs to the 1km2

model output.

3.3.4. Uniform Factor

To improve the hydrographs shown in Figure 3.6a and 3.6b, surface roughness values

from the TMM are multiplied a uniform scale factor (λ). To estimate the scale factor for

each model resolution, two error measurements are considered: Nash-Sutcliffe efficiency

67

(NSE) (Legates and McCabe, 1999) and difference in peak discharge using the fine model

resolution as the reference. For the uniform slope scenario, the calibration criteria is to

match the peak (i.e., minimize the difference in peak discharge). For the varied slope case,

which has two peaks in the simulated hydrographs at 1 km2, the criterion is to match the

larger peak and maximize NSE. NSE is used evaluate the performance of time to peak.

Figure 3.9. Hydrographs with the application of uniform scale factor for (a). uniform and

(b). varied slope scenarios for different model resolutions.

Figures 3.9a and 3.9b show the hydrographs at the outlet of Ohio River Basin after

applying the uniform scale factors for both uniform and varied slope cases at different

model resolutions. For the uniform slope condition, both peak flow and time to peak are

now nearly identical. For the varied slope condition, most of the coarse model resolutions

match both peaks except 3,200 km2, which does not match the second peak. This suggests

that 3,200 km2 maybe too coarse to capture the distributed response pattern for the basin.

Table 3.1 presents the uniform factors and goodness of fit measures for all model

resolutions at the outlet of the Ohio River Basin. Here, the peak difference (Ep) is

determined as |N’ / NZ|NZ , where Q1 is the peak discharge from reference model resolution and

68

Q’ is the peak discharge from the coarse model resolution after TTM method. After

applying the TTM method, both the peak flow difference and NSE improved for all model

resolutions. In addition to good performance at the outlet, NSE at five upstream locations

(Figure 3.1a) are all greater than 0.9 for all model resolution with a range of 0.914 ~ 0.999

for uniform slope scenario and 0.909 ~ 0.998 for varied slope scenario.

Table 3. 1. Difference in peak discharge from the outlet of Ohio River Basin and NSE for all model resolution during the calibration

process.

Slope

condition

Model

resolution, km2

Uniform

factor Ep

original

Ep w/

TTM Ep w/ λ

NSE

original

NSE w/

TTM

NSE

w/ λ

Uniform

3200 0.23 72% 23% 0% 0.02 0.88 0.98

1000 0.23 56% 18% 0% 0.23 0.89 0.99

320 0.21 41% 16% 0% 0.49 0.92 0.99

100 0.30 28% 14% 0% 0.69 0.92 1.00

32 0.35 18% 12% 0% 0.85 0.93 1.00

10 0.39 10% 10% 0% 0.95 0.95 1.00

Varied

3200 0.32 59% 19% 0% -0.12 0.94 0.97

1000 0.28 42% 16% 0% 0.16 0.93 0.98

320 0.27 27% 15% 0% 0.44 0.93 0.98

100 0.24 18% 14% 0% 0.65 0.91 0.99

32 0.24 15% 14% 0% 0.82 0.91 0.99

10 0.27 14% 14% 0% 0.92 0.92 0.99

3.3.5. Scaled Surface Roughness

Combining all steps, the final adjusted surface roughness ([\,)] ) is:

[\,)∗ = ^87\,)[\ 3.13

where ^8 is the uniform scale factor, kj,i is the adjusted surface roughness factor at location

i along the hillslope in model unit j, and Nj is the original surface roughness (assumed to

be 0.8). Figure 10a and 10b shows the mean value of the final adjusted surface roughness

(N’) from each section in each model unit for all model resolutions. In general, as the

model resolution gets coarser, the average hillslope length gets longer, and the surface

roughness on the hillslope must decrease to increase the hillslope velocity. The hillslope

velocity must increase in the coarse models to account for the combined flowpath processes

(hillslope runoff and channel flow) simulated as only one process (hillslope runoff). The

results for the varied and uniform slope cases are similar with the varied slope case showing

slightly larger roughness values are the coarser scale, which can be attributed to the

differences in simulated hillslope slopes. For the varied slope case, slope decreases as

model unit scale increases which is not the case for the uniform slope case. Figure 3.10

shows how surface roughness changes with model resolutions, which can be useful for

other modeling applications.

71

Figure 3.10 Mean surface roughness from all model units at different model resolutions

after applying the TTM method for (a) uniform and (b) varied slope scenarios.

The ratio of mean landscape flowpath to mean model-based flowpath (Rp), ratio of

mean surface roughness with and without application of TTM method (RN), and the ratio

of mean model hillslope velocity with and without TTM method (RV) are analyzed (Figure

3.11). As discussed above, the final surface roughness decreases as model resolution

coarsens to increase hillslope velocity. Meanwhile, as shown in Figure 3.11a, as model

resolution becomes coarser, Rp increases, which indicates that the model plane length

increases less than the landscape flowpath length (i.e., model approximation of an open

book with two parallel planes results in flowpaths that are much shorter than observed in

the landscape). In Figure 3.11b, as Rp increases (i.e., as the model resolution becomes

coarser), the relative change in required surface roughness decreases. A similar pattern is

shown in Figure 3.11d, where RN decreases as Rp increases. The combined effects on the

required hillslope velocity are shown in Figure 3.11c, where both roughness changes and

model vs. landscape flowpath differences are integrated into net changes in hillslope

velocity.

72

Figure 3.11. Relationships for ratio of flowpath lengths (Rp) with the final surface

roughness (N’) and ratios of surface runoff velocity (RV) and surface roughness (RN).

Figure 3.12 shows the density of required surface roughness values for 3 model

resolutions with corresponding model flowpath lengths for the uniform and varied slope

cases. For coarse model resolutions, the required roughness tends to decrease as the

hillslope length increases which is consistent with the pattern shown in Figure 3.11a. For

both constant and varied slope scenarios, the highest density of surface roughness

corresponds to larger roughness values as the model resolution becomes finer. However, it

also suggests something happens when plane length is less than about 1 km. For lengths

less than 1 km, the spread of surface roughness increases with no clear patterns. This could

be due to limitation in the kinematic wave method solution used in HRR. The

computational time step is this study is 1 hour which may be too long for these shorter

distance steps. Note that, the plane length of densest regions of modified surface roughness

is similar to the average plane lengths in Table 2.1. For example, the plane length with

73

densest area 3 km for the 100 km2 resolution model, which has an average plane length

2.74 km.

Figure 3.12. Distribution and density of surface roughness and model flowpath length at

different model resolutions after applying the TTM method for the uniform (a,c,e) and

varied (b,d,f) slope scenario. Color indicates the density of the surface roughness.

74

3.4. Conclusion

In this study, surface roughness is upscaled in the HRR model using the Travel Time

Matching (TTM) method described in (Zhao and Beighley, 2017) with: (1) spatially varied

velocities based on flowpath length and slope; and (2) the exclusion of travel time in

channels, which are contained in both the fine and coarse model resolutions. The upscaling

method is applied in the Ohio River Basin using two test cases: constant and varied slope,

and a synthetic 24-hr rainfall-runoff event (Zhao and Beighley, 2017). The reference

model resolution is assumed to be 1km2, and seven model resolutions are investigated: 3.2,

10, 32, 100, 320, 1000, 3200 km2.

After applying the TTM method, hydrographs from coarse model resolutions are

much closer to matching hydrographs from the reference model resolution for both uniform

and varied slope cases. However, they still do not exactly match the reference model

resolution (1km2). Further investigation shows that the landscape-based and 1km2 model-

based travel time distributions do not agree. Although the landscape-based travel time is

derived from the 1km2 model output, differences in flowpath lengths and velocity dynamics

result in the landscape-based travel time being rough 1.3 times longer than the reference

model. This finding indicates that surface roughness in the coarser model resolutions,

which are determined using the landscape-based travel time, need further reductions to

match the hydrograph from the 1km2 model. Thus, a uniform scale factor is determined

manually by minimizing peak flow differences and maximizing NSE between coarse and

reference model streamflow. Using the uniform scale factor, all simulated hydrographs

from the coarser models are shown to approximately match the output from the reference

model. The 3200 km2 model resolution for the varied slope case has the lowest NSE

75

compared to other model resolutions, suggesting the spatial scale may be too coarse to

effectively capture the response pattern of the basin.

After examining the distribution of surface roughness along the hillslope flowpath,

surface roughness decreases as the ratio of landscape and model flowpath increases. As

model resolution coarser, the landscape flowpaths are much longer than the model

flowpaths, even both landscape and model flowpaths increase. The ratio of landscape and

model hillslope velocity increases larger as the surface roughness decreases to minimize

the travel time difference. For the coarsest model resolution 3200 km2, the landscape

hillslope velocity is 14 times faster than the model hillslope velocity while the ratio of

landscape and model flowpaths is 2.5 and the surface roughness is decreased by 90%.

There are still several limitations in this study. The TTM method has been only

investigated for the surface runoff. Future efforts will investigate if the method can be

applied to subsurface or ground water flow. The study is based on the synthetic runoff

experiment, which limits our ability to compare results to observed streamflow. The

assumption that model travel time can be reasonably represented by landscape travel time

at 1 km2 using 50% of max model velocity is likely not optimal. Further study will explore

alternative methods for determining a representative velocity (e.g., changing percentage of

the max velocity). Finally, the rectangular shape assumption for the catchment is

questionable. Future study will explore possibilities of other shapes for simplification of

the model units in HRR model (e.g. triangular or irregular shapes).

76

4. SCALING SURFACE AND SUBSURFACE

ROUTING PROCESSES IN HYDROLOGIC

MODELS

Abstract

Hydrologic scaling studies have often focused on forcings (e.g., precipitation and

evapotranspiration) or stores (e.g., soil moisture, snow), but few have investigated hillslope

and channel routing processes. This study presents a scaling method for both surface and

subsurface flow routing processes in the Hillslope River Routing model that results in

nearly identical streamflow response (magnitude and timing) characteristics regardless of

model resolution. Here, a reference scale (i.e., resolution for which model and actual

flowpaths are similar) model resolution of 1 km2 is used as the benchmark. An application

is presented to illustrate how coarse scale model routing parameters are initialized by

upscaling reference model resolution response characteristics, calibrated using observed

streamflow, and downscaled to revise the reference model parametrization. Here, scaling

is performed by matching travel time distributions from DEM-derived and model-derived

flowpaths, which vary based on model resolution, by adjusting surface and channel

roughness and lateral hydraulic conductivity. To isolate routing processes in the model,

observed runoff from 90 U.S. Geological Survey (USGS) streamflow gauges in the Ohio

River Basin is used to force the model. USGS streamflow is separated into surface and

subsurface components using a recursive digital filtering method. Hourly surface and

subsurface runoffs are then distributed throughout the Ohio River Basin, assuming runoff

is spatially uniform over each gauge’s contributing area. Spatial interpolation is used to

77

estimate runoff for ungauged land areas. In this study, the reference model resolution (1

km2) and six coarser scale model resolutions are investigated: 10, 32, 100, 320, 1000, and

3200 km2. Results show that the coarser scale models have nearly identical response

characteristics to the reference scale model. A resolution of 320 km2 is selected as the

optimal model resolution for calibration to selected U.S. Geological Survey gauges based

on tradeoffs between computational efficiency and RMSE improvements. The routing

parameters in the 320 km2 model are calibrated to USGS streamflow and transformed back

to the reference model. The findings support that coarser model resolutions can be used for

calibration and multi-scale parameterizations.

78

4.1. Introduction

Hydrologic modeling has transformed from largely empirical to more physically-based

approaches over the past 50 years and has come to focus more on Earth system science

rather than engineering applications (Hall et al., 2014; Sivapalan, 2018). In addition,

hydrologic models are often integrated with models describing many biogeochemical

processes to enable understanding of more complex problems in both the natural and built

environments (Wagener et al., 2010). However, the balance between system spatial

heterogeneity (e.g., precipitation, soils, land cover) and model process representation (e.g.,

length and time scales in modeling frameworks) is still a challenge; often referred to as

scaling (Bloschl, 2001; Bloschl and Sivapalan, 1995; Kitanidis, 2015).

Downscaling and upscaling are the two main approaches to overcoming challenges

associated with mismatches between observation and model resolutions. Because of the

critical role of precipitation in rainfall-runoff modeling, downscaling is widely used for

meteorological data such as precipitation and temperature. For example, Maurer and

Hidalgo (2008) applied two different statistical method to downscale the monthly

temperature and precipitation gridded data to daily temporal scale for western US. Bieniek

et al. (2016) proposed a dynamic downscaling scheme to disaggregate precipitation and

temperature data in cold regions. Seyyedi et al. (2014) proposed a stochastic downscaling

scheme applicable to Global Reanalysis Precipitation Datasets (1°x1°) using finer-

resolution satellite and radar-gauge rainfall data products. A monthly high resolution

global precipitation database was created by Karger et al. (2017) using the statistical

downscaling and orographic enhancements.

79

Unlike fully distributed physically-based hydrologic models, computational units

in lumped and semi-distributed models (Krysanova et al., 1999) are conceptual and rely on

the simplification of catchment heterogeneity (i.e., uniformly distributed parameters). The

advantages are reduced parameter requirements and high computational efficiency.

However, the resolution of simplified model units is generally coarser than soil, landscape

and meteorological data, which requires these data to be aggregated to the same or a similar

spatial resolution to produce meaningful hydrologic output. Challenges associated with

upscaling are bias and uncertainty in the resulting model outputs (Ichiba et al., 2018).

Upscaling is often applied to soil parameters, soil moisture (Crow et al., 2005; Mohanty et

al., 2017; Qin et al., 2013; Vereecken et al., 2014), and topographic characteristics (Ozgen

et al., 2015; Pau et al., 2016; Shi et al., 2015). Given the complexity of many hydrologic

models, downscaling and upscaling are often utilized simultaneously (Pau et al., 2016;

Rakovec et al., 2016).

Numerous studies have used models to investigate subsurface process to monitor

the fluid dynamics and biogeochemical reactions (Binley et al., 2015). However, few have

focused on upscaling subsurface flow characteristics due to the complexity of subsurface

conditions (e.g., different soil types such as bedrock or aquifer). Most studies have focused

on soil porous media, i.e. pore-scale (Aguilar-Madera et al., 2019; Blunt et al., 2013;

Farmer, 2002; Frippiat and Holeyman, 2008; Gueguen et al., 2006; Konyukhov et al., 2019).

Vermeulen et al. (2006) reviewed several upscaling techniques for Darcy’s law and the

Richard’s equation and concluded that heterogeneity of hydraulic conductivity and the

boundary condition are key factors in subsurface flow upscaling. Hydraulic conductivity

in Darcy’s law has also been investigated in terms of upscaling (Bierkens and van der Gaast,

80

1998; Ghanbarian et al., 2017; Wen and GomezHernandez, 1996). However, methods have

either focused on soil pore to small catchment scales without considering large-to-regional

numerical modeling or have only been used in fully distributed models. Moreover, some

upscaling methods rely on overly complicated statistical or geostatistical techniques that

significantly increase computational demand and limit applicability to larger regions

(Andra et al., 2013; Zinn and Harvey, 2003). In addition, some upscaling methods lack

application to subsurface flow simulation in hydrologic models and fail to consider

parameter uncertainty and/or bias (Fatichi et al., 2016). Yet, it is critical to understand how

scale or model resolution influence uncertainty and bias for both model inputs and outputs

(Heuvelink, 1998; Saint-Geours et al., 2014; Verburg et al., 2011).

This study has three objectives: (1) integrate subsurface flow processes in the

Travel Time Matching (TTM) method presented in Zhao and Beighley (2017) for upscaling

routing parameters in a semi-distributed hydrologic model; (2) generate spatial-temporal

surface and subsurface runoff using hourly streamflow data from 90 USGS gauges

throughout the Ohio River Basin; and (3) combine both upscaling and downscaling of

surface, subsurface and channel routing parameters in a model calibration application.

4.2. Methodology

In this study, we apply the Hillslope River Routing (HRR) model (Beighley et al., 2009;

Beighley et al., 2015; Yoon and Beighley, 2015), a semi-distributed, physically-based

hydrologic model, to the Ohio River Basin. The model uses kinematic wave routing to

transform lateral surface and subsurface runoff and diffusion wave routing to for channel

and floodplain flows. The key computational units are hillslopes and channel reaches,

81

where hillslopes are approximated as rectangular planes and each catchment is divided into

two identical hillslopes with a channel (Figure 4.1). To reduce the computational cost,

surface and subsurface flow are assumed to be uniformly distributed along the channel

(Figure 4.1b–4.1d). Plane and channel slopes are determined by averaging pixel slopes for

the catchment or only pixels along the channel, and pixel slopes are determined using a

90m Digital Elevation Modeling (DEM). Six USGS gauges are used for calibration (Figure

4.1a).

Figure 4.1. The Ohio River Basin and landscape partitioning in the hillslope river routing

model. (a) A river network of 1000 km2 with six selected U.S. Geological Survey gauges.

(b) One model unit (catchment). (c) A catchment split by a channel. (d) A conceptual

illustration of hillslope and channel routing.

82

4.2.1. Travel Time Matching Framework

The Travel Time Matching (TTM) method (Zhao and Beighley, 2017) adjusts routing

parameters in the model to match travel time distributions generated from landscape (e.g.,

90-m DEM) and model scale flowpath assumptions. To develop the landscape-based travel

time, a reference scale model resolution is used to develop hillslope and channel flow

velocity functions based on flowpath length or contributing drainage area (see Chapter 3).

Previously, only overland flow was considered. The following sections provide a

framework for estimating travel time distribution for subsurface flow and an application

where surface and subsurface routing parameters are upscaled independently in a case

study using measured streamflow in the Ohio River Basin.

4.2.2. Travel Time Distributions for Subsurface Runoff

Similar to the surface flow experiment in Chapter 3, to evaluate the TTM method for

subsurface flow, we apply a synthetic subsurface runoff of 0.254 cm for 1 month to the

entire Ohio River Basin (i.e., roughly 520 m3/s at the outlet). Subsurface flow in the HRR

model is simulated based on the Dupuit approximation with an assumed kinematic wave

that is equal to the head gradient for the slope of the model unit plane slope. Based on

Darcy’s law, the subsurface flow rate (qss) per unit width along a catchment’s hillslope is:

qss = _T�ℎ* 4.1

where K is saturated hydraulic conductivity, Sp is surface slope of the catchment which is

assumed to be the subsurface surface slope, h* is the hydraulic flow depth which is h/Φ

where h is the depth of saturated flow in the aquifer and Φ is the effective porosity of the

subsurface layer. Saturated hydraulic conductivity and effective porosity are obtained from

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the global data set of soil hydraulic and thermal parameters for earth system modeling (Dai

et al., 2013). From equation (4.1), the subsurface flow velocity (u) is:

a = _T� 4.2

Channel velocities are determined using identical procedures from Zhao and

Beighley (2017). Because the Muskingum–Cunge routing method is used in the HRR

model, the velocity in the channel cannot be exported directly from the model. Instead, the

channel discharge from the channel segment (i.e., 10) is exported. The average discharge

for the channel segment of each model unit (Qa,c) is calculated as half of the maximum

discharge (Qm,c):

Qa,c =

NK,b� 4.3

assume that the channel is wide and rectangular, the channel velocity (Vc) is calculated

using Manning’s equation:

� = 1Q %1/R S TA/�

4.4

where n is channel roughness, D is average water depth, W is average channel width, and

S is the slope of the channel. Note that the average channel width is derived from Allen

and Pavelsky (2015). The power function is fit to generate the relationship between the

average channel width and the accumulated area as explained in Chapter 3. From equation

4.2, the velocity of subsurface flow varies for each model unit. To be consistent with the

use of half velocity in the channel, we divide the velocity of subsurface flow by 2 as the

average velocity of subsurface flow.

There are two travel times in this study. One, model-based travel time from the

HRR model, which is based on the assumption of rectangular model unit shape. Two,

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landscape-based travel time based on the velocities and flowpath lengths. Model-based

travel time for a given model unit (��) is:

�� = U ∆��,)AB

)CA 4.5

where M is represents the model, ∆� = ��/10 and is the plane flow length for one length

step along the hillslope, and �,) is the flow velocity at location i along the hillslope

obtained from the reference model. Because the travel time matching method focuses on

the plane subsurface flow travel time, travel time in the channel is ignored.

Landscape-based travel time ( �' ) is determined based on cumulating time

associated with DEM pixel flow lengths and velocities. The pixels velocities are derived

from the reference scale model as described above. A travel time grid is constructed and

the travel times for each pixel contained within a model unit boundary are used to derive

the travel time distribution.

4.2.3. Matching Travel Times by Adjusting Hydraulic Conductivity

In the Travel Time Matching (TTM) approach, the travel time distribution extracted from

the landscape-based travel time pixels within the coarse resolution model boundary is

considered to be the “true” travel time. If the model-based travel time is different from the

true travel time, the hydraulic conductivity of the model unit is adjusted. The goal is to

adjust the CDF of �� to match the CDF of �' by modifying the hydraulic conductivity in

the model along each section of the hillslope to increase or decrease the velocity of

subsurface flow.

85

The travel time CDF modification procedure from (Zhao and Beighley, 2017) is

applied here. For each model unit, only one kinematic wave routing solution is

implemented, and the plane response to the channel is assumed to be uniform along the

channel. Ten quantiles of CDF are used to evaluate the travel time matching: 10%, 20%,

30%, 40%, 50%, 60%, 70%, 80%, 90%, and 99%. The travel time matching procedure

starts from the bottom of the plane. The difference between the CDF of model- and

landscape-based travel time is

∆� (<%) = $%&�(<%) − $%&'(<%) 4.6

where M and L are model- and landscape-based travel time, respectively, and i is the

number of 10 quantiles of the CDFs. The adjusted model-based average plane velocity for

segment i can be determined as

�,)∗ = �∆X�∆X?,) − ∆�(<%)

4.7

where �∆X is the model-based plane segment length and ?,) is the original plane velocity

exported from the HRR model. The velocity modification ratio 2) is determined as:

2) = 4.,6∗4K,6. 4.8

The hydraulic conductivity adjustment factor for segment kd is set to Rd, and 7) is used to

increase or decrease hydraulic conductivity in the kinematic wave solution. Note that 7) is

adjusted for each segment from bottom to top, so the model-based travel time CDF is

recalculated with every new kd generated. To obtain the optimal combination of 10 kd values, the procedure is repeated until the root mean square error (RMSE) of CDFM is less

than 1% of the RMSE of CDFL.

86

4.2.4. Runoff Generation

The second goal of this study is to evaluate the TTM method for both surface and

subsurface runoff. For this experiment, spatial-temporal runoff for a 1-year period

distributed throughout the Ohio River Basin is developed based on USGS streamflow

measurements. Ninety USGS gauges were selected. All gauges have discharge data for

2015 and are located on tributaries to the mainstem of the Ohio River. The USGS gauges

provide daily and 15-min discharge data in most cases. If available, 15-min discharges

were averaged to 1-hr discharge. Otherwise, the daily discharge was used to determine the

hourly discharge, which was used for roughly 10% of the total hourly runoff values that

were generated. For each USGS drainage area, runoff (:f,)(�)) is:

:f,)(�) = H)(�)E) 4.9

where H)(�) is discharge from USGS gauge i at time t and E) is the drainage area for USGS

gauge i. In this research, the time period is 01/01/2015 through 12/31/2015, a period for

which all selected USGS gauges have daily or hourly discharge data.

Because the data from USGS gauges include both surface and subsurface flow, it

is necessary to separate the streamflow. Here, we use the separation technique from (Ayers

et al., 2019; Nathan and Mcmahon, 1990). This method is derived from signal processing,

which considers the hydrograph as the signal and is based on a recursive digital filter. The

filter is described as:

g� = �g�/A + (1 + �)2 (h� − h�/A) 4.10

87

where g� is the filtered quick response at the kth sampling instant, h� is the original

streamflow, and α is the filter parameter; base flow is thus defined as h� - g�. Here α and

k are parameters that must be determined.

Next, the TTM method was applied for both surface and subsurface flow

independently. Each model unit was assigned to one USGS gauge based on its location

(discussed in results section). The surface and subsurface runoffs were then simulated in

HRR for the calendar year 2015.

4.2.5. Model Calibration

Two calibration procedures are investigated. First, with the synthetic subsurface runoff, we

upscale the subsurface hydraulic conductivity for coarse model resolutions to match the

hydrologic responses from reference model resolution using a uniform scale factor. The

calibration is based on minimizing the peak discharge error between the coarse and

reference model resolutions. The peak discharge error (Ep) is:

�� = |H� − HA|HA 4.11

where Qc is the peak discharge at coarse model resolution and Q1 is the peak discharge at

1 km2 model resolution (i.e., reference resolution).

Secondly, we calibrate both surface and subsurface flow routing parameters from

the coarse and reference model resolutions using the runoff generated from the USGS

gauges in the Ohio River Basin (Figure 4.5). For this process, one coarse resolution model

is selected for calibration to USGS streamflow based on computational efficiency and

changes model performance as compared to the reference model. To evaluate model

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performance in the calibration process, we use two goodness-of-fit indices, the Nash–

Sutcliffe Efficiency coefficient (NSE) and Root Mean Squared Error (RMSE):

[T� = 1.0 − ∑ (ij − :j)�k)CA∑ (ij − il)�k)CA 4.12

where t is the time, O is an observation, P is a prediction, and the overbar denotes the mean

for the entire period of the evaluation. The NSE ranges from minus infinity to 1.0, where a

higher value indicates better model performance. Note that, because NSE provides a

dimensionless measurement of model performance, many argue that it should not be used

exclusively (Legates and McCabe, 1999). RMSE is thus used in this research to quantify

the error in units of the variable:

2mT� = n∑ (ij − :j)�k)CA Q 4.13

where n is total number of observation or simulated flow data.

4.3. Results and Discussion

4.3.1. Travel Time Matching for Subsurface Runoff

As discussed previously, the velocity of subsurface flow is determined by saturated

hydraulic conductivity and plane slope (equation 4.2). The TTM method was successfully

applied in cases of both constant and varied slopes for surface runoff in Chapter 3 and

(Zhao and Beighley, 2017). Figure 4.2 shows how the TTM method improves the

simulated streamflow response for each model resolutions. The TTM method increases the

peak flow from all coarse model resolutions except 10 km2. However, the peak discharges

are still not large enough, which is similar to the issue noted in Chapter 3, due to travel

89

time differences between the reference model resolution and landscape-based travel time

used for the TTM method.

Figure 4.2. Hydrographs from the outlet of the Ohio River Basin with synthetic

subsurface runoff (Wei et al., 2014)(Wei et al., 2014)(Wei et al., 2014)(Wei et al.,

2014)at 1000 km2 for (a) before and (b) after apply the TTM framework.

Figure 4.3 shows the mean modified value the saturated hydraulic conductivity (Kh)

for each section from all model resolutions. The bottom section changes (increases) the

most compared to the other sections, which is the same trend as was found for surface

runoff in (Zhao and Beighley, 2017). The figure also shows that saturated hydraulic

conductivity increases more at a coarser model resolution. When the model resolution is

coarser, the plane length is longer, which indicates a longer travel time for subsurface flow.

Increasing the saturated hydraulic conductivity increases the velocity of subsurface flow.

To account for the difference between the reference model resolution and

landscape-based travel time distributions, the hydraulic conductivity is modified by

multiplying it by the uniform scale factor (^o). For each coarse model resolution, the model

is calibrated based on the minimizing peak discharge error (Ep) and maximizing NSE. The

90

Figure 4.3. The mean modified hydraulic conductivity (Kh) along the hillslope for each

model resolution.

resulting scale factors are show in Figure 4.4a. The scale factor increases (i.e., increases

the velocity of subsurface flow) for coarser model resolution, which decreases the travel

time for subsurface runoff. The average scaled hydraulic conductivity for each section of

each model unit is shown in Figure 4.4b. The scaled hydraulic conductivity K* is

calculated as:

_∗ = ^o_o_ 4.14

where K is the original data inputs of hydraulic conductivity, Kh is the modification value

of hydraulic conductivity for the section and ^o is uniform factor. As shown in the Figure

4.4b, scaled hydraulic conductivity increases as the model resolution increases, which

accelerates subsurface flow. The final hydrographs for different model resolutions for

varied effective porosity are shown in Figure 4.4c. Now, simulated discharges from the

coarse model resolution match the discharges from the reference resolution model.

91

Figure 4.4. (a) uniform scale factors, (b) mean model unit scaled hydraulic conductivity,

and (c) simulated discharges for all model resolutions.

92

4.3.2. Ohio River Basin Runoff

Figure 4.5 shows the river network derived from the HRR model at 320 km2 with the 90

USGS gauges selected. The drainage area was delineated for each USGS gauge. The range

of the drainage area is 115 ~ 13,732 km2, with a mean area of 965 km2. Each HRR model

unit was assigned to one USGS gauge. If a model unit is inside a gauge drainage area, that

gauge is used. If a model unit contains multiple gauges the gauge located closest to the

geographic center of the model unit is used. If the model unit does not contain a gauge or

is not within a gauged watershed, the nearest gauge is used.

Figure 4.5. U.S. Geological Survey (USGS) tributary gauges and their contributing land

area (90) selected to derive runoff throughout the Ohio River Basin.

93

The subsurface flow is hard to measure especially in a large basin like the Ohio.

Depending on factors (e.g., season, soil types, rainfall, etc.), the percentage of subsurface

flow in total streamflow can vary significantly (Miller et al., 2016; Sklash and Farvolden,

1979). Chen and Kumar (2001) applied a basin scale hydrologic model to estimate the

contribution of surface and subsurface runoff to streamflow in Mississippi River Basin.

Based on their study, the range of subsurface runoff fraction for Ohio River Basin is 4 ~

65%. Here, the average ratio for the 90 USGS gauges is assumed to be 25%. For baseflow

separation using equation 4.10, values for α and k were determined as 0.9975 and 4,

respectively, providing an annual averaged subsurface runoff fraction of 25%. The

separated baseflow and total runoff are shown in Figure 4.6.

Figure 4.6. Separation of surface and subsurface flow for the Ohio River Basin using

recursive digital filter.

94

4.3.3. TTM Method for both Surface and Subsurface Flow

Based on USGS streamflow and baseflow separation, surface and subsurface runoff time

series were generated throughout the Ohio River Basin. The TTM method was applied to

each model resolution to upscale surface roughness (Chapter 3) and subsurface hydraulic

conductivity (above) separately. The HRR model was then used to simulate streamflow

from the coarse and reference model resolutions using surface and subsurface runoff as

forcings.

Figure 4.7 shows simulated hydrographs with (including uniform scale factors) and

without TTM method for the coarse and reference resolutions models. Note that, the

uniform scale factor is not applied yet and results are only compared to the reference model

to assess TTM method for combined surface and subsurface routing parameters. The first

month of 2015 is used for model warm-up and excluded in the assessment. The TTM

method improves both peak discharge and baseflow, which is clearly seen for the April

through May period. Overall, the pattern is identical to the experiments in (Zhao and

Beighley, 2017) and Chapter 3. However, Figure 4.7d shows that two peak flows from

the 3200 km2 model resolution in April are higher than in the 1 km2 model after adjustment

for surface roughness and hydraulic conductivity. In the previous two studies with synthetic

runoff, peak flow from the coarse model resolution increased but always remained lower

than the peak from the 1 km2 model. This finding suggests that calibration based on peak

error may be not applicable.

95

Figure 4.7. Simulated flow at the outlet of the Ohio River Basin at various model

resolutions using a U.S. Geological Survey Ohio River Basin runoff (a and c) without and

(b and d) with the travel time matching method.

Table 4.1 shows the average NSE, RMSE, and peak error for the six USGS gauges

from the different model resolutions as well as the change in these three goodness-of-fit

indices. Note that, we convert RMSE to mm/day by dividing by the drainage area for each

gauge. For the no adjustment case, all goodness-of-fit indices improve as the model

resolution decreases because there are more channels in the finer model resolution, which

for unscaled surface roughness and subsurface conductivity provides better agreement to

the timing of the observed streamflow. After we adjust surface roughness and hydraulic

conductivity, all evaluation measures improve except for the 10 km2 model resolution. The

96

maximum increases in NSE and the peak error are 13% and 67% at 3200 km2, respectively.

The largest decrease in RMSE is 59% for 3200 km2.

Table 4. 1. Average Nash–Sutcliffe efficiency coefficient (NSE), root mean square error

(RMSE), and peak error (Ep) for six U.S. Geological Survey gauges from the different

model resolutions with and without application of Travel Time Matching (TTM).

Model

resolution,

km2

Without TTM After TTM

Peak

Error NSE

RMSE,

mm/day Peak

Error NSE

RMSE,

mm/day

3200 26% 0.87 0.566 9% 0.98 0.235

1000 25% 0.91 0.460 11% 0.98 0.212

320 14% 0.94 0.385 6% 0.98 0.196

100 10% 0.96 0.304 6% 0.99 0.189

32 7% 0.98 0.226 5% 0.99 0.172

10 4% 0.99 0.153 5% 0.99 0.153

Next, the uniform scale factors for surface roughness (λs) and hydraulic

conductivity (λh) are estimated. Although surface roughness and hydraulic conductivity

were upscaled independently, the two uniform scale factors, surface (λs) and subsurface

(λh), are determined simultaneously. For subsurface flow, hydraulic conductivity is

multiplied by the uniform scale factor (i.e., scale factor directly impacts conductivity; if

λh > 1, conductivity increases). For surface flow, roughness is also multiplied by a scale

factor. However, roughness is inversely related to velocity (i.e., scale factor inversely

impacts surface roughness; if λs < 1, roughness increases). Based 100’s of combination of

the two scale factors, Figure 4.8 shows the peak error, NSE, and RMSE for different

combinations of surface and subsurface scale factors using the 3200 km2 model resolution.

The peak discharge error shows the opposite trend from NSE and RMSE. For example, if

the subsurface factor is fixed at 10, NSE and RMSE continue to improve as the surface

scale factor increases but the peak discharge error increases. Recall that the peak error is

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calculated using the only using the largest peak. Because this study aims to match the

overall hydrograph, the peak ratio is not used as a goodness-of-fit indicator in the

calibration procedure below. The optimal range in the surface scale factor is 0.6 to 0.8 and

2 to 5 for subsurface scale factor.

Figure 4.8. Impacts of surface (λs) and subsurface (λh) uniform scale factors on peak

discharge error, Nash–Sutcliffe efficiency coefficient (NSE), and root mean square error

(RMSE) for the 3200 km2 model resolution.

Numerous combinations of the surface and subsurface factors are simulated to find

the optimal values. A two-step procedure is used to find the optimal combination of

uniform surface and subsurface factors. First, RMSE is used to select the target factors

from the factor ensemble simulations, Next, the target factors are altered slightly and NSE

is used to select the optimal values. The procedure is applied for all model resolutions.

Table 4.2 shows the optimal combinations of the calibrated uniform factors from the

different model resolutions. The calibration criteria are minimum RMSE and maximum

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NSE. For all model resolutions except 3200 km2, NSE is ≥0.99. The resulting scale factors

and TTM adjustments to hillslope roughness and hydraulic conductivity provide simulated

streamflow that from any of the coarse scale models that matches the reference scale model.

Table 4.2. Combinations of surface (λs) and subsurface (λh) uniform scale factors at

different model resolutions with the optimal Nash–Sutcliffe efficiency coefficient (NSE)

and root mean square error (RMSE).

model

resolution,

km2 λs λh NSE

RMSE,

mm/day

3200 0.68 2.63 0.979 0.224

1000 0.30 3.33 0.995 0.104

320 0.24 3.57 0.998 0.058

100 0.20 3.13 0.999 0.040

32 0.22 2.94 0.999 0.037

10 0.20 3.33 0.999 0.037

4.3.4. Calibration Using USGS Streamflow

In the discussion above, TTM method is used for surface and subsurface flow to match

hydrographs from the coarse model resolutions to the fine model resolution. The next step

is to calibrate a coarse resolution model with USGS streamflow measurements and

downscale the calibrated model parameters to the reference model for validation. This

concept is referenced as multi-scale calibration, herein. While multi-scale calibration can

be applied using any of the coarse resolution models, the optimal coarse resolution model

for calibration is identified based on two criteria: (i) model run time (i.e., computational

efficiency); (ii) RMSE between coarse model resolution and 1 km2. Table 4.3 shows

RMSE and model run time from the coarse resolution models and 1 km2 reference model

resolution. Figure 4.9 shows the percent increase in simulation time and percent decrease

in RMSE from the different model resolutions. For 100 and 3200 km2, the average RMSE

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is much higher than other model resolutions. For 10 and 32 km2, although the average

RMSE is the lowest, the model run time is roughly 4-10 times longer. The 320 km2 model

resolution is selected as the optimal calibration model resolution because of the balance

between slightly lower RMSE and short run time.

Table 4.3. Comparison of average root mean square error (RMSE) and model run time

for selected U.S. Geological Survey gauges for the different model resolutions.

Model

resolution,

km2

RMSE,

mm/day RMSE

decrease

Run

time,

sec

Run

time

increase

3200 0.224 100% 9.9 0%

1000 0.104 54% 10.4 5%

320 0.058 44% 15.4 48%

100 0.040 31% 37.3 142%

32 0.037 7% 169.7 355%

10 0.037 2% 1961.3 1056%

Figure 4.9. Percent change in root mean square error (RMSE) and model run time from

the different model resolutions.

0%

20%

40%

60%

80%

100%

120%

0%

200%

400%

600%

800%

1000%

1200%

1 10 100 1000 10000

Pe

rce

nt

cha

ng

e,

RM

SE

Pe

rce

nta

ge

cha

ng

e,

com

pu

tati

on

tim

e

Model resolution, km2

Computation Time RMSE

100

The parameters used for calibration are surface roughness, hydraulic conductivity,

and channel roughness. First, surface roughness and hydraulic conductivity are calibrated

because they are scale-dependent and have potentially large parameter ranges. Then,

channel roughness is calibrated to fine-tune model performance. The 3 parameters are

calibrated in the HRR model for the 320 km2 model resolution using uniform correction

factors for hydraulic conductivity (fh), surface roughness (fs), and channel roughness (fn),

where the simulated parameter is the upscaled value times the correction factor. Here, we

use parameter-after-parameter calibration. That is, the values of two parameters are locked

and only the parameter calibrated is modified in the calibration process. In this study, the

initial factor ranges are 0.1–1000 for fh, 0.00001–10,000 for fs, and 0.1–3 for fn. Figure

4.10 shows the calibration process for the three factors. A fh value of 40 was selected based

on minimum RMSE. Although RMSE continues to improve slightly as fs decreases, a fs

value of 0.1 was selected because there is no significant improvement after 0.1. For channel

roughness, optimal average RMSE is 0.51 mm/day for fn = 1.5. The net effect of these three

factors are to decrease surface roughness (increase surface flow velocity), increase

subsurface conductivity (increase subsurface flow velocity) and increase channel

roughness (decrease channel flow velocity).

101

Figure 4.10 Calibration of the hillslope river routing model at 320 km2 for all five selected

U.S. Geological Survey gauges based on average root mean square error (RMSE) for three

parameters: (a) a uniform parameter for hydraulic conductivity (fh), (b) a uniform

parameter for surface roughness (fs), and (c) a uniform parameter for channel roughness

(fn).

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Because surface roughness and hydraulic conductivity were initially upscaled in

the 320 km2 model using equations 3.13 ([\,)∗ = ^87\,)[\) and 4.14 (_∗ = ô_o_), the

calibration provides:

[∗∗ = g8[\,)∗ = g8^87\,)[\ = ^87\,) × g8[\ 4.15

_∗∗ = go_∗ = goô_o_ = _oô × go_ 4.16

where N** and K** are the model parameters simulated in the coarse scale model resolutions

for surface roughness and hydraulic conductivity. Note that surface roughness and

hydraulic conductivity vary along hillslopes and between model units. Here, the calibration

is intended to adjust the reference model parameter values (i.e., the initial surface

roughness and hydraulic conductivity) as shown in equations 4.15 and 4.16. Thus, the

factors calibrated above can be directly applied to the 1 km2 model resolution parameter

values. The results (Table 4.4) show that RMSE for all gauges from the 1 km2 model are

improved and similar to the 320 km2 model with 39.4% less average RMSE. As shown in

Table 4.3, the minimum achievable RMSE for 320 km2 model resolution is 0.058 mm/day.

Of the three parameters calibrated for the 320 km2 model, fh and fs are uniform factors for

lateral flow (e.g., surface and subsurface) and can be applied to other model resolutions. In

contrast, channel roughness for the 320 km2 model can be applied to other model

resolutions but not directly because the channel network is varied for different model

resolutions.

103

Table 4.4. Root mean square error (RMSE) for five selected gauges at 320 km2 model

resolution and a comparison of the same gauges at 1 km2 with and without the same

calibrated parameters.

USGS

gauge

320 km2 original,

mm/day

320 km2 final,

mm/day

1 km2 original,

mm/day

1 km2 final,

mm/day

3086000 0.343 0.368 0.420 0.404

3216600 0.636 0.618 0.684 0.631

3277200 0.640 0.623 0.690 0.635

3294500 0.521 0.473 0.489 0.486

3303280 0.545 0.534 0.569 0.545

Average

RMSE 0.537 0.523 0.570 0.540

Average

NSE 0.838 0.846 0.816 0.838

The calibration process for the 320 km2 model resolution discussed above involves

calibrating factors one by one. Figure 4.11a shows that the optimal parameters determined

previously (i.e., fh - 40, fs - 0.1, fn - 1.5) are within the optimal range based on Monte Carlo

type simulations where all model parameters are changed randomly within their respective

ranges. Figure 4.11 shows there are many combinations of fh and fs that result in the optimal

RMSE, but a specific range for fn. This suggests that RMSE may not be ideal for

determining fh and fs because they both contribute to streamflow. Increasing one and

decreasing the other can lead to limited net change in RMSE. The importance of fn also

suggests that the TTM should be further modified to allow for channel roughness scaling.

Based on these calibration results, Figures 3.10b and 4.6c are updated to represent how

calibrated surface runoff and subsurface hydraulic conductivity vary with model resolution.

Based on comparisons to USGS streamflow, Figures 4.12a&b provide estimates of surface

roughness and subsurface hydraulic conductivity applicable to semi-distributed hydrologic

models for the Ohio River Basin. The change in model parameters with resolution may

provide insights for scaling behavior in other watersheds.

104

Figure 4.11. (a) Four-dimensional and (b–d) three-dimensional plots of the root mean square error from various ranges of three

parameters during the HRR calibration process after application of the travel time matching method.

105

Figure 4.12. Estimated (a) surface roughness (N**) and (b) hydraulic conductivity (K**)

based on the TTM framework and calibration to USGS streamflow for different model

resolutions.

4.4. Conclusion

This study demonstrates that the TTM method, which was developed for the surface runoff

routing, can be applied to subsurface routing in the HRR model. Furthermore, the method

can be applied to surface and subsurface routing simultaneously. Using the Ohio River

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Basin as case study, relationships between surface roughness and hydraulic conductivity

and model resolution are presented and intended to provide insight on how lateral runoff

routing parameters scale in hydrologic models.

An analysis of model run time and improvements in RMSE suggests that the 320

km2 model resolution is ideal for calibration. Surface roughness, hydraulic conductivity,

and channel roughness were calibrated using the 320 km2 resolution model, with surface

roughness and hydraulic conductivity upscaled based on the TTM, and USGS streamflow

from six gauges along the Ohio River Basin. The calibrated model parameters were then

transformed to the 1 km2 resolution model, resulting in minimal changes in calibrated

RMSE and NSE (i.e., no loss in model performance from calibration resolution to reference

resolution). This application suggests that TTM method can be used for parameterization

and calibration in hydrologic modeling. Because the current method focuses on surface and

subsurface flow routing, future work will focus on methods to integrate runoff generation

model parameters and forcing data (e.g., precipitation and evapotranspiration) into the

scaling framework.

107

5. SUMMARY AND FUTURE WORK

5.1. Summary

This dissertation presents a scaling framework (Travel Time Matching) for lateral surface

and subsurface runoff routing in hydrologic models. The framework is demonstrated using

synthetic rainfall-runoff experiments and observed streamflow in the Ohio River Basin. A

multiscale calibration experiment is presented where a coarse resolution model is

parameterized using Travel Time Matching and calibrated using USGS streamflow. The

calibrated parameters are then transformed to a fine spatial resolution model without

degraded model performance. The findings from this research are used to answer the three

research questions:

(1) How do simulated flowpath characteristics and runoff response timing changes with

spatial model resolution?

With model resolution becomes finer (i.e., smaller spatial resolution), the mean model unit

area, plane length, and channel length become smaller or shorter (Figure 2.4 and Table

2.1). Here, model resolution corresponds to the threshold area used to define the river

network and corresponding model unit boundaries. For a threshold area of 1 or 1000 km2,

the mean model unit area increases from 1.5 km2 to 1,510 km2, which is similar but not

exactly the underlying threshold area. Here, we use the threshold area to define model

resolution. Changing model resolution from 1 km2 to 1000 km2, the mean plane length

108

increases from 0.73 to 7.41 or by a factor of 10.2. However, the cumulative length of

channels within the Ohio River Basin decreases from 671,000 km to 35,400 km. This

increased hillslope length and loss of channel density leads to surface and subsurface runoff

taking longer to reach a channel, increasing the time to peak discharge and decreasing the

peak discharge resulting from both surface and subsurface flow (Figure 2.7, 3.5, and 4.3).

For example, the peak discharge decreases from 56,800 to 13,500 m3/s (from 1 to 1000

km2 model resolution) for the synthetic rainfall-runoff experiment with constant velocity

assumption in Chapter 2. The time to peak increases from 38 to 59 hours. Although results

for only two resolutions are presented here, the findings presented in Chapters 2 and 3

provide details on how simulated flowpath characteristics and runoff response timing

changes with spatial model resolution.

(2) Can representative travel time characteristics be used to estimate scale-dependent

process parameters in semi-distributed hydrologic models?

Travel time estimates are used to alter surface roughness and hydraulic conductivity to

ensure similar response magnitude and timing regardless of model resolution. The time

difference between model- and landscape-based travel time is minimized by modifying the

surface roughness and hydraulic conductivity (i.e., adjusting surface and subsurface flow

velocities) along model unit hillslopes. The travel time matching method effectively

upscaled and transformed the information from finer to coarser model resolutions. In the

synthetic surface and subsurface runoff experiments, results show that hydrologic

responses from all coarse model resolutions match the reference model response with a

peak discharge error ≤ 1% and NSE ≥ 0.98. Over the range of model resolutions from 1 to

109

3200 km2, surface roughness and conductivity must be reduced a factor of 0.07 (i.e., from

0.8 to 0.056) and increased by a factor of 7 (i.e., from 0.59 to 4.23 cm/hr), respectively.

Based on mean model unit values, relationships are present to estimate surface roughness

and conductivity based on model resolution (Figure 4.12). These findings suggest that

representative travel time characteristics can be used estimate scale-dependent process

parameters in semi-distributed hydrologic models.

(3) Can scaling be used to transfer calibrated model parameters across model resolutions?

The upscaling framework was applied for both surface and subsurface flows using runoff

derived from observed USGS flow data in Ohio River Basin. Root Mean Squared Error

(RMSE) and Nash–Sutcliffe Efficiency (NSE) were used as goodness-of-fit indicators. The

upscaling results show that hydrologic responses from the coarse model resolution matched

the reference model resolution with all NSEs ≥ 0.95 and RMSEs ≤ 0.3 mm/day. A model

resolution of 320 km2 was selected based on a balance between changes in RMSE and

computational efficiency. The selected coarse model resolution (i.e., 320 km2), which was

parameterized by upscaling surface roughness and hydraulic conductivity values from the

reference model resolution, was calibrated using USGS streamflow measurements for a

one-year period by uniformly adjusting surface roughness and hydraulic conductivity to

minimize RMSE and maximize NSE. Given the upscaling approach maintains the initial

reference model parameter value (i.e., P* = ^ × &? × : ; see equation 3.14 and 4.14,

where P is the initial coarse scale model parameter), the calibrated model parameters (i.e.,

P** = f x P* = [f × P] × [^ × Fm]) can be used to estimate the reference model values. Using

this approach, the calibrated parameters were applied to reference model resolution and the

110

resulting NSE and RMSE between the reference model and USGS streamflow were similar

(NSE of 0.838 and RMSE of 0.54) to the values resulting from the calibrated 320 km2

model resolution (NSE of 0.846 and RMSE of 0.523). In other words, there was no loss

of model performance when using the parameter factors obtained from calibration at

resolution of 320 km2 in the reference 1 km2 model resolution. Thus, these findings suggest

that scaling can be used to transfer calibrated model parameters across model resolutions.

5.2. Limitations

In the velocity and travel time estimation process, there are several key assumptions. In

addition, several limitations have been identified and are discussed below:

(1) Several key assumptions are applied to estimate velocities. First, the velocity is assumed

to be steady state to estimate the travel time, e.g. 0.01 m/s for surface flow and 1 m/s for

channel flow in Chapter 2. The average velocity is used and defined as the 50% of the

maximum velocity for both hillslope and channel to simplify the calculation because

velocity is changeable with time. There are other options to determine the average velocity.

For example, instead of 50%, the percentage of the maximum velocity can be adjusted

based on optimal RMSE and NSE for travel time matching. An alternative approach is to

export the velocities during actual event periods (i.e., 1 day or 1 month) and calculate the

average velocity during that specific time period. For the channel velocity estimates,

channel width is derived using data from (Allen and Pavelsky, 2015) and drainage area.

However, in their study, there is no data for small channels with widths less than 30 meters,

because of the resolution of satellite images. In this dissertation, for the channel width less

111

than 23 meters (i.e., all rivers draining less than 1000 km2), we directly applied that derived

relationship. For example, the developed relationship (Figure 3.3) results in a width of 1.1

m for a river draining 1 km2, which is much less than the minimum width in the (Allen and

Pavelsky, 2015) dataset.

(2) In the travel time matching process, the CDF of landscape-based travel time is

approximated using a beta distribution because it is computationally expensive to extract

the pixel-based travel time CDF for each coarse model unit. For the coarser resolutions,

each model has hundreds of thousands of pixels. For the model-based travel time estimates,

there are only 10 segments for the HRR hillslope. Thus, the model-based travel time can

only be estimated from 10 segments. Although the velocity for each segment is interpolated

to generate the travel time CDF, and the CDF matching scheme is only based on the 10

segments. The number of segments on the plane could be increased to obtain more accurate

travel time CDF.

(3) In this study it is assumed that the landscape-based travel time represents the model-

based travel time for the reference model resolution. Plus, the hillslope velocities are

estimated as function of hillslope length derived from the HRR model and applied to the

landscape (i.e., lengths are not the same). In the travel time matching procedure, the model-

based travel time from the coarse model resolutions match the landscape-based travel time

at the reference model resolution. However, the discussion in Chapter 3 indicates that the

model-based and landscape-based travel time are different at the reference model

resolution (i.e., model-based travel time is 1.3 times shorted than landscape-based travel

112

time for just the hillslope portion). Thus, a uniform scale factor is applied to coarse model

resolutions to account for the difference between model-based and landscape-based travel

time at reference model resolution.

5.3. Future Work

The scaling framework presented herein can be further improved and integrated with other

research. Below are the suggestions for future work.

(1) The model-based travel time is generated using the open book assumption with the

rectangular planes. Based on the discussion in Chapter 2 (Figure 2.9 and 2.10), results

show that the rectangular shape is not an appropriate assumption. The average drainage

area ratio (defined as average ratio of mean landscape and model-based drainage area) is

not equal to 1 for all model resolutions, which suggests that the drainage area is not

uniformly distributed along the channel. The ratio varies from 0.93 to 1.31 among all model

resolutions. In general, as model resolution increases, the average drainage area ratio tends

to decrease, suggesting that rectangular shape assumption is less ideal as model resolution

increases. A model resolution of 10 km2 results in a ratio close to 1. An alternative approach

is to use a triangular shape, with the vertex at the outlet of the catchment, the plane length

at the upstream end would be longer than the downstream end. Another method is irregular

section based on the distribution of the cumulated area along the channel. First, the channel

could be broken into sections, e.g., 10 sections of channel in HRR. Then, the cumulated

area for each section could be estimated, and the plane length of each section could be

calculated based on the percentage of the section’s contributing area relative to the total

113

catchment drainage area. In general, future efforts are needed to better represent flowpath

characteristics in larger scale models.

(2) The runoff series derived from USGS streamflow data considers only 90 gauges from

tributary catchments. To improve runoff estimates, more gauges could be used. Although

the upscaling framework in this research focuses on runoff routing process, future research

is needed to integrate runoff generation processes and associated forcings such as

precipitation.

(3) In the TTM method, there are multiple assumptions related to the velocity and

flowpaths, uncertainties resulting from both those assumptions will be investigated in the

future. Instead of providing one value for scaled surface roughness or hydraulic

conductivity, the modified factors could be expressed as a range, and used for simulating

ensembles in the coarser scale models. Because of the computational efficiency of the

coarser models, the upscaling framework could be integrated with other uncertainty

analyses related to calibrated parameters, initial conditions, or multiple forcings.

(4) This dissertation only investigates routing parameter scaling in the Ohio River Basin.

It can also be applied to other hydrologic regions or globally. Developing relationships

between surface roughness, soil properties and spatial model resolution can be useful for

many modeling efforts. Global scaling relationships could provide insights for how to

account for sub-grid scale routing processes in current Earth System Models.

114

(5) The TTM framework can be extended and integrated with other interdisciplinary

studies. For example, the human impact has become an important factor in hydrologic cycle

(Aerts et al., 2018; Barnett et al., 2008; Fatichi et al., 2016), which is defined as ‘socio-

hydrology’. Sivapalan et al. (2012) suggested that socio-hydrology faces more complicated

prediction challenge across space and time scales, such as the urbanization development

that the urban area and population will increase in the future (Fletcher et al., 2013). It is

necessary to consider such scenarios for the improvement of the TTM framework. Such

improvement can also be valuable for investigation of climate change issues as TTM

framework can be integrated with other Earth System Models.

115

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135

APPENDIX

A.1 USGS Gages in Ohio River Basin

This section provides information about the USGS gages.

Table A.1 shows detailed information about the 6 USGS gages used in TTM

method.

Table A.2 shows detailed information about the 90 USGS gages which are used to

generate the runoff map for Ohio River Basin.

Table A. 1. Detailed information about the 6 USGS gages in Ohio River Basin used in

TTM method.

Gauge ID Latitude Longitude Drainage

area, km2

03086000 -80.21 40.55 50424

03216600 -82.86 38.65 160532

03277200 -84.96 38.77 214718

03294500 -85.80 38.28 236027

03303280 -86.71 37.90 252134

03611500 -88.74 37.15 525341

136

Table A. 2. Information for 90 USGS gauges used in the generation of runoff map for

Ohio River Basin

Gauge ID Latitude Longitude

Drainage

area, km2

03010820 42.07 -78.45 1192

03015000 41.94 -79.13 816

03015500 41.85 -79.32 321

03020000 41.48 -79.44 479

03020500 41.48 -79.70 283

03024000 41.44 -79.96 1028

03030500 41.19 -79.44 951

03032500 40.99 -79.39 528

03036000 40.93 -79.29 344

03039000 40.72 -79.51 278

03048500 40.60 -79.55 1825

03049000 40.72 -79.70 137

03056000 39.32 -80.03 1182

03061000 39.42 -80.28 759

03070260 39.49 -79.64 1044

03070500 39.62 -79.70 200

03072000 39.76 -79.97 229

03083500 40.24 -79.81 1715

03085500 40.40 -80.10 257

03106000 40.82 -80.24 356

03106500 40.88 -80.23 398

03105500 40.89 -80.34 2235

03108000 40.63 -80.34 178

03109500 40.68 -80.54 496

03110000 40.54 -80.73 147

03111500 40.19 -80.73 123

03112000 40.04 -80.66 281

03114500 39.48 -81.00 458

03115786 39.51 -81.42 260

03139000 40.48 -81.99 464

03155220 39.08 -81.21 229

03155000 39.06 -81.39 1516

03164000 36.65 -80.98 1141

03167000 36.94 -80.89 258

03170000 37.04 -80.56 309

03173000 37.27 -80.71 299

03175500 37.31 -80.85 223

137


Drainage

area, km2

03179000 37.54 -81.01 395

03184000 37.64 -80.81 1619

03192000 38.23 -81.18 1317

03197000 38.47 -81.28 1145

03200500 38.34 -81.84 862

03202000 38.87 -82.36 585

03202400 37.60 -81.65 306

03205470 38.60 -82.50 302

03216500 38.33 -82.94 400

03217000 38.56 -82.95 242

03221646 39.99 -83.07 1050

03229500 39.86 -82.96 544

03229796 39.71 -82.96 274

03230500 39.70 -83.11 534

03234300 39.32 -82.98 1136

03247500 39.14 -84.24 476

03245500 39.17 -84.30 1203

03250500 38.42 -84.00 1785

03251200 38.59 -84.02 226

03253000 38.66 -84.35 915

03259000 39.20 -84.47 115

03266000 39.87 -84.29 650

03263000 39.87 -84.16 1149

03270000 39.80 -84.09 635

03272000 39.64 -84.40 275

03276500 39.41 -85.01 1224

03291500 38.71 -84.82 437

03280000 37.55 -83.39 1101

03281000 37.56 -83.59 537

03281500 37.48 -83.68 722

03283500 37.86 -83.93 362

03289500 38.27 -84.81 473

03303000 38.24 -86.23 476

03314500 37.00 -86.43 1849

03373500 38.67 -86.79 4927

03376500 38.39 -87.55 822

03343010 38.68 -87.54 13732

03346500 38.72 -87.66 2333

03381500 38.06 -88.16 3102

03384100 37.40 -87.85 605

03430200 36.19 -86.63 934

138


Drainage

area, km2

03434500 36.12 -87.10 683

03436100 36.55 -87.14 926

03438000 36.78 -87.72 244

03532000 36.54 -83.63 685

03540500 35.98 -84.56 764

03566000 35.30 -84.76 2298

03567500 35.01 -85.21 428

03571000 35.21 -85.50 402

03584600 35.01 -86.99 1805

03592500 34.66 -88.12 667

03604400 35.81 -87.78 702

03603000 35.93 -87.74 2557

139

A.2 Sample Code

The sample code for the entire TTM procedure is provided in this appendix, including the

code used to setup, run and calibrate the HRR model. For more information, please go to

github: github.com/yownho.

HRR Setup:

Step 1:

"""

GIS setup for Hillslope River Routing Model (HRR) step 1

Parts:

1. Creation of Flow Accumulation Threshold Grid, Stream Link, Watershed, Watershed

Polygon,

and Derived River Network;

2. Create longest flow path shapefile. Unlike stream shapefile, the lfp is based on 1sqkm

(or even smaller

drainage area).

Hydro-Geo-Spatial Research Lab

Website: http://www.northeastern.edu/beighley/home/

By: Yuanhao Zhao

Email: [email protected]

"""

import arcpy, os.path

from arcpy import env

from arcpy.sa import *

from operator import itemgetter, attrgetter

import sys

arcpy.env.overwriteOutput = True

arcpy.CheckOutExtension("Spatial")

#####***** input parameters *****#####

unit = 'Meter' # Unit for DEM grid, Meter or Degree

DEMcellSize = 30 # Grid size of DEM data decimal degrees

targetWorkspace = r"C:\Research\HRR_python_example\MissionCreek\GIS_working"

# Folder. Output workspace

flowAccumulation = r"C:\Research\HRR_python_example\MissionCreek\GIS_basic\fac"

# Raster file of flow accumulation

140

drainageDirection = r"C:\Research\HRR_python_example\MissionCreek\GIS_basic\fdr"

# Raster file of flow direction

A_thrhld = 1.0 # Threshold area to determine stream network

tip area, sqkm

A_thrhold_lfp = 0.1 # Threshold area for longest flow path,

sqkm

num_tip = 1.0 # Threshold to determine longest flow path

(LFP) for headwater catchments. Here the number is

# number of pixels, determined by user (please

check lfpstr.shp in GIS after)

#####****************************#####

#####*****First part*****#####

if unit == 'Meter':

lngThreshold = int (A_thrhld/(DEMcellSize*0.001)/(DEMcellSize*0.001))

lfpThreshold = int(A_thrhold_lfp/(DEMcellSize*0.001)/(DEMcellSize*0.001))

lfptip = num_tip*DEMcellSize

elif unit == 'Degree':

lngThreshold = int

(A_thrhld/(DEMcellSize*60*60*30*0.001)/(DEMcellSize*60*60*30*0.001))

lfpThreshold =

int(A_thrhold_lfp/(DEMcellSize*60*60*30*0.001)/(DEMcellSize*60*60*30*0.001))

lfptip = num_tip*DEMcellSize

else:

print 'Error: Units are not set'

sys.exit()

arcpy.env.workspace = targetWorkspace

# Set output variables, no need to modify

strGrid = "StrGrid"

streamLink = "StrLink"

streams = "Streams.shp" #stream network feature

watershed = "Watersheds"

catchmentsAll = "Catch_many.shp"

catchments = "Catchments.shp" #catchments feature

maxFacc = "MaxFAcc.dbf"

rivPt = "River_Pts.shp"

lfpTable = "lfp.dbf"

maxfl = "maxfl"

outlfp = "lfp"

lfp_str = "lfpstr.shp" #longest flow path for headwater catchments. Same for inter basin

catchments.

desc = arcpy.Describe(targetWorkspace)

isGDB = desc.workspaceType # FileSystem if not GDB, else type of GDB.

141

if isGDB != "FileSystem":

catchments = catchments [:-4]

streams = streams [:-4]

catchmentsAll = catchmentsAll [:-4]

maxFacc = maxFacc [:-4]

rivPt = rivPt [:-4]

# Execute and Save Stream Grid file of all streams in catchments greater than lngThreshold

outFlowAccumulationRC = Raster(flowAccumulation) >= lngThreshold

outFlowAccumulationRC.save(strGrid)

# Print Message

arcpy.AddMessage("Stream Grid grid created successfully!")

print arcpy.GetMessages()

# Execute and Save Stream Link Grid

outStreamLink = StreamLink(strGrid, drainageDirection)

outStreamLink.save(streamLink)

# Print Message

arcpy.AddMessage("Stream link grid created successfully!")


# Execute Stream to Feature

StreamToFeature(streamLink, drainageDirection, streams, "NO_SIMPLIFY")

# Print Message

arcpy.AddMessage("Derived streams feature class created successfully!")


# Execute and Save Watershed Grid

outWatershed = Watershed(drainageDirection, streamLink)

outWatershed.save(watershed)

# Print Message

arcpy.AddMessage("Watershed grid created successfully!")


# Convert watershed grid to polygons

arcpy.RasterToPolygon_conversion(watershed, catchmentsAll, "NO_SIMPLIFY",

"VALUE")

# Print Message

arcpy.AddMessage("Watershed grid converted to polygons successfully!")


# Dissolve Watershed polygons

arcpy.Dissolve_management(catchmentsAll, catchments, "GRIDCODE")

# Print Message

142

arcpy.AddMessage("Watershed polygons dissolved successfully!")


arcpy.RasterToPoint_conversion (streamLink, rivPt, "VALUE")

arcpy.AddMessage("Created stream link point file.")


arcpy.AddMessage(catchments + "GRIDCODE"+ flowAccumulation+ maxFacc)


arcpy.sa.ZonalStatisticsAsTable (catchments, "GRIDCODE", flowAccumulation,

maxFacc, "DATA", "MAXIMUM" )

arcpy.AddMessage ("Max Flow Accumulation table created")

print arcpy.GetMessages ()

#####*****Goal 2*****#####

print 'Create upd raster'

fdir1 = SetNull(flowAccumulation <= lfpThreshold,drainageDirection)

downl = FlowLength(fdir1, "DOWNSTREAM", "")

upl = FlowLength(fdir1, "UPSTREAM", "")

upd = downl + upl

print 'zonal'

ZonalStatisticsAsTable(catchments, "GRIDCODE", upd, lfpTable, "DATA",

"MAXIMUM")

arcpy.JoinField_management (catchments, "GRIDCODE", lfpTable, "GRIDCODE")

print 'Get maxfl raster'

arcpy.PolygonToRaster_conversion(catchments, "MAX", maxfl, "CELL_CENTER",

"NONE", DEMcellSize)

print 'Get LFP raster'

lfp = (upd + lfptip) > maxfl

#lfp.save(outlfp) #LFP grid

#Create LFP feature shapefile

print 'make raster to feature'

lfpR = SetNull(lfp, lfp, "Value = 0")

arcpy.RasterToPolyline_conversion(lfpR, lfp_str,"ZERO","","NO_SIMPLIFY","")

print 'Success!'

143

Step 2:

"""

GIS setup for Hillslope River Routing Model (HRR) Step 2

Parts:

1. Takes catchments table, streams table, Flow accumulation grid. Output is HRR setup

tables, with each catchment

grouped by Watershed IDs. Table is ordered by unique HRRID. In first table, HRRID

sorted in MAX. In final table,

HRRID is sorted on 1) WID and 2)Cumulative Area. Area is in number of grid pixels.

2. Calculate lfp length for each catchment, in km.

3. Takes HRR table, catchments shapefile projected, streams shapefile projected. Add

fields to catchments (Area sqkm) and streams (Length km) and CumA Sqkm.

Fill first two from joined fields. Cum A from variation of CumA HRR.



By: Yuanhao Zhao


"""

import arcpy, os.path






#####************************************* input parameters

******************************************#####

cellSize = 30 #Raster size, in meter or degree

targetWorkspace = r"C:\Research\HRR_python_example\MissionCreek\GIS_working" #

Output workspace

flowAcc = r"C:\Research\HRR_python_example\MissionCreek\GIS_basic\fac" # flow

accumulation raster

region = 'MC' #two letters represent simulated bas

zone = '01' #two numbers represent the model run

projection = r"C:\Users\Yuanhao\Google

Drive\Research_Yuanhao\HRR_Py_YZ\Raster\Lambert Azimuthal Eq Area N America

(Flood).prj" #shapefiles need to be projected in meters

projected = 'false' #True if streams and catchments already projected in meters

#####*******************************************************************

******************************#####

144

def main ():


place = region + zone

#files generated from step1, no need to modify

streamsFC = "Streams.shp" #stream shapefile from step 1

maxFacc = "MaxFAcc.dbf" #dbf file from step 1

catch = "Catchments.shp" #HRR catchments

LFP = "lfpstr.shp" #LFP shapefile

#out feature, no need to modify

lfp_m = "LFPstr_m.shp"

lfpits = "lfpits.shp"

StrDis = "lfpstrd.shp"

#####***** part1 *****#####

#Check workspace type, and set output names




newTableFinal = "HRR_Table2_" + place

newTable = "HRR_Table1_" + place

else:

newTableFinal = "HRR_Table2_" + place + ".dbf"

newTable = "HRR_Table1_" + place + ".dbf"

arcpy.CopyRows_management (streamsFC, newTable)

joinTable (newTable, maxFacc)

addFieldsTable (newTable)

deleteFields (newTable)

fillZeroes (newTable)

buildChannels (newTable, 1)

cumArea (newTable)

assignWID (newTable)

arcpy.Copy_management (newTable, newTableFinal)

buildChannels (newTableFinal, 2)

cumArea (newTableFinal)

assignWID (newTableFinal)

145

relateHRR (newTableFinal)

arcpy.AddField_management(newTableFinal, "Error", "FLOAT")

expression = 'float(!CumArea!*1.0 - !MAX!) / float (!CumArea!)'

arcpy.CalculateField_management (newTableFinal, 'ERROR', expression, 'PYTHON')

print "Error calculated"

#####***** Part2 *****#####




hrr3 = "HRR_Table3_" + region + zone

else:

hrr3 = "HRR_Table3_" + region + zone + ".dbf"

arcpy.Copy_management (newTableFinal, hrr3)

arcpy.Intersect_analysis([LFP,catch], lfpits)

arcpy.Dissolve_management(lfpits, StrDis, "GRIDCODE", "", "MULTI_PART",

"DISSOLVE_LINES")

print 'Pjoject to meters'

if (str(projected) == 'false') or (projected == False):

print "Projecting streams and catchments"

arcpy.Project_management(StrDis, lfp_m, projection)

#calculate the channel length, add to the HRR3 table

print 'Calculate LFP'

fillFieldsLFP (hrr3, lfp_m)

#####***** Part3 *****#####

if (str (projected) == 'false') or (projected == False):

print "Projecting streams and catchments"

catch, streamsFC = projectFCs (catch, streamsFC, projection, targetWorkspace)

fillFields (hrr3, catch, streamsFC, region, zone)

arcpy.AddMessage ("Success")


def checkGC (table):

""" Returns correct Grid Code field. Can be either GRIDCODE or GRID_CODE """

fields = arcpy.ListFields (table)

#Get correct name for gridcode field

for f in fields:

146

if f.name.upper() == "GRID_CODE":

return "GRID_CODE"

elif f.name.upper() == "GRIDCODE":

return "GRIDCODE"

def joinTable (streamstable, table):

"""Joins streams shapefile to MaxFAcc on Grid Code, for max FAcc by

stream/catchment."""

fields = ['COUNT', 'MAX']

gcTable = checkGC (table) # Get correct grid code name

gcStream = checkGC (streamstable)

arcpy.JoinField_management(streamstable, gcStream, table, gcTable, fields)

def addFieldsTable (table):

"""Add new fields"""

#HRR_ID is the ID in order of sort from low MAX to high MAX

# WID is watershed ID

# Down_ID is the next grid code downstream

# NumUp is the number of watersheds directly upstream

# Up1, Up2, Up3 are grid codes of watersheds directly upstream

# CumArea is the cumulative area of the upstream watersheds.

fieldNames = [["HRR_ID", "LONG"], ["WID", "LONG"], ["Down_ID","LONG"],

["NumUp","SHORT"], ["Up1ID","LONG"],

["Up2ID", "LONG"], ["Up3ID", "LONG"], ["CumArea", "FLOAT"]

]

for f in fieldNames:

arcpy.AddField_management (table, f[0], f[1])

def deleteFields (table):

""" Delete unneeded fields"""

fieldNames = ['AREA', 'GRID_COD_1', 'SHAPE_LENG']


arcpy.DeleteField_management (table, f)

def fillZeroes (table):

""" Fill zeroes into columns where zero is the default value """

fieldNames = ["NumUp", "Up1ID", "Up2ID", "Up3ID", "WID"]


arcpy.CalculateField_management (table, f, 0)

def buildChannels (table, n):

#Build channels- associate from-to nodes with Grid Codes up and downstream,

#associate watershed values."""

numRec = int (arcpy.GetCount_management (table).getOutput (0))

147

##NumRec needs to be at least highest number found in from/to, because to and from

nodes labels can be > number of records.

numRec += numRec*10

gcNewTable = checkGC (table)

toFrom =[0 for x in range (numRec)] #List where record number n is the from value

fromTo = [0 for x in range (numRec)] #List where record number n is the to value

sink = [0 for x in range (numRec)] #List to hold values for all records that are sinks or

outlets.

downID = [-1 for x in range (numRec)]

numUp = [0 for x in range (numRec)]

up1 = [0 for x in range (numRec)]



hrr = [0 for x in range (numRec)]

dict = {} #Will contain {grCode:[0 downID, 1 numUp, 2 up1, 3 up2, 4 up3, 5 sink, 6

hrr]}

print 'new table grid code is', gcNewTable

fields = [gcNewTable, "MAX", "FROM_NODE", "TO_NODE", "HRR_ID",

"DOWN_ID", "NUMUP", \

"Up1ID", "Up2ID", "Up3ID", 'WID', 'CumArea']

with arcpy.da.SearchCursor (table, fields) as cursor:

# Stores all records referenced to grCode in a list of dictionaries.

for row in cursor:

grCode = row[0]

dict[grCode] =[0 for x in range (5)]

#Sorts cursor by MAX

cursor.reset ()

#Fills toFrom

for row in cursor:

fromID = int (row[2]) #From_Node

grCode = row[0]

# index fromID = grCode

toFrom [fromID] = grCode #c #ToFrom goes current from node to current grid

code.

cursor.reset ()

#Fills fromTo

m = 1 #sink num

148

# Sort records

if n == 1:

cursor = sorted (cursor, key = itemgetter (1)) # Sort on MAX

else:

cursor = sorted (cursor, key = itemgetter (10,11)) #sort on WID, then CumArea

for row in cursor:

grCode = row[0]

toID = int (row[3]) #To_Node

k = toFrom [toID] #k = grid code at the To_Node

if k == 0:

fromTo [grCode] = 0 #There is no down unit

sink [grCode] = m #This is a sink or terminus.

m +=1

else:

fromTo [grCode] = k #Row ID for the down unit (dpfaf)

sink [grCode] = 0 #This is not a sink or terminus.

#Fills column downValue

# Sort records

for row in cursor:

grCode = row[0]

downID [grCode] = fromTo [grCode] #Assigns DownID

if n == 1:

print "n = 1, sort on MAX"

cursor = sorted (cursor, key = itemgetter (1)) # Sort on MAX

else:

print "n != 1, sort on WID & CumArea"

cursor = sorted (cursor, key = itemgetter (10,11)) #sort on WID, then CumArea

#Fills upID values. Next two loops are where data MUST be sorted by area (MAX)

c = 1

for row in cursor:

grCode = row[0]

dstr = downID [grCode]

hrr[grCode] = c

if up1[dstr] == 0: #If up1 at the next downstream is 0

up1 [dstr] = grCode #upID1 at row num downID = current row (c)

numUp [dstr] = 1

elif up1[dstr] > 0:

if up2 [dstr] == 0:

up2 [dstr] = grCode

numUp [dstr] = 2

elif up3 [dstr] == 0:

149

up3 [dstr] = grCode

numUp [dstr]= 3

elif dstr > 0:

numUp = 9999

print (str (dstr) + "has more than 3 watersheds flowing into it")

c +=1

# Sort records

# fills dictionary with values for use in update cursor.

for row in cursor:

grCode = row[0]

dict[grCode] = [downID[grCode], numUp [grCode], up1[grCode], up2[grCode],\

up3[grCode], sink[grCode], hrr[grCode]]

print "Channels determined"

#Update rows

with arcpy.da.UpdateCursor (table, fields) as cursor:

for row in cursor:

grCode = row[0]

row [4] = dict [grCode] [6]

row [5] = dict [grCode][0]





row [10] = dict [grCode] [5]

cursor.updateRow (row)

print "Channels Built"

if cursor:

del cursor

def cumArea (table):

""" Calculates cumulative area of watershed at current catchment for each catchment in

a watershed"""


fields = [gcNewTable, "COUNT", "UP1ID", "UP2ID", "UP3ID", "CumArea",

"HRR_ID"]


numRec += numRec*10

countL = [0 for x in range (numRec)] #List of all areas in Count field

sumArea = [0 for x in range (numRec)]


# Makes a list of all areas in order of Grid Code

150

for row in cursor:

id = row[0]

countL [id] = row[1]

cursor.reset()

#Sort on HRR_ID

cursor = sorted (cursor, key = lambda row:row[6])

# get all cumulative areas

for row in cursor:

# sumArea = area in count field + area in each Up field.

id = row [0]

sumArea[id] = countL [row[0]] + countL [row[2]] + countL [row[3]] \

+ countL [row[4]]

countL[id] = sumArea [id]

print "Cumulative area determined"


for row in cursor:

id = row[0]

row[5] = sumArea [id]


print "Cumulative Area entered"

if cursor:

del cursor

def assignWID (table):

""" Assigns watershed ID to each catchment"""


fields = [gcNewTable, "UP1ID", "UP2ID", "UP3ID", "WID", "HRR_ID"]


numRec += numRec*10

wid = [0 for x in range (numRec)]


# Makes a list of all areas in order of Grid Code

for row in cursor:

id = row[0]

wid [id] = row[4]

cursor.reset()

151

#Sort on HRR_ID

cursor = sorted (cursor, key = lambda row:row[5], reverse = True)

for row in cursor:

# fills list with appropriate watersheds.

id = row[0]

up1 = row[1]

up2 = row[2]

up3 = row[3]

if up1 > 0:

wid[up1] = wid[id]

if up2 > 0:

wid[up2] = wid[id]

if up3 > 0:

wid[up3] = wid[id]

print "WID determined"

#updates WID column in table


for row in cursor:

id = row[0]

row [4] = wid[id]


print "WID entered"

if cursor:

del cursor

def relateHRR (table):

""" Relates up and down IDs on HRRID instead of Grid Code"""

gcNewTable = checkGC (table) # Get correct grid code name

fields = [ gcNewTable, "HRR_ID", "UP1ID", "UP2ID", "UP3ID", "DOWN_ID"]


allCodes = {} # dictionary relating grid codes to HRRID

for row in cursor:

# {grid code: hrr}

allCodes[row[0]] = row[1]

cursor.reset()

allCodes[0] = 0 # Takes care of entries with no up or down ID.

152

# update table replaceing grid code with HRRID in up and down IDs


for row in cursor:

# up1 = allCodes[grid code from up1 column]= HRR at that column

row[2] = allCodes[row[2]]#up1



row[5] = allCodes[row[5]]#down


#Adds fields to feature class

def addFields (fc, fieldList):

""" Adds fields in a list of fields"""

for field in fieldList:

print "Adding field " + field + " to " + fc

arcpy.AddField_management (fc, field, "FLOAT", "", "", "", "", "NULLABLE",

"NON_REQUIRED", "")

def fillFieldsLFP (hrr3, stream):

fieldsTable = ["Lc_LFP_km"]

addFields (stream, fieldsTable) #channel length by LFP

#Update new fields

print "Updating simple fields"

arcpy.CalculateField_management (stream, "Lc_LFP_km",

"!SHAPE.LENGTH!/1000", "PYTHON")

newGC = checkGC (hrr3)

strGC = checkGC (stream)

arcpy.JoinField_management (hrr3, newGC, stream, strGC, "Lc_LFP_km")

def prjNames (workspace):

""" Check workspace type, and set output names """

desc = arcpy.Describe(workspace)


m = isGDB, 'is the workspace type.'

arcpy.AddMessage (m)


catch_m = 'catchments_m'

153

str_m = 'streams_m'

else:

catch_m = 'catchments_m.shp'

str_m = 'streams_m.shp'


return catch_m, str_m

def projectFCs (catch, stream, prj, workspace):

""" Projects feature classes and returns names """

c_m, s_m = prjNames (workspace)

m = c_m, s_m, "Projecting catchments and streams, in ProjectFCs"

arcpy.Project_management(catch, c_m, prj)

arcpy.Project_management(stream, s_m, prj)

return c_m, s_m

def cumFields (table, count, cumulative ):

""" Calculates cumulative area of each catchment and all catchments upstream in sqkm.

"""

fields = [count, "UP1ID", "UP2ID", "UP3ID", cumulative, "HRR_ID"]

# Check for 4 up column

allFields = arcpy.ListFields (table)

for f in allFields:

if f.name.upper == "UP4ID":

check4up = True

break

else:

check4up = False

# Add up4ID to fields if it exists

if check4up:

fields.append ("UP4ID")

countArea = [0] #List of all areas in Count field. HRR IDs start at 1, so 0 is a filler. If no

HRRID listed, area is 0.

sumArea = {} #dictionart of cumulative sum of all areas.


#Sort on HRR_ID

cursor = sorted (cursor, key = lambda row:row[5])

# Makes a list of all areas at list index HRRID

for row in cursor:

countArea.append (row[0])

# get all cumulative areas

154

for row in cursor:

# sumArea = area in count field + area in each Up field.

id = row [5]

# sumArea = area at currentHRRID + area in HRRID in up1+ area in HRRID in

up2 + Aaea in HRRID in up3

sumArea[id] = countArea [row[5]] + countArea [row[1]] + countArea [row[2]] +

countArea [row[3]]

# Add up4ID to sum if it exists

if check4up:

sumArea [id] += countArea [row[6]]

countArea[id] = sumArea [id] # current cumulative area updated.

if cursor:

del cursor

print "Cumulative determined"


for row in cursor:

id = row[5]

# cumulative area at current HRRID

row[4] = sumArea[id]


print "Cumulative entered"

def fillFields (hrr3, catch, stream, region, zone):

""" Fills in length, area, and cumulative length and area fields."""

#Add fields to both tables

fieldsTable = ["CumA_sqkm","CumL_km","cumLfp_km"] #added by YZ

addFields (hrr3, fieldsTable)

addFields (catch, ["A_sqkm"])

addFields (stream, ["L_km"])

addFields (hrr3, ["Lp_km"])

#Update new fields

print "Updating simple fields"

arcpy.CalculateField_management (stream, "L_km", "!SHAPE.LENGTH! / 1000",

"PYTHON") #GIS channel length

arcpy.CalculateField_management (catch, "A_sqkm",

"!SHAPE.AREA@SQUAREKILOMETERS!", "PYTHON")

155

newGC = checkGC (hrr3)

strGC = checkGC (stream)

catchGC = checkGC (catch)

arcpy.JoinField_management (hrr3, newGC, stream, strGC, "L_km")

arcpy.JoinField_management (hrr3, newGC, catch, catchGC, "A_sqkm" )

expression = "getClass(float(!Lc_LFP_km!),float(!A_sqkm!),cellSize)"

codeblock = """def getClass(lpkm,asqkm,dx):

if lpkm < dx:

return asqkm/dx/2

elif lpkm >= dx:

return asqkm/lpkm/2"""

arcpy.CalculateField_management (hrr3, "Lp_km", expression, "PYTHON", codeblock)

#EB

#arcpy.CalculateField_management (hrr3, "Lp_km", "!A_sqkm!/!Lc_LFP_km!/2",

"PYTHON") #yz

arcpy.JoinField_management (hrr3, newGC, catch, catchGC, "Lp_km" )

arcpy.DeleteField_management (catch, "A_sqkm")

arcpy.DeleteField_management (catch, "Lp_km")

arcpy.DeleteField_management (stream, "L_km")

print ("updating Cum fields")

cumFields (hrr3, "A_sqkm", "CumA_sqkm")

cumFields (hrr3, "L_km", "CumL_km")

cumFields (hrr3, "Lc_LFP_km", "cumLfp_km")

if __name__ == "__main__":

main ();

156

Step 3.1:

###########################

#read the nc file of hydraulic conductivity

# and make the raster of harmonic mean.

#By Yuanhao Zhao

###########################

rm(list = ls())

require(ncdf4)

require(maps)

require(raster)

require(rgdal)

#--------- INPUT ------------#

# Set netCDF folder path, put all nc files and this R code in fdir folder

fncdir <- "D:\\Data\\BNU\\K_sFromBNU\\k_s" #, Data source folder, Must use '\\'

# f_tiff <- 'C:\\Research\\Congo\\Congo_Lake2\\GlobalData\\k_s\\ks_1.tiff' #In case user

want to write a geotiff raster file

# working directory

wkdir <- 'C:\\Research\\HRR_python_example\\MissionCreek\\Soil_rast' #Must use '\\'

# Note: Put 'Catchments.shp in the wkdir folder' !!!!!!

#----------------------------#

#####***** MAIN *****#####

# Names of all nc files

names_ksat <- list.files(fncdir, pattern = '.nc')

# Read catchments shapefile, dsn is the folder name, layer is the shapefile name

catch <- readOGR(dsn = wkdir, layer = "Catchments")

prj <- "+proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0"

#Project catchment to wgs84

catch <- spTransform(catch, prj)

# loop to generate ascii raster

for (i in 1:length(names_ksat)){

# Generate the name of the nc file

nc_f <- paste(fncdir, names_ksat[i], sep='\\')

# Make the nc file to raster

157

ras_nc<-raster(nc_f, varname="k_s")

# ras_nc<- projectExtent(ras_nc, crs = prj_m)

# If want to write the raster to a tiff file, uncomment next line

# writeRaster(rast, filename = f_tiff, format = 'GTiff', overwrite = T)

# Extract the nc raster by catchments

nc_extr <- crop(ras_nc, extent(catch)+0.05, snap="out")

#ksat raster

ksat_lay <- paste('ksat',i,sep='_')

assign(ksat_lay, nc_extr)

#Name of the output raster, in ascii format

ext_ncras <- paste("ext_ncras",i,sep="_")

ext_nc <- paste(wkdir, ext_ncras,sep = "\\")

#Save the raster of each layer, comment next line if unnecessary

writeRaster(nc_extr, filename = ext_nc, format = 'ascii', overwrite = TRUE)

}

# Ksat harmonic mean

# The vertical variation of soil property was captured by eight layers to the depth of 2.3 m

# (i.e. 0- 0.045, 0.045- 0.091, 0.091- 0.166, 0.166- 0.289, 0.289- 0.493, 0.493- 0.829,

# 0.829- 1.383 and 1.383- 2.296 m).

ksat_hm <- 2.296/(0.045/ksat_1 + 0.046/ksat_2 + 0.075/ksat_3 + 0.123/ksat_4 +

0.204/ksat_5 + 0.336/ksat_6 + 0.554/ksat_7 + 0.913/ksat_8)

# SoilD <- 0.045*ksat_1/ksat_1 + 0.046*ksat_2/ksat_2 + 0.075*ksat_3/ksat_3 +

0.123*ksat_4/ksat_4 +

# 0.204*ksat_5/ksat_5 + 0.336*ksat_6/ksat_6 + 0.554*ksat_7/ksat_7 +

0.913*ksat_8/ksat_8

# Name of output ksat raster

name_kshm <- paste(wkdir,"ksat_hm_cm_d", sep="\\")

# name_soilD <- paste(wkdir, "soilD_m", sep="\\")

# Write raster, harmonic mean of ksat and soil depth

# Seems all layers have depth (2.296)

writeRaster(ksat_hm, filename = name_kshm, format = 'ascii', overwrite = TRUE)

# writeRaster(SoilD, filename = name_soilD, format = 'ascii', overwrite = TRUE)

158

Step 3.2:

###########################

#read the nc file of hydraulic conductivity

# and make the raster of harmonic mean.

#By Yuanhao Zhao

###########################

rm(list = ls())

require(ncdf4)

require(maps)

require(raster)

require(rgdal)

#--------- INPUT ------------#

# Set netCDF folder path, put all nc files and this R code in fdir folder

fncdir <- "D:\\Data\\BNU\\theta_s" #Data source folder, Must use '\\'

# working directory

wkdir <- 'C:\\Research\\HRR_python_example\\MissionCreek\\Soil_rast' #Must use '\\'

# Note: Put 'Catchments.shp in the wkdir folder' !!!!!!

#----------------------------#

#####***** MAIN *****#####

# Names of all nc files

names_theta <- list.files(fncdir, pattern = '.nc')

# Read catchments shapefile, dsn is the folder name, layer is the shapefile name

catch <- readOGR(dsn = wkdir, layer = "Catchments")

prj <- "+proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0"

#Project catchment to wgs84

catch <- spTransform(catch, prj)

# loop to generate ascii raster

for (i in 1:length(names_theta)){

# Generate the name of the nc file

nc_f <- paste(fncdir, names_theta[i], sep='\\')

# Make the nc file to raster

ras_nc<-raster(nc_f, varname="theta_s")

# Extract the nc raster by catchments

159

nc_extr <- crop(ras_nc, extent(catch) + 0.05, snap="out")

#theta raster

theta_lay <- paste('theta',i,sep='_')

assign(theta_lay, nc_extr)

#Name of the output raster, in ascii format

ext_ncras <- paste("ext_ncras",i,sep="_")

ext_nc <- paste(wkdir, ext_ncras,sep = "\\")

#Save the raster of each layer, comment next line if unnecessary

writeRaster(nc_extr, filename = ext_nc, format = 'ascii', overwrite = TRUE)

}

# theta mean

# The vertical variation of soil property was captured by eight layers to the depth of 2.3 m

# (i.e. 0- 0.045, 0.045- 0.091, 0.091- 0.166, 0.166- 0.289, 0.289- 0.493, 0.493- 0.829,

# 0.829- 1.383 and 1.383- 2.296 m).

theta_hm <- (0.045*theta_1 + 0.046*theta_2 + 0.075*theta_3 + 0.123*theta_4 +

0.204*theta_5 + 0.336*theta_6 + 0.554*theta_7 +

0.913*theta_8)/2.962

# SoilD <- 0.045*theta_1/theta_1 + 0.046*theta_2/theta_2 + 0.075*theta_3/theta_3 +

0.123*theta_4/theta_4 +

# 0.204*theta_5/theta_5 + 0.336*theta_6/theta_6 + 0.554*theta_7/theta_7 +

0.913*theta_8/theta_8

# Name of output theta raster

name_kshm <- paste(wkdir,"theta", sep="\\")

# name_soilD <- paste(wkdir, "soilD_m", sep="\\")

# Write raster, harmonic mean of theta and soil depth

# Seems all layers have depth (2.296)

writeRaster(theta_hm, filename = name_kshm, format = 'ascii', overwrite = TRUE)

# writeRaster(SoilD, filename = name_soilD, format = 'ascii', overwrite = TRUE)

160

Step 4.1:

# -*- coding: utf-8 -*-

"""

Note: Please extract soil raster files based on catchment before this step.

In: Take soil raster files, project them using flow direction raster file.

Out: Projected soil raster files have same coordinate system as flow direction raster

@author: Yuanhao

"""

import arcpy, os, os.path






targetWorkspace = r"C:\Research\HRR_python_example\MissionCreek\Soil_rast" #

Working folder



global_rastPath = r"C:\Research\modelsetupcode\HWSD" # Folder, contains all origin

golbal soil raster files

rast_global = ['soild_cm'] # Soil properties raster file in global raster path folder (above)

that user wants to extract by

# catchments.shp

rast_cat = ['ksat_hm_cm_d.asc',

'theta.asc',

'lc_cat',

'soild_cm_cat'] # Names of raster files for catchments will be projected

using

# flow direction raster

#####****************************#####


arcpy.env.snapRaster = drainageDirection # Snap raster - fdir

#%% Part 1: extract soil property raster files by flow direction raster of basin

161

for name in rast_global:

print name

rast = os.path.join(global_rastPath, name)

outras = ExtractByMask(rast, drainageDirection)

outras.save(targetWorkspace+'\\'+name+'_cat')

#%% Part 2: Project the soil raster files which are not in projection of flow direction

fdircellsize = arcpy.GetRasterProperties_management(drainageDirection, "CELLSIZEX")

# cell size

desc_fdir = arcpy.Describe(drainageDirection)

coor_system = desc_fdir.spatialReference

print 'Start to project...'

for name in rast_cat:

print name

rast = os.path.join (targetWorkspace, name)

desc_rast = arcpy.Describe(rast)

if desc_rast.extension == 'asc':

rastN = rast[:-4]

arcpy.ASCIIToRaster_conversion(rast, rastN, "FLOAT")

desc_rastN = arcpy.Describe(rastN)

spatialRef_rastN = desc_rastN.spatialReference

if spatialRef_rastN.Name == 'Unknown':

arcpy.DefineProjection_management(rastN, '4326')

rastp = rastN+'p' # p means projected

arcpy.ProjectRaster_management(rastN, rastp, drainageDirection, 'BILINEAR',

fdircellsize)

else:

rastp = rast+'p'

if rast[-9:] == 'cover_cat':

arcpy.ProjectRaster_management(rast, rastp, drainageDirection, 'NEAREST',

fdircellsize)

else:

arcpy.ProjectRaster_management(rast, rastp, drainageDirection, 'BILINEAR',

fdircellsize)

print 'Success!'

162

Step 4.2:

"""


Parts:

1. Extract DEM data from longest flow path (LFP), measure the slope of LFP for each

model unit in percent rise.

2. Extract information from HWSD for soil properties. Write to HRR3 table.



By: Yuanhao Zhao


"""





#cellsize = 0.00083333333




#Output workspace folder

DemRas = r'C:\Research\HRR_python_example\MissionCreek\GIS_basic\dem_m' # dem

raster file for whole basin, 90m X 90m

CatSlope = r"C:\Research\HRR_python_example\MissionCreek\GIS_basic\slope" # slope

raster for whole basin

rastPath = r"C:\Research\HRR_python_example\MissionCreek\Soil_rast" #Soil property

data raster folder path, user can create a folder which has the raster data

hrr3 = "HRR_Table3_MC01.dbf" #HRR3 table in 'GIS_working' folder

#####****************************#####

def main ():





catchments = "Catchments.shp" #shapefile of catchments

lfp = "lfpstrd.shp" #longest flow path shapefile

163

#####***** part1 *****#####

isGDB = checkGDB (targetWorkspace) # True if output workspace a geodatabase

# Create copy of HRR table to add new field to.

if isGDB == False:

StrslpStat = 'StrslpStat.dbf'

slopeStat = 'slope_stats.dbf'

hrr4 = 'HRR_Table4.dbf'

else:

StrslpStat = 'StrslpStat'

slopeStat = 'slope_stats'

hrr4 = 'HRR_Table4'

StrslpStat = os.path.join (targetWorkspace, StrslpStat) #Stream (LFP) slope

slopeStat = os.path.join (targetWorkspace, slopeStat) #Catchment slope

print 'Slope for lfp'

StrDem = ExtractByMask(DemRas, lfp)

slp_str = Slope(StrDem, "PERCENT_RISE")

hrr4 = hrr3 # Commented out code above creates a new HRR table. Not needed,

since nothing is being removed, just added.

gridCode = checkGC (catchments)

m = ('zonal stats parameters : ' + catchments, gridCode, slp_str, StrslpStat, 'DATA',

'MEAN')


arcpy.GetMessages ()

arcpy.sa.ZonalStatisticsAsTable (catchments, gridCode, slp_str, StrslpStat,

'DATA', 'MEAN')

# Join fields from catchments and slope with HRR

slopeField (hrr4, StrslpStat)

print 'slope for catchment'

m = ('zonal stats parameters : ' + catchments, gridCode, CatSlope, slopeStat,

'DATA', 'MEAN')



arcpy.sa.ZonalStatisticsAsTable (catchments, gridCode, CatSlope, slopeStat,

'DATA', 'MEAN')

# Join fields from catchments and slope with HRR

slopeFieldCat (hrr4, slopeStat)

164

#####***** Part2 *****#####

#arcpy.env.cellSize = cellsize

print 'Soil properties'

names = [

["KSat_cm_d", "FLOAT", "ksat_hm_cm_dp" , 1.0],

["Eff_Por", "FLOAT", "thetap", 1.0],

["depth10km", "SHORT", "soild_cm_catp", 1.0]

]

# These are other rasters of depth which are not used in the model at this time.

notUsed = [["Ref_Val", "FLOAT", "Ref_Depth" , 1000.0],

["Roots_Val", "FLOAT", "Roots_Depth", 1000.0],

["Suction_cm", "FLOAT", "suction_0", 1000.0],

["MDMax", "FLOAT", "mdmax_0", 100000.0],

["Imp_Wr", "FLOAT", "imp_water", 1.0],

["Imp_GG", "FLOAT", "imp_gg", 1.0],

["Imp_Rock", "FLOAT", "imp_rock", 1.0],

["Imp_Urban", "FLOAT", "imp_urban", 1.0],

["Min_Depth", "FLOAT", "Min_Depth_0", 1000.0],

["IL_Val", "FLOAT", "IL_Depth", 1000.0]

]

addFields (hrr3, names)

fillFields(catchments, hrr3, rastPath, names)

print 'Success!'

def addFields (table, names):

#print ("Adding fields")

for n in names:

arcpy.AddField_management (table, n[0], n[1])





for f in fields:


return "GRID_CODE"


return "GRIDCODE"

def checkGDB (workspace):

""" Returns true if GDB, false if not. """



165


return True

return False

# gets slope by stream, joins it to HRR table

def slopeField (hrrTable, StrslpStat):

print StrslpStat, 'is channel slope stat'

hrrGC = checkGC (hrrTable)

slopeGC = checkGC(StrslpStat)

f1 = arcpy.ListFields(hrrTable)

for f in f1:

if f == 'Slope_str' or f == 'Slope_cat':

arcpy.DeleteField_management (hrrTable, 'Slope_str')

# f2 = arcpy.ListFields (slopeStat)

fields = ['MEAN']

print 'adding field'

arcpy.AddField_management (hrrTable, 'Slope_str', 'FLOAT')

print 'joining mean'

arcpy.JoinField_management (hrrTable, hrrGC, StrslpStat, slopeGC, fields)

arcpy.CalculateField_management (hrrTable, 'Slope_str', '!MEAN!*0.01', 'PYTHON')

arcpy.DeleteField_management (hrrTable, fields)

def slopeFieldCat (hrrTable, slopeStat):

print slopeStat, 'is catchment slope'

hrrGC = checkGC (hrrTable)

slopeGC = checkGC(slopeStat)

f1 = arcpy.ListFields(hrrTable)

for f in f1:

if f == 'Slope_cat':

arcpy.DeleteField_management (hrrTable, 'Slope_cat')

fields = ['MEAN']

print 'adding field'

arcpy.AddField_management (hrrTable, 'Slope_cat', 'FLOAT')

print 'joining mean'

arcpy.JoinField_management (hrrTable, hrrGC, slopeStat, slopeGC, fields)

expression = '!MEAN!'

arcpy.CalculateField_management (hrrTable, 'Slope_cat', '!MEAN!', 'PYTHON')

arcpy.DeleteField_management (hrrTable, fields)

166

def fillFields (fc, outTable, rastPath, names):

"""Performs zonal statistics on all fields"""

outGC = checkGC(outTable)

fcGC = checkGC (fc)

for item in names:

field = item[0]

file = item[2]

divisor = item[3]

statTable = file

expression = "(!MEAN!) / " + str (divisor)

rast = os.path.join (rastPath, file)

print rast

desc_rast = arcpy.Describe(rast)

spatialRef_rast = desc_rast.spatialReference

# If it's ascii file, it doesn't have spatial reference, then define projection

if spatialRef_rast.Name == 'Unknown':

arcpy.DefineProjection_management(rast, '4326')

# IF it's asciii file, convert it to raster then perform zonal

if desc_rast.extension == 'asc':

rastN = rast[:-4]

arcpy.ASCIIToRaster_conversion(rast, rastN, "FLOAT")

statTableN = statTable[:-4]

desc_rastN = arcpy.Describe(rastN)

spatialRef_rastN = desc_rastN.spatialReference

if spatialRef_rastN.Name == 'Unknown':

arcpy.DefineProjection_management(rastN, '4326')

arcpy.sa.ZonalStatisticsAsTable (fc, fcGC, rastN, statTableN, "DATA", "MEAN")

statGC = checkGC (statTableN)

arcpy.JoinField_management (outTable, outGC, statTableN, statGC, "MEAN")

print ("calculating field")

arcpy.CalculateField_management (outTable, field, expression, "PYTHON")

arcpy.DeleteField_management (outTable, "MEAN")

arcpy.Delete_management(statTableN)

else:

arcpy.sa.ZonalStatisticsAsTable (fc, fcGC, rast, statTable, "DATA", "MEAN")

statGC = checkGC (statTable)

167

arcpy.JoinField_management (outTable, outGC, statTable, statGC, "MEAN")

print ("calculating field")



arcpy.Delete_management(statTable)

if __name__ == "__main__":

main ();

168

Step 5:

"""


Procedure:

1. Take landcover, Ksat and slope raster of the basin, reclassify these 3 rasters and

combine them to 1 raster.

2. Reclassify the combined raster to n rasters (n as categories).

3. Run zonal statistics for each category to get weight in catchment, write to HRR table3.

4. Also determine surface roughness based on HECHMS.



By: Yuanhao Zhao


"""




#####***** Input parameters *****#####

drainageDirection =

r"C:\Research\HRR_python_example\MissionCreek\GIS_basic\fdr" # Raster file of flow

direction


#Output workspace folder

LandCover = r"C:\Research\HRR_python_example\MissionCreek\Soil_rast\lc_catp"

#land cover raster from MODIS for modeling basin

#these should be raster exactly like fdir grid (coordinate system, cell size and snapped

to fdir)

ksatras =

r"C:\Research\HRR_python_example\MissionCreek\Soil_rast\ksat_hm_cm_dp" #ksat

raster for modeling basin, from HWSD or defined by user

planeslope = r"C:\Research\HRR_python_example\MissionCreek\GIS_basic\slope"

#slope raster for modeling basin

region = 'MC' # Modeling basin

zone = '01' # Two numbers represent the model run

# Below are the runoff coefficients for different categories of landcover, ksat and plane

slope,

# please see user manual for details.

169

# RC - runoff coefficient

# slope: Fl - Flat, M - Moderate, S - Steep

# Ksat group: g1 - group 1, g2-group 2, g3-group 3

# Land cover: F-Forest, AGB-Agr/Grass/brush, U-Urban

RCFlg1F= 0.36

RCFlg1AGB= 0.52

RCFlg1WU = 0.68

RCFlg2F = 0.194

RCFlg2AGB = 0.357

RCFlg2WU = 0.512

RCFlg3F = 0.154

RCFlg3AGB = 0.2355

RCFlg3WU = 0.45

RCMg1F = 0.43

RCMg1AGB = 0.59

RCMg1WU = 0.745

RCMg2F = 0.2665

RCMg2AGB = 0.41

RCMg2WU = 0.5815

RCMg3F = 0.2

RCMg3AGB = 0.305

RCMg3WU = 0.48

RCSg1F = 0.586

RCSg1AGB = 0.746

RCSg1WU = 0.89

RCSg2F = 0.4225

RCSg2AGB = 0.5825

RCSg2WU = 0.7375

RCSg3F = 0.25

RCSg3AGB = 0.461

RCSg3WU = 0.66

#####*****************************#####



catchments = "Catchments.shp"

#arcpy.env.mask = catchments

#output files, no need to modify

rasgdb1 = "reclass1.gdb" #This GDB file contains first step of reclassify

rasgdb2 = "reclass2.gdb" #This GDB file contains second step of reclassify

outLC = "ReclaLC" #land cover category raster

outSoil = "ReclaSoil" #soil type category raster

170

outSlp = "ReclaSlp" #slope type categoty raster

outSR = "ReclaSR" #surface roughness raster based on land cover

CatComb = "CatComb" #combined 3 catogeries raster

def main ():



#Create gdb

gdb1path = os.path.join(targetWorkspace,rasgdb1)

gdb2path = os.path.join(targetWorkspace,rasgdb2)

HRR3 = "HRR_Table3_" + region + zone + ".dbf"

if not os.path.exists(gdb1path):

arcpy.CreateFileGDB_management(targetWorkspace,rasgdb1)

if not os.path.exists(gdb2path):

arcpy.CreateFileGDB_management(targetWorkspace,rasgdb2)

#####***** part1-reclassify *****#####

# ---reclassify land cover type to 3 categories:Forest, urban, Agr/Grass/brush

# Data source:

https://lpdaac.usgs.gov/dataset_discovery/modis/modis_products_table/mcd12c1

# Use Layer 0 for land cover grid

# We use classification type1 (IGBP)

remap = RemapValue([[1,1],[2,1],[3,1],[4,1],[5,1], #forest

[6,2],[7,2],[8,2],[9,2],[10,2],[12,2],[14,2],

#Agr/Grass/brush

[15,3],[16,3],[13,3],[0,3],[11,3]])

#Urban,water

print 'start land cover reclassify'

outReclassify = Reclassify(LandCover, "VALUE", remap)

outLCras = os.path.join(gdb1path,outLC)

outReclassify.save(outLCras)

# ---reclassify ksat to 3 categories:loam, clay and sand. ksat is in cm/day

print 'start soil reclassify'

remap = RemapRange([[0,6,10], #ksat group 1

[6,24,20], #ksat group 2

[24,504,30]]) #ksat group 3

outReclassify = Reclassify(ksatras, "VALUE", remap)

outSoilras = os.path.join(gdb1path,outSoil)

outReclassify.save(outSoilras)

171

# ---reclassify plane slope to 3 categories

print 'start plane slope reclassify'

remap = RemapRange([[0,2,100], #flat

[2,10,200], #moderate

[10,1000,300]]) #steep

outReclassify = Reclassify(planeslope, "VALUE", remap)

outSlpras = os.path.join(gdb1path,outSlp)

outReclassify.save(outSlpras)

# ---reclassify land cover type to surface roughness raster

# based on Table6-1 in hecHMS mannual, P61.

remap = RemapValue([[1,5,600], #forest, 0.6

[6,10,180],[12,180],[14,180],

#Agr/Grass/brush, 0.18

[15,11],[16,11],[13,11],[11,11],[0,11]])

#Urban, 0.011

print 'start surface roughness reclassify'

outReclassify = Reclassify(LandCover, "VALUE", remap)

outSRras = os.path.join(gdb2path,outSR)

outReclassify.save(outSRras)

#%% Generate new raster, add three rasters to create a new raster

ReclaLC=Raster(outLCras)

ReclaSoil=Raster(outSoilras)

ReclaSlp=Raster(outSlpras)

ReclaSR=Raster(outSRras)

desc_soil = arcpy.Describe(ReclaSoil)

spatialRef_soil = desc_soil.spatialReference

if spatialRef_soil.Name == 'Unknown':

arcpy.DefineProjection_management(ReclaSoil, '4326')

ReclaSoil_N = os.path.join(gdb1path, 'ReclaSoil_N')

cellsize = arcpy.GetRasterProperties_management(ReclaSlp,

"CELLSIZEX")

arcpy.ProjectRaster_management(ReclaSoil, ReclaSoil_N, ReclaSlp, "",

cellsize)

arcpy.env.snapRaster = ReclaSlp

arcpy.env.extent = "MINOF"

CateCombination = ReclaLC+ReclaSoil_N+ReclaSlp

CatCombras = os.path.join(gdb1path,CatComb)

CateCombination.save(CatCombras)

else:

CateCombination = ReclaLC+ReclaSoil+ReclaSlp

CatCombras = os.path.join(gdb1path,CatComb)

CateCombination.save(CatCombras)

172

#####***** Part2 *****#####

print '1'

remap = RemapValue([[111,1], #flat, group 1, forest

[0,110,0],[112,1000,0]])

outReclassify = Reclassify(CatCombras, "VALUE", remap)

outReclassify.save(os.path.join(gdb2path,'RclsFlg1F'))

print '2'

remap = RemapValue([[112,1], #flat, group 1, AGB

[0,111,0],[113,1000,0]])


outReclassify.save(os.path.join(gdb2path,"RclsFlg1AGB"))

print '3'

remap = RemapValue([[113,1], #flat, group 1, WU

[0,112,0],[114,1000,0]])


outReclassify.save(os.path.join(gdb2path,"RclsFlg1WU"))

print '4'


[0,120,0],[122,1000,0]])


outReclassify.save(os.path.join(gdb2path,"RclsFlg2F"))

print '5'


[0,121,0],[123,1000,0]])



print '6'

remap = RemapValue([[123,1], #flat, group 2, WU

[0,122,0],[124,1000,0]])



print '7'


[0,130,0],[132,1000,0]])


outReclassify.save(os.path.join(gdb2path,"RclsFlg3F"))

print '8'

173


[0,131,0],[133,1000,0]])



print '9'

remap = RemapValue([[133,1], #flat, group 3, urban

[0,132,0],[134,1000,0]])



print '10'

remap = RemapValue([[211,1], #moderate, group1, forest

[0,210,0],[212,1000,0]])


outReclassify.save(os.path.join(gdb2path,"RclsMg1F"))

print '11'

remap = RemapValue([[212,1], #moderate, group1, AGB

[0,211,0],[213,1000,0]])


outReclassify.save(os.path.join(gdb2path,"RclsMg1AGB"))

print '12'

remap = RemapValue([[213,1], #moderate, group1, WU

[0,212,0],[214,1000,0]])


outReclassify.save(os.path.join(gdb2path,"RclsMg1WU"))

print '13'


[0,220,0],[222,1000,0]])



print '14'


[0,221,0],[223,1000,0]])



print '15'


[0,222,0],[224,1000,0]])



174

print '16'


[0,230,0],[232,1000,0]])



print '17'


[0,231,0],[233,1000,0]])



print '18'


[0,232,0],[234,1000,0]])



print '19'

remap = RemapValue([[311,1], #steep, group1, forest

[0,310,0],[312,1000,0]])


outReclassify.save(os.path.join(gdb2path,"RclsSg1F"))

print '20'

remap = RemapValue([[312,1], #steep, group1, AGB

[0,311,0],[313,1000,0]])


outReclassify.save(os.path.join(gdb2path,"RclsSg1AGB"))

print '21'

remap = RemapValue([[313,1], #steep, group1, WU

[0,312,0],[314,1000,0]])


outReclassify.save(os.path.join(gdb2path,"RclsSg1WU"))

print '22'


[0,320,0],[322,1000,0]])



print '23'


[0,321,0],[323,1000,0]])

175



print '24'


[0,322,0],[324,1000,0]])



print '25'


[0,330,0],[332,1000,0]])



print '26'


[0,331,0],[333,1000,0]])



print '27'


[0,332,0],[334,1000,0]])



#####***** Part3 *****#####

names = [

["Flg1F", "FLOAT", "RclsFlg1F", 1.0],

["Flg1AGB", "FLOAT", "RclsFlg1AGB", 1.0],

["Flg1WU", "FLOAT", "RclsFlg1WU", 1.0],







["Mg1F", "FLOAT", "RclsMg1F", 1.0],

["Mg1AGB", "FLOAT", "RclsMg1AGB", 1.0],

["Mg1WU", "FLOAT", "RclsMg1WU", 1.0],





176



["Sg1F", "FLOAT", "RclsSg1F", 1.0],

["Sg1AGB", "FLOAT", "RclsSg1AGB", 1.0],

["Sg1WU", "FLOAT", "RclsSg1WU", 1.0],







#surface roughness

["SRtemp", "FLOAT", "ReclaSR", 1000.0]

]

addFields(HRR3, names)

fillFields(catchments, HRR3, gdb2path, names)

arcpy.AddField_management (HRR3, "runco", "FLOAT")

arcpy.AddField_management (HRR3, "SR", "FLOAT")

print ("Calculate runoff coefficient")

rows = arcpy.SearchCursor(HRR3)

expression = "(!Flg1F!) * " + str (RCFlg1F) + " + (!Flg1AGB!) * " + str

(RCFlg1AGB) + " + (!Flg1WU!) * " + str (RCFlg1WU) + \

" + (!Flg2F!) * " + str (RCFlg2F) + " + (!Flg2AGB!) * " +

str (RCFlg2AGB) + " + (!Flg2WU!) * " + str (RCFlg2WU) + \

" + (!Flg3F!) * " + str (RCFlg3F) + " + (!Flg3AGB!) * " +

str (RCFlg3AGB) + " + (!Flg3WU!) * " + str (RCFlg3WU) + \

" + (!Mg1F!) * " + str (RCMg1F) + " + (!Mg1AGB!) * " +

str (RCMg1AGB) + " + (!Mg1WU!) * " + str (RCMg1WU) + \





" + (!Sg1F!) * " + str (RCSg1F) + " + (!Sg1AGB!) * " + str

(RCSg1AGB) + " + (!Sg1WU!) * " + str (RCSg1WU) + \


(RCSg2AGB) + " + (!Sg2WU!) * " + str (RCSg2WU) + \


(RCSg3AGB) + " + (!Sg3WU!) * " + str (RCSg3WU)

arcpy.CalculateField_management (HRR3, "runco", expression, "PYTHON")

arcpy.CalculateField_management (HRR3, "SR", "!SRtemp!", "PYTHON")

177

print 'Success!'

#------------------------------------------------------------

#functions

def addFields (table, names):

for n in names:

arcpy.AddField_management (table, n[0], n[1])





arcpy.AddMessage (isGDB)


if isGDB == "FileSystem":

arcpy.AddMessage (isGDB)


return False

else:

return True





for f in fields:


return f.name.upper ()



def fillFields (fc, outTable, rastPath, names):

#fc - catchments, outTable - HRR table, rastpath - folder save rasters

#"""Performs zonal statistics on all fields"""

outGC = checkGC(outTable)

fcGC = checkGC (fc)

for item in names:

field = item[0]

filex = item[2]

divisor = item[3]

178

expression = "(!MEAN!) / " + str (divisor)

rast = os.path.join (rastPath,filex)

statTable = os.path.join (targetWorkspace, filex)

print rast

print "Zonal stats on " + field

arcpy.sa.ZonalStatisticsAsTable (fc, fcGC, rast, statTable, "DATA", "MEAN")

statGC = checkGC (statTable)

print "joining field " + field

arcpy.JoinField_management (outTable, outGC, statTable, statGC, "MEAN")

print "calculating field"


print "Deleting Mean field"


arcpy.Delete_management(statTable)

def delFields (table, names):

for n in names:

arcpy.DeleteField_management (table, n[0])

if __name__ == "__main__":

main ();

179

Step 6:

"""


Objectives:

1. Take HRR3 table, Returns 3 tab delimited .txt files for HRR model to run: channels.txt,

planes.txt. output_calibration.txt



By: Yuanhao Zhao


"""







outputPath = r'C:\Research\HRR_python_example\MissionCreek\Input' #Path with

HRR table (see next line) and location to write text files

hrr = "HRR_Table3_MC01.dbf" #Final HRR table with all soil property fields, slopes,

lengths and areas

###******************************#####

def main ():

arcpy.env.workspace = outputPath

print ' running hrr to text on', hrr

# Fill lists with appropriate data

count = sum((1 for row in arcpy.da.SearchCursor(hrr, ['HRR_ID'])))

numRec = count + 1

gridCode = checkGC (hrr) ##""" only if split"""

dict = fillLists (hrr, numRec)

dict = removeFirst (dict)

#Write to files

makeFiles (outputPath, dict, numRec)

180

print 'Success!'






return True

return False




for f in fields:

if "GRID_CODE" in f.name.upper ():

return "GRID_CODE"

elif "GRIDCODE" in f.name.upper ():

return "GRIDCODE"

def checkNumUp (hrrTable):

"""Check for up4 field"""

fields = [f.name for f in arcpy.ListFields(hrrTable)]

if 'UP4ID' in fields:

return True

else:

return False

#Recalculates null values to -999

def nullCheck (dict):

"""Recalculates slope from null to -999 where catchment has no null value in

raster."""

for id in dict['hrrID'][0]:

#slope

if not isinstance (dict['slope_ch'][0][id], float):

dict['slope_ch'][0][id] = -999

if not isinstance (dict['slope_p1'][0][id], float):

dict['slope_p1'][0][id] = -999

#HWSD

if not isinstance (dict['kSat'][0][id], float):

dict['kSat'][0][id] = -999

if not isinstance (dict['effPor'][0][id], float):

dict['effPor'][0][id] = -999

181

#depth10km

if not isinstance (dict['dep10km'][0][id], int):

dict['dep10km'][0][id] = -999

return dict

def fillLists (hrrTable, numRec):

""" Creates data structure to hold final output."""

# Data fields needed for final output, or needed to calculate final output.

# Fills with default of -999 so it is obvious when a record does not exist for

# a particular grid code.

dict = {'gridCode': [[0 for x in range (numRec*10)], 1, 'all'], #arc

'hrrID': [[0 for x in range (numRec)], 0, 'all'], #arc

'length_p1': [[-999 for x in range (numRec)], 2, 'planes'], #calc

'slope_p1': [[-999 for x in range (numRec)], 3, 'planes'], #arc, calc

'n_surface': [[0.8 for x in range (numRec)], 4, 'planes'], #constant

'kSat': [[-999 for x in range (numRec)], 5, 'planes'], #arc

'effPor': [[-999 for x in range (numRec)], 6, 'planes'], #arc

'dep10km': [[-999 for x in range (numRec)], 7, 'planes'], #arc

'runco': [[-999 for x in range (numRec)], 8, 'planes'], #calc

'downID': [[-999 for x in range (numRec)], 2, 'channels'], #arc

'numUp': [[-999 for x in range (numRec)], 3, 'channels'], #arc

'up1': [[-999 for x in range (numRec)], 4, 'channels'], #arc



'a_km2': [[999 for x in range (numRec)], 8, 'channels'], #arc

'cumA_km2': [[999 for x in range (numRec)], 9, 'channels'], #arc

'len_ch': [[-999 for x in range (numRec)], 10, 'channels'], #arc

'slope_ch': [[0.01 for x in range (numRec)], 11, 'channels'], #constant

'n': [[0.025 for x in range (numRec)], 12, 'channels'], #constant

'width_ch': [[-999 for x in range (numRec)], 13, 'channels'], #calc

'q_r': [[-999 for x in range (numRec)], 14, 'channels'], #calc

'guageA': [[-999 for x in range (numRec)], 2, 'output'] } #calc

# Add entry for 4up if it exists.

up4 = checkNumUp (hrrTable)

if up4:

dict [up4] = [[-999 for x in range (numRec)], 7, 'channels'], #arc, or none

# fill values directly from Arc

182

dict = fillArcLists (hrrTable, dict)

# Fill lists with calculated values

dict = nullCheck (dict)

dict = calcChannelsLists (dict)

return dict

def calcChannelsLists (dict):

"""Calculates values for fields with calculated values. """

hrrID = dict['hrrID'][0]

for id in hrrID:

dict['length_p1'][0][id] = dict['length_p1'][0][id] * 1000 #(m)

dict['len_ch'][0][id] = dict['len_ch'][0][id] * 1000 #(m)

dict['slope_p1'][0][id] = dict['slope_p1'][0][id] / 100 #(percent)

dict['slope_ch'][0][id] = dict['slope_ch'][0][id] / 1 #(percent)

dict['kSat'][0][id] = dict['kSat'][0][id] / 24 # ksat, cm/day to cm/hour

dict ['width_ch'][0][id] = 0.5 * ((dict['cumA_km2'][0][id]) ** 0.6)

dict ['q_r'][0][id]= 0.75 * (0.1 * ((dict['cumA_km2'][0][id]) ** 0.95))

dict ['guageA'][0][id] = int (dict['cumA_km2'][0][id])

return dict

def fillArcLists (hrrTable, dict):

""" Takes data from arc table and puts it into a list in memory."""

# Create lists of correct length

#list of fields in HRR3

gridCode = checkGC (hrrTable)

arcFields = [gridCode, 'HRR_ID', 'DOWN_ID', 'NUMUP', 'UP1ID',

'UP2ID', 'UP3ID', 'CUMA_SQKM', 'A_SQKM', 'LC_LFP_KM',

'LP_KM','KSAT_CM_D','EFF_POR','SLOPE_STR','SLOPE_CAT',

'DEPTH10KM','RUNCO','SR'

]

# Check if 4 upID fields

up4 = checkNumUp (hrrTable)

if up4:

arcFields.append ('UP4ID')

# list of lists

arcLists = [dict['gridCode'][0], #1

dict['hrrID'][0], #2

dict['downID'][0], #3

dict['numUp'][0], #4

dict['up1'][0], #5

dict['up2'][0], #6

183

dict['up3'][0], #7

dict['cumA_km2'][0], #8

dict['a_km2'][0], #9

dict['len_ch'][0], #10

dict['length_p1'][0], #11

dict['kSat'][0], #12

dict['effPor'][0], #13

dict['slope_ch'][0],#14

dict['slope_p1'][0], #15

dict['dep10km'][0], #16

dict['runco'][0], #17

dict['n_surface'][0] #18

]

if up4:

arcLists.append (dict ['UP4ID'][0])

with arcpy.da.SearchCursor (hrrTable, arcFields) as cursor:

for row in cursor:

hrrINT= row [1]

# Fill all lists, with HRRINT as index

for i in range(len(arcLists)):

arcLists[i][hrrINT] = row [i]

dict['gridCode'][0] = arcLists [0]

dict['hrrID'][0] = arcLists [1]

dict['downID'][0] = arcLists [2]

dict['numUp'][0] = arcLists [3]

dict['up1'][0] = arcLists [4]



dict['cumA_km2'][0] = arcLists [7]

dict['a_km2'][0] = arcLists [8]

dict['len_ch'][0] = arcLists [9]

dict['length_p1'][0] = arcLists [10]

dict['kSat'][0] = arcLists [11]

dict['effPor'][0] = arcLists [12]

dict['slope_ch'][0] = arcLists [13]

dict['slope_p1'][0] = arcLists [14]

dict['dep10km'][0] = arcLists [15]

dict['runco'][0] = arcLists [16]

dict['n_surface'][0] = arcLists [17]

if up4:

184

dict['up4'[0]] = arcLists [18]

return dict

def makeFiles (outPath, dict, numRec):

"""Creates and opens channels, planes, and ouput_calibration .txt files."""

channels = os.path.join (outPath, 'channels.txt')

planes = os.path.join (outPath, 'planes.txt')

output = os.path.join (outPath, 'output_calibration.txt')

input = os.path.join (outPath, 'input.txt')

# Put data into lists for files

chList, plList, outList = toLists (dict)

chList = sorted (chList, key = lambda ch:ch[1])

plList = sorted (plList, key = lambda pl:pl[1])

outList = sorted (outList, key = lambda ou:ou[1])

# make files

with open (planes, 'w') as handle:

wrFile (plList, handle)

with open (channels, 'w') as handle:

wrFile (chList, handle)

with open (output, 'w') as handle:

wrFile2 (outList, numRec, handle)

with open (input, 'w') as handle:

wrInput (numRec, handle)

def wrFile (dataLists, handle):

"""Writes data to open file"""

n = 0

#Iterate number of records in HRRID

#

hrrID = dataLists [0][0]

print len (dataLists)

while n < len (hrrID):

#Iterate fields for current file

i = 0

while i < (len (dataLists)):

handle.write (str (dataLists[i][0][n]))

if i == len (dataLists) - 1:

handle.write ('\n')

else:

handle.write ('\t')

185

i += 1

n += 1

def wrFile2 (dataLists, numRec, handle):

"""Writes data to open file"""

n = 0

#Iterate number of records in HRRID

hrrID = dataLists [0][0]

print len (dataLists)

handle.write (str (numRec-1)+ '\n')

while n < len (hrrID):

#Iterate fields for current file

i = 0

while i < (len (dataLists)):

handle.write (str (dataLists[i][0][n]))

if i == len (dataLists) - 1:

handle.write ('\n')

else:

handle.write ('\t')

i += 1

n += 1

def toLists (dict):

"""Creates list of data to be written to files from dictionary."""

ch = []

pl = []

out = []

all = []

for k, v in dict.iteritems ():

if v[2] == 'planes':

pl.append (v)

elif v[2] == 'channels':

ch.append (v)

elif v[2] == 'output':

out.append (v)

else:

all.append (v)

ch = all + ch

pl = all + pl

out = all + out

return ch, pl, out

# Removes first item of each list, where HRRID = 0. These are not valid datapoints

186

def removeFirst (dict):

for k, v in dict.iteritems():

v[0] = v[0][1:]

return dict

# Writes fill of inputs used to create data.

def wrInput (numRec, handle):

handle.write (str (numRec-1) + '\n' + str (10) + '\n' + str (122736) + '\n' + str (3600)

+ '\n' + str (2000) + '\n' + str (100) + '\n' + str (0.001)

+ '\n' + str (1) + '\n' + str (700) + '\n' + str (4.0)

+ '\n' + str (1.0) + '\n' + str (1.0) + '\n' + str (0.75)

+ '\n' + str (4.0))

main ()

187

Step 7:

"""


Objectives:

1. Take catchment, met polygon IDs. Calculate area of each part of the catchment, then

calculate

weight (wt) by percent area for each part of the catchment. Sort by catchment ID

(GRID_CODE), small to large.

2. Output text file contains met data.



By: Yuanhao Zhao


"""

import arcpy, csv, os, os.path, subprocess, shutil, time




zone = '01'

region = 'MC'

outputSpace = r'C:\Research\HRR_python_example\MissionCreek\Met' #Location for

final text files contain met data

arcpy.env.workspace = outputSpace


fortSpace = r'C:\Research\HRR_python_example\MissionCreek\Met\Met_bas' # Folder

contains origianl met data, location of overlay4.exe

hrr =

r"C:\Research\HRR_python_example\MissionCreek\Input\HRR_Table3_MC01.dbf"

#Location of final HRR 3 table in GIS folder

catchments =

r"C:\Research\HRR_python_example\MissionCreek\GIS_working\Catchments.shp"

#Fianl catchments shapefile in GIS folder

gridList = ['TRMM','MODIS'] # Name of met data, must match the met data grid in

'met_bas' folder.

#For example, 'TRMM' matches

'TRMM_Grid.shp'. If want to use other data source, the format must be ####_Grid.shp

#####****************************#####

188

def main ():

#Start run

place = '{1}{0}'.format (zone, region)

for cpcet in gridList:

# Run code for grid

cpcName = cpcet + '_Grid.shp'

cpcPoly = os.path.join(fortSpace,cpcName)

intTable = os.path.join (outputSpace, "{}_Zones_{}.shp".format (cpcet, place))

#intersected table, output

print 'working on', place, cpcet

setup (catchments, cpcPoly, intTable, hrr)

dataRec = getData (intTable, cpcet, cpcPoly)

dataRec = calcWt (dataRec)

writeCSV (dataRec, fortSpace, cpcet)

fortranCall (fortSpace, outputSpace, place, cpcet)

print 'success!'

def addFields (table, fields):

for f in fields:

arcpy.AddField_management (table, f[0], f[1])





for f in fields:





def setup (catch, cpc, iTable, hrr):

""" Creates intersected, projected shapefile, adds and calculates

weight field, and adds weight (wt) field. """

arcpy.Intersect_analysis ([catch, cpc], iTable)

print 'intersect done'

189

fields = ['AP_sqkm', "DOUBLE"]

arcpy.AddField_management (iTable, fields[0], fields[1])

print 'fields added'

iTableGC = checkGC (iTable)

hrrGC = checkGC (hrr)

arcpy.JoinField_management (iTable, iTableGC, hrr, hrrGC, "HRR_ID")

print "joined hrr"

expression = "!SHAPE.AREA@SQUAREKILOMETERS !"

arcpy.CalculateField_management (iTable, fields [0], expression, "PYTHON")

print 'field calculated'

print 'Setup completed'

def getData (table, cpcet,cpc):

""" Reads data from the intersected cpc/grid table. """

gc = checkGC (table)

print 'gridcode is ', gc

field_names = [f.name for f in arcpy.ListFields(cpc)]

metID = field_names[2]

print metID

fields = ["HRR_ID", gc, metID, "AP_SQKM", "SHAPE@AREA"]

data = {"grid": [],

"hrr": [],

"cpc": [],

"ap": [],

"area": [],

"wt": []

}


# Sort on HRR_ID

cursor = sorted(cursor, key = itemgetter(0))

# extract data to lists

for row in cursor:

190

data["cpc"].append (row[2])

data["grid"].append (row[1])

data["hrr"].append (row [0])

data["ap"].append (row[3])

data["area"].append (row [4])

print 'cursor run'

return data

def calcWt (data):

numRecs = len(data["hrr"])

areaDict = {} # Dictionary of total areas by grid code

for n in range (numRecs):

# fill gridDict with sum of areas by grid code

hrr = data["hrr"][n]

# if the 2nd or later entry of a grid code, cumulative sum of area,

# else add entry for that grid code.

if hrr in areaDict:

areaDict [hrr] = areaDict [hrr] + data ["ap"][n]

else :

areaDict [hrr] = data ["ap"][n]

for n in range (numRecs):

# Calculate weighted average of areas

hrr = data["hrr"][n]

data ["wt"].append (round((data ["ap"][n] / areaDict [hrr]), 3))

return data

def writeCSV(data, workspace, cpcet):

# Writes data to Pgrid.txt

numRecs = len(data["grid"])

csvFile = os.path.join(workspace, "Pgrid.txt")

print "file name is", csvFile

with open(csvFile, "w") as myFile:

writer = csv.writer(myFile, delimiter = ",", lineterminator = "\n")

# Header row

writer.writerow(["ID", "HRR_ID", "wt"])

for n in range(numRecs):

row = [data["cpc"][n], data["hrr"][n], data["wt"][n]]

191

writer.writerow (row)

myFile.close()

def fortranCall (fortSpace, outPath, place, cpcet):

""" Runs overlay4.exe, and puts the output in the current workspace"""

newPgrid = 'Pgrid_{}_{}.txt'.format (cpcet, place)

newOverlay = 'Grid_overlay_{}.txt'.format (cpcet)

pGrid = 'Pgrid.txt'

overlayGrid = 'Pgrid_overlay.txt'

exe = os.path.join (fortSpace, 'overlay4.exe')

fromFile = [os.path.join (fortSpace, pGrid),

os.path.join (fortSpace, overlayGrid)

]

toFile = [os.path.join (outPath, newPgrid),

os.path.join (outPath, newOverlay)

]

subprocess.Popen (exe, cwd = fortSpace)

time.sleep(20) # Without this, computer would sometimes have Pgrid.txt open,

# or would not recognize Pgrid_overlay.txt

# Move results to output location and rename.

for n in range (2):

print 'moving ', toFile [n]

shutil.copy (fromFile [n], toFile [n])

time.sleep(20)

print 'have run overlay4.exe'

if __name__ == '__main__':

main ()

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