Zong-Liang Yang, Guo-Yue Niu and Robert E. Dickinson*

The University of Texas at Austin

* Georgia Institute of Technology

Modeling Runoff in CLMModeling Runoff in CLM

Prepared for Hydrology Project, CCSM Land Model Working Group MeetingMarch 27, 2006

www.geo.utexas.edu/climate

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

1. Introduction

2. Design of a Simple TOPMODEL-Based runoff Scheme (SIMTOP)

3. Validate SIMTOP against GRACE ΔS

4. Development of a Simple Groundwater Model

5. Assess Model against GRACE ΔS

6. Conclusions

Outline

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

Design of the Simple TOPMODEL-Based Runoff Scheme (SIMTOP)

Surface Runoff : Rs = P Fmax e – C f zwt

p = precipitation

zwt = the depth to water table

f = the runoff decay parameter which determines recession curve

Fmax and C = topographic parameters

Subsurface Runoff : Rsb= Rsb,maxe –f zwt

Rsb,max = the maximum subsurface runoff when the grid-mean water table is zero. It should be related to lateral hydraulic conductivity of an aquifer and local slopes. Rsb,max=1.0x10-4 mm/s through sensitivity experiments.

SIMTOP parameters:

Two calibration parameters Rsb,max and f Two topographic parameters Fmax and C

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

Relationship Between the Saturated Area and Water Table Depth

Map of saturated areas showing expansion during a single rainstorm. [Dunne and Leopold, 1978]

zwt

fsat

fsat

fsat = Fmax(λ) e –C f zwt

λ – topographic wetness index derived from DEM

Justification of Surface Runoff Formulation and Derivation of Topographic parameters

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

Topographic Wetness Index: λ = ln(a/tanβ) = ln(a) – ln(S)

DEM –Digital Elevation Model

ln(a) – contribution area

ln(S) – local slope

The higher topographic wetness index, the wetter the pixel

1˚ x 1˚

Justification of Surface Runoff Formulation and Derivation of Topographic parameters

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

1˚

1˚

TOPMODEL (Beven and Kirkby, 1979; Sivapalan et al., 1987) :

zi – zm = – (λi – λm) / f

where zi and λi are water table depth and topographic index at a pixel; while zm and λm are their grid-cell (catchment) mean values.

The Saturated Fraction the Grid-Cell:

Fsat = Prob { zi < 0 } or Prob { λi > λm – fzm } zi, λi

λ

PD

F

0.1

0.2

λm

1.0

0.5

CD

F

λλm

Fmax

zm λm

Lowlandhighland

Justification of Surface Runoff Formulation and Derivation of Topographic parameters

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

A 1 ˚x 1˚ arid-cell in the Amazon River basin

Both Gamma and exponential functions fit for λi > λm

Fmax = 0.45; C = 0.6

Justification of Surface Runoff Formulation and Derivation of Topographic parameters

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

A 1 ˚x 1˚ arid-cell in Northern Rocky Mountain

Gamma function fails, while exponential function works.

Fmax = 0.30; C = 0.5

Justification of Surface Runoff Formulation and Derivation of Topographic parameters

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

Woods and Sivapalan (2003) Fmax=0.35; C = 0.51 to 1.10

C ~ 0.6

Exponential function fits very well in well-developed catchments.

The larger the catchment, the better the fitting.

Justification of Surface Runoff Formulation and Derivation of Topographic parameters

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

Global Fmax

a: Discrete Distribution

b: Gamma Function

c: Error of Gamma (b -- a)

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

Justification of Subsurface Runoff Formulation

TOPMODEL (Beven and Kirkby, 1979)

Rsb= Rsb,max e fS

where S is the deficit of the subsurface water storage

Sivapalan et al., (1987) and Stieglitz et al. (1997 )

Rsb= K0/f e –λ e –f zwt

It needs very large K0, which is justified by soil surface macropore (1000 times lager than in LSM);

Chen and Kumar (2001):

Rsb = α K0/f e –λ e –f zwt (where αK0 is the lateral K)

Difficulties in determining α globally; λ needs very high resolution DEM (30 m or finer) to determine slopes.

Niu et al. (2005):

Rsb = Rsb,max e –f zwt (Rsb,max= 1.0x10-4 mm/s)

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

The Exponential Relationship between Streaflow and Water Table Depth

Groundwater level is highly correlated with streamflow in a strong nonlinear manner and

explains 2/3 of the streamflow (Yeh and Eltahir, 2005)

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

Diagnostic Water Table Depth from Soil Moisture Profile

Water profile under

gravity

Soil water profile when gravity equals

to capillary force

Ψi – zi

Ψsat – zwt

GravityGravity

Capillary

Chen and Kumar (2001)

Koster et al. (2000);

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

Validation Against GRACE Terrestrial Water Storage Change Data

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

Validation Against GRACE Terrestrial Water Storage Change Data

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

Validation Against GRACE Terrestrial Water Storage Change Data

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

Validation Against GRACE Terrestrial Water Storage Change Data

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

Prognostic Water Table: A Simple Groundwater Model

bot

botbota zz

zzKQ

)(

Water storage in an unconfined Aquifer:

Recharge Rate:

)1(bot

bota zzK

Gravitational Drainage

sba RQ

dt

dW ya SWz /

Upward Flow under capillary forces

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

fzsbsb eRR max,

Groundwater Discharge (Baseflow or Subsurface Runoff)

Properties of the Aquifer

1. Hydraulic Conductivity:

2. Specific Yield:

SIMTOP (Niu et al., 2005)

)(,

botzzfbotsatsat eKK

2.0yS

Model Design: A Simple Groundwater Model (SIMGM)

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

Validate the Model against the Valdai Data

The model reproduces SWE, ET, runoff, and water table depth.

The water table depth has two peaks and two valleys in one annual cycle

WTD is very sensitive to soil permeability (sand percentage, frozen soil), Runoff, and ET parameters.

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

Validate the Model against GRDC Runoff

Good agreements between the modeled runoff and GRDC Runoff;

Runoff ~ exp(- f *wtd)

The modeled water table depth ranges from 2.5m in wet regions to 30m in arid regions.

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

Regional Averaged Runoff

Agreement between the modeled runoff and GRDC runoff in most regions except for mid-latitudes;

Surface runoff accounts for about 20%;

Groundwater discharge accounts for about 80% of the total runoff.

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

Validate the Model Against GRACE ΔS Anomaly

The modeled ΔS anomaly agrees very well with GRACE data in river basins where ΔS is not affected by frozen soil;

Groundwater ΔS anomaly accounts for about 60-80% of the total ΔS anomaly;

The model capture the inter-annual and inter-basin variability of the ΔS anomaly .

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

Validate the model Against GRACE WTD Anomaly

GRACE ΔS / 0.2

The modeled water table depth agrees very well with GRACE data in terms of inter-annual and inter-basin variability in river basins where ΔS is not affected by frozen soil;

The uncertainty in GRACE data is mainly the attenuation effects induced by smoothing.

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

P – E, Groundwater Recharge, and Discharge

Phase lags in P – E, groundwater recharge and discharge;

Negative recharge in dry seasons when P – E is negative

Variations of P – E, groundwater recharge, discharge are consistent with the groundwater storage anomalies and WTD in terms of the inter-annual and inter-basin variability.

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

The Impacts of Groundwater Model on SM and ET

It has a large impact on bottom-layer soil moisture, most obviously in cold regions (30% globally);

It has a smaller impacts on surface-layer soil moisture (5% globally);

The impacts on ET are mostly in arid-to-wet transition zones, i.e., the “hot spots” (20% in sensitive zones).

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

Soil Moisture Profiles in Selected Regions

It has a large impacts on the soil moisture profile in most regions;

It has a relative small impacts in arid regions because the WTD is very deep and thus the capillary forces are weak.

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

Transpiration vs. Soil Surface Evaporation

Groundwater has a negligible impacts on transpiration, although it greatly increases deep soil moisture;

It enhanced the ground-surface evaporation in dry seasons corresponding to the increases in the surface-layer soil moisture.

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions

Conclusions

1. We developed a simple groundwater model (SIMGM) for use in GCMs by representing the recharge and discharge processes in an unconfined aquifer, which is added as a single integration element.

2. It is first validated against the observed water table depth in a small cold-region watershed. It captures not only the summer valley also the winter valley of the observed water table.

3. On the global scale, it reproduces the GRDC runoff; Groundwater discharge accounts for about 80% of the total runoff.

4. The modeled ΔS anomaly agrees very well with GRACE data in terms of inter-annual and inter-basin variability in most river basins.

5. Groundwater ΔS anomaly accounts for about 60-80% of the total ΔS anomaly; The modeled water table depth agrees very well with that converted from GRACE. The groundwater storage and WTD anomalies are mainly controlled by P – E, or climate.

6. It produces a much wetter soil globally except for arid regions; It produces about 4 – 20% more annual ET mainly through the enhanced ground surface evaporation instead of transpiration in humid-arid regions.

Introduction | SIMTOP | Validation | SIMGM | Validation | Conclusions