www.csiro.au

Erin E. Peterson

Postdoctoral Research Fellow

CSIRO Mathematical and Information Sciences Division

Brisbane, Australia

May 18, 2006

Regional GIS-based Geostatistical Models for Stream Networks

The work reported here was developed under STAR Research Assistance Agreement CR-829095 awarded by the U.S.

Environmental Protection Agency (EPA) to Colorado State University. This presentation has not been formally reviewed by

EPA. EPA does not endorse any products or commercial services mentioned in this presentation.

Space-Time Aquatic Resources Modeling and Analysis Program

This research is funded by

U.S.EPA凡Science To AchieveResults (STAR) ProgramCooperativeAgreement # CR -829095

This research is funded by

U.S.EPAScience To AchieveResults (STAR) ProgramCooperativeAgreement # CR -829095

Dr. David M. TheobaldNatural Resource Ecology LabDepartment of Recreation & TourismColorado State University, USA

Dr. N. Scott UrquhartDepartment of StatisticsColorado State University, USA

Dr. Jay M. Ver HoefNational Marine Mammal Laboratory, Seattle, USA

Andrew A. MertonDepartment of StatisticsColorado State University, USA

Collaborators

Overview

Introduction~

Background~

Develop and compare geostatistical models

~Visualizing model predictions

~Current and future research in

SEQ

Challenges

Challenges are similar to states attempting to comply with the Clean Water Act

Anadromous Waters Catalog (AWC)

Large number of water bodies within AK

~ 20,000 unidentified anadromous water bodies

Need spatially explicit, unambiguous field observations of anadromous fish

Cost (time and $$) of field surveys is high

“… We recognize a pressing need for approaches that predict the distribution of salmon in Alaska’s extensive unsurveyed freshwaters.”

My Goal

Demonstrate a geostatistical methodology based on

Coarse-scale GIS data

Field surveys

Predict stream characteristics for individual segments throughout a region

How are geostatistical models different from traditional statistical models?

Traditional statistical models (non-spatial)

Residual error (ε) is assumed to be uncorrelated

ε = unexplained variability in the data

Geostatistical models

Residual errors are correlated through space

Spatial patterns in residual error resulting from unidentified process(es)

Model spatial structure in the residual error

Explain additional variability in the data

Generate predictions at unobserved sites

Y X

( ) ( ) ( )Y s X s s

Geostatistical Modeling

Fit an autocovariance function to data Describes relationship between observations based on separation distance

Separation Distance

Sem

ivar

ian

ce

Sill

Nugget Range

10000

0

103 Autocovariance Parameters

1) Nugget: variation between sites as separation distance approaches zero

2) Sill: delineated where semivariance asymptotes

3) Range: distance within which spatial autocorrelation occurs

Distance Measures and Spatial Relationships

Straight Line Distance (SLD)

As the crow flies

A

B

C

Symmetric Hydrologic Distance (SHD)

As the fish swims

A

B

C

Distance Measures and Spatial Relationships

Weighted asymmetric hydrologic distance (WAHD)

As the water flows

Incorporate flow direction & flow volume

A

B

C

Distance Measures and Spatial Relationships

Ver Hoef, J.M., Peterson, E.E., and Theobald, D.M. (2006) Spatial Statistical Models that Use Flow and Stream Distance, Environmental and Ecological Statistics, to appear.

Fit a mixture of covariances

A

B

C

Cressie, N., Frey, J., Harch, B., and Smith, M.: 2006, ‘Spatial Prediction on a River Network’, Journal of Agricultural, Biological, and Environmental Statistics, to appear.

Based on more than one distance measure

Distance Measures and Spatial Relationships

Site’s relative influence on other sites Dictates form and size of spatial neighborhood

Important because… Impacts accuracy of the geostatistical model predictions

Distance measure influences how spatial relationships are represented in a stream network

SHD WAHDSLD

Distance Measures and Spatial Relationships

Demonstrate how a geostatistical methodology can be used to identify ecologically significant waters

Example:

Develop and compare geostatistical models for DOC

Predict regional DOC levels

Identify the spatial location of stream segments with high levels of DOC

Dissolved Organic Carbon (DOC) Example

N 0 20

Kilometers

n Min 1st Qu. Median Mean 3rd Qu. Max σ2312 0.6 1.2 1.7 1.9 2.7 15.9 1.8

N 0 20

Kilometers

0 20

Kilometers

n Min 1st Qu. Median Mean 3rd Qu. Max σ2312 0.6 1.2 1.7 1.9 2.7 15.9 1.8n Min 1st Qu. Median Mean 3rd Qu. Max σ2

312 0.6 1.2 1.7 1.9 2.7 15.9 1.8

N 0 20

Kilometers

n Min 1st Qu. Median Mean 3rd Qu. Max σ2312 0.6 1.2 1.7 1.9 2.7 15.9 1.8

N 0 20

Kilometers

0 20

Kilometers

n Min 1st Qu. Median Mean 3rd Qu. Max σ2312 0.6 1.2 1.7 1.9 2.7 15.9 1.8n Min 1st Qu. Median Mean 3rd Qu. Max σ2

312 0.6 1.2 1.7 1.9 2.7 15.9 1.8

Study Area

Maryland Biological Stream Survey (MBSS) Data

Create data for geostatistical modeling

1. Calculate watershed covariates for each stream segment2. Calculate separation distances between sites

SLD, Asymmetric hydrologic distance (AHD)3. Calculate the spatial weights for the WAHD4. Convert GIS data to a format compatible with statistics software

FLoWS website: http://www.nrel.colostate.edu/projects/starmap

1 2

3

1 2

3

SLD

1 2

3

SHD AHD

Functional Linkage of Watersheds and Streams (FLoWS)

Spatial Weights for WAHD

Proportional influence (PI): influence of each neighboring survey site on a downstream survey site Weighted by catchment area: Surrogate for flow volume

1. Calculate the PI of each upstream segment on segment directly downstream

2. Calculate the PI of one survey site on another site Flow-connected sites Multiply the segment PIs

BA

C

Watershed Segment B

Watershed Segment A

Segment PI of A

Watershed Area A

Watershed Area A+B=

A

BC

DE

F

G

H

survey sitesstream segment

Spatial Weights for WAHD

Proportional influence (PI): influence of each neighboring survey site on a downstream survey site Weighted by catchment area: Surrogate for flow volume

1. Calculate the PI of each upstream segment on segment directly downstream

2. Calculate the PI of one survey site on another site Flow-connected sites Multiply the segment PIs

A

BC

DE

F

G

H

Site PI = B * D * F * G

Spatial Weights for WAHD

Proportional influence (PI): influence of each neighboring survey site on a downstream survey site Weighted by catchment area: Surrogate for flow volume

1. Calculate the PI of each upstream segment on segment directly downstream

2. Calculate the PI of one survey site on another site Flow-connected sites Multiply the segment PIs

Data for Geostatistical Modeling

Distance matrices

SLD, AHD

Spatial weights matrix

Contains flow dependent weights for WAHD

Watershed covariates

Lumped watershed covariates

Mean elevation, % Urban

Observations

MBSS survey sites

Geostatistical Modeling Methods

Autocorrelation Function SLD WAHD

Exponential

Spherical

Mariah

Hole Effect

Linear with Sill

Rational Quadratic

Fit the correlation matrix for SLD and WAHD models

Maximized profile-log likelihood function Estimate model parameters

Comparison within model set Spatial AICC

Comparison between model set Universal kriging MSPE

R2 = 0.7221

0

18

0 5 10 15Observed DOC mg/l

Pre

dic

ted

DO

C m

g/l r2 = 0.7221R2 = 0.7221

0

18

0 5 10 15Observed DOC mg/l

Pre

dic

ted

DO

C m

g/l r2 = 0.7221

r2 Observed vs. Predicted values

SLD Mariah Model

1 influential site r2 without site = 0.66

Spatial Patterns in Model Fit

Squared Prediction Error (SPE)

Generate Model Predictions

Prediction sites Study area

– 1st, 2nd, and 3rd order non-tidal streams– 3083 segments = 5973 stream km

ID downstream node of each segment– Create prediction site

Generate predictions and prediction variances

SLD Mariah model Universal kriging algorithm

DOC Predictions (mg/l)

Weak Model Fit

Strong Model Fit

Apply this methodology to salmon or salmon habitat

Identify habitat conditions necessary for spawning, rearing, or migration of anadromous fish Based on ecological & biological knowledge

Identify watershed conditions that may influence those conditions Watershed geology type ~ substrate type Derive watershed characteristics using GIS/remote sensing

Generate predictions and estimates of uncertainty for potential salmon habitat

Categorize predictions into low, medium, or high status Probability of supporting anadromous fish

Implications for Anadromous Fish Conservation

Tradeoff between cost-efficiency and model accuracy One model can be used throughout a large region Regions may be ecologically unique May need to generate separate models for AWC regions

Allocate scarce sampling resources efficiently Target areas with a high probability of supporting anadromous fish Identify areas where more information would be useful

Implications for Anadromous Fish Conservation

Advantages of GIS

Identify spatial patterns in model fit

Evaluate habitat at multiple scales Feature scale and regional scale Help prioritize fish habitat restoration Help prioritize land/conservation easement

acquisitions

Easily communicate with community, environmental, and government groups

Implications for Anadromous Fish Conservation

www.csiro.au

Questions? Comments?

Erin E. Peterson

Phone: +61 7 3214 2914

Email: Erin.Peterson@csiro.au