Regional GIS-based Geostatistical Models
for Stream Networks
Erin E. Peterson
Postdoctoral Research Fellow
CSIRO Mathematical and Information Sciences Division
Brisbane, Australia
May 18, 2006
www.csiro.au
Space-Time Aquatic Resources
Modeling and Analysis Program
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.
This research is funded by
U.S.EPA 凡Science
Science To
ToAchieve
Achieve
Results (STAR) Program
Cooperative
Agreement # CR - 829095
Collaborators
Dr. David M. Theobald
Natural Resource Ecology Lab
Department of Recreation & Tourism
Colorado State University, USA
Dr. N. Scott Urquhart
Department of Statistics
Colorado State University, USA
Dr. Jay M. Ver Hoef
National Marine Mammal Laboratory,
Seattle, USA
Andrew A. Merton
Department of Statistics
Colorado State University, USA
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
Y  X 
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 ( s )  X ( s )    ( s )
Geostatistical Modeling
Fit an autocovariance function to data

Describes relationship between observations based on separation
distance
3 Autocovariance Parameters
2) Sill: delineated where semivariance
asymptotes
3) Range: distance within which spatial
autocorrelation occurs
Sill
Semivariance
1) Nugget: variation between sites as
separation distance approaches zero
10
Nugget
0
0
Range
Separation Distance
1000
Distance Measures and Spatial Relationships
B
A
C
Straight Line Distance (SLD)
 As the crow flies
Distance Measures and Spatial Relationships
B
A
C
Symmetric Hydrologic Distance (SHD)
 As the fish swims
Distance Measures and Spatial Relationships
B
A
C
Weighted asymmetric hydrologic distance (WAHD)
 As the water flows
 Incorporate flow direction & flow volume
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.
Distance Measures and Spatial Relationships
B
A
C
Fit a mixture of covariances
 Based on more than one distance measure
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.
Distance Measures and Spatial Relationships
Distance measure influences how spatial relationships are
represented in a stream network


Site’s relative influence on other sites
Dictates form and size of spatial neighborhood
Important because…

Impacts accuracy of the geostatistical model predictions
SLD
SHD
WAHD
Dissolved Organic Carbon (DOC) Example
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
Maryland Biological Stream Survey (MBSS) Data
Study Area
Kilometers
0
N
Kilometers
20
0
N
n
312
n
312
Min
0.6
Min
0.6
Qu.
1st
1.2
1st Qu.
1.2
Median
1.7
20
Median
1.7
Mean
1.9
Mean
3rd Qu.
1.9
3rd Qu. 2.7
Max
2.7
15.9
Max
15.9σ2
1.8
σ2
1.8
Functional Linkage of Watersheds and Streams (FLoWS)
Create data for geostatistical modeling
1. Calculate watershed covariates for each stream segment
2. Calculate separation distances between sites
 SLD, Asymmetric hydrologic distance (AHD)
3. Calculate the spatial weights for the WAHD
4. Convert GIS data to a format compatible with statistics software
FLoWS website: http://www.nrel.colostate.edu/projects/starmap
2
1
3
SLD
1
2
3
SHD
1
2
3
AHD
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
Watershed
Segment B
Watershed
Segment A
A
2. Calculate the PI of one survey site on
another site
 Flow-connected sites
 Multiply the segment PIs
B
C
Segment PI
of A
=
Watershed Area A
Watershed Area A+B
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
A
C
B
E
2. Calculate the PI of one survey site on
another site
 Flow-connected sites
 Multiply the segment PIs
D
F
G
H
survey sites
stream 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
A
C
B
E
2. Calculate the PI of one survey site on
another site
 Flow-connected sites
 Multiply the segment PIs
D
F
G
H
Site PI = B * D * F * G
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
Fit the correlation matrix for SLD and
WAHD models
Maximized profile-log likelihood function

Estimate model parameters
Autocorrelation
Function
Exponential
Spherical
Comparison within model set
 Spatial AICC
Mariah
Hole Effect
Linear with Sill
Comparison between model set
 Universal kriging
 MSPE
Rational Quadratic
SLD
WAHD
SLD Mariah Model
r2 Observed vs. Predicted values
 1 influential site
 r2 without site = 0.66
18
Predicted DOC mg/l
rR2 2==0.7221
0.7221
0
0
5
10
Observed DOC mg/l
15
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
Implications for Anadromous Fish Conservation
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
Questions? Comments?
Erin E. Peterson
Phone: +61 7 3214 2914
Email: Erin.Peterson@csiro.au
www.csiro.au