Erin E. Peterson

1
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

2
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.
3
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
4
Overview
Introduction Background Develop and compare
geostatistical models Visualizing model
predictions Current and future research in SEQ
5
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
  Alaskas extensive unsurveyed freshwaters.

6
My Goal

• Demonstrate a geostatistical methodology based on
• Coarse-scale GIS data
• Field surveys
• Predict stream characteristics for individual
  segments throughout a region

7
How are geostatistical models different from
traditional statistical models?

• Traditional statistical models (non-spatial)
• Residual error (e) is assumed to be uncorrelated
• e 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

8
Geostatistical Modeling

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

• 3 Autocovariance Parameters
• Nugget variation between sites as separation
  distance approaches zero
• Sill delineated where semivariance asymptotes
• Range distance within which spatial
  autocorrelation occurs

9
Distance Measures and Spatial Relationships

• Straight Line Distance (SLD)
• As the crow flies

10
Distance Measures and Spatial Relationships

• Symmetric Hydrologic Distance (SHD)
• As the fish swims

11
Distance Measures and Spatial Relationships

• 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.
12
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.
13
Distance Measures and Spatial Relationships
14
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

15
Maryland Biological Stream Survey (MBSS) Data
Study Area
16
Functional Linkage of Watersheds and Streams
(FLoWS)

• Create data for geostatistical modeling
• Calculate watershed covariates for each stream
  segment
• Calculate separation distances between sites
• SLD, Asymmetric hydrologic distance (AHD)
• Calculate the spatial weights for the WAHD
• Convert GIS data to a format compatible with
  statistics software
• FLoWS website http//www.nrel.colostate.edu/proje
  cts/starmap

17
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

18
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

survey sites stream segment
19
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

A
C
B
E
D
F
G
H
20
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

21
Geostatistical Modeling Methods

• 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

22
SLD Mariah Model
r2 Observed vs. Predicted values

• 1 influential site
• r2 without site 0.66

23
Spatial Patterns in Model Fit
24
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

25
DOC Predictions (mg/l)
26
Weak Model Fit
27
Strong Model Fit
28
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

29
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

30
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

31
Questions? Comments?
Erin E. Peterson Phone [phone] Email
Erin.Peterson_at_csiro.au