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 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 Achieve Results (STAR) Program Cooperative Agreement # CR This research is funded by U.S.EPAScience To Achieve Results (STAR) Program Cooperative Agreement # CR

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 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

Geostatistical Modeling Fit an autocovariance function to data  Describes relationship between observations based on separation distance Separation Distance Semivariance Sill Nugget Range 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 SHDWAHD SLD 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

Study Area Maryland Biological Stream Survey (MBSS) Data

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: SLD 12 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 B C D E 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 2.Calculate the PI of one survey site on another site  Flow-connected sites  Multiply the segment PIs

A B C D E 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 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

r 2 Observed vs. Predicted values SLD Mariah Model  1 influential site  r 2 without site = 0.66

Spatial Patterns in Model Fit Squared Prediction Error (SPE)

Generate Model Predictions Prediction sites  Study area –1 st, 2 nd, and 3 rd 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

Questions? Comments? Erin E. Peterson Phone: