1. Ecologically representative distance measures for spatial modeling in stream networks Erin Peterson, David M. Theobald, and Jay Ver Hoef Natural Resource Ecology Laboratory Colorado State University Fort Collins, Colorado

2. The work reported here was developed under STAR Research Assistance Agreements 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

3. Overview ~ Introduction Background Objective Methodology Products Improvements

4. Spatial Models and Terrestrial Systems Wildlife –Reich et al., 2000; Pleydell et al., 2004; Carroll, 1998 Vegetation –Chong et al., 2001; Hudak et al, 2002; Merganic et al., 2004 Fire –Robichaud and Miller, 2003; Flores-Garnica and Omi, 2003 Agriculture –Dobermann and Ping, 2004; Jurado-Exposito et al, 2003; Van Bergeijk et al., 2001 Snow –Erxleben et al., 2002; Josberger and Mognard, 2002; Bales et al. 2001

5. Spatial Models and Aquatic Systems Lakes and Estuaries Little et al., 1997; Rathbun, 1998; Altunkaynak et al., 2003 Stream Networks Spatial dependence –Dent and Grimm, 1999  Nutrient availability –Torgensen et al., In Press  Cutthroat trout Hydrologic distance –Gardner et al., 2003  temperature Euclidean, symmetrical hydrologic, and symmetrical hydrologic weighted by stream order Prediction –Yuan, 2004  Euclidean distance –Kellum, 2003  Acid neutralizing capacity

6. Distance measures for stream data Stream data: chemical, physical, biological Functional distances: Must represent the biological or ecological nature of the variable of interest Euclidean distance: Is it an appropriate measure of distance? –Influential continuous landscape variables: geology or agriculture Symmetrical hydrologic distance –Hydrologic connectivity: Fish movement Asymmetrical hydrologic distance –Longitudinal transport of material: Benthic macroinvertebrates or water chemistry

7. A B C Distances and relationships are represented differently depending on the distance measure Applying Spatial Statistical Models to Stream Networks Distance measures for spatial modeling in stream networks Must represent the biological or ecological nature of the dependent variable

8. Distances and relationships are represented differently depending on the distance measure Applying Spatial Statistical Models to Stream Networks A B C Distance measures for spatial modeling in stream networks Must represent the biological or ecological nature of the dependent variable

9. Distances and relationships are represented differently depending on the distance measure Applying Spatial Statistical Models to Stream Networks A B C Distance measures for spatial modeling in stream networks Must represent the biological or ecological nature of the dependent variable

10. Distances and relationships are represented differently depending on the distance measure Applying Spatial Statistical Models to Stream Networks A B C Distance measures for spatial modeling in stream networks Must represent the biological or ecological nature of the dependent variable

11. A B C Distances and relationships are represented differently depending on the distance measure Applying Spatial Statistical Models to Stream Networks Challenge: Spatial autocovariance models developed for Euclidean distance may not be valid for stream distances Distance measures for spatial modeling in stream networks Must represent the biological or ecological nature of the dependent variable

12. New Spatial Statistical Models for Stream Networks Developed by Jay Ver Hoef, Alaska Department of Fish and Game (Ver Hoef et al., Submitted) Spatial statistical models for stream networks –Moving average models –Incorporate flow and use hydrologic distance –Represents discontinuity at confluences Important for pollution monitoring Flow

13. Measuring Hydrologic Distance On the ground –Hip chain or tape measure Manually using a map –Topographic maps or air photos –Scale master, string, straight edge Geographical information system (GIS) –Gardner et al., 2003 ArcView script –Rathbun, 1998 Estuaries: Digitizing shoreline, partition estuary and streams into convex polygons, and finding shortest path through polygons –Torgensen et al., In Press Coastal cutthroat trout in Oregon ArcInfo AML

14. Objective To develop the tools needed to programmatically extract and format the spatial data necessary for spatial interpolation along stream networks

15. Flow Dependent Example Asymmetric hydrologic distance Weight tributaries by flow volume Methodology A B C

16. Calculate reach contributing areas (RCAs) for each stream segment Accumulating RCAs: Calculate digitally derived explanatory variables and spatial weights Calculate hydrologic distance Calculate proportional influences GIS Tools

17. Automated = more efficient for large datasets –MAHA National Hydrography dataset (NHD) = 186,290 stream segments –Sample points Hydrologic distance between every sample point and every other connected point –Written in Visual Basic for Applications (VBA) using ArcObjects and ArcGIS version 8.3 Use easily accessible input data with national coverage –NHD –Digital elevation model (DEM) Free data! –Makes regional analysis more cost effective Tool Requirements

18. Create reach contributing areas (RCAs) Methods and VBA program developed by David M. Theobald and John Norman Input Data: –NHD waterbodies and reaches, DEM, & flowdirection grid “Grows” contributing areas away from each stream segment using WATERSHED command –Stops at a depression in DEM “Bumps” RCA boundary at each iteration –Prevents boundary delineation at slight depression in DEM Output: –Overland hydrologic contributing area for each NHD segment

19. Framework of RCAs Non-overlapping, contiguous tessellation of RCAs RCAs are networked up & downstream based on stream network topology Conceptually similar to HUCs –Represents hydrologic connectivity –Finer set of analytical units 1 to 1 relationship –Reaches are linked to catchments –For each RCA, attributes such as: Area Topography Land use, soils, geology, vegetation, etc. Efficient method for calculating catchment attributes –Flexible: can be used for multiple datasets

20. Stream Segments RCA boundaries RCA boundaries and NHD stream segments

21. RCA Example US ERF1.2 & 1 km DEM: 60,833 RCAs

22. Accumulating RCAs: Calculating digitally derived explanatory variables Input Data: Geometric network –Retains topological relationships –Created using NHD data & sample sights –RCA attributes contained as segment weights –Set flow direction Accumulate RCA attributes downstream IForwardStar and INetTopology provide access to logical network Catchment attribute = Local RCA attribute + Sum of upstream RCA attributes Flexibility Can be used for multiple datasets Many sample points fall midway on a segment Interpolate % distance along arc and calculate % catchment attribute Final Output: Cumulative catchment attributes stored in edge attribute table –Explanatory variables in spatial models

23. Calculating Catchment Attributes From RCAs

24. Catchment attribute = Local RCA attribute + Sum of upstream RCA attributes

25. Calculating Catchment Attributes From RCAs

26. Catchment attribute = Local RCA attribute + Sum of upstream RCA attributes

27. Catchment attribute = % Local RCA attribute + Sum of upstream RCA attributes

28. Catchment attribute = % Local RCA attribute + Sum of upstream RCA attributes

29. Methodology GIS Tools: Calculate reach contributing areas (RCAs) for each stream segment Accumulating RCAs: Calculate digitally derived explanatory variables and spatial weights Calculate hydrologic distance Calculate proportional influences

30. Input Data: NHD and sample sites Methods: Set flow direction  NHD segments digitized against flow Geometric network tracing functions Find Path Output: Flexible Contains upstream, downstream, and total hydrologic distance between sample sites User defines functional distance measure All information provided in 1 distance matrix Format: NxN distance matrix used in spatial interpolation Comma delimited text file Compatible with statistics software Programmatically calculate hydrologic distances and relationships

31. A C B D AB CD A 0257 B 3068 C 3305 D 0000 Records downstream distance only Contains information for: Downstream, upstream, and total distance Distance Matrix

32. A C B D AB CD A 0257 B 3068 C 3305 D 0000 C B D Downstream distance A  B = 2 A Distance Matrix

33. A C B D AB CD A 0257 B 3068 C 3305 D 0000 C B D Upstream distance A  B = Downstream distance B  A = 3 A Distance Matrix

34. A C B D AB CD A 0257 B 3068 C 3305 D 0000 C B D Total distance A  B= Downstream A  B + Downstream B  A = 5 A

35. A C B 1.0 0.6749 0.3251 0.5612 0.4312 0.1982 0.8018 1.0 Edge proportional influence Sample point Stream network A  C = 0.3251 * 0.8018 * 1.0 B  C = 0.6749 * 0.8018 * 1.0 Proportional Influence Proportional influence of one point on another = Product of edge proportional Influences in downstream path Output: NxN weighted incidence matrix Proportional influence: influence of each neighboring sample site on a downstream sample site Weighted by catchment area: Surrogate for flow Calculate influence of each upstream segment on segment directly downstream Find Path function in ArcGIS

36. Products Data Required for Spatial Modeling 1.Observed values Sample points 2.Explanatory variables Catchment attributes: Area, landuse type, topography 3.NxN distance matrix Hydrologic distance from every sample point to every other sample point Represents flow relationships 4.NxN weighted distance matrix Neighbors weighted by catchment area Surrogate for flow

37. ArcGIS Version 9 GeoNetwork –Not ESRI’s Geometric Network –Replaces the IForwardStar Object –Faster and more efficient Python scripts allow faster development & better user documentation Building the Functional Linkage of Watersheds and Streams (FLOWS) toolbox Improvements

38. Future Research Collaborations between ecology, GIS, and statistics –Functional distances Can new functional distance measures be applied using existing statistical methods? Develop new statistical methods –Allow spatial models to more accurately represent processes in aquatic systems

39. Questions?