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

This research is funded by

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

This research is funded by

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

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

Overview~

IntroductionBackground

ObjectiveMethodology

ProductsImprovements

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

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

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

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

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

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

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

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

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

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

Objective

To develop the tools needed to

programmatically extract and format the spatial data necessary for spatial interpolation along stream networks

Flow Dependent Example

• Asymmetric hydrologic distance

• Weight tributaries by flow volume

Methodology

A

B

C

• 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

• 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

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

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

Stream Segments RCA boundaries

RCA boundaries and NHD stream segments

RCA Example

• US ERF1.2 & 1 km DEM: 60,833 RCAs

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

Calculating Catchment Attributes From RCAs

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

Calculating Catchment Attributes From RCAs

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

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

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

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

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

A

C

B

D

A B C D

A 0 2 5 7

B 3 0 6 8

C 3 3 0 5

D 0 0 0 0

Records downstream distance only• Contains information for:

• Downstream, upstream, and total distance

Distance Matrix

A

C

B

D

A B C D

A 0 2 5 7

B 3 0 6 8

C 3 3 0 5

D 0 0 0 0

C

B

D

Downstream distance A B = 2

A

Distance Matrix

A

C

B

D

A B C D

A 0 2 5 7

B 3 0 6 8

C 3 3 0 5

D 0 0 0 0

C

B

D

Upstream distance A B = Downstream distance B A = 3

A

Distance Matrix

A

C

B

D

Distance Matrix

A B C D

A 0 2 5 7

B 3 0 6 8

C 3 3 0 5

D 0 0 0 0

C

B

D

Total distance A B= Downstream A B + Downstream B A = 5

A

AC

B1.0

0.6749

0.3251

0.5612

0.4312

0.1982

0.80181.0

1.0

Edge proportional influenceSample pointStream network

AC = 0.3251 * 0.8018 * 1.0BC = 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

ProductsData 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

• 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

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

Questions?