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
Space-Time Aquatic Resources
Modeling and Analysis Program
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.
This research is funded by
U.S.EPA ・Science To Achieve
Results (STAR) Program
Cooperative
Agreement # CR - 829095
Overview
~
Introduction
Background
Objective
Methodology
Products
Improvements
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
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
B
A
Distances and relationships are
represented differently depending on
the distance measure
C
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
B
A
Distances and relationships are
represented differently depending on
the distance measure
C
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
B
A
Distances and relationships are
represented differently depending on
the distance measure
C
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
B
A
Distances and relationships are
represented differently depending on
the distance measure
C
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
B
A
Distances and relationships are
represented differently depending on
the distance measure
C
Challenge:
• Spatial autocovariance models developed for Euclidean
distance may not be valid for stream distances
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
Methodology
Flow Dependent Example
• Asymmetric hydrologic distance
• Weight tributaries by flow volume
B
C
A
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
Tool Requirements
• 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
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
RCA boundaries and NHD stream segments
Stream Segments
RCA boundaries
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:
Programmatically calculate hydrologic
distances and relationships
• 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
Distance Matrix
B
A
B
C
D
A
0
2
5
7
B
3
0
6
8
C
3
3
0
5
D
0
0
0
0
A
C
D
Records downstream distance only
• Contains information for:
• Downstream, upstream, and total distance
Distance Matrix
B
A
B
C
D
A
0
2
5
7
B
3
0
6
8
C
3
3
0
5
D
0
0
0
0
A
C
D
Downstream distance A  B = 2
Distance Matrix
B
A
B
C
D
A
0
2
5
7
B
3
0
6
8
C
3
3
0
5
D
0
0
0
0
A
C
D
Upstream distance A  B = Downstream distance B  A = 3
Distance Matrix
B
A
B
C
D
A
0
2
5
7
B
3
0
6
8
C
3
3
0
5
D
0
0
0
0
A
C
D
Total distance A  B= Downstream A  B + Downstream B A = 5
Proportional Influence
•
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
Proportional influence of one point on another
=
Product of edge proportional Influences in
downstream path
0.4312
0.5612
C
0.8018
A
AC = 0.3251 * 0.8018 * 1.0
BC = 0.6749 * 0.8018 * 1.0
•
Output: NxN weighted
incidence matrix
0.1982
1.0
0.3251
1.0
0.6749
1.0
B
Edge proportional influence
Sample point
Stream network
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
Improvements
• 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
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?