Ecologically representative distance measures for spatial modeling in stream networks

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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

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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.
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• Overview
• Introduction
• Background
• Objective
• Methodology
• Products
• Improvements

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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

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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

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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

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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
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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
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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
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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
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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

• Challenge
• Spatial autocovariance models developed for
  Euclidean distance may not be valid for stream
  distances

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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

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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

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Objective

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

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Methodology

• Flow Dependent Example
• Asymmetric hydrologic distance
• Weight tributaries by flow volume

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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

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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

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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

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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

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RCA boundaries and NHD stream segments
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RCA Example

• US ERF1.2 1 km DEM 60,833 RCAs

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Accumulating RCAsCalculating 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

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Calculating Catchment Attributes From RCAs
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Catchment attribute Local RCA
attribute Sum of upstream RCA attributes
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Calculating Catchment Attributes From RCAs
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Catchment attribute Local RCA
attribute Sum of upstream RCA attributes
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Catchment attribute Local RCA
attribute Sum of upstream RCA attributes
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Catchment attribute Local RCA
attribute Sum of upstream RCA attributes
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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

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Programmatically calculate hydrologic distances
and relationships

• 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

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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

• Records downstream distance only
• Contains information for
• Downstream, upstream, and total distance

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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
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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
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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
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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
A?C 0.3251 0.8018 1.0 B?C 0.6749 0.8018
1.0

• Output NxN weighted incidence matrix

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Products

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

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Improvements

• ArcGIS Version 9
• GeoNetwork
• Not ESRIs 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

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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

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Questions?