Terrain Analysis Tools for Routing Flow and Calculating Upslope Contributing Areas

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Terrain Analysis Tools for Routing Flow and
Calculating Upslope Contributing Areas

• John P. Wilson
• Terrain Analysis for Water Resources Applications
  Symposium 2002

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Todays Topics

• Guiding principles
• Proposed flow routing algorithms
• Flow routing methods implemented in TAPES-G
• Sensitivity of computed topographic attributes to
  choice of flow routing method
• Key decisions, problems, and challenges

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Scales / Processes / Regimes
Cloud cover and CO2 levels control primary energy
inputs to climate and weather patterns Prevailing
weather systems control long-term mean
conditions elevation-driven lapse rates control
monthly climate and geological substrate exerts
control on soil chemistry Surface morphology
controls catchment hydrology slope, aspect,
horizon, and topographic shading control surface
insolation Vegetation canopy controls light,
heat, and water for understory plants vegetation
structure and plant physiognomy controls nutrient
use Soil microorganisms control nutrient
recycling
Global Meso Topo Micro Nano
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Water Flow on Hillslopes
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Land Surface Shape
Courtesy Graeme Aggett 2001
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Terrain Shape

• Terrain shape / drainage structure important at
  toposcale
• Locally adaptive gridding procedures work well
  with contour and stream line data
• Need filtering / interpolation methods that
  respect surface structure for remotely sensed
  elevation sources
• Choose resolution based on data sources / quality
  and not the application at hand

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Flow Direction / Catchment Area

• Flow direction shows path of water flow
• Upslope contributing area A is area of land
  upslope of a length of contour l
• Specific catchment area is A/l

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Proposed Flow Routing Algorithms

• Vary depending on granularity with which aspect
  is computed and whether single or multiple flow
  paths are allowed
• Single flow direction algorithms
• D8 (OCallaghan and Mark 1984)
• Rho4 / Rho8 (Fairfield and Leymarie 1991)
• Aspect-driven (Lea 1992)

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Flow Routing Algorithms (2)

• Multiple flow direction algorithms
• FD8 (Quinn et al. 1991)
• FMFD (Freeman 1991 Holmgren 1994)
• DEMON (Costa-Cabral and Burges 1994)
• R.flow (Mitasova and Hofierka 1993 Mitasova et
  al. 1995, 1996)
• D8 (Tarboton 1997)
• Form-based method (Pilesjo et al. 1998)

Courtesy Qiming Zhou and Xuejun Liu 2002
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TAPES-G Algorithms

• Single-flow-direction D8 method
• Randomized single-flow-direction Rho8 method
• Multiple-flow-direction FD8 and FRho8 methods
• DEMON stream-tube method

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TAPES-G Inputs

• Square-grid DEM
• Important decisions about extent of study area
  and how to handle edge effects, spurious sinks or
  pits, etc.
• Interested in hydrologic connectivity of
  topographic surface

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TAPES-G Outputs
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Final Cottonwood Creek DEM
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Aspect / Primary Flow Direction?

• Shows aspect computed using finite difference
  method
• Poor choice of scale bar?

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Primary Flow Direction (FLOWD)

• Approximate surrogate for aspect since it
  identifies direction to the nearest neighbor with
  maximum gradient
• FLOWD 2j - 1
• where j arg max
• i 1,8
• The approximate aspect corresponding to this flow
  direction is ?D8 45j

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D8 SFD Algorithm

• Does well in valleys
• Produces many parallel flow lines and problems
  near catchment boundary
• Cannot model flow divergence in ridge areas

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D8 SFD Algorithm

• Diagram shows detail near catchment boundary
• Dark cells not located on boundary due to
  subtle change in aspect as it swifts from south
  to southeast

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Rho8 SFD Algorithm

• Breaks up parallel flow paths / produces mean
  flow direction equal to aspect
• More cells with no upslope connections
• Produces unique result each time

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FD8 MFD Algorithm

• Distributes flow on hillslopes to each downslope
  neighbor on a slope-weighted basis
• Specify cross-grading threshold to disable this
  feature in valleys

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FD8 Flow Dispersion Weights
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DEMON Algorithm

• Flow generated at each source pixel and routed
  down a stream tube until edge of DEM or a pit is
  encountered
• Stream tubes constructed from points of
  intersections of a line drawn in gradient
  direction and a grid cell edge

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DEMON Stream-Tube Algorithm

• Three variants used in TAPES-G related to
• Choice of DEM
• Use of grid centroids in place of vertices
• Definition of aspect

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Upslope Contributing Area

• Computed with contour-based stream tubes in
  northern part of catchment

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TAPES-C Element Network
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Contour DEM Elements

• Set of elements formed by contours and flow lines
• Proceeding uphill, flow lines are terminated (A)
  and added (B, C) to maintain even spacing
• Lines are constructed using either a minimum
  distance (BD) or orthogonal (CE) criterion

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Specific Catchment Area

• 105 km2 Squaw Creek catchment in Gallatin
  National Forest, Montana
• Results derived from 30 m DEMS for 3 USGS
  124,000 scale map quadrangles

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Specific Catchment Area Maps
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Secondary Topographic Attributes
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Secondary Topographic Attributes
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Sediment Transport Capacity Index
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Grid Comparisons
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Key Decisions and Challenges

• Methods can be distinguished based on equation
  used to estimate aspect and whether or not they
  permit flow to two or more downslope cells
• Most of the results produced thus far relate to
  coarse resolution DEM products
• Sensitivity analysis results are difficult to
  extrapolate to new study sites

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New Data Sources

• Several presentations about SAR and LIDAR
  technology data at this conference
• Must develop and/or find methods for filtering
  and interpolation that respect surface structure
  for these remotely sensed elevation sources

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Interpolation Results
TIN
IDW
Surf.tps (GRASS)
Thin plate spline
TOPOGRID
Courtesy Graeme Aggett 2001
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Better Sensitivity Analyses?
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Topographic Attributes

• Elevation
• Slope
• Profile curvature
• Plan curvature
• Distance from ridge lines
• Incident solar radiation
• Topographic wetness index
• Sediment transport capacity index

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Fuzzy Classification

• Split study area into three equal parts
• Took stratified random sample and
• extracted topographic attributes
• Performed several fuzzy k-means classifications
• Calculated confusion index and F and H parameters
  and generated fuzzy and crisp landform class maps

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Final Landform Classes

• Valley bottoms
• Main drainage lines
• Lower slopes
• Steep, shaded north-facing slopes
• Narrow ridge lines
• Steep, south-facing, drier upper slopes and broad
  ridges

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Cluster Centers and Ranges
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Summary Data for Six Classes
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Final Map?
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Closing Comments

• Several graduate students working on new data
  sources and fuzzy classification of landscapes
• One is looking at performance of five flow
  routing algorithms in different landform classes
  with 5 m SAR DEM for example
• May be able to answer one or two questions if
  there is time available