creating a topographic index - cornell universitysoilandwater.bee.cornell.edu/tools/ti.pdf ·...

Biological and Environmental Engineering

Soil & Water Research Group

Creating a Topographic Index

So you can spend the next 3 yrs of you life figuring out what to do with it



•  Topographic Index maps are grids derived from digital elevation models (DEMs). These grid include only topographical information. It makes use of an index of hydrological similarity based on topographic data. •  Originally developed in the TOPMODEL framework (Beven

et al., 1984). •  TOPMODEL was one of the first attempts to model

distributed hydrological responses based on variable contributing area concepts.

•  Has since been applied outside of the TOPMODEL framework in GWLF, SWAT.



•  Topographic Indices assume that topography drives flows. •  Thus, the index may not capture conditions in areas

where there are other more dominant processes governing the flow.

•  However, it generally correctly predicts the accumulation of flow in topological low spots (e.g., areas where the flows accumulate).



⎟⎟⎠

⎞⎜⎜⎝

⎛=

βα

λtan

ln

where λ is the topographic index, α is the upslope contributing area per unit length of contour, and β is the topographic slope of the cell.

The Topographic Index



1) Begin with a DEM:



• Since raster processing can be computationally intensive, we will work with a single sub watershed • We need to clip the larger DEM to the extent of the Town Brook watershed



There are several ways to do this. 1. Open spatial analyst options and set the Analysis mask. Here we use a shape file of the watershed boundary previously defined by the USGS



Open the raster calculator and select the raster, and hit evaluate.

Now we have a well defined watershed to work with.



2) In Arc Catalog create a new shapefile under “file> new”, make it a point file. Import into Arc Map and digitize a point at the outlet of the watershed. Open Arc ToolBox and “Spatial Analyst”, and “Watershed” and input the flow direction raster and the point shapefile. Note, you will need to calculate the flow directions first, so it is a bit more intensive.

There are several other ways to extract various shapes and sizes and attributes in the DEMs. Explore.



Creating a TI 2) Open ArcTool Box “Spatial Analyst Tools” under “Hydrology” select fill to fill any sinks in the DEM:



3) In “Spatial Analyst Tools” under “Hydrology” select flow direction map:



4) In “Spatial Analyst Tools” under “Hydrology” select flow accumulation:



5) In “Spatial Analyst Tools” under “Surface” select slope map in degrees (from filled DEM):



6) Calculate tangent of slope (radians), by typing “Tan(([TB_Slope] * 1.570796) / 90)” in Raster Calculator:



7) Remove zeros values by typing “con(TB_Rads == 0, 0.0001, [TB_Rads])” in Raster Calculator: This prevents any undefined cells in the final output.



8) Calculate TI by typing “Ln((([FlowAcc_flow1] + 1) * 10) / [TB_Rads_No0] )” in Raster Calculator (note that 10 is cell size in meters):



Notice that in areas with complex topology or on divergent hillslopes there is a “streaking” effect. This is due to the flow accumulation algorithm used in Arc, which uses a computationally efficient single direction flow algorithm. That is, if water were placed on a cell, it is only allowed to flow down slope in one direction based on the path of steepest decent, and not in several or many directions like we might expect. Thus, on simple hillslopes the single direction method works fine, but in complex basins it is lacking.



• Using the single direction flow routing, slope is evaluated in the direction of steepest descent and is reported as drop/distance, i.e. tangent of the angle. • All flow leaving any given pixel with the single direction method (or the area contributing flow to the pixel) is assumed to flow into a single downstream neighbor pixel. • While these simplifications are valid in regions where the flow is convergent, such as the channelized portion of the landscape, they do not work well on divergent hillslopes. • This leads to potentially large errors in the calculation of contributing area (or basin area) for hillslope pixels, even though computed values for channel pixels are correct. • Accurate contributing areas for hillslope pixels are needed for process-based models of erosion, landslide potential, or source areas.



• So we need a better flow partitioning methods to capture complex landscapes. We have gone through the basics of topographic indices, and their calculation. Now comes the easy part, where we download an extension for Arc that incorporates a more robust flow direction method. This extension “TauDEM” is available free at http://hydrology.neng.usu.edu/taudem/90info.htm and uses what is called a multi-direction flow algorithm. • The methodology is outlined at http://hydrology.neng.usu.edu/taudem/



Method: The D-Infinity (dinfi) algorithm was proposed by Tarboton (1997) in an effort to compute contributing area more accurately on divergent hillslopes. While it does not provide a completely rigorous solution to this challenging "flow tube" problem, it is a fairly robust and pragmatic approach and gives visually appealing results. The dinfi (infinity) flow routing is encoded as an angle 'ang' in radians counter-clockwise from east as a continuous (floating point) quantity between 0 and 2 pi. The flow direction angle is determined as the direction of the steepest downward slope on the eight triangular facets formed in a 3 x 3 grid cell window centered on the grid cell of interest. A block-centered representation is used with each elevation value taken to represent the elevation of the center of the corresponding grid cell. Eight planar triangular facets are formed between each grid cell and its eight neighbors. Each of these has a downslope vector which when drawn outwards from the center may be at an angle that lies within or outside the 45o (pi/4 radian) angle range of the facet at the center point. If the slope vector angle is within the facet angle, it represents the steepest flow direction on that facet. If the slope vector angle is outside a facet, the steepest flow direction associated with that facet is taken along the steepest edge. The slope and flow direction associated with the grid cell is taken as the magnitude and direction of the steepest downslope vector from all eight facets. Slope is measured as drop/distance, i.e. tan of the slope angle. In the case where no slope vectors are positive (downslope), the flow direction is set using the method of Garbrecht and Martz (1997) for the determination of flow across flat areas. This makes flat areas drain away from high ground and towards low ground.



Flow direction defined as steepest downward slope on planar triangular facets on a block centered grid.



We install the interface



Select the DEM, and let the program run

You will get lots of maps as output. You need only the flow accumulation grid “…sca”, which uses the multi-direction flow method, and the slope grid “…slp”, which is already the tangent of the slope. Therefore, you now have everything you need to calculate a TI. In the raster calculator type “Ln(([flowAcc_flow] * 10) /[slope_tb_dem))” (note that 10 is cell size in meters):



The resulting TI appears much “smoother” because flow is now partitioned among several cells



References: Beven, K.J., M.J. Kirkby, N. Schofield, A.F. Tagg, (1984), “A physically based flood forecasting model (TOPMODEL) for 3 UK catchments”, Journal of Hydrology, 69:119-143. Garbrecht, J. and L. W. Martz, (1997), "The assignment of drainage direction over flat surfaces in raster digital elevation models," Journal of Hydrology, 193: 204-213. Tarboton, D. G., (1997), "A new method for the determination of flow directions and contributing areas in grid digital elevation models," Water Resources Research, 33(2): 309-319.

creating a topographic index - cornell universitysoilandwater.bee.cornell.edu/tools/ti.pdf ·...

Documents