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Topographic Flammability Index

Topographic Flammability Index

Dec 25, 2015

In an effort to improve the dNBR predictive surface I wondered whether I could further inform the model based on an index of topographic position. The question: how does topography redistribute heat energy along a hill slope of increasing height and angle of repose, and does this feature lead to different burn severity in the observed dNBR data? I calculated an inverse DEM's catchment catchment area using the Catchment Area (recursive) SAGA module. Slope was calculated in radians using Tarboton (1997) triangular slope option with the Slope, Aspect, Curvature module. Essentially the model is an inverse topographic wetness index (TWI). Traditionally TWI (TOPMODEL, Beven and Kirkby 1979) is calculated as:

 TWI = log( Upslope Area / tan(Slope) )

where log is the natural logarithm of local upslope area (catchment area) over the tangent of slope (in radians). For the conditionally named topographic flammability index (TFI) I used the inverse DEM to calculate downslope area in the numerator, and because TWI has a declining index value for increasing slope I took the cotangent of the slope; the value of the denominator can also use tangent calculated by subtracting the slope angle from  ?/2 = 1.57079632679.

 TFI = log( Downslope Area / cotan(Slope) )

where the Downslope area is the inverse DEM Catchment area (in meters squared), ?/2 minus Slope is the value in radians (1 degree = 0.0174532925 radians). Quick trigonometry refresher:

tan A = sin A / cos A

cotan A = cos A / sin A = tan( pi/2 - A) = 1 / tan A

Identifying topographically related trends in the MTBS dNBR data.

After I generated TFI I use the Grid Value to Points command in QGIS (via SAGA) to generate points at every pixel for the 30 m MTBS dNBR layers clipped to the vector fire perimeter. I use the Point Sampling Tool to sample dNBR, Northness, Elevation, and TWI and saved those outputs as *.CSV files.

I then open the data in Matlab and run the grpstats() tool on each set of independent variables (elevation, northness, TWI, TFI) for median, mean, max, and standard deviation.

(Right Click and Open Image in New Window to view full size)

           

Box plots of dNBR by slope, aspect, northness, catchment height, and upslope and downslope catchment area.

Workflow in QGIS/SAGA

  1. In SAGA import raster using GDAL Import Raster.
  2. In QGIS open the raster file by dragging it into the console, or by clicking on the raster import button.
  3. Reproject (Warp) the Raster to make sure that the units are in meters (instead of decimal degrees, e.g. SRTM or NED DEM data).
  4. Flip the sign of the raster using Raster Calculator in QGIS.
  5. Note: SAGA Grid Calculator does not support cotangent (cot); so use 1/tan = cot to calculate.
  6. Run Catchment Area (Recursive) on the negative DEM.
  7. Run Slope, Aspect, Curvature - make sure to select units in 'Radians'.

  8. Calculate TFI using Grid Calculator or Raster Calculator: 

    ln ( Catchment_Area / cot (Slope))
%% Or
ln ( Catchment_Area / (1/tan(Slope)))