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Surface area processing in GIS
Surface Area from SHR (surface to horizontal area ratio)
Extending the areal parameter, SHR (Surface to Horizontal area Ratio) was conceived, which has a potential to accurately approximate surface area. The algorithm developed was a 3 by 3 roving window operator that triangulates the pixels in the window into eight triangles and then extracting the elevation values from the nine pixels calculates the surface area for each of the 8 triangular faces (Fig. 2).  Figure 2: Pixel base (left) & Surface (right) in a DEM The equivalent horizontal area was then calculated for the equivalent region within the window (i.e. 4 times the pixel area) and then its ratio to the former (i.e. the SHR value) was stored in the central pixel.  Figure 3: The 3 by 3 roving window for SHR calculation  Figure 4: The DEM and the watershed basin This operator was programmed in JDK1.3 and was run on the available DEM of the region. The program operates on a 3 by 3 window basis and calculates the surface area of the window by the triangulation (Fig. 3). The ratio (SHR) actually is stored as a percentage so as to minimise errors in float to integer conversions. SHR = {(SA)/(HA)}× 100 Where SA is summation of surface area for each 8 triangles (Fig. 2) & HA is 4 times the pixel resolution area The surface area (SAP) for each pixel was calculated from the SHR by the equation below SAP = {SHR × Res}/100 Where Res is the area of each pixel for the Raster The value of SHR can never be less than one since the surface area is greater than or equal to the horizontal area. Moreover the upper limit of this value though theoretically is infinity but practically it is finite since a slope value of 90 0 is not practically derivable from a DEM. SHR, being the focal function equivalent of the areal parameter (which is a global function), is suitable for further overlaying operations (local, focal, zonal or global). This was essence of its conception in this research. Test Case The algorithms discussed above were applied on a given zone in the study region and a statistical-based comparative study was undertaken to determine their performance and suitability. Surface area as calculated for a delineated watershed basin for the area (Fig. 4) using the aforesaid discussed algorithms were used for pixel based comparative study. The test area (for which a DEM was readily available) was chosen for its rough topography depicted by a greater range for slope (0 0 -79 0 ). |