Single-input, multiple-output iterative algorithm for the volume, area, elevation, and shape calculation using 3D topobathymetric models

Abstract

Most methods for estimating the morphometric values of water bodies use equations derived from hypsographic curves or digital terrain models (DTMs) that relate depth, volume (V), and area (A), and that model the uncertainty inherent in the complex underwater morphology. This work tests the performance (precision and processing time) of an algorithm to calculate morphometric parameters of a lake that uses bathymetry and topography of the surrounding water body area. The projection of the water surface height (H) on each DTM pixel generates a water column with intrinsic attributes such as volume and area. The process is replicated among all cells and estimates the total area and volume of the water body. If the V or A is the input data, an algorithm that iterates height values is used to generate the new data, which is compared to the entered value that functions as a reference. If the difference between the reference value and the calculated value is less than an error threshold, the iteration stops, and the maximum and average depths are calculated. The raster and the shape that represent the body of water are created. The crosscomparison of H-V-A showed that there is an error between 0.0034% and 0.000039% when any of the parameters are used as input data. Performance tests determined that pixel dimensions are directly proportional to the processing time for each iteration. The results of the implementation of this algorithm were satisfactory since, for the DTM of Bustillos Lake, Chihuahua, Mexico, the simulation took less than 17 seconds in at most 22 iterations.