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

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 research focuses directly on the use of topobathymetric models that include the bathymetry and topography of the surrounding area next to the water body. 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 with 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 cross comparison 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 Lagoon, Chihuahua, Mexico, the simulation took less than 17 seconds in at most 22 iterations.