Water Balance Simulations
This schematic view of the basin shows the underlying maze-like structure. The basin is built by constructing spanning tree across a rectangular grid. The resulting tree can then be solved by recursively solving the maze with a “rat”. As the “rat” solves the maze it determines all of the basin’s geometric and topographic characteristics. From these data, the elevation and drainage characteristics of the basin can similarly be simulated. Generation and solution of these trees is extremely fast - much less than a second even for much larger mazes than the one shown.
The image below is a three-dimensional view of the simulated basin rendered in OpenGL. The elevations for the basin were determined from the simulated stream channel geometry, which were in turn determined from the basin geometry using common geomorphologic principles. The hues and values of the rendering were controlled by the elevation and aspect of each slope element.
The hydrographs below were generated by running a 365 day water balance on the basin shown above. The basin is 64x64 elements or 65536 basin elements. Precipitation and temperature were simulated for each grid element for each day and a water balance derived for each element using standard hydrologic models, with storage for surface (green), vadose (yellow), and phreatic zones (red) as well a snow pack (cyan). By routing these storages within each element the water balance for each element was generated. Then, based on the channel geometry, the surplus (channel storage) for each element was routed down through the whole basin using the spanning tree’s geometry. All of the estimates were made using 4th order Runge-Kutta approximations.
The lower graph shows the precipitation inputs to each basin element and the outflow at the basin outlet. Flow rates at any point in the basin can be easily obtained as well
The water balance model is remarkably fast. The annual balance shown below is 365 days run across 65536 elements with two iterations per time step (day). It takes approximately 20 seconds to run and display on a 333 MHz PII.