Analytical Methods and Field Applications to Test the TVDLF Method in Hillslopes and Wetlands

Abstract

With the increased emphasis on developing integrated models capable of simulating runoff through hydrologic systems that include hillslopes and wetlands, analytical solutions have become useful in analyzing and testing numerical models applied to both. An analytical solution in algebraic form is developed in this paper to describe a sinusoidal moisture profile migrating through a wetland or a hillslope, the magnitude of the peak runoff, and the phase lag. The solution is obtained for an instantaneous sinusoidal recharge signal, and results are expressed in terms of the basin geometry and flow resistance parameters. The analytical solution is used to verify the accuracy of a numerical model based on the implicit total variation diminishing Lax-Friedrichs (TVDLF) method. This method is used in the Regional Simulation Model (RSM) developed at the South Florida Water Management District (SFWMD) to simulate the complex hydrologic system of south Florida. The runoff peak, phase lag, propagation speed, and decay rate over a range of Péclet numbers are used in the comparison of analytical and numerical solutions. The numerical model using the TVDLF method is tested by applying to the Boggy Creek watershed in central Florida, and the wetland stormwater treatment area (STA)-3/4 in south Florida to simulate storm runoffs and water levels. Results show that the model using a general power-law equation to represent flow resistance, and a conceptual model consisting of a canallike drainage feature to represent rapid drainage can be used to simulate the hydrology in both the watershed and the wetland.