A. M. Wasantha Lal

Numerical errors in groundwater and overland flow models

Numerical error estimates are useful to evaluate the applicability of overland and groundwater flow models and verify the validity of their results. In this paper, methods of estimating numerical errors are developed and then applied to evaluate the numerical accuracy of the South Florida Water Management Model. Analytical expressions for errors generated during the propagation of disturbances due to well pumping, boundary water level changes, and rainfall are obtained for steady and transient conditions using Fourier analysis of the linearized governing equations. Different situations under which truncation errors are introduced into models and their variation with the spatial and temporal discretization are discussed. Numerical experiments are carried out with the three-dimensional groundwater flow model MODFLOW and a number of implicit and explicit models to verify the results. Dimensionless parameters are used in the expressions so that the results can be used to determine discretization errors in any existing or new finite difference model of regional or local scale.

Implicit TVDLF Methods for Diffusion and Kinematic Flows

AbstractDiffusion-wave and kinematic-wave approximations of the St. Venant equations are commonly used in physically based, regional hydrologic models because they have high computational efficiency and use fewer equations. Increasingly, models based on these equations are being applied to cover larger areas of land with different surface and groundwater regimes and complicated topography. Existing numerical methods are not well suited for multiyear simulation of detailed flow behavior unless they can be run efficiently with large time steps and control numerical error. A numerical method also should be able to solve both diffusive and kinematic wave models. A total variation diminishing Lax-Friedrichs type method (TVDLF) that is stable and accurate with both diffusive- and kinematic-wave models and large time steps is presented as a means to address this problem. It uses a linearized conservative implicit formulation that makes it possible to avoid nonlinear iterations. The numerical method was tested su...

ERROR ANALYSIS OF THE FINITE VOLUME BASED REGIONAL SIMULATION MODEL, RSM

A fully integrated regional simulation model (RSM) has been developed to simulate the complex hydrologic system of South Florida. The South Florida system consists of a large integrated overland flow system, a groundwater flow system and a canal flow system. Implicit solution methods, efficient sparse solvers, and object oriented methods have made it possible to solve large complex systems simultaneously with practically any time step and cell size, even when the numerical errors can be extremely large. The current study is aimed at understanding the numerical error due to a boundary disturbance under a variety of spatial and temporal discretizations and solution characteristics. The errors are compared with the analytical estimates obtained by Lal (2000) for finite difference problems. Results of the study are useful in determining optimal spatial and temporal discretizations for model applications.

Mapping Vegetation-Resistance Parameters in Wetlands Using Generated Waves

AbstractConstructed wetlands, referred to as stormwater treatment areas (STAs), are important components of the water management infrastructure in south Florida. These systems have complex internal...

Calibration of Bulk Aquifer Parameters of Regional Models Using Hydraulic Disturbances

Calibration of integrated hydrologic models of managed systems just using historical data is a difficult task because these systems have a large number of structures and pumps operated by multiple government agencies, utilities and the public based on a variety of rules and guidelines that change over time. The operations of the facilities are too complex and unrecorded at times. Water level and discharge data collected for such managed systems with mixed urban-agricultural-natural land use types often contain unrecorded local effects that are considered as errors if the model is not intended to simulate it. Data collected for such systems have a high level of noise that cannot be easily traced to the source. A method is proposed in the paper to solve the problem of the calibration of such systems by using the existing pumps and structures to generate specific identifiable hydraulic signatures in the system that also have analytical solutions. If data related to causal stress and the resulting hydraulic signal are collected free of noise, they can be used to calculate parameters directly using analytical methods or optimization methods. The paper describes such a test carried out in South Florida, and the use of an analytical method to obtain the parameters. INTRODUCTION Accurate estimation of aquifer parameters is important for calculating groundwater flow and canal seepage. Seepage computed using computer models is inaccurate if the aquifer parameters are inaccurate, regardless of the accuracy of the algorithms. In South Florida, calibration of regional parameters is not a simple process considering that the physical system itself is complex, and the state variables of the system depend heavily on complicated operational rules. A typical water level or discharge time series record in South Florida shows primarily the effects of rainfall and evapotranspiration (ET) on the surface and sub-surface system, and superimposed over it, the effects of local and regional stresses due to structure and pump operations by utilities and agricultural users, among others. Under these complex conditions, calibrations based on optimization or manual methods may be difficult at times. A key reason for the difficulty is the lack of understanding of the cause and effect relationships between

Simulation of Canal Network Flow in the South Florida Regional Simulation Model

ABSTRACT The weighted implicit finite volume approach for 2-D flow is extended to model canal flow in the South Florida Regional Simulation Model (SFRSM). St Venant equations with the diffusion approximation are used as governing equations. The water body and water mover base classes are used to represent canal segments and junctions in the 1-D model in an object oriented framework. Ground water and surface water flow is integrated with canal flow through flow functions attached to segment walls. The model uses an external sparse solver to solve overland, ground and canal flows simultaneously. The method is stable because of the implicit formulation. This paper describes the theory and provides a sample application.