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The ability to better quantify resistance to water flow exerted by vegetation is receiving increased attention due to ongoing worldwide efforts to restore natural vegetation communities in the wetlands and use of vegetation for environmental benefits in streams and wetlands. In south Florida, vegetation resistance affects discharge through shallow wetlands of the Everglades and projects under way in the system to restore remaining natural systems. A more detailed knowledge of the flow dynamics in these wetlands is required to improve modeling of these systems that supports restoration and management efforts. The goal of this investigation is to understand the flow dynamics and the vegetation resistance within a 3 km by 7 km area in the Everglades referred to as STA-3/4 Cell 3A. Methods are developed to demonstrate the use of analytical solutions of partial differential equations (PDEs) and inverse methods to obtain bulk and spatially varying resistance parameters. To achieve this goal, a field test was conducted using sinusoidal discharge disturbances capable of creating water waves in the storm water treatment area (STAs). The discharges, wave speeds, and the wave attenuation rates from the test are used to develop graphical and empirical functions expressing discharge in terms of water depth and energy slope. The empirical functions developed are power law type, and different functions are developed for different depths. The results show that the Manning's equation is not applicable for wetlands with thick emergent vegetation, as well as the difficulty of applying a single power law-type expression for vegetation resistance over a wide range of depths and energy slopes without errors. This is partly due to the existence of multiple flow regimes and different power exponents over depth and energy slopes in these regimes. Results show that the flow regime at low depths is similar to porous media flow, and the flow regime at higher depths is more turbulent.

Diffusion-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...

Summary A primary advantage in using the finite volume method for simulating groundwater flow and overland flow is the conservation property or the ability to conserve mass. However, when implicit finite volume methods are used with large time steps, small cell areas, or parameters with extreme value ranges, the conservation of mass equation becomes slightly unbalanced with a residual. Problems with large mass residuals can be predicted using the condition number of the solution matrix, and the convergence criterion used in the sparse matrix solver. The amount of practical guidance available on how to manage the magnitude of the mass residual or the matrix condition number is limited. To address this need, the current paper shows the usefulness of the mesh ratio. The mesh ratio is a dimensionless number that is a function of the mesh resolution and the temporal resolution. It is directly related to the condition number of the matrix, which in turn affects the mass residual and the model run time. During the current study, several numerical experiments are carried out to determine how the mesh ratio and the water level are related to the condition number, how the critical mesh ratio is related to the number of cells, how the run time is related to the mesh ratio, and how the mass residual is related to the mesh ratio. The results are useful in creating guidelines for mesh design during large-scale model applications. These guidelines can be applied to reducing the mass residual and the run time. The usefulness of the mesh ratio is illustrated using a Regional Simulation Model (RSM) (Lal, A.M.W., Van Zee, Randy, Belnap, Mark, 2005. Case study: model to simulate regional flow in South Florida. Journal of Hydraulic Engineering 131 (4), 247–258) application in south Florida.

South Florida has a complex regional hydrologic system that consists of thousands of miles of networked canals, sloughs, highly pervious aquifers, open areas subjected to overland flow and sheet flow, agricultural areas and rapidly growing urban areas. This region faces equally complex problems related to water supply, flood control, and water quality management. Advanced computational methods and super fast computers alone have limited success in solving modern day problems such as these because the challenge is to model the complexity of the hydrologic system, while maintaining computational efficiency and acceptable levels of numerical errors. A new, physically based hydrologic model for South Florida called the regional simulation model ~RSM! is presented here. The RSM is based on object oriented design methods, advanced computational techniques, extensible markup language, and geographic information system. The RSM uses a finite volume method to simulate two-dimensional~2D! surface and groundwater flow. It is capable of working with unstructured triangular and rectangular mesh discretizations. The discretized control volumes for 2D flow, canal flow and lake flow are treated as abstract "water bodies" that are connected by abstract "water movers." The numerical procedure is designed to work with these and many other abstractions. An object oriented code design is used to provide robust and highly extensible software architecture. A weighted implicit numerical method is used to keep the model fully integrated and stable. A limited error analysis was carried out and the results were compared with analytical error estimates. The paper describes an application of the model to the L-8 basin in South Florida and the strength of this approach in developing models over complex areas.

Traditional delivery of water to farmers in the Maduru Oya river basin in Sri Lanka is based on seasonal reservoir releases into diversion canals and distribution canals that gravity-feed the farms. Usually water delivery schedules for the main canal are decided by the Mahaweli Authority. These schedules do not give incentives for the farmers to save water, or make improvements to delivery system efficiency. This paper describes a computer based water-quota system that relies on SMS (text) messages sent by the farmers requesting water, and a computer based water delivery system that calculates hydraulic structure gate openings for the water managers. As the first step, an unsteady flow model is developed based on the solution of the St Venants equations to analyze the hydraulics in the canal. Hydraulic transients due to inflow and outflow gate operations are investigated using this model. The results are used to develop a simple operational model for the canal system that can calculate the gate openings necessary for quota based water deliveries. The project makes use of recent advances in information technology (IT) and cheapening of computational capabilities to assist water management and farm water delivery.

Unsteady canal flow in an integrated canal-flow-groundwater-flow system is analyzed by solving the coupled equations governing canal flow, groundwater flow and the seepage between them. Analytical solu- tions are obtained for the coupled system for small water-level disturbances using Fourier analysis methods and complex variables. Dimensionless parameter groups characterizing the aquifer, the canal, and the sediment layer are identified using the governing equations and the solution. The influence in the aquifer and the semipermeable bottom sediment layer due to disturbances in canal flow is studied. The analytical solutions are compared to numerical solutions obtained using the MODFLOW model and the Hydrologic Simulation Engine of the South Florida Regional Simulation Model. Results of the analysis are useful in determining the range of aquifer, sediment, and canal characteristics for which stream-aquifer interaction is important. The results can be used to determine the conditions for which the canal is hydraulically disconnected from the aquifer because of the sediment layer. The analytical solution is useful to understand the propagation characteristics of small-amplitude water-level disturbances in the canal and the aquifer. The characteristics studied include the amplitude decay constant and the speed. The solution can be used to design benchmark problems that can be used to evaluate integrated canal-flow-groundwater-flow models. The results of the study can be used to estimate the space and time steps needed in the canal and the aquifer when simulating stream-aquifer interaction. As part of the overall effort to restore the Everglades eco- system in South Florida, and to meet its regional water man- agement responsibilities, the South Florida Water Management District (SFWMD) (SFWMD 1999) and other organizations have developed a number of mathematical models to simulate the water management system. One important requirement of these models is the capability to simulate stream-aquifer in- teraction or stream-wetland interaction. A significant part of the South Florida landscape is covered with a network of ca- nals that extends for thousands of miles through wetlands, ag- ricultural areas, and urban areas. The behavior of water levels in the canals, when areas adjacent to canals are subjected to water-level changes, is not completely understood. The influ- ences of the highly conductive surface aquifer and the less conductive bottom sediment layer of the canal on the overall hydrology are also not completely known. These behaviors influence a significant part of South Florida hydrology. The current study provides a method to understand the basic pa- rameters that govern the problem and to obtain an analytical solution. Stream-aquifer and stream-wetland interactions have previ- ously been studied by a number of researchers. The study by Pinder and Sauer (1971) was conducted by using a coupled numerical model for canal flow and 2D groundwater flow. The objective was to study the influence of bank storage on the modification of flood waves. The example used by Pinder and Sauer (1971) served as a benchmark test for integrated mod- els such as MODBRANCH (Swain and Wexler 1996) and MODNET (Walton et al. 1999). These models consist of a MODFLOW model (McDonald and Harbaugh 1988) coupled with either the BRANCH model (Schaffranek 1987) or the UNET model (HEC 1996). The comparison between the so- lution obtained by Pinder and Sauer (1971) and the solutions obtained using MODBRANCH or MODNET was not perfect 1

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.

A weighted implicit finite-volume model is developed to simulate two-dimensional diffusion flow in arbitrarily shaped areas. The model uses a mixture of unstructured triangles and quadrilaterals to discretize the domain, and a mixture of cell wall types to describe structures, levees, and flow functions that characterize two-dimensional flow. The implicit formulation makes the model stable and run faster with very large time steps. The sparse system of linear equations that results from the implicit formulation is solved by using iterative solvers based on various preconditioned conjugate gradient methods. The model was tested under a variety of conditions. The results were compared with results from known models applied to axisymmetric and other test problems that had known solutions. The model was applied successfully to the Oxbow section of the Kissimmee River in Florida, and the results were compared with results from physical and numerical modeling studies. This analysis indicated that the circumcenter-based flow function for walls that is used in the model gives overall superior results in all the cases considered. Results of the numerical experiments showed that the use of weighted implicit methods and iterative solvers provide modelers with improved flexibility and control of the overall accuracy and the run time. The method is to be used as an efficient solution method for local and regional modeling problems in south Florida.

Two regional models, the South Florida Water Management Model (SFWMM) and the Natural System Model (NSM), are applied to analyze and predict water conditions in the Everglades and South Florida. Both of these models use an alternating direction explicit (ADE) type method to solve diffusion flow. In this paper, three finite-difference algorithms based on explicit, alternating direction implicit (ADI) and successive over relaxation (SOR) methods are examined as possible replacements for the ADE method. Various model solutions are verified using an axisymmetric test problem that is solved using an axisymmetric test model. A comparison of run time versus error plots proved that the ADI method has the best overall performance. The study includes a description of the relationship between the accuracies and run times of different algorithms and their spatial and temporal discretizations in dimensionless form. Linear and spectral analyses are used to derive theoretical expressions for numerical error, run time, and stability. Comparisons indicate that theoretical estimates of numerical error and run times closely approximate the experimental values. Results of this study are valuable as methods to determine optimum space and time discretizations of future modeling applications when the maximum allowable numerical error and the dimensions of the flow features to be simulated are known. Results can also be used to understand the magnitudes of numerical errors in existing modeling applications.

This paper presents the formulation of a one-dimensional river-ice simulation model RICEN. The model consists of two major parts: (1) An unsteady flow model for a channel network with ice; and (2) ...

Singular value decomposition is used to calibrate the Manning's roughness coefficients in a one-dimensional unsteady flow model of the Upper Niagara River. The method is used to solve for the parameters after formulating the calibration problem as a generalized linear inverse problem. Singular value decomposition is useful in solving underdetermined, overdetermined or even-determined problems, and can provide information to compute matrices describing parameter resolution, covariance, and correlation. This information is useful in identifying the important parameter groups in the model. Calibration is repeated with different numbers of parameter groups to determine the variation of the output error and uncertainty of the parameters with the parameter dimension. For purposes of comparison, the model with a selected group of parameters is calibrated using the Gauss-Newton method and minimax methods. The study shows the relationship of the parameters to the geometric layout of the river and the gauging stations.

A computer model RICE is developed for simulating ice processes in rivers. In the riverhydraulics component, the flow condition is determined from onedimensional unsteady flow equations. In the the...

Determining the spatial and temporal discretization is an important part of setting up a model. As a general rule for numerical models, the discretization has to be fine enough to show most of the details of the solution, but at the same time, it cannot be too fine to prevent excessive demand for run time and computer resources. In this paper, analytical expressions are obtained for optimal mesh size using the physical parameters of the governing ipartial differential equation (PDE), space and time scales under investigation, and run time constraints. The paper describes how sensitive the discretization is to each of the attributes around the optimum.

[1] A method was developed to determine bulk values of aquifer and sediment resistance parameters in a coupled canal-aquifer system using generated sinusoidal hydraulic disturbances. The method is based on analytical solutions to the canal-aquifer interaction problem derived assuming small perturbations, linear analysis, and spectral methods. Results were obtained in terms of dimensionless parameters so that they can be applied to many practical problems. Numerical models were used to verify the solutions in selected test problems. The method was applied to determine physical parameters of the L-31W canal in Miami-Dade County, Florida, near the Everglades in both dimensionless and dimensional forms. The field experiment was carried out using operational control features of the south Florida conveyance system. Results of the analysis show that various dimensionless parameter groups determine various dynamic behaviors in both confined and unconfined aquifers. Which flow component dominates in the system depends on the range of a particular dimensionless parameter. The analytical solutions derived during the analysis are useful in calculating parameters in regional systems where the historical data are noisy or questionable. Calculation of parameters is accomplished by designing field experiments in which input and output signals of a particular frequency can be used with analytical equations to obtain parameters.

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

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.

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.