Modified method of characteristics for the shallow water equations

Flow in open channels is frequently modelled using the shallow water equations (SWEs) with an up-winded scheme often used for the nonlinear terms in the numerical scheme (Delis et al., 2000; Erduran et al., 2002). This paper presents a mathematical model based on the SWEs to compute one dimensional (1-D) open channel flow. Two techniques have been used for the simulation of the flood wave along streams which are initially dry. The first one uses up-winding applied to the convective acceleration term in the SWEs to overcome the problem of numerical instabilities. This is applied to the integration of the shallow water equations within the domain, so the scheme does not require any special treatment, such as artificial viscosity or front tracking technique, to capture steep gradients in the solution. As in all initial value problems, the main difficulty is the boundaries, the conventional method of characteristics (MOC) can be applied in a straight forward way for a lot of cases, but when dealing with a very shallow initial depths followed by a flood wave, it is not possible to overcome the problem of reflections. So a modified method of characteristics (MMOC) is the second technique that has been developed by the authors to obtain a fully transparent downstream boundary and is the main subject of this paper. The mathematical model which integrates the SWEs using a staggered finite difference scheme within the domain and the MMOC near the boundary has been tested not only by comparing its results with some analytical solutions for both steady and unsteady flow but also by comparing the results obtained with the results of other models such as Abiola et al. (1988)

Mitigation of flash floods in arid regions using adjoint sensitivity analysis

This paper presents an analysis of the sensitivities of flood wave propagation to variations in certain control variables and boundary conditions by means of the adjoint method. This uses a variational technique to find the relationships between changes in predicted flood water levels and changes in control variables such as the inflow hydrograph, bed roughness, and bed elevation. The sensitivities can be used for optimal control of hydraulic structures, for data assimilation, for decision makers' procedures, for the analysis of the effects of uncertainties in control variables on the predictions of floods water levels, and for investigating both the sensitivities of model flood forecasts to model parameters, boundary and initial conditions. Example of the last application of the sensitivity analysis is presented and discussed These methods are developed and implemented through a numerical hydraulic model of channel flow based on the Shallow Water Equations (SWEs) and the corresponding adjoint model. The equations are integrated using finite difference methods and a new modified method of characteristics is used to define the open boundaries. Results of validation tests on both the forward hydraulic model and on the adjoint model are presented

Modelling uncertainty for flash floods in coastal plains using adjoint methods

This paper shows the application of adjoint sensitivity analysis to flash flood wave propagation in a river channel. The adjoint sensitivity analysis is used to assess flood hazard in a coastal area caused by river discharge. The numerical model determines the sensitivities of predicted water levels to uncertainties in key controls such as inflow hydrograph, channel topography, frictional resistance and infiltration rate. Sensitivities are calculated using the adjoint equations and are specified in terms of water levels being greater than certain safe threshold levels along the channel. The flood propagation model is based on the St. Venant equations while the propagation of sensitivity information is based on the corresponding adjoint equations. This analysis is achieved using a numerical model that integrates The St. Venant equations forward in time using a staggered finite difference scheme. An enhanced method of characteristics at the downstream boundary provides open boundary conditions and overcomes the problem of reflections from the boundaries. Then, the adjoint model is integrated backwards in time to trace the sensitivity information back through the model domain towards the inflow control boundary. The adjoint model has been verified by means of an identical twin experiment

Computer modelling of channel flow using an inverse method

We may not be able to command the water to stop but we can take steps to predict when and where it will invade and attack our lives, and provide solutions to deal with the problem. The research project reported in this paper is concerned with a study of unsteady free surface water flow, a hydrograph, resulting from a watershed just after the outlet station. The quality of flood predictions by numerical models depends on the accuracy of the inflow hydrograph, other control variables such as bed roughness, infiltration rate, and channel topography. However, none of these are well known, the values of each are uncertain. This research examines what effect these uncertainties have on the flood prediction. That is we find out how the uncertainties in control values propagate through the model. This is achieved by calculating the sensitivities of the flood predictions to changes (uncertainties) in control variables. The adjoint method is used to study the sensitivity of the flow to changes in the boundary and initial conditions. To achieve this aim we constructed a numerical hydraulic model to simulate the flow of water in the main stream based on the shallow water equation (SWE). The sensitivities are determined using the adjoint method which uses a variational technique to find the relationships between changes in channel flow conditions and changes in control variables such as the inflow hydrograph. This could be done at significant computational expense using multiple runs and ensemble techniques however the adjoint method presented here determines these sensitivities analytically in one run of the model

Flash floods simulation using Saint Venant equations

Flash floods prediction is considered one of the important environmental issues worldwide. In order to predict when and where the flood wave will invade and attack our lives, and provide solutions to deal with this problem it is essential to develop a reliable model that simulates accurately this physical phenomena. The research project reported in this paper is concerned with a study of unsteady free surface water flow, a hydrograph, resulting from a watershed just after the outlet station. To achieve this aim a numerical hydraulic model has been constructed to simulate the flow of water in the main stream based on the Saint Venant equations (SVES) using a staggered finite difference scheme to evaluate the discharge, the water stage, and the cross section area within the domain. While the Method Of Characteristics (MOC) is applied to achieve open boundary downstream and overcome the problem of reflections there. The developed model had passed a series of tests which indicated that this model is capable of simulating different cases of water flow that contain both steady and unsteady flow. Once the flood had been predicted it could be used as a stepping stone for different purposes including parameter identification (Ding et al. 2004), evaluating the sensitivity of the flood to some control variables (Copeland and Elhanafy 2006), Flood risk assessment (Elhanafy and Copeland 2007) ,uncertainty in the predicted flood (Elhanafy and Copeland 2007) and (Elhanafy et al. 2007)

The effect of water stage on the infiltration rate for initially dry channels

Several hydrological models that are used for simulating the water flow in rivers and channels are based on the shallow water equations as in Copeland and El-Hanafy, (2006) or Saint Venant equations (El-Hanafy and Copeland, 2007a). Both the shallow water equations and the Saint Venant equations form a system of partial differential equations which presents mass and momentum conservation along the channel and include source terms for the bed slope and bed friction. This paper presents a staggered finite difference scheme for the channel routing based upon Saint Venant equations and the well know method of characteristics after modifying it to suit the case of a shallow water depth initially followed by a flood event (El-Hanafy and Copeland, 2007b). The modified method of characteristics is implemented to achieve a transparent down stream boundary. The relation between the water depth and the infiltration rate have been derived for Saint Venant equations and it is concluded that the effect of water stage have a positive effect on the infiltration rate as it was expected

Neonatal adrenal hemorrhage presenting as acute scrotum

Neonatal adrenal hemorrhage may rarely present as acute scrotum,  mimicking the conditions that require an immediate operative intervention. The authors report one such case and discuss the importance of clinical examination and ultrasonography to avoid an unnecessary surgical  exploration.Keywords: neonatal acute scrotum, neonatal adrenal hemorrhage, scrotal  hematoma, testicular torsio