Muthiah Perumal

Hydrodynamic derivation of a variable parameter Muskingum method: 1. Theory and solution procedure

Abstract An approach is presented for directly deriving a variable parameter Muskingum method from the St. Venant equations for routing floods in channels having any shape of prismatic cross-section and flow following either Mannings or Chezys friction law. The approach also allows the simultaneous computation of the stage hydrograph corresponding to a given inflow or the routed hydrograph. This first paper also describes the solution procedure for routing the discharge hydrograph. A second paper (Perumal, 1994b) presents a verification of the methodology.

Multilinear discrete cascade model for channel routing

Abstract A method for flood routing in rigid bed channels using multilinear modelling based on a time distribution scheme is presented. The discrete cascade model with its parameters related to channel and flow characteristics through a moment-matching technique is used as the linear submodel. The particular advantage of using this two-parameter submodel is that it simulates the outflow hydrograph in a realistic way unlike the Muskingum model which produces a ‘dip’ or ‘reduced outflow’ at the beginning of routing. The suitability of this method for routing floods in uniform rectangular channels is studied by routing a mathematically defined inflow hydrograph. The solutions obtained using this model are compared with the corresponding solutions of the St. Venant equations. The study reveals that the proposed multilinear model reproduces the St. Venant solutions closely when the rating curve corresponding to the inflow hydrograph is characterized by a narrow loop.

Multilinear muskingum flood routing method

Abstract In a study of multilinear modelling of flood wave propagation based on a time distribution scheme, an attempt is made to overcome certain limitations of the currently available multilinear models. The physically based Muskingum method is used as the linear sub-model. Unlike the currently available multilinear models, wherein the parameters are held constant for routing prescribed flow zones of the inflow hydrograph, in the proposed method they vary at each routing time step. This allows better modelling of the non-linear behaviour of the flood wave movement and eliminates the subjectivity of deciding on the number of flow zones to be used for routing the given inflow hydrograph. The suitability of this method for routing floods in wide uniform rectangular channels without lateral flow is studied using hypothetical data. The study reveals that the proposed method is capable of describing flood wave movement in open channels, as a result of a flood hydrograph characterized by narrow loop rating curve.

Hydrodynamic derivation of a variable parameter Muskingum method: 2. Verification

Abstract The hydrodynamic derivation of a variable parameter Muskingum method and its solution procedure for estimating a routed hydrograph were presented in Part I of this series (Perumal, 1994a). In this paper, the limitations of the method, the criterion for its applicability and its accuracy are discussed based on the assumptions used. The method is verified by routing a given hypothetical inflow hydrograph through uniform rectangular cross-section channels and comparing the results with the corresponding numerical solutions of the St. Venant equations. The stage hydrographs as computed by the method are also compared with the corresponding St. Venant solutions. It is demonstrated that the method closely reproduces the St. Venant solutions for the discharge and stage hydrographs subject to the compliance of the assumptions of the method by the routing process.

The cause of negative initial outflow with the Muskingum method

The cause of negative or reduced outflow formation at the beginning of a Muskingum solution is examined in two steps. The first step involves a physical interpretation of the Muskingum weighted discharge and the storage equation, using theory based on an extension of the Kalinin-Milyukov method. The second step involves the derivation of an analytical solution for the weighted discharge based on linear systems analysis theory, and then subsequently the Muskingum solution from that analytical solution using the assumption of linear variation of discharge within the reach. It is proved that this assumption causes the formation of negative or reduced outflow at the beginning of a Muskingum solution.

Multilinear Muskingum Method for Stage-Hydrograph Routing in Compound Channels

A multilinear stage-hydrograph routing method based on time distribution scheme is analyzed. The framework of the multilinear method is based on the Muskingum-type routing method, which is used as the linear submodel. The proposed method can implicitly model the nonlinear dynamics of the flood wave propagation by varying the model parameters at each routing time step. The suitability of this flood routing method is verified using a set of laboratory experimental data and the field data of the Tiber River in central Italy.

Genetic Algorithms and Their Applications to Water Resources Systems

Real-life water resource problems such as optimal allocation of scare water, watershed management, conjunctive use of surface and groundwater, reservoir operation, water distribution systems, and management of water quality have many complex features. The variables involved may be discrete, discontinuous, or both; frequently the variables are stochastic and highly nonlinear. These typical problems limit the use of traditional nonlinear algorithms, such as the gradient-based algorithms, since the solution may converge to local optima and the computational requirements may be very high. Evolutionary algorithms, such as genetic algorithms (GAs), do not rely on any mathematical properties of the functions employed in the model. This feature makes them robust and more generally applicable than the other directed search methods. GAs are a particular class of evolutionary algorithm based on mechanics of natural selection and natural genetics, and they use techniques inspired by evolutionary biology such as inheritance, mutation, selection, crossover, and survival of the fittest. Since GAs are heuristic search techniques, the global optimum solution is not guaranteed. Nevertheless, GAs give alternative solutions that are close to the optimum after a reasonable number of evolutions, which is acceptable for most real-life problems. This chapter introduces the art and applications of GAs to water resource optimization problems. An illustrative example of reservoir operation optimization has been included to clarify the concepts.

Rating Curve Development at Ungauged River Sites using Variable Parameter Muskingum Discharge Routing Method

A physically based simplified discharge routing method, namely, the variable parameter Muskingum discharge-hydrograph (VPMD) routing method, having the capability of estimating the stage hydrographs simultaneously in channels with floodplains is presented herein. The upstream discharge hydrograph is routed using this VPMD method in different two-stage symmetrical trapezoidal compound cross section channel reaches. The performance of the VPMD method is evaluated by numerical experiments using the benchmark MIKE11 hydrodynamic model and the field data of the Tiber River in central Italy. The proposed method is capable of accurately routing the discharge hydrographs, corresponding stage hydrographs and synthesizing the normal rating curves at any downstream ungauged river site which is not affected by any downstream effects. This study can be helpful for various planning and management of river water resources in both the diagnostic and prognostic modes.

Appraisal of overland flow modeling using HEC-HMS and a variable parameter Muskingum method

The present study was undertaken with the objective of evaluating the simulation capabilities of the variable parameter Muskingum discharge (VPMD) routing methods, proposed) for channel routing and that of the kinematic wave based method adopted in the US Army Corps of Engineers HEC-HMS model for simulating overland flow over unit width plane strips. The solutions obtained from the above two methods were also compared with the corresponding benchmark solutions obtained by solving the full Saint-Venant equations. A total of 60 simulations were made by each of these three methods for evaluating their performances. Accordingly, a total of 60 unit width overland flow strips with the length of 100 m each were considered for study. Each of these strips were characterized by a set of uniform Manning’s roughness coefficient and uniform slope with the former selected from six values varying from 0.02 to 0.4 and the latter selected from ten overland flow plane slopes varying from 0.0005 to 0.005. The comparison of the VPMD and HEC-HMS based solutions with the corresponding benchmark solutions of the Saint-Venant equations reveal that the overland flow simulated using the VPMD method is more accurate and robust in comparison with the corresponding solutions based on the Kinematic Wave method of the HEC-HMS model in simulating the benchmark solutions for a wide range of flow conditions, except for the flow conditions characterized by the criterion , where k is the kinematic wave number and F is the Froude number. Further, the severe restriction on the temporal grid size as employed in the HEC-HMS model for obtaining stable solutions is not needed for obtaining solutions using the VPMD method.

Study of overland flow phenomenon using experimental and modelling approaches

Rainfall-runoff analysis of a watershed is needed for the purposes of water resources planning, design flood estimation, flood forecasting, study of movement of pollutants, and many other applications. For a mathematical simulation of this phenomenon, controlled rainfall-runoff experimental runs were conducted on the V-catchment system placed over the advanced hydrologic system to obtain runoff hydrograph data. The approximate convection–diffusion (ACD) equation–based overland flow model was used for simulation of these observed hydrographs. Considering various combinations of runoff simulation scenarios, a total of 111 laboratory experiments were conducted on two types of overland flow and channel flow roughness conditions generated (1) on a V-catchment model made up of acrylic sheet surface and (2) with artificial roughness surface generated with the help of sand paper pasted on the acrylic V-catchment model. These 111 experimental runs were made corresponding to six rainfall intensity inputs, that is, varying from 54 to 84 mm/hour, and for four overland plane slope conditions varying from 0.22% to 1.54%, for each of the three channel slopes used. Overall, it is demonstrated that the ACD equation–based overland flow model is able to reproduce the observed hydrographs closely, in many cases with Nash–Sutcliffe efficiency greater than 90%. But in all the experiments, the recession limb of the observed hydrographs could not be reproduced very closely because of prolonged flow of water. The reason behind this behaviour could be attributed to the retention of runoff of the recession limb because of surface water tension prevailing over the overland flow bed, channel bed and even over the weir model used for flow measurement. Except for this problem, the experimental set-up established in the laboratory reasonably generates overland flow hydrographs which could be reproduced by the overland flow model developed based on the ACD equation, including those cases of diffusion behaviour of the V-catchment experimental hydrographs.