General Review of Calibration Process of Nonlinear Muskingum Model and Its Optimization by Up-to-Date Methods

Introduction

Flood routing techniques are user-friendly tools in estimation of downstream hydrograph by given upstream hydrograph and practically utilized in engineering issues such as designing flood control facilities and used for warning the people living in the flood regions in order to prevent them from loss of life and property as well. They are separated into two categories as hydraulic and hydrological models. Hydraulic models are built upon Saint Venant equations in which principle of mass and momentum conservation are taken into consideration. The use of momentum conservation principle introduces the flood routing processes into tedious struggle. Moreover, hydraulic models require thorough data measurement of multiple variables in the related river reach (Papaioannou et al., 2017). In view of these conditions, the hydrological methods such as Muskingum model are sufficient such that linear reservoir concept based on only principle of mass conservation is taken into consideration (Barati, 2011).

Floods are natural hazards which come to existence frequently around the world such that they have disastrous effects on human life, animals, agricultural fields, etc. Hence, it is crucial to implement planning studies about flood risk managements and vulnerability. The studies about flood risk managements deal with flood hazard prediction, its effects on human society and how to minimize flood risk (Schanze, 2006; Nikoo et al., 2016). In this respect, the methods such as flood routing specifies characteristics of a river channel by modeling the temporally or spatially varying flood wave. The flow rate is measured at a cross-section of the channel and it is predicted at an outlet point. Thus, this method enables decision makers to take measure right after a storm which may give rise to flood events. In the literature, Muskingum model is one of the well-known flood routing methods frequently used in the literature.

The linear Muskingum model in which only streamflow measurement data are utilized is the most frequently used method in natural channels and rivers among all hydrolgical models with regard to its ease of use. The model is presumed to capture the river characteristics in the routing process by means of its inherent parameters. A linear storage-discharge relationship is set up in the linear Muskingum model, however, it is highly possible to experience the linear Muskingum model to be insufficient in many flood events. That is, the nonlinear structure of streamflow with respect to time gives rise to inadequacy in estimation of outflow by linear model. Hence, a nonlinear Muskingum model in which a nonlinear storage-discharge relationship is involved in the process is more appropriate to use at this stage. Following the this idea, a three-parameter model which is frequnetly utilized in the literature is derived. The parameters to be estimated are storage time constant, absolute channel storage and an exponential constant which captures the nonlinearity in the model.

With the increase of parameter number and degrees of freedom, the calibration process of the model turns into more complex form when compared to the linear model. In this respect, it is considered that parameter estimation of the nonlinear model becomes more striving while the precision of downstream hydrograph estimations increases. Hence, it is required to use an efficient optimization procedure to estimate model parameters.