Physically-based models

Physically-based models, knowing also as “distributed” or “deterministic” models, simulate the complex hydrological process in the catchment mathematically. These models consist of nonlinear partial differential equations which spatially represent the physical process of runoff generation in a catchment. They improve our understanding of hydrological system by representing interaction of the spatial- temporal variables. The drawback of deterministic models is that they are very costly and time consuming (Chau, et al., 2005). They require a large amount of data, such as catchment characteristics and meteorological parameters to represent sub-surface and surface runoff generation and routing. For solving of the complex equations of the hydrological process, numerical solutions like finite element, finite difference, boundary integral and integral finite difference must be implemented (Gosain, et al., 2009).

Several physically-based distributed models have been developed and applied in hydrological forecasting. One of the pioneering physically-based models is European Hydrological System - Système Hydrologique Européenne (SHE). SHE has been developed by three European institutions, namely SOGREAH (France), Danish hydraulic institute and UK institute of hydrology (Beven, et al., 1980). SHE is a distributed physically-based model which simulates water movement in the hydrological cycle by applying a grid-based finite difference method. Partial equations of mass, energy conservation or momentum are derived based on the

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spatially distributed data of catchment parameters, precipitations and catchment hydrological response in the orthogonal grid network (Abbott et al., 1986). Catchment parameters are assumed constant within each grid but could be different from other girds. Based on SHE model, an integrated hydrological modelling system of MIKE SHE has been further developed by DHI water and environment (Refsgaard and Storm, 1995). MIKE SHE represents hydrological process, including evapotranspiration, surface flow, unsaturated flow, sub surface, channel flow and their interactions (Butts et al., 2004). Figure 2.1 illustrates the schematic of MIKE SHE model and its numerical solutions for different hydrological process.

Another well known physically-based model is the Institute of Hydrology Distributed Model (IHDM) (Beven, 1985). This model uses two-dimensional finite element approach. Compared to SHE model, it needs less computational time and parameters as it does not forecast the hydrological response of every point in the catchment. Another example of such simplified model is the popular TOPMODEL (Beven and Kirkby, 1979). This model assumes that the hydraulic gradient of subsurface saturated zone is similar to the local surface slope. It also considers similar hydrological respond for the points with same topographic index and thereby eliminates the need for calculations in every point of the watershed. This model also minimizes the number of parameters by simplifying surface flow and unsaturated zone routing algorithms. O’Connor (2006) argues that these kinds of model are not truly physically-based model as they actually apply conceptual model to each grid of the watershed. Many other physically-based models have been developed and applied in various case studies. Some of the most widespread among all are as follows;

ECOMAG model is developed by Motovilov et al. (1999) and consists of hydrological, geochemical and biological process in daily time scale. HYDROTE distributed model is developed in 2001 (Fortin et al., 2001a, b). This model is GIS compatible and its hydrological unit is a small vertical homogenous unit. Downer and Ogden (2004) are developed fully distributed GSSHA model by improving the older two-dimensional model of CASC2D (Julien and Saghafian, 1991). The main improvement was in discharge prediction, when runoff is not produced by Hortonina process. In 2004, MODHMS model with the ability of three-dimensional subsurface

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modelling and two-dimensional surface modelling was developed (Panday and Huyakorn, 2004). This model is capable of simulating complex surface and groundwater interactions (Donn et al., 2012).

Figure 2. 1 Schematic of MIKE SHE distributed model structure (Graham and Butts, 2005).

Although physically-based models are more sophisticated than the other types of models, they are not applicable and accurate enough for flood forecasting due their complexity and extensive data demands. The main drawbacks of the physically- based models are as follows;

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- They are not the exact representation of the hydrological process as it is very difficult to measure and understand catchment parameters such as soil parameters and determine their variation over the time (Liu, et al., 2011).

- There are difficulties in solving catchment descriptive equations. Even applying various available numerical techniques may not lead to convergence of solutions due to complexity of nonlinear partial differential equations.

- They are not cost-effective. Considerable costs are involved in setting up these models including measuring an extensive set of parameters from the field, appropriate softwares and training time.

- They are not suitable for large catchments due to their high-resolution data requirement.

- The accuracy of the model depends on grid size. Most of hydrological data are measured in points and could be homogenous in small scale while grid scale often covers a much bigger area.

- Due to time-consuming nature of complex numerical simulations, physically- based models may not be suitable for real-time flood forecasting.

- Physically-based forecasts are subject to high level of uncertainty as there are many possible sources of error in calibrating the model (Huang and Liang, 2006).

In conclusion, physically-based models can be considered as a powerful tool for providing spatial information of the hydrological parameters within the catchment. Their outcomes would be beneficial for solving many water management problems such as assessing water storage within the catchment rather than river flow forecasting (O’Connor, 2006).