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Physically based hydrological modelling.

S.M. Seth
Director, National Institute of Hydrology
Roorkee-247667 (U.P.), INDIA
[email protected]

Hydrological modelling is a powerful technique in the planning and development of integrated approach for management of water resources.

The scope of hydrological applications has broadened dramatically over the past four decades. Although the problems of flood protection and water resourcesmanagement continue to be of importance and relevance for the security of communities and for human, social and economic development, many applied problems relating to the wider role of hydrology have come into focus.

Physically based distributed models of the hydrological cycle can in principle be applied to almost any kind of hydrological problem. These models are based on our understanding of the physics of the hydrological processes which conrol catchment response and use physically based equations to describe these processes. Some typical examples of field applications include study of effect of catchment changes, prediction of behaviour of ungauged catchment, of spatial variability in catchment inputs and outputs, movement of pollutants and sediment etc.

Hydrological modelling is a powerful technique of hydrologic system investigation for both the research hydrologists system investigation for both the research hydrologists and the practising water resources engineers involoved in the planning and developmetn of integrated approach for management of water resources.

The availability of remote sensing data and application of Geographical Information system provide very useful input data requirement for physically based hydrological models. The use of remote sensing and GIS facilitates hydrologists to deal with large scale, complex and spatially distributed hydrological processes.

Physically based Hydorlogical Models
The physically based models are based on our understanding of the physics of the hydrological processes which control the catchment response and use physically based equations to describe these processes. A discretization of spatial and temporal coordinates is made and the solution is obtainhydrological applications has broadened dramatically over the past four decades. Although the problems of flood protection and water resources management continue to be of importance and relevance for the security of communities and for human, social and economic development, many applied problems relating to the wider role of hydrology have come into focus.

Physically based distributed models of the hydrological cycle can in principle be applied to almost any kind of hydrological problem. These models are based on our understanding of the physics of the hydrological processes which control catchment response and use physically based equations to describe these processes. Some typical examples of field applications include study of effect of catchment changes, prediction of behaviour of ungauged catchment, of spatial variability in catchment inputs and outputs, movement of pollutants and sediment etc.

Hydrological modelling is a powerful technique of hydrologic system investigation for both the research hydrologists and the practising water resources engineers involved in the planning and development of integrated approach for management of water resources.
ed at the node points of this discretized representation. Physically based distributed models do not consider the transfer of water in a catchment to take place in a few defined storage as in case of lumped conceptual models. From their physical basis such models can simulate the complete runoff regime, providing multiple outputs (e.g. river discharge, phreatic surface level and evaporation loss) while black box models can offer only one output. In these models transfer of mass, momentum and energy are calculated directly from the governing partial differential equations which are solved using numerical methods, for example the St. Venant equations for surface flow, the Richards equation for unsaturated zone flow and the Boussinesq equation for ground water flow. As the input data and computational requirements are enormous, the use of these models for real-time forecasting has not reached the ‘production stage’ so far, particularly for data availability situations prevalent in developing countries like India.

Physically-based distributed models can in principle be applied to almost any kind of hydrological problem. Some examples of typical fields of application are:

  • Catchment changes
  • Ungauged Catchments
  • Spatial variability
  • Movement of Pollutants and Sediments

Topmodel and SHE Model
The TOPMODEL is a variable contributing area conceptual model in which the predominant factors determining the formation of runoff are represented by the topography of the basin and a negative exponential law linking the transmissivity of the soil with the vertical distance from the ground level. In this model the total flow is calculated as the sum of two terms: surface runoff and flow in the saturated zone. The TOPMODEL is frequently described as being ‘physically based’, in the sense that its parameters can be measured directly in situ. This definition is somewhat optimistic, in veiw of the doubts and uncertainties encountered even in defining the parameters of the ‘physically based models’, as already mentioned.

The Systeme Hydrologique Europeen (SHE), the Institute of Hydrology Distributed Model (IHDM), and the USDAARS small watershed model are the familiar models from this group. Because of their inherent structure these models also make very little use of contour, soil and vegetation maps, or of the increasing body of information in such areas as soil physics and plant physiology. Similarly, much historical information frequently consulted during project planning, for example crop yields over specific periods, survival patterns of particular types of vegetation and characteristics events occurring during floods and droughts, is not used directly. These observations do not imply any criticism of conventional rainfall-runoff models in relation to the more traditional applications in which they have clearly been successful, for example real-time flow forecasting and the extension of short stream flow records using longer rainfall records. However, they serve to underline some of the potential which a new approach in hydrological modelling might be able to fulfil. In particular physically-based, distributed models can in principle overcome many of the above deficiencies through their use of parameters which have a physical interpretation and through their representation of spatial variability in the parameter values. Role of Remotely Sensed Data
The land cover maps derived by remote sensing are the basis of hydrologic response units for modelling units. For an understanding of the hydrology of areas with little available data, a better insight into the distribution of the physical characteristics of the catchments is provided by image processing techniques. Some of the new measurement methods (photographic systems, active radar systems etc.) could yield assessment of areal distribution or atleast to some extent reliable areal totals or averages of hydrologic variable such as precipitation, evapotranspiration and soil moisture. Some of the main hydrological application field of remote sensing are:

  • Spatial rainfall patterns
  • Evaporation and soil moisture
  • Snow cover extent
  • Groundwater
  • Topography
  • Water Bodies
  • Vegetation

GIS Applications
Since, GIS does not directly land itself to time varying studies, its features are utilised in hydrological studies by coupling it with hydrological models. Two types of approaches are possible for this purpose. In the model driven approach, a model or set of models is defined and thus the required spatial (GIS) input for the preparation of the input data and output maps. The other approach is the data driven approach. It limits the input spatial data to parameters which can be obtained from generally available maps, such as topographic maps, soil maps etc. The possibility of rapidly combining data of different types in a GIS has led to significant increase in its use in hydrological applications. It also provides the opportunities to combine a data from different sources and different types. One of the typical applications is use of a digital terrain model (DTM) for extraction of hydrologic catchment properties such as elevation matrix, flow direction matrix, ranked elevation matrix, and flow accumulation matrix.

Application of TOPMODEL
Calibration and validation of the TOPMODEL was carried out on Hemavati catchment situated in Western Ghats. Raster DEM input for the model is generated through ILWIS after digitization contour map from Survey of India toposheets. In all 5 years of data was available for simulation study. Available data series was broken in two parts and first part i.e. June 1975-December 1977 was used for model parameter calibration and remaining data series i.e. January 1978 to December 1980 was used for model validation. Simulation results are encouraging. Model efficienty was more than 0.84 both for model calibration and validation on independent data series.

The TOPMODEL has been applied to Malaprabha catchment in Karnataka to simulate the daily flows at Khanapur. River Malaprabha is a tributary of river Krishna. The catchment area of Malaprabha upto discharge measuring site Khanapur is 520 Sq. Km. The model uses topographic index for the formation of runoff. The topographic index for Malaprabha catchment was derived by developing a Digital Elevation Model (DEM) by interpolating the contours in the basin at 300 m grid size.The results indicate that the model can be used to simulate the flows in the catchment quite accurately (the efficiency of the model is 0.89 and 0.79 respectively in calibration and validation run).

Application of SHE model for sub-basins of river Narmada
The distributed and physically based nature of the SHE requires that in each application study a vast amount of data and parameters describing the physical characteristics of the catchments are available. This includes data for catchment geometry, land use and soil parameters, surface flow characteristics and input data of rainfall, evapotranspiration, stream flow etc. The data handling package of the SHE Model has therefore been organised on the lines of a typical GIS format. A brief processor package produces maps of spatially distributed data and enables an automatic setup of input data for the SHE at a desired grid square scale. Digitised data such as contour lines from toposheets are transformed to average elevation values compatible with the chosen grid square size. Also soil land-use maps are digitised and codes attached to each type are allocated to each grid square. The SHE model was applied to six sub-basins of river Narmada namely – Kolar, Barna, Sher, Ganjal, Hiren and Narmada upto Manot. The SHE model has been found to be successful for modelling the rainfall, runoff process in these sub-basins within data availability constraint. These studies have also provided useful guidelines for carrying out systematic field investigations for determination of various parameters for application of a physically based modelling approach.

Typical studies were also carried out for Kolar basin to consider the effect of changes in soil depth, soil properties, vegetation, surface roughness characteristics etc. on water yield from the catchment. Some simple studies for hypothetical irrigation systems were carried out for Barna basin. These clearly demonstrated capabilities of physically based distributed models using spatial information in typical GIS type framework.

Discussion
Until very recently, GIS was a tool for managing and analysing spatial data and hydrologists were collecting their own data and sharing it in a format specific to the model they worked with. The integration of these two technologies began slowly as GIS was used to perform overlays of basin characteristics for further analysis by FORTRAN programme or a statistical package. However, now significant developments have already taken place for the integration of GIS and hydrological modelling. The basin characteristics for use in hydrological modelling is now being readily derived from digital elevation models. GIS is a valuable tool for use in parameterization for large scale physically based distributed models and significant developments in this area are taking place. These would result in corresponding increase in operational use of such models. There is however, need for considerable efforts to obtain representative hydrological data and information for use in such applications.