A STUDY OF MATHEMATICAL MODELS FOR DERIVING UNIT GRAPHS

Abstract

Considering linear input-output relation, where input is rainfall and output is runoff, the catchment or drainage basin as a system can be described by its response, or output, to an input of unit magnitude applied for an infinitesimally small duration of.time. This response to a unit input is thetinstantaneous unitgraph' of the catchment. If the unit input extends over a finite period of time 6 T, it produces the ' b t unit graph' . Once the unit graph of a catchment is known, it is possible to find the output or runoff for any given net rainfall. Many models have been developed to generate this unit graph. In this dissertation , the Ramganga drainage basin (catchment area 1210 sq. mile) and Brahman' drainage basin (catchment area 277.5 sq, min) are taken as a linear systems and three techniques of mathematical modelling known as conceptual model, polynomial method and Bieck box method have been applied to generate unit graphs for the system. Finding average unitgraph for the three storms of Ramganga basin and two storms of Brahmani basin, the flood hydrograph for each storm have been developed for the comparison of the methods. It is found that the polynomial method is better suited to the Ramganga basin and blackbox method to the Brahmani basin.