DP-2 : Rating curve analysis

Abstract

Many hydrologic analyses are made using discharge data of a river at a site. Often these discharge values are obtained from stage measurements. In order to compute the discharge from the stages a rating curve is used. A rating curve is a steady-state relation between the complex inter-relations of stages and discharges. When rating curves are available one can go in for interpolation methods. Some time physically sound rating curves may have to be established before computation of discharge is taken up. Two computer programmes for this purpose are given in this documentation.

In the case of use of available rating curves, a rating table is prepared. This table consists of stage and discharge values. After removal of data error in the table by finding first and second differences of the discharge values this table can be used as interpolating table. The Hermition method, which provides a smooth curve taking continuity of slope and curvature is used. A FORTRAN subroutine capable of interpolating discharge values for given stage values has been developed and documented.

For the establishment of rating curve from the measured discharge and the corresponding water level, after data processing, the available data is plotted on a simple graph and also on double logarithmic paper. This helps in grouping the data and to find its suitability for fitting simple curve. The grouped data is used to fit a relationship of the following form Q = a (S-e)b where, Q is the discharge, S is the stage and ‘a',’b’,’e’ are parameters defining the relation. The well known method fitting a curve is to minimise the sum of squares of differences between observed and computed Q using least squares criterion. Assuming a value of parameter ‘e’ and taking logarithms of Q and (S-e) the parameter ‘a’ and ‘b’ are found. For different values of ‘e’ the method is repeated and various sets of parameter ‘a’ and ‘b’ along with the sum of square of departures are found. The set having minimum of above departure can be taken to define the relation. But a physical interpretation of the results may suggest different set of parameters.

The stage and discharge data is given as input to the programme and it gives values of parameters ‘a’ and ‘b’ using least squares method. Necessary flow charts, input specifications and sample output are given in the documentation. Interpretation of the physical information regarding the cross section for arriving at appropriate values of parameters ‘a’ and ‘b’ of the rating curves are also provided.