TR-15 : Mathematical modelling of moving storms

Abstract

The magnitude of peak flood and the shape of a flood hydrograph depend not only on the magnitude of total storm rainfall depths but also on its distribution in space and with time. Improvements of the accuracy and timeliness of hydrological forecasting would thus largely depend on the prediction of rainfall distribution in space and with time.

It is common knowledge that in India, tropical disturbances popularly known as storms and cyclones originate in the Bay of Bengal and Arabian Sea prior to, during and after the monsoon season, and move over the mainland of India. The direction of storm movement has the greatest effect on large elongated catchments like Narmada. During a given storm period for the same amount of total storm rainfall, the magnitude of the flood peak would be greater and the rising limb steeper if the storm moves down the valley.

Modelling of moving storms has been attempted by several authors using both dynamical and statistical approaches. Some of these methods are reviewed in the report and the statistical technique of interstation cross correlation has been applied to model the movement of four historical storms in Narmada basin which had caused critical floods in Narmada river. Hourly rainfall data recorded at a number of self recording rain gauges in the Narmada catchment has been used for the analysis. The storms considered for the analysis were, (i ) 2-6 Sept 1970, (ii) 28-31 August. 1973, (iii) 28-31 August 1978 and (iv) 6-10 August 1979.

The hourly rainfall data are scrutinized by visual observation for each of the storms and the storm period at each of the SRRG stations was identified. The hourly rainfall data at each of the SRRG stations has been input to the cross correlation programme incorporating the lag observed through the visual observation. During the analysis, the inter-station correlation is computed for all pair wise combination of SRRG stations lagging the rainfall data at stations down the storm track in successive increments of 1 hour up to a maximum lag of 18 hours.

The results have indicated the usefulness of the statistical model based on cross correlation, in modelling the movement of the tropical storms in spite of the rather poor network of self recording stations in the Narmada basin.

The study further strengthened the theory regarding the size of the storm cell which has been reported in various studies to be of the order of about 5 km. The lag zero correlation obtained at any pair wise combination in all the four stations is rather poor, the maximum correlation coefficient obtained being only 0. 7200.