Parametric and power regression models: New approach to long range forecasting of monsoon rainfall in India

Abstract

Monsoon is a complex system. As such it is not yet possible to develop a deterministic model for long range forecasting of monsoon rainfall. An attempt h!1.s been made here to develop a parametric and a power regression model to predict monsoon rainfall by utilising signals from 15 parameters known to be related with the Indian summer monsoon rainfall. Some of the parameters are global and others are regional in nature. These parameters also have physical links with the Indian summer monsoon. Some of these parameters are inter-related. The parametric model, which analyses the monsoon rainfall vis-à-vis  the 15 parameters for the last 37 years (1951.-1987), shows encouraging results. It is observed that whenever more than 70% parameters showed favourable signals, the monsoon rainfall in India was not only normal (percentage departure of rainfall -+10% of normal), but it was towards the positive side of the normal. In .1988, a large number (87%) of parameters were favourable. Based on this analysis the long range forecast for monsoon 1988 was estimated towards the positive side of the normal and actually the monsoon rainfall in 1988 was above normal (+19% of the normal) .

This parametric model is purely a qualitative decision making tool where equal weightage has been given to all the 15 parameters. However, the relationship of monsoon rainfall with individual predictors exhibits a nonlinear relationship. To take care of this non-linearity, a curvilinear relationship has been determined by fitting the equation of different degrees. The best fit degree of relationship with all the 15 parameters has been combined and a power regression model has been developed. The forecasts from this power regression model have been found encouraging both during the sample period (1958-1980) on which the model is developed, as well as during the independent test period (1981-1988). The power regression model has correctly predicted the drought and large excess rainfall during the sample and independent test periods.

The performance of the power regression model has been compared with that of the multiple linear regression model, formed by utilising exactly the same set of data which was used for formulating the power model. Comparison of two models shows that the performance of power regression model is better than that of the multiple regression model