New models for long range forecasts of summer monsoon rainfall over north west and peninsular India

New models based on (a) Multivariate Principal Component Regression (PCR) (b) Neural Network (NN) and (c) Linear Discriminant Analysis (LDA) techniques were developed for long-range forecasts of summer monsoon (June-September) rainfall over two homogeneous regions of India, viz., North West India and Peninsular India. The PCR and NN models were developed with two different data sets. One set consisted 42 years (1958-1999) of data with 8 predictors and the other, 49 years (1951-1999) of data with 6 predictors. The predictors were subjected to the Principal Component Analysis (PCA) before model development. Two different neural networks were designed with 2 and 3 hidden neurons. To avoid the nonlinear instability, 20 ensemble runs were made while training the network and the ensemble mean results are discussed. The LDA model was developed with 42 years of data (1958-1999) for classifying three rainfall intervals with equal prior probability of 0.33. Both the PCR and NN models showed useful forecast skill for NW India and Peninsular India. Models with 8 predictors performed better than the models with only 6 predictors. The NN model with 3 hidden neurons performed better than model with 2 hidden neurons. For NW India, the NN model performed better than the PCR model. The RMSE of the NN model and PCR model with 8 predictors for NW India (Peninsular India) during the independent period 1984-99 was 12.5% (12.2%) and 12.6% (11.5%), respectively. Corresponding figures for the models with 6 predictors are 15.0% (13.0%) and 13.9% (11.4%) respectively. During the independent period, model errors were large in 1991, 1994, 1997 and 1999. However all the models showed deteriorating predictive skill after 1988, both for NW India and Peninsular India. The LDA model correctly classified 62% of grouped cases for NW India and Peninsular India. The LDA model showed better skill in classifying deficient rainfall (<-8%) over NW India and excess rainfall (>3%) over Peninsular India