A graphical sensitivity analysis for statistical climate models: Application to Indian monsoon rainfall prediction by artificial neural networks and multiple linear regression models

A form of sensitivity analysis is described that illustrates the effects that inputs have on outputs of statistical models. The strength and sign of relationships, the types of nonlinearity, and the presence of interactions between inputs can be diagnosed using this technique. Intended for interpreting flexible nonlinear models, the graphical sensitivity analysis is applied to artificial neural networks (ANNs) in this study. As ANNs are increasingly being used for climate prediction, the discussion focuses on specific problems associated with their use in this context. The technique is illustrated using a real-world, long-range climate prediction example. Principal components (PCs) of circulation fields prior to the Indian summer monsoon are related to rainfall during monsoon months for the 1958-98 period. The skill of multiple linear regression and ensemble ANNs are compared using a resampling procedure. Interpretation of the models is then conducted using traditional diagnostic tools and graphical sensitivity analysis. This provides an improved investigation of precursor circulation field-summer monsoon rainfall relationships identified in a previous modelling study. The relatively stable, linear relationship identified between the May 200 hPa geopotential height field and summer monsoon rainfall is confirmed. Correlations previously identified between 850 hPa geopotential heights during January and rainfall by ANNs are shown to be the result of a weakly nonlinear, interactive relationship involving the first and second PCs of this field. An analysis of out-of-sample model predictions suggests that this relationship does not persist over the entire study period. This may result from a modulation of the strength of the circulation-rainfall relationship by El Nino-southern oscillation. Stratification of the results also reveals a relatively strong, nearly linear relationship with monsoon strength during years exhibiting positive scores of the second PC. On extending the analysis to longer lead-times, the surface pressure and 850 hPa geopotential height fields during November show relatively strong, persistent precursor relationships with summer monsoon rainfall. Sensitivity analyses suggest a mildly nonlinear relationship that is common to both fields. Copyright (C) 2002 Environment Canada. Published by John Wiley Sons, Ltd.