Prediction of the January to March Rainfall of South Africa, Botswana and Namibia Using CCA

contributed by Willem A. Landman¹ and Simon J. Mason²

¹South African Weather Bureau, Private Bag X097, Pretoria 0001, South Africa

²International Research Institute for climate prediction, Scripps Institution of Oceanography,

University of California San Diego, Mail Code 0235, La Jolla, CA92093-0235, USA

The Research Group for Seasonal Climate Studies of the South African Weather Bureau issues seasonal forecasts for South Africa, Botswana and Namibia. Forecasts are made for 3-month periods using canonical correlation analysis (CCA; Barnett and Preisendorfer, 1987; Graham et al., 1987a, 1987b; Barnston and Smith, 1996; Barnston et al., 1996).The predictor (global-scale sea-surface temperatures (Smith et al., 1996) and predictand data (regional rainfall indices) sets are first standardized, resulting in correlation matrices on which the EOF (Jackson, 1991) analysis is performed. The standardization ensures that all the grid points and homogeneous region indices have equal opportunity to participate in the prediction process (Barnston, 1994; Jackson, 1991). EOF analysis is performed separately for each of the predictor and predictand fields. An EOF analysis performed on the same variable measured at different time periods, which is the case for the predictor field, is known as extended empirical orthogonal function (EEOF) analysis (Weare and Nasstrom, 1982). The leading patterns within one EEOF can be interpreted as the propagation or evolution of the patterns in time, for example a cooling trend in the equatorial Pacific Ocean.

The African sub-continent is divided into nine homogeneous rainfall regions (Landman and Mason, 1998; Mason, 1998) on the basis of the inter-annual rainfall variability. Canonical variates are then used to make 3-month aggregate precipitation forecasts for January-February-March 1999 for South Africa, Botswana and Namibia from global-scale sea-surface temperatures. Four consecutive 3-month mean periods (D₉₇JF₉₈, MAM₉₈, JJA₉₈ and SON₉₈) of sea-surface temperatures are used to incorporate evolutionary features as well as steady-state conditions in the global oceans.

Cross-validation was used to estimate the model's performance (Barnett and Preisendorfer, 1987; Ward and Folland, 1991; Elsner and Schmertmann, 1994) over a 45-year training period (1951/52 to 1995/96) and model skill was estimated using the Pearson correlation coefficient between the predicted and observed indices for each homogeneous rainfall region. In effect, the correlation coefficient is a variance-adjusted measure of model skill (Ward and Folland, 1991). The number of modes to be retained in the analysis (i.e. those that will be used in the CCA eigenanalysis problem) is determined using forecast skill sensitivity tests. This is performed by cross-validation with varying number of retained predictor and predictand EOF modes. The combination producing the highest average correlation is used as the best estimate of the number of predictor and predictand EOF modes. For the predictand the number of retained EOF modes explain about 60-80% of the predictand variance and for the predictor, about 40% of the predictor variance. The truncation for the number of CCA modes retained is determined by using the Guttman-Kaiser criterion (Jackson, 1991) where only those modes having an eigenvalue larger that the average eigenvalue is retained.

The forecast for January to March 1999 (Fig. 1) is for above-normal rainfall to occur over the region. However, modest skill (correlation > 0.4) is found over mainly the central and western regions, with poor skill over the north-eastern regions, south coast and south-western Cape. Regions where the skill is statistically significant (using the Student's t-test) at the 95% level are shaded.

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