[Previous Article] [Next Article]


Multiple Regression and Discriminant Analysis Predictions
of Jul-Aug-Sep 1997 Rainfall inthe Sahel and Other
Tropical North African Regions
contributed by Andrew Colman1, Michael Davey1,
Michael Harrison2, Tony Evans2 and Ruth Evans2
1Ocean Applications Branch 2NWP Division
UK Meteorological Office, Bracknell, United Kingdom

The UK Meteorological Office has produced experimental forecasts for summer wet season rainfall in tropical North Africa using multiple linear regression and linear discriminant analysis since 1986 (see Ward and Folland 1991 or the March 1993 issue of this Bulletin for information on these two statistical methodologies). Specifically, forecasts have been experimentally issued for the Sahel region of Africa since 1986, based preliminarily on March-April SST predictors (for an early May forecast) and then updated with the availability of May-June SST (for an early July forecast). The latter is effectively a zero-lead forecast, as most rain in the Sahel falls in the July-September period. In 1992 the forecasts were expanded to cover four regions located from the Sahel southward to the Guinea Coast. The current forecast regions (Fig. 1) are referred to below as regions 1 (SAH-G), 2 (SAH-G), 3 (SDN), and 4 (GUI).

African rainfall forecasts for regions 1, 2, and 3 are made here using three distinct components of SST forcing as predictors. The first and most important is an inter-hemispheric contrast in SST anomaly. A warm Northern Hemisphere relative to Southern Hemisphere tends to accompany increased rainfall in the Sahel and Soudan. The second predictor represents the local SST anomaly in the south tropical Atlantic, which accom-panies more rain in the Guinea Coast region, less in the Sahel, and slightly less in the Soudan. The third SST predictor is related to ENSO, as the warm phase of ENSO accompanies reduced rainfall in the Sahel and especially the Soudan. The importance of each of these SST predictors (which are conveniently expressed as EOFs of the SST fields over various regions) for rainfall in each of the four regions is shown by standardized regression coefficients in multiple regression, which are discussed in the June 1993 issue of this Bulletin. Rainfall in the Guinea Coast region is best predicted, however, by the SST anomaly immediately adjacent to the west coast of Africa south of the Guinea Coast (Ward et al. 1993).

Independent forecast skill was estimated by developing multiple regression coefficients on a different period than that used for hindcast testing. Table 1 shows the skill of hindcasts for 1901-45 made using a regression model based on 1946-92 data, and vice versa, for two of the target regions.

Table 1. Independent hindcast skill (temporal correlation between forecasts and observations) in forecasting two of the four North African rainfall regions. The skill of persistence forecasts is shown in parentheses.

African 

Region

Forecasting 1901-1945 

Using 1946-92 

Regr. Model

Forecasting 1946-1992 

Using 1901-45 

Regr. Model

SAH-N .51 (.10) .68 ( .66)
GUI .44 (.02) .53 (-.33)




The correlations are fairly good, suggesting usable forecast skill. The high persistence skill for the SAH-N region in the later period arises because of the marked interdecadal component of variability, with relative wetness before the early 1970s versus relative dryness after that time.

The accuracy of the SAH-N forecasts issued since their inception in 1986 has generally been within one quint except for 1988 when there was a sudden development of La Niña after the forecast was made and the forecast was much too dry ("very dry" versus a verification of "wet"), and for 1994 when the forecast was again too dry.

Real-time atmospheric general circulation model (AGCM) forecasts have been run with some success for the last several years, using persisted SST anomalies from April to forecast Jul-Aug-Sep northern African rainfall (Folland et al. 1991). The model forecasts have been considered in conjunction with the multiple regression and discriminant analysis forecasts even though the expected skill of the latter two are better known.

In March and April 1997, SST was well below average in the Gulf of Guinea and below average in the tropical south Atlantic. These conditions usually favor above average seasonal rainfall in the Sahel and Soudan (regions 1, 2 and 3) and below average rainfall in the Guinea coast region (region 4). The contrast between northern and southern hemisphere SST is quite weak at present, favoring average rainfall. (This situation differs from that seen for most of the past 25 years, in which the interhemispheric contrast in SST has usually favored below average rainfall for regions 1 ,2, and 3.) A warm ENSO episode is developing in the tropical Pacific. Historically, warm ENSO conditions weakly favor below average rainfall in regions 1, 2, and 3.

When linear discriminant analysis and linear multiple regression are applied to the values of the March-April SST predictors summarized above, resulting rainfall forecasts are as shown in Tables 2 and 3, respectively. To reduce noise, forecasts made using models with two different training periods and (for Sahel, Soudan) two different sets of predictors are averaged.

Table 2. Probability of July through September 1997 rainfall in each of five equiprobable (with respect to 1941-85 data) categories in four regions in tropical North Africa, according to linear discriminant analysis prediction models.
Very Dry Dry Average Wet Very Wet
SAH-N .34 .20 .09 .16 .20
SAH-G .12 .32 .14 .10 .33
SDN .32 .15 .18 .12 .23
GUI .52 .37 .05 .04 .01






Table 3. Prediction of July to September 1997 rainfall in four regions in tropical North Africa, based on multiple linear regression models.
Region 1 

SAH-N

Region 2 

SAH-G

Region 3 

SDN

Region 4 

GUI

% of 1951-80 mean 95% 97 95 77
% of 1971-90 mean 131 122  109 77




For regions 2, 3 and 4 experimental ensemble predictions have been made using the UKMO climate AGCM with persisted April 1997 SST anomalies. This model, its skill, and further 1997 results are discussed in detail in a separate article by Harrison et al. in this issue. The AGCM predictions are summarized in Table 4. For the inflated predictions, the predicted anomalies have been rescaled such that model variance matches observed variance in 1979-93.

Table 4. Prediction of July to September 1997 rainfall in three regions in tropical North Africa, based on the UKMO climate AGCM with persisted April 1997 SST anomalies. The dynamical 9-ensemble predictions are expressed as a percentage of model climatology based on simulations for 1979-93.
Region 2 

SAH-G

Region 3 

SDN

Region 4 

GUI

Ensemble Prediction 85% 85 64
Inflated Prediction 80 74 44


The discriminant analysis forecasts indicate that for regions 1 and 3 the very dry category has the largest probability, but there are substantial values also for the other categories. For region 2 the highest probabilities are for the dry and very wet categories. The spread of substantial probabilities between different categories reflects the contrasting influences of SST anomalies in different oceanic areas. For region 4, only south Atlantic SST is used as a predictor, and here the dry and very dry categories are clearly favored. The multiple regression prediction is close to the (1951-80) average/wet category boundary for region 2, in the average category for region 1, close to the dry/average boundary for region 3, and in the dry category for region 4. The dynamical forecasts indicate below average rainfall for regions 1, 2 and 3 and well below average rainfall for region 4. [Note: with the newest set of historical data, the quint boundaries have been revised such that the very dry/dry, dry/average, average/wet, and wet/very wet boundaries are as follows for the four regions (with respect to 1951-80): region 1: 75, 91, 103, 117; region 2: 80, 87, 97, 111; region 3: 90, 94, 101, 105; region 4: 73, 87, 101, 110.]

Because the predictive skill of the dynamical model in these African regions has not been fully tested, the overall forecast is based mainly on the linear discriminant and multiple regression results. Our best estimate forecasts, based on all the prediction methods and the current evolution of SST, are shown in the following table:

FORECASTS FOR 1997 RAINY SEASON
Region Forecast Confidence
1 SAH-N  dry low
2 SAH-G dry/avg low
3 SDN dry moderate
4 GUI dry /very dry moderate




Three notes: (1) A forecast for, e.g., dry/very dry means that the dry and very dry categories are equally likely. (2) the forecast for regions 1, 2 and 3 is below average relative to the 1951-80 mean, but near-average relative to the drier 1971-90 means. (3) These forecasts are experimentaland should be used with caution.

Folland, C.K., J.A. Owen, M.N. Ward, and A.W. Colman, 1991: Prediction of seasonal rainfall in the Sahel region of Africa using empirical and dynamical methods. J. Forecasting., 10, 21-56.

Nicholson, S.E., 1985: Sub-Saharan rainfall 1981-84. J. Clim. Appl. Met., 24, 1388-1391.

Ward, M.W. and C.K. Folland, 1991: Prediction of seasonal rainfall in the north Nordeste of Brazil using eigenvectors of sea-surface temperature. Int. J. Climatol., 11, 711-743.

Ward, M.N., C.K. Folland, K. Maskell, A.W. Colman, D.P. Rowell and K.B. Lane, 1993: Experimental Seasonal Forecasting of Tropical Rainfall at the U.K. Meteorological Office. In:Prediction of Interannual Climate Variations (J. Shukla, Ed.), NATO ASI Series, Vol. 16, Springer-Verlag, Berlin, 197-216.

Fig. 1. Locations of the North African forecast regions for Jul-Aug-Sep rainfall. Region 1 (SAH-N) is the Sahel as defined by Nicholson (1985), for which forecasts have been made since 1986. Region 2 is a redefined Sahel (SAH-G), region 3 covers the Soudan zone (SDN) and region 4 covers the Guinea Coast (GUI).

[Previous Article] [Next Article]