Seasonal rainfall in the north Nordeste in northeast Brazil occurs mainly from February to May, with heaviest amounts in March and April. Experimental forecasts of north Nordeste rainfall at 1 and 0 month leads are issued using November-January and January-February predictor data, respectively. Two predictors found to deliver substantial forecast skill are (1) the 30N-30S portion of the third covariance-based EOF of Atlantic SST for all seasons, and (2) the first EOF of Pacific SST for Dec-Jan-Feb. Both of these EOF patterns are shown in the March 1993 issue of this Bulletin. The Atlantic EOF pattern reflects the SST anomaly immediately off the North Nordeste east coast and the large scale north-south SST gradient structure, while the Pacific EOF pattern serves mainly as an index of the ENSO situation. The amplitude time series of each of these predictors are used to predict north Nordeste rainfall both with multiple regression (giving a point forecast) and discriminant analysis (giving probabilities for each of five climatologically equiprobable [for 1951-1980] rainfall amount categories).

Details about the EOF analyses, the physical relevance of the predictors, and the two forecasting methods are given in Ward and Folland (1991). Multiple regression develops optimal weights for each predictor in order that the resulting linear equation minimizes squared errors between forecasts and corresponding observations over the training periods (1912-95, 1946-95). In discriminant analysis, categories of rainfall amount are defined, and, given values of the predictors, probabilities of each of the rainfall categories are determined using Bayes' theorem. Less linear constraint is imposed here than in multiple regression, as the probabilities do not necessarily change smoothly as a function of category.

Forecasts are made for three separate North Nordeste predictands: Nobre (for Feb-May), Hastenrath (Mar-Apr) and Fortaleza/Quixeramobim (FQ) (Mar-May). These are illustrated in Fig. 1. Each of these forecasts is done using both multiple regression and discriminant analysis. The forecasts presented here are only for the two predictands whose periods begin in March, (Hastenrath and FQ), making for a long-lead forecast. The Hastenrath rainfall area occupies a central portion of the north Nordeste, while FQ is the rainfall averaged over the two stations, both of which are in the Hastenrath area.

If the amplitudes of the predictor EOFs are changing rapidly during the Nov-Jan period, values from Dec-Jan or only January may be used as predictors, if the more recent SST anomalies are expected to persist. In early March updated forecasts for the predictand periods are issued, using SST data through February. While this is not a long-lead forecast, it is presented here following the 1-month lead forecast for comparitive purposes.

To estimate forecast skill, multiple regression and discriminant analysis hindcasts for the FQ and Hastenrath indices based on the SST for Nov-Jan were made for the 1912-54 period using data from 1955-97 and vice versa. Forecasts were also made for the 1981-1997 period using data from 1912-80. There is an overlap of the SST EOF analysis period (1901-80) and the first experiment's period (1912-1997) but the second experiment's period is completely independent of the SST EOF analysis. The discriminant analysis forecast skill was assessed by comparing the observed category with the most likely category according to the hindcasts over the period 1912-97 (Table 1), while the point estimate rainfall amounts predicted by multiple linear regression were correlated with observed values (Table 2). The correlations and the contingency tables show significant (5% level) prediction skill, particularly for the extreme (very dry and very wet) categories and no depreciation in skill for the fully independent years (1981-1997).

Table 1:Contingency table showing performance of discriminant analysis hindcasts of rainfall categories during 1912-97. Q1=very dry, Q2=dry, Q3=average, Q4=wet,Q5=very wet.

(a) FQ

(b) Hastenrath

Table 2: Verification of hindcasts made using multiple regression against observed (obs.) values using correlation, forecast bias and Root Mean Square Errors (RMSE).

Experimental real-time forecasts for the FQ, Hastenrath and Nobre indices using the methods discussed here have been made for each rainfall season since 1987. The forecasters combined the forecasts from discriminant analysis and multiple regression to determine the official forecast category. The forecast-observation correspondence from 1987 to 1997 is good with 35 of the 40 issued forecasts being within 1 category of correct, (chance=21). The correct category is also predicted much more often than expected by chance, i.e., 8 times out of 19 by the preliminary forecast, (chance =4/19), and 8 times out of 21 for the updated forecasts, (chance =4/21). (Over a large number of cases the updated forecasts would of course be expected to have more skill.)

Table 3 shows the record of real-time forecasts for 1987-97.

Table 3:Verification of experimental real-time forecasts of NE Brazil rainfall 1=Q1=very dry etc.

FQ March-April Rainfall

Hastenrath March-April Rainfall

nb. No 1 month lead forecast issued in 1997 due to disagreement amoung prediction methods.

At the time of forecast, Atlantic SST anomalies were positive between 0 and 20S and negative to the southwest which favour above average rainfall in NE Brazil. The signal from the Atlantic has weakened during January relative to November and December. In the Pacific, a very strong EL Nino favours below average in NE Brazil.

Figures 2 and 3 show the monthly timeseries of the Atlantic and Pacific SST anomaly EOF predictors used in the regression and discriminant analysis prediction models.

Example multiple regression equations for the 1-month lead forecast for the Hastenrath (for Mar-Apr) and FQ (for Mar-May) rainfall indices (standardised rainfall anomaly units) based on 1912-1995 data are:

Hastenrath: 24.9 -67.0 A -9.9 P

FQ: 23.3 -88.1 A -7.5 P

where the EOF time coefficients (A = Atlantic EOF, P=Pacific EOF) are not standardised. (Between 1981 and 1997, The Atlantic series varies between about -2 and +2 and the Pacific series varies between -5 and +10.

For the 1-month lead linear regression predictions, the average of predictions made using training periods 1912-95 and 1946-95 and SST anomalies for November, December and January was calculated. The result is:

The multiple regression prediction for the February-May Nobre series was for the average quint (quint 3). The following forecast probabilities produced by discriminant analysis show the probability of the 1998 Hastenrath and FQ index being in each of the quintiles:

The statistical predictions reflect the influence of large and opposing predictor values for the Pacific and Atlantic. This results in bimodal discriminant forecasts and regression forecasts of near average rainfall.

Predictions of NE Brazil rainfall were also produced from an ensemble of "dynamical" Atmospheric Global Circulation Model (AGCM) runs. These dynamical predictions are described in detail by Evans et al. also in this bulletin. All the dynamical ensemble members consistently predict seasonal rainfall well above average. The wetness of the dynamical forecasts relative to the statistical forecasts may be due to nearby warm SST anomalies to the south-east enhancing rainfall over NE Brazil.

Available predictions of the current El Nino event indicate that the large east equatorial Pacific SST anomalies are likely to decline through the Mar-Apr-May forecast period.

Our best estimate forecast for the most likely category is WET (category 4) for the 'Hastenrath' and 'FQ' rainfall indices. However, given the continuing strong El Nino, and the fact that the atmospheric model placed positive (wet) anomalies only over the Nordeste, the possibility of a dry or very dry season should also be considered.

An updated forecast was prepared in early March using February SST.

The Atlantic SST anomalies in February favored drier conditions in NE Brazil compared with the previous months SST anomalies. The main cause of this change is warmer SST relative to normal in the north Atlantic off the coast of Africa. Meanwhile, in the Pacific, the very strong El Nino event slowly weakens. These SST anomalies indicate that it will be slightly drier in NE Brazil than expected at the time of the preliminary forecast.

Regression predictons: quints are based on the period 1951 to 1980.

Discriminant predictions: probabilities that rainfall will be in the five categories Very Dry; Dry; Average; Wet; Very Wet

Dynamical predictions: A revised version of the AGCM used to make the dynamical forecast above was forced with February SST and early March initial atmospheric conditions. The prediction from a 9member ensemble was for near average rainfall, drier than theJanuary SST forecasts. There is less certainty about the climatology of this new AGCM however. With these updated predictions using February SST,Our best estimate forecasts are:

DRY (category 2) for the 'Hastenrath' rainfall index.

DRY/AVERAGE for the 'FQ' index:

References:

Ward, M.N. 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. 

Figure captions:

Fig. 1: Locations of the stations used in the Hastenrath rainfall timeseries, and the Fortaleza and Quixeramobim stations. The Nobre rainfalltimeseries is based on stations throughout the bounded region indicated.

Fig. 2: Amplitude timeseries for the Atlantic eigenvector for Jan 1990 to Feb 1997. Positive values (e.g. SST anomalies warm in north tropical Atlantic, cool in south tropical Atlantic) are associated with drier conditions.

Fig. 3: Amplitude timeseries for the Pacific eigenvector for Jan 1990 to Feb 1997. Positive values (e.g. SST anomalies warm in the central-east equatorial Pacific, cool in the north-west and south-west Pacific) are associated with drier conditions.