Statistical Prediction of March-May 2000 Rainfall in Northeast Brazil

from SST up to the end of January using Linear Regression

and Discriminant Analysis.

contributed by A.W. Colman, M.K. Davey, R.J. Graham and R.T. Clark

The Met Office, Bracknell, United Kingdom

1. Introduction

Real-time forecasts of rainfall during the NE Brazil rainy season (March-May approx.) have been issued by the UK Meteorological Office (UKMO) for each season since 1987 following research by Ward and Folland (1991).

In 1999, the forecasts were revised and extended to cover a region from 2.5^o to 10^o south and from the Atlantic coast west to 50^o west. Forecasts are now for gridpoint mean rainfalls. The grid used is the same as that of the Atmospheric General Circulation Model (AGCM) used for seasonal prediction. Empirical forecasts will now be made for exactly the same predictands as AGCM forecasts.

Included with the forecast are assessments of deterministic forecasts using correlation, and the Root Mean Square Skill Score (RMSSS) which is proposed as a WMO standard assessment measure. Also included are assessments of probability forecasts using Linear Error in Probability Space (LEPS).

2. Predictors

The empirical forecast is based on the same predictors as previous forecasts; (see Experimental Long Lead Bulletin March issues 1993 to 1999, an index of Atlantic Sea Surface Temperature (SST) and an index of Pacific SST. The AGCM forecast is largely controlled by sea temperature anomalies world-wide.

This year, the La Niña SST pattern in the Pacific is very strong, which clearly favours above average rainfall in NE Brazil. The Atlantic SST anomalies are not as strong as those in the Pacific but also favor above average rainfall. The anomaly centres in the Atlantic are about 10^o northward of where they usually occur prior to an anomalously wet NE Brazil rainfall season. There is a small area of below average SST to the East of NE Brazil, which favours below average rainfall in NE Brazil. Recent predictor values are plotted in figure 1.

3. Northern Brazil Regions

Our forecast area consists of 12 rectangular regions each covering 3.75^o longitude x 2.5^o latitude. Grid point rainfalls at the corner points are averaged to calculate values for the region. This smoothing reduces local errors and improves skill scores. The rainfall data used to make and assess the forecasts were supplied to us by the Climate Research Unit at the University of East Anglia, by Prof. Hastenrath at the University of Wisconsin and by INPE in Brazil.

Regions extend westward to 50^oW, northward to the equator and south to 10^oS. Observational data for at least 2 of the grid points at opposite corners is required for a region to be considered for the forecast. The regions were selected only if the correlation between independent forecasts and observed values exceeded 0.5 over the period 1948-1997.

Region number 8 centered at 39.375^oW, 6.25^oS is the closest to the regions used previously for issued forecasts and is referred to as the Standard NE Brazil region (SNEBR).

The forecast period is for March-May but similar anomalies can be expected in all months up to June.

As in previous years, the rainfall for each region is categorized into 5 equiprobable categories (over 1961-1990) called quints and referred to as Very Dry, Dry, Average, Wet and Very Wet Quints.

4. Empirical Forecasts

Empirical forecasts consist of forecasts made using historical data back to 1913. Probability forecasts are produced using discriminant analysis and deterministic forecasts are produced using linear regression.

Probability Forecast Summary (fig. 2a-e):

The discriminant forecasts are all favouring the wetter categories though with some differences in preferred quint. For all regions, the highest probability is for the wet or very wet category.

Regression Forecast Summary (fig. 2g-j):

The linear regression forecasts favor the very wet category for all regions. The regressions show a clearer signal of above average rainfall than the discriminant predictions.

See TABLE 4 for forecast skill assessments

Probability forecasts produced using discriminant analysis (fig. 2f) are assessed using LEPS (See Potts, Folland, Jolliffe and Sexton; Journal of Climate, 1996, Vol 9 page 34) and deterministic forecasts produced using regression are assessed using correlation and RMSSS (fig 2k,l).

RMSSS=100*(1-(persistence refers to persistence from the previous year's rainfall season) RMS error (forecasts)/ RMS error (persistence))

5. Dynamical Forecasts

Dynamical forecasts are produced as an ensemble of 9 AGCM runs started at 6 hourly intervals between 2^nd and 4^th February and run for 4 months. The GCMs were initialised with the observed atmospheric data at the starting time and forced throughout the run with sea temperature anomalies observed in the 4 week period preceding the start time.

The dynamical forecasts are presented as ensemble mean (fig. 3f-i) and as probability forecasts (fig.3 a-e). The ensemble mean predictions are presented below as a percentage of a 1961-1990 climatology, and as a percentage of standardised units relative to this climatology. The 1961-1990 climatology was calculated by running the same GCM over this period forcing it with observed SST. The Quint categories in fig. 3i were calculated from dynamical model rainfall simulations for 1961-1990. Hence, these model quints are based on the probability distribution function of model rainfall.

Probability forecasts for the observed data quints presented in fig. 3a-e can be directly compared with the empirical discriminant analysis forecasts in fig. 2a-e. The probabilities in fig 3a-e make use of a contingency table of forecast and observed quints for 1961-90, to adjust the probabilities from the AGCM ensemble predictions for March-May 2000. Hence these probabilities reflect the skill of the model simulations over 1961-1990.

Dynamical Summary:

The dynamical ensemble mean predictions are for above average rainfall in the western regions and near average in the more eastern regions including SNEBR. A small area of below average SST to the east of NE Brazil (referred to in the predictors section) may have contributed to the relatively dry forecast for the more eastern and south-eastern regions. Large (ocean) scale patterns are used in the statistical methods to predict rainfall hence these methods are not sensitive to small region SST anomalies.

6. Overall Summary

SNEBR: The regression forecast is for the VERY WET category, the discriminant forecast equally favors the WET and VERY WET categories as the most probable and the dynamical forecasts favour the AVERAGE category. If the statistical and dynamical probabilities were averaged, then the WET category would be most probable. Therefore, our best estimate for this region is for the WET category.

REGIONS 1 &,2: The dynamical and statistical forecasts all favour the VERY WET category. Hence, our best estimate forecast for regions 1 and 2 is for the VERY WET category with MODERATE confidence.

REGIONS 3,4,6,7 & 9: The statistical forecasts favour the WET or VERY WET categories for these regions while the dynamical forecasts favour the AVERAGE or WET category. Our best estimate for these regions is for the WET category.

REGIONS 10 and 11: The Statistical forecasts favour the WET or VERY wet category while and the dynamical forecasts favour the AVERAGE or DRY category. These south-eastern most regions are closest to the region of below average SST anomalies in the South Atlantic which are associated with below average rainfall in NE Brazil. Our best estimate for these regions is for the AVERAGE category.

Note: These Forecasts are Experimental and Should Be Used with Caution

References:

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

Appendix: Statistical Prediction for Fortaleza and Quixeramobim (FQ)

For consistency with and continuation of forecasts issued in previous years (1987-1998), predictions of the standardised index of March-May rainfall at Fortaleza and Quixeramobim are being included here.

The linear regression forecast based on an average Nov-Jan, Dec-Jan and Jan SST is:

1.69 +standardised units (in Quint category 5 relative to 1951-1980 or 1961-1990, 1951-1980 Quint 4-5 boundary=0.71, 1961-1990 boundary=1.03).

Probabilities calculated from the same data using discriminant analysis are for the 5 (1951-80) quint categories:

V Dry	Dry	Average	Wet	Very Wet
0.004	0.021	0.103	0.122	0.750

and for 5 (1961-90) quint categories:

V Dry	Dry	Average	Wet	Very Wet
0.001	0.010	0.091	0.065	0.832

Note: The FQ forecast is for the very wet quint with respect to 1951-80 and with respect to 1961-90.

Figure 1: SST EOF time series used as predictors. * marks January values

Figure 2: Empirical forecasts for March-May 2000 and forecast skill

Figure 3: Dynamical forecasts for March-May 2000 and forecast skill