An assessment of the value of

1. Introduction

Real-time forecasts of rainfall during the NE Brazil rainy season (March-May approx.) have been issued by the Met Office 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 rainfall. The grid used is the same as that of the Met Office Atmospheric General Circulation Model (AGCM) used for seasonal prediction. This allows presentation of both empirical and dynamical forecasts for the same region.

Also in 1999, long lead forecasts were introduced for January-June rainfall from November SST. The longer period (January-June) rainfall averages are slightly more predictable than the March-May averages from November SST hence the change in season definition, however January-June and March-May rainfall totals are quite highly correlated. For the 2000 and 2001 seasons, predictions were only issued for one (SNEBR, see definition below) region. This year the long lead forecast format has been revised to be the same as the updated forecast format. This has been made possible by the availability of longer (6-month) lead dynamical forecasts. The forecast period has been shortened to February-May to be compatible with the NE Brazil regional climate outlook product and be within the dynamical forecast range (6 months).

This year we have introduced probability forecasts of terciles (for compatibility with the NE Brazil Regional Climate Outlook Forum) and probability forecasts of extreme season defined as a season wetter or drier than any during the past 10 years.

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, Potts et al. 1996).

2. Predictors

The empirical forecast is based on the same predictors as previous forecasts; (see Experimental Long Lead Bulletin March issues 1993 to 2001 published by NWS, NOAA USA and currently by COLA, USA). They are an index of Atlantic Sea Surface Temperature (SST) and an index of Pacific SST. The AGCM forecast is largely controlled by sea temperature anomalies worldwide.

Current SST patterns

SST anomaly pattern indices in the Pacific and tropical Atlantic which are linked to NE Brazil rainfall continue to be quite weak so rainfall is still expected to be quite close to the 1961-1990 average. Recent values of the two SST EOF predictor indices are plotted in figure 1.

3. Northern Brazil Regions

Our forecast area consists of 11 rectangular regions each covering 3.75^o longitude x 2.5^o latitude which are displayed in figure 2. 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. GPCP (Global Precipitation Climatology Project) data were used to fill data gaps for recent years. Observational data for at least 2 of the grid points at opposite corners are 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 centred 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 February-May but the heaviest rains usually occur in March and April. February-May totals are quite highly correlated with January-June totals predicted in 2000 and 2001 (r=0.97).

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

3.1 Predictions of terciles and extremes

This year we have added predictions of terciles and 10-year extremes to our forecasts. These predictions are shown in figures 3 and 5. The terciles are evaluated over the same period as the quints, 1961-1990 and enable the forecast to be compatible with NE Brazil Climate Outlook Forum (contact www.funceme.br for details). Predictions of the probability of a rainfall total greater or less than the most extreme year in the past 10 years (1992-2001) and the probability of a rainfall total greater than last year (FMAM 2001) are presented.

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. 3, 4a-e):

Probabilities of terciles and year extremes are shown in figure 3. The near AVERAGE tercile is most probable in most regions. An extreme dry season is less likely than usual (chance probability is just below 10%) in all regions. An extreme wet season is less likely than usual in most regions except region 8 (SNEBR) where the probability of exceeding the 1992-2001 decadal maximum (p=0.13) is slightly higher than the chance probability (p=<0.10). The probability of exceeding the decadal maximum in region 10 (p=0.37) is very high relative to chance. This is due to rainfall in this region being somewhat lower during the past 10 years than during the previous 30 years. For most regions, 2002 rainfall is more likely to be higher than it was last year.

The average quint category is most probable for most regions including SNEBR (fig. 4a-e) . Exceptions are the south-westernmost region (region 6), where the wet category is favoured the north-easternmost region (region 1) where the dry category is favoured and the southern region (region 10) where the very dry category is most probable.

Regression Forecast Summary (fig. 4g-j):

The linear regression forecasts favour the average category for most regions. The wet category is favoured in the far Southwest.

Empirical Forecast assessments (fig. 4f,k,l):

Probability forecasts produced using discriminant analysis are assessed using LEPS (See Potts, Folland, Jolliffe and Sexton; Journal of Climate 1996 Vol 9 page 34) (fig. 4f) and deterministic forecasts produced using regression are assessed using correlation and RMSSS (fig 4k,l).

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

A score of 100% indicates a perfect set of forecasts. Random forecasts are expected to have a LEPS and correlation score of 0. Persistence forecasts have a RMSSS skill of 0. The northern Brazil forecast skill (LEPS around 45%, RMSSS around 55%, correlation around 80%) is very high for seasonal forecasts.

5. Dynamical Forecasts

Dynamical forecasts are produced as an ensemble of 9 AGCM runs started at 6 hourly intervals between 12^th and 14^th December and run for 6 months. The model runs were initialised with the observed atmospheric data at the starting time and forced throughout the run with sea temperature anomalies observed at the start time.

The dynamical forecasts are presented as ensemble mean (fig. 6f-i) and as probability forecasts (fig. 5,6a-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. 4i were calculated from dynamical model rainfall simulations for 1961-1990. Hence, these model quints are based on the probability distribution function of model rainfall.

The probabilities in fig. 5 and 6a-e were calculated using discriminant analysis. Discriminant equations for each forecast area were calculated using model simulations as predictors and observed quint categories as predictands. The discriminant equations therefore represent any long term biases in the model simulations. Probability forecasts were calculated by substituting the current model forecast output into the discriminant equation.

Dynamical Summary:

The tercile forecast probabilities are generally highest for the middle AVERAGE tercile (fig. 5). The dynamical forecasts agree with the empirical forecasts in that a season drier than the last 10 is very unlikely. However the probability of a season wetter than the last 10 years wettest is greater than chance (>0.10) in regions 3,7,8 and 10. A wetter season than last year is expected to be more likely in the more southern and eastern regions but a drier season than last year is more probable further west.

The dynamical forecasts are in agreement with the empirical forecasts in favouring the average quint category for most regions (fig. 6a-e). The exception is the easternmost regions (5 and 8) were the wet quint category is favoured.

Dynamical forecast skill assessment (fig. 6j):

Correlations between dynamical simulations using observed SST and observed February-May rainfall, 1961-1990 range from 0.87 near and to the north of SNEBR to 0.59 in the north-western most region. The skill level is similar to or slightly higher the empirical forecasts.

6. Overall Summary and ”BEST ESTIMATE” quint category forecast

All regions including SNEBR: The regression forecasts favour the AVERAGE quint category for all regions except the south-westernmost region, region 6. The AVERAGE category has the highest discriminant probabilities too for most regions. The dynamical forecasts favour the AVERAGE category in most regions except for the north-easternmost regions where the wetter categories are favoured. Given that the long lead of this forecast requires caution, the lack of strong SST anomalies that are related to NE Brazil rainfall and the lack of a consistent signal for any other quint category than average, our best estimate for all regions is for the AVERAGE quint category.

An extreme wet year (wetter than the wettest of the last 10 years) is slightly more likely (probability 0.10-0.15) than usual for the SNEBR region

References:

Potts, J.M., Folland, C.K., Jolliffe, I. and D. Sexton, 1996: Revised “LEPS” scores for assessing climate model simulations and long-range forecasts. J. Climate, 9, 34-53.

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.