An assessment of the value of

1. Introduction

Real-time forecasts of mean rainfall during the NE Brazil rainy season (approximately February-May) have been issued by the Met Office for each season since 1987 following research by Ward and Folland (1991) and by Folland et al (2001). Forecasts are issued in December and early February using the latest available ocean and atmosphere information and are provided for 11 rectangular regions located between 2.5^o and 10^o south and between the Atlantic coast and 50^o west. The corners of the rectangular region correspond with the grid used by the Met Office GLObal SEAsonal (GLOSEA) model

Forecasts are in probability format and are presented in the following ways: probabilities for tercile and quintile categories; the probability of an extreme season, defined as a season wetter or drier than any during the past 10 years; and the probability of a wetter season than last year.

Dynamical model output from the GLOSEA coupled ocean-atmosphere general circulation model and SST based statistical predictors have been combined using a multi-variate discriminant equation to produce one set of probability forecasts.

Included with the forecasts are assessments of the probability forecasts using the Relative Operating Characteristic (ROC) skill measure, a WMO standard assessment measure for probability forecasts.

2. Forecast System

2.1 Statistical Predictors

The statistical forecast is based on the same two predictors as in previous forecasts; (see Folland et. al.,2001). The two predictors used are an index derived from Atlantic Sea Surface Temperature (SST) patterns and an index derived from Pacific SST patterns.

Current SST patterns

SST is currently slightly below average in the East Tropical Pacific, which favours above average rainfall over NE Brazil .In the Atlantic, SST is currently slightly above average just north of the equator and there is an area of below average SST in South-East tropical Atlantic. These Atlantic anomalies favour below average rainfall, thus there are contrasting signals from the two predictors.

Predicted SST

Time coefficients of the Atlantic and SST patterns are also calculated using predicted SST using the statistical forecast system described in Colman and Davey (2003). SST predictions are produced from earlier SST observations using an equally weighted average of forecasts from 3 methods, persistence of box area average SST anomaly, Global Scale Canonical Correlation Analysis and linear regression from neighbouring boxes. Predicted SST are used in a 2 tier approach to seasonal forecasting. Firstly the SST prediction system is used to produce forecasts of 10 degree latitude x longitude box anomalies for February from November anomalies. Secondly, the February anomalies are used to evaluate the SST pattern indices which are substituted into regression or discriminant prediction equations to make rainfall forecasts.

For this forecast we use Atlantic and Pacific index values calculated from latest available SST observations (i.e. for November 2005) and index values calculated using predicted SST for February 2006. These make up 4 of the predictors used in the discriminant equation described in section 2.3.

2.2 GLOSEA Dynamical Forecasts

The GLOSEA forecasts are produced monthly as an ensemble of 40 members. The members are generated from slightly perturbed ocean initial conditions (for more about GLOSEA see http://www.metoffice.gov.uk/research/seasonal/technical.html ) . The model is run out to 6 months ahead. The model output is calibrated in the discriminant equation using hindcasts from 43 years (1960-2002) produced as part of the DEMETER project (see http://www.ecmwf.int/research/demeter/) for more information about DEMETER).

For this forecast we use the GLOSEA prediction initialised in early December which covers the period March to May.

2.3 Content of Discriminant Forecast Equation

The forecast is produced using an equation of the form

Tercile probability for gridbox g = 1/40 x SUM (f ( a x November Atlantic SST index + b x November Pacific SST index + c x predicted February Atlantic SST index + d x predicted February Pacific SST index + e x GLOSEA member m forecast for gridbox g ) for 40 members m=1,40)

Where f is an exponential function adjusted so the sum of probabilities for the 3 terciles=1.

Coefficients a,b,c,d,e and function f are all evaluated using historical SST data and GLOSEA hindcasts produced using the DEMETER project.

The discriminant equation effectively calibrates the model output and corrects for any bias observed over the 1960-2002 training period. (See Afifi and Azen, 1979 for more about discriminant analysis).

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 1. 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 are a merger of data supplied to us by the Climate Research Unit at the University of East Anglia, by Prof. Hastenrath at the University of Wisconsin and by FUNCEME and 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. For the 11 regions used the correlation between independent forecasts and observed values exceeds 0.5 over the period 1948-1997 (this criteria formed the basis of selecting the regions).

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).

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. For compatibility with other forecasts including Regional Climate Outlook Fora (RCOF) products, the rainfall is also presented in terms of 3 equiprobable categories called terciles which are referred to as dry, average and wet categories.

4. Forecasts and Forecast Skill

This year, the GLOSEA forecasts are generally favouring near or above average rainfall whilst the Statistical forecasts are favouring average or below average rainfall. The GLOSEA forecasts are consistent with the signal from the Pacific whilst the Statistical forecasts are more consistent with the signal from the Atlantic.

4.1 Quint Probability forecasts (Figure 2a-e)

Quint probabilities are presented in figure 2a-e, note that for quint categories the climatological expectation is 20%. The average category is most probable except for north-westernmost regions 1 and 2 and south-easternmost region 11 where the dry category is most probable and for north-easternmost region 5 where the wet category is most likely. In region 11, the WET category probability is also greater than chance.

4.2 Quint forecast ROC assessments (fig. 2f-j):

The ROC skill of probability forecasts for the 5 quints for the 11 regions is presented in figure 2f-j. ROC scores (Stanski et. al. 1989, Graham et. al. 2000) are a widely used measure for probability forecasts and are a WMO standard measure. The expected ROC score from random chance is 0.5. If the ROC score is greater than 0.5 there is evidence of skill. Skill tends to be highest for the outer category forecasts (DRY, VERY DRY and VERY WET).

4.3 Probabilities of terciles, extreme seasons and of a wetter season than last year (Figure 3)

Forecast probabilities are displayed in graphical format in figure 3. The tercile probabilities are consistent with the quint forecasts in that the average category is generally the most probable. The only exception is region 2 where the dry category is most probable. An extreme dry season (drier than the last 10 years) is less likely than expected from climatology (i.e. less than 10%) in all regions. An extreme wet season is also less likely than expected from climatology in all regions except 8 and 10. The high probability for an extreme wet season in region 10 should be regarded with caution. It is linked to a lack of wet seasons in this region in recent years and consequently a low 10 year maximum threshold. There is an elevated chance that the 2006 season will be wetter than the 2005 season in the regions 2, 7, 8, 9, 10 and 11 but drier than 2005 in other regions.

4.4 ROC skill of tercile, extreme season and wetter season than last year probabilities

The ROC skill of probability forecasts for the 3 terciles is presented in figure 4. Monte Carlo tests have been used to locate the 5% significance levels for these probability ROC scores. Significant skills are marked by * on fig 4. Skill is mainly confined to the outer categories (DRY and WET).

5. Overall Summary and “best estimate” Quint categories

All Regions including SNEBR but excluding 1,2 and 5: The average category is most probable in all these regions except region 11 where there is a relatively broad distribution of probabilities. For these regions, our best estimate category is the AVERAGE category.

Regions 1,2: In these regions there is a tendency for a skew in probabilities to the drier categories, with dry most favoured. Our best estimate category for these regions is the DRY category.

Regions 5: In region 5 the wet category is the most probable. Hence, our best estimate category for this region is the WET category.

REFERENCES

Afifi, A.A. and Azen, S.P. 1979: Statistical Analysis – a computer oriented Approach. Academic Press, New York.

Colman, A.W., Davey M.K. 2003: Statistical Prediction of Global Sea-Surface Temperature Anomalies. Int. J.Climatology, 23 1677-1697.

Folland, C.K., Colman, A.W., Rowell, D.P & Davey M.K. 2001: Predictability of northeast Brazil rainfall and real-time forecast skill, 1987-98. J.Climate, 14 1937-1958.

Graham,R.J., Evans, A.D.L, Mylne,K.R., Harrison, M.S.J. and Robertson, K.B. 2000: Assessment of seasonal predictability using atmospheric general circulation models. Q.J.Royal.Met.Soc.,126 2211-2240.

Potts, J.M., Folland, C.K., Jolliffe, I. and Sexton, D. 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. Climatology.,11,711-743.

FIGURES

FIGURE 1: Forecast regions

FIGURE 2: Combined GLOSEA/statistical discriminant Probability forecasts of quints for February-May 2006.

FIGURE 3: Combined GLOSEA/statistical discriminant Probability forecasts of terciles, 10 year extremes and of a wetter season than last year for February-May 2006.

FIGURE 4: ROC Skill of GLOSEA/statistical discriminant tercile forecasts (1960-2002)