Statistical Forecast of North Brazil Seasonal Rainfall for March to May 2001 Based on Sea Temperature Anomaly Patterns Up to February 2001
contributed by A.W. Colman, M.K. Davey and R.J. Graham
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 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 2.5o to 10o south and from the Atlantic coast west to 50o 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 published by NWS, NOAA USA and currently by COLA, USA) 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.
As in the period prior to the February forecast, SST anomalies 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 3.75o longitude x 2.5o 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. 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 39.375oW, 6.25oS 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. 3a-e):
These forecasts are similar to the February equivalent with the average category being most probable for most regions including SNEBR. Exceptions are the most southwestern region where the wet category is most probable and one of the southernmost regions where the dry category is most probable.
Regression Forecast Summary (fig. 3g-j):
The linear regression forecasts favor the average category for most regions. The wet category is favoured in the far Southwest and northeast.
Empirical Forecast assessments (fig. 3f,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. 3f) and deterministic forecasts produced using regression are assessed using correlation and RMSSS (fig 3k,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 7th and 9th March and run for 4 months. The GCMs were initialized 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. 4f-i) and as probability forecasts (Fig. 4a-e). The ensemble mean predictions are presented below as a percentage of a 1961-1990 climatology, and as a percentage of standardized 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. 4a-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 200. Hence these probabilities reflect the skill of the model simulations over 1961-1990.
Dynamical Summary:
The dynamical forecasts are in agreement with the empirical forecasts in favoring the average category around SNEBR. However the dynamical forecasts show a strong E-W gradient with very wet category favored for the most western regions and the dry category for the south-easternmost region.
Dynamical forecast skill assessment (Fig. 3j):
Correlations between dynamical simulations using observed SST and observed March-May rainfall, 1961-1990 range from 0.87 near and to the north of SNEBR to 0.59 in the northwestern most region. The skill level is similar to or slightly higher the empirical forecasts.
6. Overall Summary
SNEBR + regions 5,9,10: The regression, discriminant analysis and dynamical forecasts are all for the AVERAGE category. Therefore, our best estimate for these regions is for the AVERAGE category.
Regions 1,2,3,4,6,7: The empirical forecasts favor the AVERAGE category in all but region 6. The dynamical forecasts favor the WET or VERY WET category. While there is some variation in the forecasts for these regions, there is no clear pattern so our best estimate is for the WET category for all these regions; a compromise between the different forecast input.
Region 1: The empirical forecasts favor the AVERAGE category and the dynamical forecasts the DRY category. We prefer the dynamical forecasts for this region because the dynamical forecast skill (r=0.74, Fig. 4j) is slightly higher than empirical forecast skill (r=0.68, Fig.3k) and may be showing predictability not represented by the empirical forecasts. Hence, our best estimate is for the DRY category based on the dynamical forecasts.
The forecast methods are in agreement for SNEBR but not for some of the other regions. The empirical predictor signal is weak so confidence in the forecast is moderate for SNEBR and LOW for elsewhere.
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 of Dec-Feb, Jan-Feb and Feb SST is:
+0.41 standardised units (in Quint category 4 relative to 1951-1980 or Quint 3 relative to 1961-1990, 1951-1980 Quint 4 boundaries= 0.15 to 0.67, 1961-1990 Quint 3 boundaries= -0.14 to 0.48 )
Probabilities calculated from the same data using discriminant analysis are for the 5 (1951-80) quint categories:
| Very Dry | Dry | Average | Wet | Very Wet |
| 0.10 | 0.13 | 0.26 | 0.23 | 0.28 |
and for 5 (1961-90) quint categories:
| Very Dry | Dry | Average | Wet | Very Wet |
| 0.9 | 1.18 | 0.42 | 0.24 | 0.07 |
The best estimate FQ forecast is for the WET quint with respect to 1951-80 and For the AVERAGE quint with respect to 1961-90.
Reference:
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.
Figure 1: SST EOF time series used as predictors. *marks February values
Figure 2: Forecast Regions
Figure 3: Empirical forecasts for March-May 2001 and forecast Skill
Figure 4: Dynamical forecasts for March-May 2001 and forecast skill
