Statistical Prediction of March-May 1999 Rainfall in Northeast Brazil from SST up to the end of January using Linear Regression and Discriminant Analysis
contributed by A. Colman, M. Davey
UK Meteorological Office, Bracknell, United Kingdom
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. This year the forecast format has been updated to be a better representation of the empirical and dynamical forecasting methods used and to fit with proposed WMO guidelines on forecast assessment. This empirical forecasting scheme was originally developed by Ward and Folland (1991).
These statistical forecasts were produced concurrently with dynamical Global Circulation Model predictions discussed by Evans and Graham in this issue of the Bulletin. The forecast summary uses input from the dynamical and statistical forecasts.
New developments include:
1) 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.
2) The forecast region has been extended to cover grid points between 2.5N and 10S and west to 50W. Predictions of the March-April Hastenrath and the February-May Nobre rainfall indices (see past March issues of Bulletin) are being discontinued.
3) Included with the 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).
4) For the convenience of users, the forecasts are presented in graphical and in tabular text form. This enables the forecast to be emailed in text form to those who do not have the facility to browse graphics.
Predictors
The statistical forecast is based on the same predictors as previous forecasts; (see Bulletin March issues 1993 to 1998). The predictors are (1) the 30N-30S portion of the third covariance-based EOF of Atlantic SST for all seasons, and (2) the first Empirical Orthogonal Function (EOF) of Pacific SST for Dec-Jan-Feb. These two patterns (fig. 1), have been used to make statistical regular real-time predictions of NE Brazil seasonal rainfall. 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 1961-1990] rainfall amount categories).
This year, La Niña conditions in the Pacific and below average sea temperatures in the North Tropical Atlantic statistically favor above average rainfall in NE Brazil, while below average SST in the Tropical SE Atlantic and above average SST in the SW Atlantic near the Rio Grande weakly favor below average rainfall.
The predictor time series for the last six months are shown in Table 1 and the time series values since 1991 are plotted in figures 2a and b.
Northern Brazil Regions
This year, our forecast area has been enlarged following research at UKMO which has found predictability to extend well to the west of the region for which forecasts have previously been issued.
Our forecast area consists of 12 rectangular regions each covering 3.75 deg longitude x 2.5 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 gridded 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 50W, northward to the equator and south to 10S. 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 39.375W, 6.25S 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 categorised into five equiprobable categories (over 1961-1990) called quints and referred to as Very Dry, Dry, Average, Wet and Very Wet Quints.
The Forecasts
The forecasts consist of probability forecasts made using historical data back to 1913. Probability forecasts are produced using discriminant analysis and deterministic forecasts are produced using linear regression.
The forecasts and assessments in the tables are also displayed in graphical format on maps in figure 3 a-l.
Probability Forecast Summary:
For most regions including SNEBR, the highest probability is for the average or wet category, region 10 is an exception where the probability distribution is strongly bimodal. A very dry season is very unlikely in all regions but the probabilities for the dry and average categories combined are mostly higher than the probabilities of the wet and very wet categories combined.
Regression Forecast Summary:
The linear regression forecasts favor the wet category for SNEBR and most nearby regions. The regressions show a clearer signal of above average rainfall than the discriminant predictions which indicate just a small bias towards above average rainfall.
Prediction Skill
Probability forecasts produced using discriminant analysis 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.
RMSSS 100*( 1- RMS error (forecasts)/ RMS error persistence) (persistence refers to persistence from the previous year's rainfall season)
Assessments were made using the "Jackknife" technique where prediction equations are calculated using data for the whole period minus the predicted year and the two years subsequent to the predicted year. The two subsequent years are excluded to remove positive skill bias due to persistence. Assessments were also made for the 1981-1998 period using data from 1912-80. There is an overlap of the SST EOF analysis period (1901-80) and the first evaluation period (1948-1997) but the second evaluation period is completely independent of the SST EOF analysis.
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 continued.
The linear regression forecast based on an average Nov-Jan, Dec-Jan and Jan SST is:
+0.84 standardised units (in Quint category 5 relative to 1951-1980, Quint 4-5 Boundary 0.71)
(or Quint 4 relative to 1961-90 climatology, Quint 4-5 boundary 1.03, Quint 3-4 boundary 0.48)
Probabilities calculated from the same data using discriminant analysis are for the 5 (1951-80) quint categories shown in Table 5 and for 5 (1961-90) quint categories in Table 6.
Note: The FQ forecast is for the very wet quint with respect to 1951-80 and in the wet quint with respect to 1961-90. This is because it was wetter in Brazil overall over the period 1961-90 than over the period 1951-80. The FQ forecast is quite close to the SNEBR forecast when assessed according to the 1961-90 climatology.
Overall Summary
For our overall best estimate, dynamical predictions (see Evans et al., this issue) were considered as well as statistical predictions.
SNEBR: All the forecast types indicate above average rainfall in this region. The discrimimant analysis and regressions both indicate that the wet quint category is most likely. Hence, the best estimate for this region is for the WET category with MODERATE confidence as forecasts show good agreement.
OTHER REGIONS: The dynamical and linear regression forecast agree on above average rainfall everywhere but the discriminant forecasts show above chance probabilities of the average or dry quint in several regions. Our best estimate for all the regions is for the WET category but due to differences between the discriminant forecasts and the other forecasts, confidence for the region 1,2 and 10 forecasts is LOW while confidence for the remaining region forecasts is MODERATE.
Note: These forecasts are experimental and should be used with caution.
References
Ward, N., and V. Folland, 1991: Predictions of seasonal rainfall in north Nordeste of Brazil using eigenvectors of sea surface temperature. Int. J. Clima., 11, 711-743.
Table 1: Recent Predictor Values
|
Month |
August 98 | Sept 98 | Oct 98 | Nov 98 | Dec 98 | Jan 99 | Nov-Jan
1961-90 mean |
Nov-Jan
1961-90 SD |
| Pacific index | 1.65 | -0.22 | -1.43 | -0.11 | -2.14 | -2.75 | 0.06 | 3.51 |
| Atlantic index | -0.53 | -0.09 | 0.12 | -0.15 | 0.18 | -0.42 | -0.04 | 0.71 |
Table 2: Probability Forecasts for Regions
| Region center
No. Long Lat |
Probabilities for
Very Dry |
Dry |
Average | Wet | Very Wet |
| 1 46.875W 1.25S | 0.074 | 0.228 | 0.362 | 0.178 | 0.158 |
| 2 46.875W 3.75S
3 43.125W 3.75S 4 39.375W 3.75S 5 35.625W 3.75S |
0.074
0.093 0.077 0.083 |
0.207
0.189 0.215 0.143 |
0.344
0.359 0.348 0.266 |
0.164
0.237 0.215 0.358 |
0.211
0.121 0.145 0.151 |
| 6 46.875W 6.25S
7 43.125W 6.25S 8 *39.375W 6.25S 9 35.625W 6.25S |
0.096
0.088 0.067 0.115 |
0.153
0.197 0.159 0.129 |
0.174
0.278 0.302 0.338 |
0.400
0.212 0.344 0.179 |
0.177
0.225 0.129 0.239 |
| 10 39.375W 8.75S
11 35.625W 8.75S |
0.126
0.136 |
0.341
0.183 |
0.164
0.262 |
0.096
0.255 |
0.273
0.164 |
| chance | 0.200 | 0.200 | 0.200 | 0.200 | 0.200 |
*Marks SNEBR Region
Table 3: Deterministic Forecasts for Regions
| Region center
No. Long Lat |
Deterministic Forecasts
mm % average |
1961-90
anomaly % |
standardized
category |
Quint |
| 1 46.875W 1.25S | 1444 | 113 | 56 | Wet |
| 2 46.875W 3.75S
3 43.125W 3.75S 4 39.375W 3.75S 5 35.625W 3.75S |
993
950 870 831 |
117
119 120 123 |
64
56 59 70 |
Wet
Wet Wet Wet |
| 6 46.875W 6.25S
7 43.125W 6.25S 8 *39.375W 6.25S 9 35.625W 6.25S |
663
607 612 691 |
122
122 125 122 |
71
63 69 65 |
Wet
Wet Wet Very Wet |
| 10 39.375W 8.75S
11 35.625W 8.75S |
382
587 |
121
121 |
63
59 |
Wet
Wet |
* Marks SNEBR region
Table 4a: Forecast Assessments
| Region center
No. Long Lat |
1948-97 Jackknife skill
probability Deterministic LEPS |
correlation | RMSSS |
| 1 46.875W 1.25S | 0.246 | 0.697 | 42 |
| 2 46.875W 3.75S
3 43.125W 3.75S 4 39.375W 3.75S 5 35.625W 3.75S |
0.240
0.266 0.306 0.265 |
0.711
0.752 0.761 0.760 |
39
43 44 45 |
| 6 46.875W 6.25S
7 43.125W 6.25S 8 *39.375W 6.25S 9 35.625W 6.25S |
6.196
0.225 0.249 0.266 |
0.622
0.665 0.715 0.767 |
29
36 39 46 |
| 10 39.375W 8.75S
11 35.625W 8.75S |
0.189
0.197 |
0.522
0.645 |
28
36 |
*Marks SNEBR region
Table 4b: Forecast Assessments
| Region center
No. Long Lat |
1981-98 Independent Forecast skill
probability Deterministic LEPS |
correlation | RMSSS |
| 1 46.875W 1.25S | 0.193 | 0.789 | 44 |
| 2 46.875W 3.75S
3 43.125W 3.75S 4 39.375W 3.75S 5 35.625W 3.75S |
0.186
0.246 0.248 0.219 |
0.824
0.800 0.757 0.747 |
49
46 44 44 |
| 6 46.875W 6.25S
7 43.125W 6.25S 8 *39.375W 6.25S 9 35.625W 6.25S |
0.228
0.212 0.232 0.282 |
0.751
0.742 0.719 0.812 |
44
35 40 51 |
| 10 39.375W 8.75S
11 35.625W 8.75S |
0.185
0.207 |
0.581
0.761 |
26
46 |
* Marks SNEBR region
| Very Dry | Dry | Average | Wet | Very Wet |
| 0.035 | 0.160 | 0.102 | 0.236 | 0.467 |
| Very Dry | Dry | Average | Wet | Very Wet |
| 0.063 | 0.129 | 0.217 | 0.405 | 0.185 |
