Linear Regression Forecast of
Central England Temperature for July-August 1998
contributed by Andrew Colman
Hadley Centre for Climate Prediction and Research
UK Meteorological Office, Bracknell, United Kingdom
The UK has had some notable exceptionally warm summers in recent years prompting the question: Are seasonal summer temperatures in this region predictable? At the UK Meteorological Office empirical techniques using global scale patterns of historical sea surface temperature anomalies (SSTA) have been used successfully to make experimental predictions of seasonal rainfall in NE Brazil, tropical NW Africa and E Africa (Ward et al. 1993; see also recent March and June issues of this Long-Lead Bulletin). The problem of predicting UK climate is more difficult than that of predicting rainfall in these tropical regions: however there is some evidence that UK climate may be predictable from SST (e.g. Ratcliffe and Murray 1970, Palmer and Sun 1985).
Colman (1997) and Colman and Davey (1998) have found a statistical link between the pattern of north Atlantic SSTA in January and February and the nature of the subsequent summer in NW Europe. They found that summer temperature in NW Europe and to a lesser extent pressure and rainfall to be linearly related to the time series of the leading eigenvector of January-February north Atlantic SSTA. The leading eigenvector (Fig. 1) is the pattern which explains the most SSTA variability over the period 1901-1990 and the time series is a measure of the strength and sign of this pattern in the SSTA for individual winters. The time series is used as the independent variable in a linear regression equation to predict the subsequent July-August average Central England Temperature (CET). CET is a homogenised temperature series from 1659 to the present, first put together by Manley (1974) and updated by Parker et al. (1992) and is a good indicator of English temperature.
Similar predictions of July-August average Central England Temperature (CET) from the winter SSTA data for 1996 and 1997 were published in this bulletin (Colman & Davey, 1996,1997). The following table shows the forecast and observed values:
|
Year |
Forecast |
Observed (°C) |
|
1996 |
15.4 |
16.5 |
|
1997 |
15.25 |
17.6 |
The forecast standard error is 1.1°C and the standard deviation of observed CET 1.2 °C. These forecasts were disappointing though the 1996 forecast was just within 1 standard error of the observed value.
To provide an example of likely forecast skill, inflated regression predictions have been made for 1956-1996, using the 'jack-knife' technique. They are plotted against observed values in Fig.2. The forecasts are plotted as temperature ranges showing the standard error of the forecasts. The term 'jack- knife' refers to forecasts being made for each year using a regression equation from which the year being forecast is excluded. The subsequent two years are also excluded, as these may be related to the forecast year through persistence. The term 'inflation' indicates that a scaling factor is applied to match the variance of the predictions to that of the observed predictand. The correlation of 0.56 for 1956- 1996 is very high, considering the 6-month lead time, and compares well with other long lead extratropical statistical prediction skills (e.g. Barnston 1994).
The correlation between the January-February SST predictor and summer CET is significantly different from zero even when data back to 1871are used. The temporal correlation between the predictor time series and July-August CET over the period 1871-1995 is 0.44, which is significant (different from zero) at the 99.9% level.
An experimental forecast has been made using the regression scheme described above. To make the forecast, regression equations were made for the 117 training periods that start between 1871 and 1987 inclusive and end in 1997. 117 Predictions for 1998 were made using all 117 equations projected on to January-February 1998 data. A weighted average of these predictions was calculated, the weight being the variance explained by each equation (calculated as the dependent data correlation squared multiplied by the number of years used to calculate the equation) . A weighted mean standard error was also calculated in a similar way from the same regression equations.
The forecasts from the 117 candidate equations varied between 17.0 and 17.3 °C with the weighted average at 17.13 °C, about 1.2 °C above the 1961-90 average. The mean standard error was 1.1 °C. The forecast for 1998 is 17.1 °C +/- 1.1 °C.
NOTE: this forecast is experimental, and should be regarded with caution as the physical mechanism behind this apparent predictability is not fully understood. The method should be regarded as developmental, and practical use is not recommended.
REFERENCES
Barnston A.G., 1994: Linear statistical short-term climate predictive skill in the northern hemisphere. J.Climate, 7,1513-1564.
Colman, A.W. 1997: 'Prediction of summer central England temperature from preceding north Atlantic winter sea surface temperature.' Int. J. Climatol., 17, 1285-1300.
Colman, A.W. and Davey, M. 1996: 'Linear regression forecast of central England temperature for July-August 1996. Long lead Bull., 5, no.2 published by NOAA/ NWS USA.
Colman, A.W. and Davey, M. 1997: 'Linear regression forecast of central England temperature for July-August 1997. Long lead Bull., 6, no.2 published by NOAA/ NWS USA.
Colman, A.W. and Davey, M. 1998: 'Prediction of summer temperature, rainfall and pressure in Europe from preceding winter north Atlantic ocean temperature.' Submitted to Int. J. Climatol.
Manley G., 1974: Central England Temperatures, monthly means 1659 to 1973. Q.J.Roy.Met.Soc., 79, 242-261.
Palmer T. and Z. Sun, 1985: A modelling and observational study of the relationship between sea surface temperature in the northwest Atlantic and atmospheric general circulation. Q.J.Roy.Met.Soc., 111, 947-975.
Parker D.E., T.P. Legg and C.K. Folland, 1992: A new daily Central England Temperature series, 1772-1991. Int. J.Climatol., 12, 317-342.
Ratcliffe R.A.S and R. Murray, 1970: New lag associations between north Atlantic sea temperatures and European pressure, applied to long-range weather forecasting. Q.J.Roy.Met.Soc., 96, 226-246.
Ward M.N., C.K. Folland, K. Maskell, A.W. Colman, D.P. Rowell and K.P. Lane, 1993: Experimental seasonal forecasting of tropical rainfall at the UK Meteorological Office. In: 'Prediction of interannual climate variations', NATO ASI vol 16, pp 197-216.
FIGURE CAPTIONS:
Fig. 1: The predictor SST leading eigenvector pattern, based on 1901-1990 January-February sea surface temperature anomalies in the North Atlantic. Observed SST anomalies are projected onto this pattern to obtain a predictor value for the corresponding year. Positive (negative) predictor values are associated with warmer (colder) Central England temperature.
Fig. 2: July-August Central England Temperature, as observed (diamonds) and as forecast (vertical bars showing standard errors) using linear regression and January-February North Atlantic sea surface temperature anomalies, for 1956-1998.