Empirical Prediction of the Global Temperature

Anomaly for 2000



contributed by Chris Folland and Andrew Colman

The Met Office, Bracknell, United Kingdom



1. Introduction

Global temperature is an important indicator of global climate, and which has been at record levels in recent years. Analysis of observed and model data has linked interannual to decadal fluctuations in global temperature to various natural phenomena including ENSO, volcanic activity and, solar flux variability,. Global temperature change has also been linked to human activity including and well-mixed greenhouse gas and aerosol emissions caused by human activity, and stratospheric ozone depletion and tropospheric ozone increases. The existence of these numerous links raises the possibility of skilful predictions of global temperature. In this study, indices of the known important climate phenomena forcings and influencing phenomena are used to make empirical predictions of the global temperature anomaly from a 1961-90 average. On the interannual time scale, the state of ENSO is the most important predictor. On the multi-decadal time scale, the net change in the radiative forcing of the atmosphere is most important.

We have used multiple linear regression to make these forecasts. We use three forms (a) where predictors based on physical understanding are forced into the regression (b) an orthogonalised version where empirical orthogonal functions of the predictor time series are used instead and (c) where one of the predictors is a forecast of SST anomaly in the Nino3.4 region of the Tropical Pacific. The latter was chosen to be the forecast by made by the US National Center for Environmental Prediction (NCEP) coupled ocean-atmosphere global circulation model.



1.1 Predictors

The six predictors selected and listed below have been identified by more than one author to be related to large-scale temperature:

a) The Inter-Hemispheric Contrast (IHC) index which is the time series of the second covariance eigenvector of low frequency global SST for 1911-1995 in Folland et al (1999). This index is also highly correlated to rainfall in the Sahel on decadal time scales.

b) The High Frequency El Niño Southern Oscillation index 1 (ENSO HF 1) is the time series of the first covariance eigenvector of high frequency (<13 years) global SST for 1911-95. This eigenvector pattern is clearly strongly ENSO related.

c) The High Frequency El Niño Southern Oscillation index 2 (ENSO HF 2) is the time series of the second covariance eigenvector of high frequency (<13 years) global SST. This eigenvector pattern is also ENSO-related, but the time series is 6-9 months out of phase with HF ENSO 1. These patterns are also in Folland et al (1999).

d) An index of global volcanic dust cover (VOLCANO) produced by Sato et al (1993). Dust veils from major volcanic eruptions, particularly in the tropics, lead to a significant drop in global temperature for a year or two after the eruption.

e) An index of solar irradiance (SOLAR) as supplied by Lean (Frohlich & Lean, 1998).

f) An estimate of the global mean net radiative forcing at the tropopause from well-mixed anthropogenic greenhouse gases, the direct and indirect effects of sulphate aerosol emissions and from stratospheric and tropospheric ozone concentration changes (GSO). This index was calculated using the Hadley Centre's current Coupled Ocean-Atmosphere general circulation model, HADCM3. It is expressed as the annual mean forcing at the top of the troposphere in wm-2 (Johns, personal communication).

g) In some one of the of the forecasts, predictions of the Nino3.4 area (170-120oW, 5oN-5oS) SST anomaly made by the NCEP coupled ocean-atmosphere global circulation model (NCEP NINO3.4).

Over the jackknife testing period, 1949-1998, our knowledge of the state of the North Atlantic Oscillation in the current year did not add skill. Tests also showed that the current state of the Interdecadal Pacific Oscillation added no interannual skill over and above that of ENSO. We chose this period because the predictor and predictand data are best then, though in the near future, current advances in data set analysis might allow this period to be substantially extended.



Predictor data for the following periods are used. The examples given are for the prediction for 2000.

IHC September-November 1999

ENSO HF1 September-November 1999

ENSO HF2 September-November 1999

VOLCANO November 1999

SOLAR January-December 1999

GSO December 1998 - November 1999

NCEP NINO3.4 January-June 2000 (used in place of ENSO HF1)



The predictor periods chosen were selected to extract the maximize available skill from data available at the time of the forecast. Note that for the observed predictors, use of predictor values simultaneous with the forecast in the training equations did not produce more than a marginal increase of skill. Use of such predictors in real time would also involve estimating them in the year ahead. So only observed predictor values are used, except for the small annual SOLAR radiation index which can be estimated quite accurately for the current year.. So far, no lags have been introduced into the radiative forcing data predictors other than an effective lag of about one year due to the choice of predictor values that centre on middle of the year prior to that being predicted. This will be investigated in future.



1.2 Predictand

The predictand variable is mean global land and sea surface temperature for the forthcoming year chosen to be the IPCC series produced by the Hadley Centre and the Climatic Research Unit. Anomalies from the 1961-90 average are predicted.



1.3 Forecast Method

Three Forecasts are made using multiple linear regression. A global temperature forecast is produced by applying the regression equation to the 86 predictor indices described above. Two of the regression equations are calculated using historical data for 1949-1998 while the third uses 1899-1998. The three regression equations are:

(i) An equation using predictors a-f, calculated using data for 1949-1998.

(ii) An equation using predictors a-f, orthogonalised using data for 1949-1998.

(iii) Equation a), but using ENSO HF1 index for January-June of the forecast year. The value for 2000 is estimated from the NCEP NINO3.4 forecast. NINO3.4 is the place where HF ENSO EOF1 has most weight. The prediction equation is calculated using data for the extended period 1899-1998, simply because this was the form available and tested by the time of this forecast. No NAO or Interdecadal Pacific Oscillation index was included for this longer period, in common with the 1949-98 period.

The forecast from each model is made using inflated linear regression, though because of he high correlation skill, the level of inflation is small. The Forecast Probability Distribution Function (FPDF) is calculated based on the standard error of the regression predictions on dependent data and assuming the forecast errors are normally distributed.



1.4 Assessment Methods

To estimate likely forecast skill, trial forecasts (hindcasts) were made using the Jackknife method in a fairly severe way. Jackknife forecasts were made for every year in the data period using equations calculated using the majority of the remaining years in the data period. Thus the coefficients of the predictors in the equations change from year to year but the predictors themselves do not as they have been chosen a priori on physical grounds. The forecast year is always excluded from the regression equation, along with data for the 5 years before and after the forecast year. During the first and last five years only a one sided exclusion of data is possible. This process minimises artificial hindcast skill due to persistence.

Two measures of forecast skill are used:

(a) Correlation: (Pearson) Correlation ignores biases between forecast and observed values and the difference in standard deviation between the forecast and the observed value. We use a total correlation score (Correlation) and a high frequency correlation (HF corr.). The latter calculates correlations on time scales less than about 10 years.

(b) RMS (Root Mean Square error): RMS scores can be misleading when the forecast standard deviation is different from the observed, but this is not true here.



2. Performance of Hindcasts, 1949-1998



2.1 Jackknife Forecast Skill from the non orthogonalised predictors

Jackknife multiple regression forecasts are plotted against observed global temperatures in figure 1. The correlation of 0.91 is very high for a climate prediction scheme, though this includes the substantial low frequency component in the predictions and predictand. Because an important aim of the forecasts is to indicate how next year will differ from this year, the high frequency correlation of 0.73 gives a more realistic estimate. Nevertheless the excellent reconstruction of the low frequency would only be possible in an empirical method if the shape of the low frequency forcing had been captured well. 20% and 40% confidence intervals are plotted as dotted lines alongside the best estimate forecasts.

In Table 1 the contribution of the different predictors is displayed. The regression equation is built up in a stepwise manner, with predictors added in order of importance. Importance is measured by the magnitude of the regression coefficient when all predictor and predictand series are standardised. These "standardised" regression coefficients are shown in table 1. The bold numbers show the skill of the complete regression equation.

The strongest predictor, the GSO index (red line), predicts the warming trend this century and the accelerated warming over the past 30 years but does not predict any variability on timescales less than 20 years. The second predictor is HF ENSO, which predicts variability on the 2-7 year timescale. The third predictor, VOLCANO, is important only during the 2 or 3 years following a major eruption.



2.2 Jackknife forecast skill from the orthogonalised predictors and from the NCEP NINO34 predictions.

The RMS skill from the NCEP model is hard to estimate from the limited hindcasts so we have provisionally used the mean values from the long tests of the empirical methods in the final forecast (+-0.16). In Table 2, the skill of the orthogonalised predictor forecasts and the forecasts using the NCEP Nino3.4 forecasts is quite similar to the skill of the non-orthogonalised predictors shown in table 1, though the assessments of forecasts using the NCEP NINO 3.4 predictions are substantially less certain due to the short period of testing.



2.3 Totally independent test for 1999:

This is a severe test, as the change in observed temperature from 1998 to 1999 was the largest since 1949, at about 0.25 oC.

We first list the best estimate forecasts of global temperature anomaly from the 1961-1990 average made by the three methods:



1. Using 6 empirical predictors and observed ENSO index, SEPT-NOV 1998- 0.36 oC

2. As above but using orthogonalised predictors-0.36 oC

3. As 1 but using NCEP NINO3.4 SST hindcast for January-June 1999 instead of HF ENSO 1 for Sep-Nov 1998-0.43 oC



The associated probability forecasts are now expressed as the boundaries corresponding to the following values of the cumulative probability of

the forecast, starting at the coldest level:
20% 40% 50% 60% 80%
Method 1 0.29 0.34 0.36 0.38 0.42
Method 2 0.29 0.34 0.36 0.38 0.43
Method 3 0.33 0.40 0.43 0.46 0.53
Mean 0.30 0.36 0.38 0.41 0.46



The forecast anomaly is 0.38oC and the observed anomaly is likely to be about 0.33 oC, so our 1999 hindcasts will be a little too warm, mainly because of the NCEP model hindcast, but an observed value of 0.33 oC (if confirmed) will be within the 20-80% confidence interval for all 3 forecasts. 80% of the observed fall in temperature was captured by the 1999 hindcast, and rather more by the empirical methods



3. The Forecast for 2000

We first list the best estimate forecasts of global temperature anomaly from the 1961-1990 average made by the three methods :



1. Using 6 Empirical Predictors and observed ENSO INDEX, Sept-Nov 1999-0.39 oC

2. As above but using orthogonalized predictors- 0.39 oC

3. As 1 but using NCEP NINO3.4 SST Forecast for January-June 2000 Instead of HF ENSO 1 for Sep-Nov 1999-0.46 oC



The associated probability forecasts are now expressed as the boundaries corresponding to the following values of the cumulative probability of the forecast, starting at the coldest level:

.
20% 40% 50% 60% 80%
Method 1 0.32 0.37 0.39 0.41 0.45
Method 2 0.32 0.37 0.39 0.41 0.46
Method 3 0.36 0.43 0.46 0.49 0.56
Mean 0.33 0.39 0.41 0.44 0.49



Our overall best estimate forecast of the temperature anomaly for the year 2000 is 0.41+-0.16 oC, or a range from 0.25 oC to 0.57 oC based on the intrinsic skill of the empirical hindcasts. The uncertainty +-0.16 oC represents approximately the 5% and 95% confidence limits of the individual forecasts. Thus there is about an 80% probability that 2000 will be warmer than 1999 but just less than a 5% probability that 2000 will be as warm or warmer than the warmest year, 1998.



References:

Folland, C.K., Parker D.E., Colman A. and R. Washington, 1999: Large scale modes of ocean surface temperature since the late nineteenth century. Chapter 4, pp73-102 of Beyond El Niño: Decadal and Interdecadal Climate Variability. Ed: A. Navarra. Springer-Verlag, Berlin, pp 374.

Frohlich, C. and Lean, J. 1998: The sun's total irradiance: cycles, trends and related climate change uncertainties since 1976. Geophysical Res. Lett., 25, pp 4377-4380.

Sato, M., J.E. Hansen, M.P. McCormick and J.B. Pollack, 1993: Stratospheric aerosol optical depths, 1850-1990. J. Geophys. Res., 98, 22987-22994.



Table 1 Performance of jackknife hindcasts 1949-1998 Adding 1 Predictor at a time, using six non-orthogonalsed predictors
Predictor added Standardised Coefficient Correlation

1949-1998

 HF Corr.

1949-98

 RMS

1949-98

 RMS S.U.
GSO 0.82 0.78 0.11 0.132 0.731
ENSO HF 1 0.33 0.83 0.55 0.108 0.600
VOLCANO -0.27 0.83 0.63 0.105 0.582
SOLAR 0.21 0.85 0.65 0.100 0.553
IHC -0.19 0.89 0.65 0.083 0.460
ENSO HF 2 -0.10 0.91 0.73 0.079 0.439



Table 2 summary performance of jackknife forecasts using orthogonal predictors and using NCEP NINO3.4 SST Forecasts as a predictor.
Predictors Assessment Period Correlation HF Corr. RMS oC RMS S.U.
Orthogonal 1949-1998 0.90 0.72 0.079 0.438
ENSO represented by 1982-1998 0.86 0.119 0.539