Empirical Prediction of the Global Temperature Anomaly for 2001

contributed by Chris Folland and Andrew Colman

Met Office, Bracknell, United Kingdom

1. Introduction

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

We use three forms of multiple linear regression to make these forecasts (a) using predictors based on physical understanding which are forced into the regression (b) an orthogonalized version where empirical orthogonal functions of the predictor time series are used instead and (c) a modified version where one of the predictors is a forecast of SST anomaly in the Niño3.4 region of the Tropical Pacific. The latter was chosen to be the forecast made by the US National Center for Environmental Prediction (NCEP) coupled ocean-atmosphere global circulation model. This model was chosen as it is possible the assess the intrinsic skill of the method from published hindcasts and previous forecasts.

1.1 Predictors

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

a) IHC: The Inter-Hemispheric Contrast (IHC) index (sometimes known as the Atlantic Multidecadal mode). This is used in the form of the time series of the second covariance eigenvector of low frequency global SEA SURFACE TEMPERATURE ANOMALIES (SSTA) for 1911-1995 as described in Folland et al (1999). (This index is highly correlated to rainfall in the Sahel on decadal time scales).

b) ENSO HF1: The High Frequency El Niño Southern Oscillation index 1 (ENSO HF 1). This is the time series of the first covariance eigenvector of high frequency (<13 years) global SSTA for 1911-95 in Folland et al (1999). This eigenvector pattern is related strongly to ENSO.

c) ENSO HF2: The High Frequency El Niño Southern Oscillation index 2 (ENSO HF 2). This 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. This pattern is also from Folland et al (1999).

d) VOLCANO: 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) SOLAR: An index of solar irradiance (SOLAR) as supplied by Lean (Frohlich & Lean, 1998) and extrapolated to the present.

f) GSO: An estimate of the global mean anthropogenic net radiative forcing at the tropopause. This comes from changing concentrations of 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) NCEP NINO 4: In one forecast, predictions of the Nino3.4 area (170-120^oW, 5^oN-5^oS) SST anomaly made by the NCEP coupled ocean-atmosphere global circulation model (NCEP NINO3.4) are used. This replaces ENSO HF1 in the previous equation, and no ENSO HF2 index is used.

The North Atlantic Oscillation does not contribute significantly in the regression method mostly probably because there are large areas of negative as well as positive anomalies. Similarly the Interdecadal Pacific Oscillation or the very similar Pacific Decadal Oscillation does not contribute because it is highly correlated with ENSO. Future work will investigate this in more detail as small residual effects on global temperature may exist.

We chose 1950-1999 as our training period because the predictor and predictand data are best at that time. Soon, advances in data sets might allow this period to be substantially extended. In the cross validation skill testing method, we allow for serial correlation on the interannual time scale as described below. The multiple regression equations include December data of the prior year (unlike the forecast issued for 2000, which used multiple regression forecasts based on data to November of the previous year).

Predictor data for the following periods are used. The examples are for the 2001 prediction.

IHC-- October-December 2000

ENSO HF1-- October-December 2000

ENSO HF2-- October-December 2000

VOLCANO-- December 2000 (extrapolated from data ending in 1997 assuming no significant recent activity)

SOLAR-- January-December 2000 (Extrapolated from data up to 1998 by Lean allowing for the solar cycle (pers. comm.)

GSO-- January-December 2000

NCEP NINO3.4-- January-June 2001 (used in place of ENSO HF1 )

Note: December 2000 SSTA are based only on observations from 2nd-11th December. In real-time forecasts this data is persisted for the whole month.

The predictor periods chosen were selected to extract maximum available skill from data available at the time of the forecast. Updating to December is only influential for SSTA based predictors. So far, no investigation of the optimum lags have been made concerning the radiative forcing data predictors, which are based on the prior year.

1.2 Predictand

The predictand is mean global land and sea surface temperature anomalies relative to 1961-90 for the forthcoming year. This chosen to be the IPCC Third Assessment Report optimally averaged series produced by the Hadley Centre and the Climatic Research Unit (Folland et al, 2001). This represents a change from the forecast for 2000. That forecast used the non-optimally averaged IPCC(1996) data based on Jones (1994) and Parker et al (1995). The IPCC(1996) method was based on the weighted averaging of available 5^o latitude x5^o longitude areas. In principle this had the problem that the weighting of the land relative to the ocean tended to be slightly too small because of a greater fraction of data gaps over land due to non receipt of data or lack of stations. Antarctica was particularly under-weighted. Optimum averaging objectively allows for data gaps as well as observational uncertainties. The changes in annual global mean temperature anomalies for recent years are, however, small.

1.3 Forecast Method

Three forecasts are made using multiple linear regression (METHODS 1-3). A global temperature anomaly forecast is produced by applying each regression equation to the predictor indices described above. All regression equations use historical data for 1950-1999. The three regression equations are:

1. An equation using predictors a-f of section 1.1, calculated using data for 1950-1999.

2. An equation using predictors a-f, orthogonalized using data for 1950-1999.

3. A modified method using NCEP couple model forecasts of the NINO3.4 SSTA index for January-June of 2001 instead of observations of HF ENSO EOF 1 for late 2000. The NCEP forecast is corrected for bias compared to observations estimated from 18 model hindcasts from 1982-1999.

The forecast from each model is modified to use "inflated" linear regression to retain the same forecast as observed variance. However because of the high correlation skill of these methods, the level of inflation is small. The Forecast Probability Distribution Function (FPDF) for each method is based on the assessed standard errors of the regression predictions, assuming the forecast errors are normally distributed.

1.4 Assessment Methods

To estimate forecast skill, trial forecasts (hindcasts) were made using the jack-knife method in a fairly severe way. Jack-knife forecasts were made for every year in the data period used to create the forecast equations using equations calculated using the majority of the remaining years in that period. Thus the coefficients of the predictors change from year to year but the predictors do not. The forecast year is always excluded from the regression equation, along with data for the 5 years before and 5 years after the forecast year. During the first and last five years of the data period only a one sided exclusion of data is possible. This process minimizes artificial hindcast skill due to persistence.

In real time forecasts, we only have an estimate of December SST up to about December 10th. To account for this, December values are only given a 50% weight relative to October and November values when calculating the October-December SSTA indices used in the hindcasts. Two measures of forecast skill are used:

(a) Correlation: Standard (Pearson) Correlation. This 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 correlation). The latter calculates correlations on time scales less than about 10 years.

(b) RMS (Root Mean Square error): RMS scores are very appropriate as the forecast standard deviation is equal to that observed.

We intend to introduce other skill measures in future.

2. Performance of hindcasts, 1950-1999 using optimally averaged global temperature estimates.

2.1 Jack-knife forecast skill from the non orthogonalized predictors.

Jack-knife multiple regression forecasts are plotted against observed global temperatures in figure 1 for Method 1. The jack-knife correlation of 0.94 is very high for a climate prediction scheme. Because an important aim of the forecasts is to indicate how next year will differ from this year, the high frequency correlation of 0.67 gives a more realistic estimate of skill on this time scale. Nevertheless the excellent reconstruction of the low frequency would only be possible if the shape of the low frequency forcing had been captured well. So our technique to some extent corroborates estimates of the time-dependent shape of the total net radiative forcing that we use. However, as long as the shape of such forcing is well captured, our method would not be sensitive to the overall magnitude of radiative forcing change. In Figure 1, 40% and 95% confidence intervals are plotted in green and the best estimate forecasts in red.

Table 1 shows the contributions of the different predictors in Method1. The regression equation is built up in a stepwise manner, with predictors incorporated in order using the results of an F test. The importance of each predictor is shown by the standardized regression coefficient. This is the coefficient estimated when both predictor and predictand index are standardized. Bold numbers show the skill of the complete regression equation.

Table 1 performance of jack-knife hindscasts 1950-1999 adding 1 predictor at a time, using six non-orthogonalzed predictors (Method 1)

The strongest predictor (over 1950-1999), the GSO index , predicts the warming trend this century and the accelerated warming over the past 30 years but does not predict variability on time scales less than 20 years. The second predictor, ENSO HF 1, contributes most to interannual skill. The third predictor, VOLCANO, is important only during the 2 or 3 years following a major eruption. It is negligible in the 2001 forecast.

2.2. Jack-knife forecast skill from the orthogonalized predictors and the NCEP NINO3.4 predictions.

Table 2 summary performance of jack-knife forecasts using orthogonal predictors and using NCEP NINO3.4 SST forecasts as a predictor.

The skill of the orthogonalised predictor forecasts is similar to that of METHOD1 while the NCEP Nino3.4 forecasts give slightly less skill. However, the latter assessments are substantially less reliable due to the short period of testing.

2.3 Assessment of forecast for 2000 (Folland & Colman, 2000)

The forecasts for 2000 were expressed as the boundaries corresponding to the following values of the cumulative probability of the forecast, tarting at the coldest level:

The forecast was made using the IPCC(1996) temperature data so is assessed using that data. The mean forecast anomaly of 0.41^oC was based on an equally weighted average of the three methods. The observed anomaly is likely to be about 0.32 or 0.33 ^oC, so the 2000 forecast was a little too warm, mainly because the methods implicitly or explicitly assumed a quicker decline of the current La Niña than has occurred, particularly the NCEP model. The error of near 0.09^oC is nevertheless well within the 95% confidence range. We were correct in giving a very low probability that 2000 could be the warmest year. 2000 is likely to be the 5th or 6th warmest year in the IPCC (1996) record. Our forecast was for the third warmest year.

3. Forecast for 2001 .

The best estimate forecasts of global temperature anomaly made by the three methods were:

1. Using six empirical predictors including observed ENSO INDEX, Oct-Dec 2000-0.51 ^oC

2. As above but using orthogonalized predictors-0.51 ^oC

3. As 1 but using NCEP NINO3.4 SST forecast for January-June 2001-0.44^oC

The associated probability forecasts are expressed as the boundaries corresponding to the following values of the cumulative probability of the forecast, starting at the coldest level. The mean and standard deviation is calculated by weighting the forecasts according to their intrinsic skill as measured by variance explained in the cross validated tests.

Our best estimate forecast of the global temperature anomaly for 2001 is 0.47+-0.14 ^oC, a 95% confidence range from 0.33 ^oC to 0.61 ^oC. The best estimate forecast would be the second warmest year in the record. There is about a 95% probability that 2001 will be warmer than the provisional 2000 anomaly of 0.32 or 0.33^oC. There is about a 5% probability that 2000 will be as warm or warmer than the warmest year, 1998 (0.59^oC in the Folland et al, 2001, data set).

Warning: the accuracy of this forecast depends on the development of a relatively strong El Niño in 2001. At the time this forecast was issued, the 1998-2000 La Niña was quite weak but no longer declining.

References

Folland, C.K & Colman, A.W. 2000. Empirical Prediction of the global temperature anomaly for 2000. Experimental Long Lead Forecast Bulletin 9 1 published by COLA, USA, www.iges.org/ellfb

Folland, C.K., Parker D.E., Colman AW. 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.

Folland, C.K, N.A. Rayner, S.J. Brown, T.M. Smith, S.S. Shen, D.E. Parker, I. Macadam, P.D. Jones, R.N. Jones, N. Nicholls and D.M.H. Sexton, 2001: A comprehensive analysis of global temperature change and its major uncertainties since 1861 (Submitted to Nature).

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.

Jones, P.D., 1994: Hemispheric surface air temperature variations: a reanalysis and an update to 1993, J. Climate, 7:1794-1802.

Parker, D.E., C.K. Folland, and M. Jackson, 1995: Marine surface temperature: observed variations and data requirements, Climatic Change, 31:559-600.

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.

Figure 1: Jack-knife hindcasts of optimally averaged global mean temperature anomalies for 1950-1999 (red) and forecasts for 2000 and 2001 (blue) using method 1. The black line represents observations based on optimal averages. The 40% and 95% confidence intervals are marked by lines in green.