Empirical Prediction of the Global Temperature Anomaly for 2006

 

contributed by Chris Folland & Andrew Colman

 

1.    INTRODUCTION

 

Global surface temperature (land surface air temperature combined with sea surface 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 on interdecadal time scales 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 skilful 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 two forms of multiple linear regression to make these forecasts (a) using observed or calculated predictors based on physical understanding which are forced into the regression and (b) a modified version where one of the predictors is a forecast of sea surface temperature anomaly (SSTA) in the Nino3.4 region of the Tropical Pacific. The latter was chosen to be the forecast made by the Met Office GLObal SEAsonal (GLOSEA) coupled ocean-atmosphere global circulation model. (see http://www.metoffice.gov.uk/research/seasonal/technical.html  for more about GLOSEA) .

 

 

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 (related to as the Atlantic Multidecadal mode). This is used in the form of the time series of the second covariance eigenvector of low frequency global 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 Nino 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 Nino 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)       GLOSEA NINO 3.4:  Predictions of the Nino3.4 area (170-120oW, 5oN-5oS) SST anomaly made by the Met Office GLOSEA coupled ocean-atmosphere global circulation model are used to replace the current observed ENSO state as measured by ENSO HF1 to make a second forecast..

 

 

Predictor data for the following periods are used.

 

IHC                        October-November-December (1st-11th) 2005

ENSO HF1            October-November-December (1st-11th) 2005

ENSO HF2            October-November-December (1st-11th) 2005

VOLCANO           December 2004 (extrapolated from data ending in 1997 assuming no significant recent activity)

SOLAR                  January-December 2005 (Extrapolated from data up to 1998 by Lean allowing for the solar cycle

                               (pers. comm.)

GSO                       January-December 2005

GLOSEA NINO3.4     January-April 2006 (used in place of ENSO HF1 )

 

The predictor periods were chosen to extract maximum skill from data available at the time of the forecast.

 

 

1.2 PREDICTAND

 

The predictand is mean global land air and sea surface temperature anomalies relative to 1961-90 for the forthcoming year. This is chosen to be the HadCRUT2vOA (Parker et al., 2004), the optimally-averaged successor to the IPCC Third Assessment Report optimally-averaged series produced by the Hadley Centre and the Climatic Research Unit (Folland et al, 2001).  Optimum averaging objectively allows for data gaps as well as observational uncertainties and, in the form used here, non stationarity of the global series. 

 

 

1.3 FORECAST METHOD

 

Two forecasts are made using multiple linear regression (METHODS 1 and 2). A global temperature anomaly forecast is produced by applying each regression equation to the predictor indices described above. The two regression equations are:

 

1.        An equation using predictors a-f of section 1.1, calculated using data for 1947-2005.

2.    An equation using predictors a, c, d, e, f and g of section 1.1 calculated using data for 1960-2002.  The shorter training period is used here as GLOSEA hindcasts have been produced for this period as part of the DEMETER project (see  http://www.ecmwf.int/research/demeter/ ) and are used to correct for bias in the GLOSEA forecast compared to observations.

 

The forecast from each model is modified to use "inflated" linear regression to retain the same total variance in the forecast as in the observations. However because of the high total 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. 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 to minimise artificial hindcast skill due to persistence. During the first and last five years of the data period only a one sided exclusion of data is possible. We used the following assessment metrics:

 

(a)     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. 

 

2.       PERFORMANCE OF HINDCASTS AND  FORECASTS  OF OPTIMALLY AVERAGED GLOBAL TEMPERATURE ESTIMATES

 

2.1 JACKKNIFE HINDCAST  SKILL 1947-2005

 

Jack-knife multiple regression forecasts are plotted against observed global temperatures in Figure 1 for METHOD 1. The total jack-knife correlation of 0.95 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 HF correlation of 0.69 gives a more realistic estimate of skill on this time scale. Nevertheless the excellent reconstruction of the low frequency is only possible because the shape of the low frequency forcing has 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 is not sensitive to the overall magnitude of radiative forcing change. In Figure 1, the 95% confidence interval is 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 standardised regression coefficient. This is the coefficient estimated when both predictor and predictand index are standardised.   Bold numbers show the skill of the complete regression equation.

 

 

TABLE 1 PERFORMANCE OF JACKKNIFE HINDCASTS 1947-2005 ADDING 1 PREDICTOR AT A TIME, USING SIX PREDICTORS  (METHOD 1)  

 

 

Predictor added

Standardised

Coefficient

(1947-2005)

Correlation

1947-2005

HF Corr.

1947-2005

RMS

1947-2005

     oC

RMS

Stand. Units

GSO

0.81

0.88

0.07

0.102

0.491

ENSO HF 1

0.30

0.89

0.57

0.096

0.464

VOLCANO

-0.23

0.93

0.67

0.077

0.374

IHC

0.14

0.95

0.65

0.068

0.329

SOLAR

0.12

0.95

0.66

0.066

0.317

ENSO HF 2

-0.07

0.95

0.69

0.064

0.308

 

 

The strongest predictor, 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 2006 forecast.       

 

 

 

TABLE 2  SUMMARY PERFORMANCE OF JACKKNIFE FORECASTS USING GLOSEA NINO3.4 SST FORECASTS AS A PREDICTOR.

 

GLOSEA hindcasts produced as part of the DEMETER project were used for these assessments.

 

Predictors

Assessment

Period

Correlation

 

HF Corr.

 

RMS

     oC

RMS

S. U.

Method 1

1947-2005

0.95

0.69

0.064

0.308

Method 2 (ENSO represented by

GLOSEA NINO 3.4)

1960-2002

0.96

0.81    

0.057

0.289

 

The skill of the 2 methods is quite similar, but the forecasts using GLOSEA Nino3.4 predictions are better at predicting the higher frequency variability over 1960-2002.

 

 

2.2 ASSESSMENT OF FORECAST FOR 2005 (http://www.metoffice.gov.uk/research/seasonal/global/pdf/global_temp_2005.pdf)

 

The forecasts for 2005 were expressed as the boundaries corresponding to the following values of the cumulative probability of the forecast, starting at the coldest level:

 

 

2.5%

25%

50%

75%

97.5%

Method 1

0.40

0.49

0.52

0.56

0.65

Method 2

0.38

 

0.47

0.50

 

0.53

 

0.62

Weighted Mean

0.39

0.48

0.51

0.54

0.63

 

 

The mean forecast anomaly of 0.51oC was based on a skill weighted average of the two methods. The observed anomaly to November is 0.48 oC, so the 2005 forecast was slightly too warm but just within the 50% confidence range and well within the 95% confidence range.. 


3.  FORECAST FOR 2006

 

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

 

1.        USING SIX EMPIRICAL PREDICTORS INCLUDING OBSERVED ENSO INDEX, OCT-NOV-  DEC (1st-11th) 2005   0.44 oC

 

2.        AS 1 BUT USING  GLOSEA NINO3.4 SST  FORECAST FOR NOVEMBER  2005- APRIL 2006                         0.45 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 total variance explained in the cross validated tests.  

 

 

2.5%

25%

50%

75%

97.5%

Method 1

0.32

0.40

0.44

0.49

0.57

Method 2

0.34

 

0.42

0.45

 

0.49

 

0.57

Weighted Mean

0.33

0.41

0.45

0.49

0.57

 

 

Our best estimate forecast of the global temperature anomaly for 2006 is 0.45-0.12oC, with a 95% confidence interval from 0.33oC to 0.57oC.  This is a forecast for the fifth warmest year on record, marginally warmer than the hitherto fifth warmest year, 2004 ( 0.44oC). There is a  30% probability that 2006 will be as warm or warmer than 2005 which is likely to be the fourth warmest year at  0.48oC but only an 5% probability that 2006 will be as warm or warmer than the warmest year (1998, 0.54oC) .

 

Cooling relative to current conditions depends on a prediction of a weak La Nina by both the statistical and dynamical methods. The consensus from most dynamical and statistical methods is for near neutral or slightly cool conditions in the Tropical East Pacific. If  the Pacific is neutral, then the forecast could be up to 0.05oC too cold.

 

References

 

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 Nino: 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.

 

Parker, D.E., L.V. Alexander and J. Kennedy, 2004: Global and regional climate in 2003. Weather, 59, 145-152.

 

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 1947-2005 (red line) and forecast for 2006 (red+) using method 1. The black line represents observations based on optimal averages and includes a preliminary estimate for 2005. The 5% and 95% confidence limits are marked by lines and crosses in green.