To separate the GHG-induced warming signal from other variations, I performed an empirical orthogonal function (EOF) analysis9 of the monthly anomalies of surface air temperature (SAT) and total water vapor content or precipitable water (PW) in an air column for 1950–2099 simulated by and averaged over all the climate models participated in the IPCC Fourth Assessment (AR4)6,10 under the IPCC A1B scenario for future emissions (a similar analysis was also done using the CMIP5 model data11). The first EOF (Fig. 1a-c,e-f) clearly represents the global warming signal with the familiar temporal and spatial characteristics that resemble the global-mean GHG forcing series and long-term change patterns6,7. Surprisingly, the EOF and long-term change patterns Fig. 1c,g for both the SAT and PW broadly resemble the spatial patterns of the standard deviation (SD) of the monthly anomalies of surface air temperature and PW, respectively, from the models during 1950–1979 when the warming trend is relatively small (thus detrending had little effect; Fig. 1). This is especially true for PW, whose future change patterns strongly correlate with the SD patterns (r = 0.86–0.93). Besides the obvious land-ocean contrasts seen in both the future change patterns and the current SD maps, the pattern correlation over land or ocean only is also strong, although not perfect. For example, the correlation coefficient between the future PW EOF change patterns and its current SD patterns is 0.87 and 0.93 over land and ocean, respectively; while these numbers are lower but still statistically significant at 0.64 and 0.41 for the SAT case. Although the pattern correlation for the SAT case is not very strong, especially over ocean, the similarities between the future change patterns and current variability patterns are remarkable considering that they are caused by totally different forcing and they result from very different physical processes (e.g., ENSO or volcano induced variations vs. GHG-induced changes).

Figure 1 Left column: The principal component (PC, (a) left ordinate) and empirical orthogonal function (EOF, (b) of the leading mode of the monthly anomalies (relative to the 1950–1979 mean annual cycle, all months combined) of surface air temperature from 22 CMIP3 models from their 20th and 21st (under the A1B scenario) century simulations. The EOF 1 pattern is compared with the patterns in (c) 2080–2099 minus 1980–1999 surface air temperature differences (dT, multiplied by 0.9) and (d) the standard deviation (S.D., multiplied by 8 and in oC) of the monthly temperature anomalies (all months combined) during 1950–1979, with the pattern correlation coefficient (r) between the dT and SD (EOF1 and SD) is shown on top of panel (c,d) for, from left to right, all areas, land and ocean only. In (a), the global-mean temperature anomalies (oC) associated with this EOF is shown on the right-side ordinate and % variance explained by the mode is given on top of the panel. Right column: same as the left column but for precipitable water (PW) from 20 CMIP3 models and the unit is millimeters. To use the same color scale, values in (f,h) were multiplied by 0.4 and 4.0, respectively. The product of the PC and EOF coefficients yields the anomalies in one tenth of the given unit associated with the mode for a given time and location. Detrending the 1950–1979 data had little effect on the S.D., which includes variations on time scales from a month to 30 years (but with the mean annual cycle excluded). All maps in this paper were created using NCAR Graphics library by the author. Full size image

The EOF represents the mean patterns averaged over the entire data period. To check whether the EOF patterns change over time, I performed the EOF analysis for three different periods from 1950–1999, 2000–2049 and 2050–2099. The results (Fig. S1) show only small changes in the EOF patterns that may be partly due to sampling errors for the relatively short periods and they are similar to the EOF patterns for the whole period from 1950–2099 (Fig. 1). The pattern correlation with the SD of 1950–1979 is still significant, ranging from 0.85–0.93 for PW and 0.30–0.71 for SAT. The correlation between the SD patterns and future change patterns also exist for each of the seasons (Fig. S2). These results show that change patterns for PW in the 21st century largely resemble the spatial patterns of their variability during 1950–1979 and this is also true for SAT to a lesser degree.

The multi-model ensemble averaging used in Fig. 1 and S1 reduces natural variations and enhances the GHG-induced warming signal, increasing the percentage variance explained by the first EOF from around 35–50% in individual models (not shown) to around 92% (Fig. 1) for 1950–2099. Without the ensemble averaging, the warming signal (EOF1) in the individual models is not separated from other modes of variability as well as for the multi-model ensemble mean case. Nevertheless, the warming patterns, as represented by the leading EOF, of the SAT and PW in the individual models (from one single run) for 1950–2099 are still strongly correlated with the spatial patterns of the SD of the SAT and PW monthly anomalies from the same model during 1950–1979, with most of the models showing a correlation around or above 0.8 for PW and 0.5–0.6 for SAT (Fig. 2). Thus, there exists a significant correlation between the future change patterns of SAT and PW and the patterns of their present-day variations in all the IPCC AR4 models and this correlation is very strong (~0.8 or higher) for PW in most of the models. I also found significant correlations between the patterns of 1950–1979 SD and the 2080–2099 minus 1980–1999 difference maps for SAT and PW for individual models, although this correlation is slightly lower than those shown in Fig. 2 due to contamination of other modes of internal variability in the simple difference maps, i.e., the 20-year difference maps from individual model runs contain varying contributions from internal decadal variability12, which may not be a major contributor for the SD pattern during 1950–1979 in many models.

Figure 2 The correlation coefficient between the spatial patterns of the standard deviation of the monthly anomalies during 1950–1979 and the leading EOF of the monthly anomalies during 1950–2099 under the A1B scenario simulated by individual CMIP3 coupled models and the multi-model averaged correlation (red bar) for (a) surface air temperature and (b) precipitable water. Also shown in (a) (black bar) is the case for observed surface monthly temperatures during 1950–2010. Full size image

I also analyzed the CMIP5 model output and found similar pattern correlations (slightly higher for SAT) between future changes and current variability (Fig. S3).

To check whether the above relationship found in models exists in the real world, I performed a similar EOF analysis of observed surface air temperature over land and sea surface temperature over ocean using the Climate Research Unit data set (HadCRUT3)13,14. I focused on the 1950–2010 period as observations for earlier years are sparse over oceans and many land areas. Data for the polar regions are sparse and thus these regions were excluded from the analysis. Compared with the EOFs from the models, the leading EOF from this data set (Fig. 3a,b) exhibits more short-term variations and more spatial noise. Nevertheless, it still represents a warming trend over most of the globe, especially over land and the Indian and Atlantic Ocean. Although the noisy EOF patterns (Fig. 3b) do not match the SD of the 1950–1979 from the same data set over the North Pacific and several other regions, they are still significantly correlated (r = 0.62) for all areas within 45oS–75oN, which is comparable to those shown in Fig. 2a.