ST and MDV of GST and their instantaneous rates of change
In Wu et al. (2007) we applied EMD to the time series of annual values of GST in order to illustrate how the method works. In Fig. 2 we use EEMD to decompose global monthly land and sea surface temperature time series derived from HadCRUT3v dataset, which cover the period of record January 1850 through December 2008. Land temperature evidently exhibits greater variability than ocean temperature in the high frequency components C1, C2, and C3. When these are filtered out, the land and ocean time series become more similar, as evidenced by the consistently high positive correlations between respective modes obtained from the two decompositions (Table 1). Thompson et al. (2010) also show evidence of strong coherence between land and ocean temperature time series on these time scales. The features of interest in this study relate to the bottom two curves, which refer to C8 and C9 in the expansion. The bottom curves are C9 alone and the curves just above them are the sum of C8 and C9. Subsequent results discussed in this paper are based on an analogous EEMD analysis of the global-mean surface temperature (GST), combined land and ocean surface temperature time series.
In “Appendix” MDV and ST of GST (based on HadCRUT3v), as defined by C8 and C9, respectively, are shown to be distinguishable from a univariate red noise at above the 99% confidence level, and are in this sense statistically significant with reference to a univariate red noise null hypothesis. Figure 3 shows time series of ST and ST + MDV, all based on EEMD of the GST time series with land and ocean data combined, superimposed on the GST time series itself. ST exhibits continuous warming from 1850 to present, with a cumulative temperature rise of 0.75°C, and inclusion of the MDV captures the stepwise character of the GST time series.
To assess the sensitivity of the estimated trends to the noise contained in GST and to the end point of the analysis, we use the down-sampling approach that was discussed in Sect. 2.3: we estimated ST and MDV based on the period of record 1850–1949, 1850–1950, …, 1850–2008 to obtain the 60 different estimates. Results of period of record 1850–1983, 1850–1988, 1850–1993, 1850–1998, 1850–2003, and 1850–2008 are shown in Figs. 4 and 5. Estimates of ST (C9) and MDV (C8) for the years prior to the 1940s are relatively insensitive to the end point, but the sensitivity is noticeably larger toward the end of the data records, as discussed in (Wu and Huang 2009). However, almost all the means of STs and of MDVs obtained based on any of these periods stay within the spreads of year 2008 (2 standard deviations) of the STs and MDVs calculated based on the down-sampled yearly time series for the period 1850–2008. In this sense, the MDV curve and the overall shape of the ST curve are robust with respect to changes in the end point despite the uncertainties toward the end of the record.
The contributions of ST and MDV to the linear trends in GST over the past 150, 100, 50, and 25 years are compared in Table 2. Notice that in the table, the linear trends in Figure TS.6 of AR4 are based on the observed GST time series ending in 2003 while our calculation is based on the same GST time series ending in 2008. The last 5 years of relatively flat GST from 1998 onward leads to relatively smaller mean trends of the last 25 years and the last 50 years in our results than in AR4. On all time scales, the trends based on the time series formed by superimposing ST and MDV (i.e., the green curve in the upper panel of Fig. 3) are in close agreement with the trends based on the raw time series, consistent with the results that the high frequency components of yearly-averaged GST resemble white noise (Huang et al. 2009b). ST alone accounts for 0.43 K of the 0.53 K temperature increase over the past 50 years, consistent with the statement in the Summary for Policymakers in AR4 that “The observed changes … support the conclusion that it is extremely unlikely that the global change of the past 50 years can be explained without external forcing and that it is very likely that it is not due to known natural causes alone”. The estimated warming rate corresponding to the sum of ST and MDV over the past 25 years is 0.15 ± 0.05 K per decade, of which 0.10 ± 0.02 K per decade of warming is associated with ST only. The shape of ST closely parallels the global annual CO2 input to the atmosphere by the fossil fuel burning (figure not shown). Therefore, the estimated global warming due to human activities over the past 25 years ranges from about 0.10 K to about 0.15 K per decade, depending on the assumed partitioning of the MDV between natural and anthropogenic aerosol-forced variability: if variations in the circulation of the Atlantic Ocean play a prominent role in causing MDV, then the value should lie toward the lower end of this range. On the other hand, if a slowdown or reversal in the buildup of aerosols was primarily responsible for the increased rate of global warming toward the end of the twentieth century, then the human contribution should lie closer to the top end of the range.
The time derivative of ST, indicated by the red curve in Fig. 1, provides an indication of the rate at which global warming induced by the buildup of greenhouse gases and long-term aerosol change in the atmosphere has been proceeding, irrespective of the MDV associated with variations in the oceanic circulation and the relatively short-term changes in the rate of emission of aerosols. It is evident from the red curve in Fig. 1 that this rate has been increasing with time. The instantaneous warming rate is largest at the end of GST with a value of 0.10 ± 0.03 K per decade. The instantaneous warming rates of ST calculated based on different periods of record of GST all stay within ± 0.03 K per decade of the warming rate of the mean ST calculated based on GST for 1850–2008.
The time derivative of ST + MDV, indicated by the blue curve in Fig. 1, replicates the step-like character of the 25-year running mean trends (the black curve) and it also captures the recent slowdown in the rate of warming.
Robustness of MDV and ST
In this section, we examine the robustness of the results, with emphasis on the sensitivity of MDV and ST with respect to (a) a spurious discontinuity in the GST time series in 1945, (b) the inclusion or removal of the cool episodes following major volcanic eruptions, and (c) the presence of noise in the GST time series. All these calculations use the down-sampling approach described in Sect. 2.3.
Effect of the spurious temperature discontinuity in 1945
A spurious temperature drop in the GST time series derived from HadCRUT3v data, with an amplitude of about 0.3°C occurs starting in August 1945, when the U.S. Naval fleet, which was measuring sea surface temperature (SST) using thermometers embedded in the condenser intake returned to port and British ships, which were taking bucket measurements of SST, replaced them as the dominant source of SST data (Thompson et al. 2008, 2009). This problem was discovered in 2008; efforts are underway to correct it, but as of this time, it is known only that the correction required to eliminate the biases associated with the use of different measurement methods aboard ships operated by different nations will be negative prior to 1945 and positive thereafter and that these corrections will probably extend over one to as much as a few decades (Thompson et al. 2008).
It has been previously demonstrated that EEMD is a temporal local analysis method. If the biases are restricted to a relatively short time span, for example, less than a decade, the extracted MDV and ST should not be noticeably affected. If the duration is longer, e.g., a few decades, it is anticipated that there will be some phase shift in the MDV. Here, we consider the impact of a hypothetical, synthetic correction for this discontinuity generated by adding an exponential decaying function with an amplitude of 0.15°C, ending in August 1945 and exponentially decaying backward in time and subtracting an exponential function with an amplitude of 0.15°C beginning in September 1945 and exponentially decaying forward in time. The e-folding time for both exponential functions is 15 years. The original GST, the GST correction function, and corrected GST are displayed in the top panel of Fig. 6.
It is clear from the bottom two panels of Fig. 6 that the MDVs of the original and “corrected” GST exhibit some differences between 1925 and 1975. The peak in the 1940s occurs a few years earlier in the “corrected” data and the minimum that appears in the original data in the 1960s is slightly shallower and shifted forward in time by about 10 years. The effect of the correction on the ST is barely discernible. Hence, unless the forthcoming real correction to the GST time series extends over time intervals substantially longer than assumed in designing this synthetic correction, it is not likely to qualitatively affect the results presented in this paper.
Inclusion or exclusion of the response to volcanic eruptions
Sulfur injected into the stratosphere by volcanic eruptions, condenses, forming long-lived layers of sulfate aerosols that reduce the shortwave solar radiation reaching the Earth’s surface. Because of the thermal inertia of the oceans, the resulting cooling of GST persists much longer than the aerosol layers that produce it. Since the volcanic eruptions occur intermittently throughout the GST record and the cool episodes following major eruptions in low latitudes can persist for up to 5–10 years, it is conceivable that volcanic forcing could affect the estimated MDV and ST.
To infer quantitatively how much this episodic volcanic forcing affects the estimated MDV and ST time series, we decompose the GST time series with the surface temperature response to the volcanic forcing removed. For this purpose we use the reconstruction of Thompson et al. (2009), in which the signatures of major low latitude volcanic eruptions of Santa Maria (1902), Agung (1963), El Chichon (1982), and Pinatubo (1991) are most clearly discernible, as indicated by the red line of the top panel of Fig. 7. The analysis is restricted for the period from 1900 onward, for which the volcanic forcing is best defined.
From the results shown in Fig. 7, it is evident that the removal of the response to volcanic eruptions in the GST time series has very little effect on the estimated ST. However, the effect on the MDV is quite significant: when the response to volcanic eruptions is removed, the MDV exhibits a pronounced peak around the year 2000, with a rapid dropoff after that time that is not present in the original GST time series. But regardless of whether the response to volcanic eruptions is included or excluded, MDV exhibits a pronounced warming trend throughout most of the 1970s, the 1980s and the 1990s.
The choice of dataset
Although various versions of HadCRUT (Jones et al. 1999; Rayner et al. 2003) are the most widely used surface temperature analysis, there are other analyses, such as those provided by Goddard Institute for Space Studies (GISTEMP) (Hansen et al. 2009), and by the NOAA National Climate Data Center (Smith et al. 2008). Since the different analyses have used different methods to homogenize the observed surface air temperature and sea surface temperature observations, each of these products is slightly different. For example, 1998 is the warmest year based on HadCRUT, while in GISTEMP, 2005 is as warm as 1998. Furthermore, each of these analyses contains a different level of noise. Since there is not enough information to assess which of these products is the most accurate, we will restrict ourselves to assessing whether the results obtained by performing EEMD on the GST time series are sensitive to the choice of dataset.
In Fig. 8, we compare the MDV and ST modes derived from the GST and GISTEMP data. Since the GISTEMP is with respect to the mean annual cycle over the 30-year period 1950–1980 and the GST represents departures from the later (and warmer) 1960–1990 climatology, GISTEMP is systematically warmer than GST. This difference is reflected by the absolute value difference between the STs based in the two different analysis products at any given time. However, the STs closely parallel one another from 1950 onward, implying that the estimated trends in that time frame are almost identical. The major difference in the results is in the extracted MDVs in the early part of the record in which the data coverage was limited. From 1930 onward the two ST curves are quite similar. The raw time series and both the MDV and ST time series derived from GISTEMP exhibit slightly larger upward trends in the last decade or two of the record.
In the sensitivity experiments described in this section, we have demonstrated that the secular trend (ST or C9) mode recovered from EEMD is robust with respect to several prescribed perturbations in the input time series. The multidecadal variability (MDV or C8) mode exhibits some sensitivity with respect to the timing of the extrema, but the character of the variations is qualitatively similar in all cases and, in particular, all variants of the analysis exhibit a strong upward temperature trend in the late twentieth century that is reflected in both MDV and ST.
Spatial structures of ST and MDV
To get some indication of the physical processes that might be contributing to the ST and MDV in GST, we regressed the global surface air temperature (SAT) and global sea surface temperature (SST) fields onto the ST and MDV time series derived from EEMD of global (land plus ocean) surface temperature. The SAT dataset, which covers a time span from 1900 to December 2006, is from the Global Historical Climatology Network, version 3 (Peterson and Vose 1997), and the SST dataset is the NOAA ERSST by Smith et al. (2008), which spans the period or record January 1880 to December 2006. Regression maps for the periods from January 1900 (SAT) to December 2006 are shown in Fig. 9. Consistent with the linear trend maps in Fig. 3.9 in AR4 (IPCC 2007) and the forced response and unforced internal variability over the most of global oceans of Ting et al. (2009), Knight (2009), and DelSole et al. (2011) the regression patterns for ST exhibit warming over the entire globe except for some spotty areas, e.g., the North Atlantic Ocean southeast of Greenland, southeastern United States and parts of China, where slight cooling has occurred. Such widespread warming is suggestive of a response to the buildup of well-mixed greenhouse gases, especially carbon dioxide. The close parallel between the ST curve and the carbon emission rate related to fossil fuel consumption after the industrial revolution also indicates that the buildup of atmospheric greenhouse gas concentrations projects almost exclusively onto ST, as does a substantial fraction of the buildup of aerosols injected into the atmosphere by human activities, activities, which can be assumed to be roughly linearly proportional to the rate of burning of fossil fuels (Crowley 2000). These results were confirmed by the analysis of CMIP3 model simulations by DelSole et al. 2011.
A noticeable feature of our regression pattern for MDV is that the dominant signals are restricted to high latitudes of the Northern Hemisphere and they appear to be more clearly defined over the ocean than over land (despite the fact that the amplitudes of surface temperature variation tend to be larger over land) and the sea surface temperature variations associated with MDV are particularly large over the Gulf Stream extension. These results are also consistent with the results of Semenov et al. (2010) which indicate that the North Atlantic-Arctic sector explains over 60% of the total Northern Hemisphere SAT response to surface flux anomalies of multidecadal timescale in their model experiments.
Both recent observational diagnoses (Zhang et al. 2007; Zhang 2008; Polyakov et al. 2009) and modeling evidence (Knight et al. 2005; Latif et al. 2006; Keenlyside et al. 2008; Semenov et al. 2010) suggest that variations in the intensity of the Atlantic meridional overturning circulation on the multidecadal time scale can give rise to episodes of rising and falling SST over the extratropical North Atlantic. In the SST pattern for the MDV shown in Fig. 9, the positive regression coefficients over the extratropical North Atlantic are accompanied by patches of negative coefficients over the Southern Ocean, a configuration reminiscent of the so-called “bi-polar seesaw” pattern inferred from paleoclimate proxies (Seidov and Maslin 2001; EPICA Community Members 2006), which is believed to be a consequence of variations in the strength of the Atlantic meridional overturning circulation. Another potential source of MDV that projects upon C8 derived from the EEMD analysis is the change in the Northern Hemisphere wintertime circulation that contributed to the rise in surface air temperature over the continents poleward of 40°N during the late twentieth century (Wallace et al. 1995; Quadrelli and Wallace 2004, Fig. 16).
To substantiate that the patches of negative regression coefficients in Fig. 9 are really a reflection of an out-of-phase relationship between SST in the North Atlantic and Southern Ocean, we show in Fig. 10 time series of SST averaged over the two regions, as indicated in the caption. The North Atlantic time series and the topmost of the two Southern Ocean time series are based on data from ERSST. The bottom curve for the Southern Ocean is based on the International Comprehensive Ocean-Atmosphere Data Set (ICOADS), which contains objectively analyzed in-situ observations of SST in 5° × 5° grid boxes (Smith and Reynolds 2005). When sampling is sparse within a grid box in a given month, the data are flagged as missing.
The two representations of the Southern Ocean time series closely parallel one another after 1930, during which time they exhibit a pronounced out-of-phase relationship with the North Atlantic time series on the multidecadal time scale. The correlation coefficient between C8 of the North Atlantic ERSST and the ERSST (ICOADS) representation of the Southern Hemisphere time series is −0.77 (−0.57). The length of these time series is not sufficient to establish the statistical significance of these multidecadal correlations, but at least it is evident that they are strong and the sign of them is consistent with the notion that the Atlantic multidecadal variability involves cross-equatorial heat fluxes associated with the thermohaline circulation, as demonstrated in Semenov et al. (2010).
The results of a climate model simulations by Semenov et al. (2010), the statistical analysis of CMIP 3 forced and unforced runs by DelSole et al. (2011) and our analysis of observational data sets all points to the MDV being largely a reflection of internal variability of the climate system. However, the possibility that shorter term variations in aerosol forcing has contributed to the MDV cannot be ruled out. For example, the leveling off of sulfate concentrations around 1970 projects positively on that segment of the MDV curve (Murphy et al. 2009); indeed, it has been argued that the MDV in the second half of the twentieth century is dominated by this feature (Mann and Emanuel 2006).