Comment on “Influence of the Southern Oscillation on tropospheric temperature” by J. D. McLean, C. R. de Freitas, and R. M. Carter



[1] McLean et al. (2009) (henceforth MFC09) claim that the El Niño–Southern Oscillation (ENSO), as represented by the Southern Oscillation Index (SOI), accounts for as much as 72% of the global tropospheric temperature anomaly and an even higher 81% of this anomaly in the tropics. They conclude that the SOI is a “dominant and consistent influence on mean global temperatures,” “and perhaps recent trends in global temperatures.” However, their analysis is inappropriate in a number of ways and overstates the influence of ENSO on the climate system. This comment first briefly reviews what is understood about the influence of ENSO on global temperatures and then shows that the analysis of MFC09 greatly overestimates the correlation between temperature anomalies and the SOI by inflating the power in the 2–6 year time window while filtering out variability on longer and shorter time scales. The suggestion in their conclusions that ENSO may be a major contributor to recent trends in global temperature is not supported by their analysis or any physical theory presented in their paper, especially as the analysis method itself eliminates the influence of trends on the purported correlations.

1. Introduction

[2] McLean et al. [2009] (henceforth MFC09) have recently argued that most of the decadal and longer-term variation in large-scale tropospheric temperatures can be explained by a single factor: the El Niño–Southern Oscillation (ENSO). They claimed that more than two thirds of the interseasonal and longer-term variability in global tropospheric temperature anomaly (GTTA) (72% using the 29 year long MSU satellite record and 68% using the longer 50 year RATPAC-A record), and an even larger 81% of the variation in tropical (20°S–20°N) tropospheric temperatures, can be explained by the long-term variations in the Southern Oscillation Index (SOI). All the data used in this paper are described more fully by MFC09.

[3] In this comment, we show that their conclusions are not valid because their analysis is based on an inappropriate filtering of the data. It is well established that ENSO accounts for much of the interannual variability in tropospheric temperatures (e.g., Newell and Weare [1976], Angell [1981], and discussion by Trenberth et al. [2002]). Jones [1989] found that roughly 30% of the variation in global annual mean surface temperature could be explained by the SOI over the period 1867–1988 (with the SOI leading temperatures by 6 months). As we show in section 2, however, the filtering of MFC09 eliminates all long-term variability from the data. Consequently, their estimates are at marked variance with essentially every other study of the connection between ENSO and large-scale temperature variability, particularly with regard to the role of ENSO in any long-term warming trends. For example, Wigley [2000] found that the lower tropospheric warming trend over the 21 year period 1979–1999 increases from 0.15°C/decade to 0.25°C/decade after the joint impacts of ENSO and volcanic aerosols are accounted for and removed. A related analysis by Santer et al. [2001] found trends of 0.210 to 0.250°C/decade at the surface, reducing to 0.056 to 0.158°C/decade in the lower troposphere, after the joint removal of both factors. Using Niño 3.4 region (170°–120°W, 5°N–5°S) sea surface temperature (SST) anomalies as an index of ENSO, Trenberth et al. [2002] found a residual global mean surface temperature trend of 0.4°C over the period 1977–1998 after ENSO impacts alone are removed. More recently, Thompson et al. [2008] removed an estimate of global temperature variations associated with both ENSO and the so-called cold ocean/warm land or “COWL” pattern of extratropical temperature variation, and found a residual global mean surface warming of 0.4°C over the 1950–2006 period.

[4] In all of these previous analyses, ENSO has been found to describe between 15 and 30% of the interseasonal and longer-term variability in surface and/or lower tropospheric temperature, but little of the global mean warming trend of the past half century. Here, we explain how MFC09 results come about from (1) inappropriate statistical averaging and differencing procedures which distort the frequency domain characteristics of the time series analyzed, effectively removing long-term trends, and (2) inappropriate splicing of different data products. We identify some additional problems in their interpretation of their analyses.

2. Method of MFC09

[5] For all monthly time series (the global and tropical MSU temperature estimates from UAH and the SOI from the Australian Government Bureau of Meteorology), the analysis of MFC09 first takes 12 month moving averages of the data, then takes differences between those values which are 12 months apart. The first step filters out the high-frequency variation from the time series, while the second step filters out low-frequency variation. The latter step is perhaps the most problematic aspect of their analysis. It approximates taking the time derivative of the smoothed series, and therefore (as we illustrate in section 4) any underlying linear trend which may be present in the original data will be replaced by an additive constant in the filtered time series. Since an additive constant makes no contribution to the variance of a time series, it can have no effect on the correlation between time series. Therefore subsequent correlation-based analysis of the differenced time series can tell us nothing about the presence or causes of trends in the original data.

[6] In more detail, the combined processing can be considered to act as a bandpass filter. An input signal consisting of a pure sinusoid at frequency ν cycles per year, given by x(t) = sin(2πνt) (with t in years), sampled monthly and subjected to the filter used by MFC09, will produce an output signal with frequency-dependent amplitude

equation image

The variance due to such a signal will, like its power in a Fourier spectrum, be proportional to the square of that factor. Hence the variation of any signal will be band-pass-filtered, by the proportions plotted in Figure 1. A comparison of the normalized power spectra for the UAH and SOI time series from December 1979 to the present, before and after filtering, computed using the date-compensated discrete Fourier transform [Ferraz-Mello, 1981], is shown in Figure 2. This shows both an increase in power in the ENSO frequency band of 0.2–0.5/year, and the removal of power at both high and low frequencies. The latter region is of course where the spectra of the original data sets exhibit strong disagreement.

Figure 1.

Squared output amplitude for a unit-amplitude input after filtering by the method used by MFC09 (a) as a function of frequency and (b) as a function of period.

Figure 2.

Fourier spectra for the UAH and SOI time series from December 1979 to the present, both (a) before filtering and (b) after filtering.

[7] The effect of the filter at low frequencies is even greater when applied to the RATPAC-A data (Figure 3). This is because the RATPAC-A data exhibit larger secular change over the observed time span, showing a larger trend and covering a longer time span. The extremely high spectral power at very low frequencies, which is the dominant feature of the spectrum due to the larger trend and longer duration of the RATPAC-A data series, is entirely eliminated by the filtering.

Figure 3.

Fourier spectra for the RATPAC-A global time series, before filtering (black curve) and after (red curve).

3. Justification for the Filter

[8] MFC09 note that even after initially taking the 12 month moving average the correlation between the SOI and GTTA remains poor, saying “A 5 month lag produced the best match of key turning points but the overall correlation of −0.223 is quite weak. This weak correlation may be due to the period during which volcanic eruptions exert an influence on temperature, or to noise caused by short-term forces such as wind, within the two data signals, both of which are given as monthly averages, from which these 12 month running averages were calculated.”

[9] They then suggest that the derivative filter is applied for the specific purpose of removing the noise: “To remove the noise, the absolute values were replaced with derivative values based on variations. Here the derivative is the 12 month running average subtracted from the same average for data 12 months later.”

[10] However, taking the derivative of a time series does not remove, or even reduce, short-term noise. It has the opposite effect, amplifying the noise while attenuating the longer-term changes. Thus, the use of the differencing filter has not been justified, as it has precisely the opposite effect to that invoked by the authors. The noise of short-term variability has already been reduced by the moving-average step. Yet even this noise should not have been removed if the authors truly wish to estimate how much of the total variation in GTTA is due to variations in the SOI.

4. Demonstration of the MFC09 Filter

[11] As an illustration, we constructed an artificial “temperature” time series as −0.02 times the SOI time series from December 1979 to the present, x(t) = −0.02 × SOI(t). Of course the correlation between x and the SOI here is precisely −1, and for this artificial variable the SOI accounts for 100% of the variation. We then added normally distributed white noise and a linear trend to generate a new series y(t) = x(t) + N(0, σ) + a(t − 1995) with σ = 0.2 and a = 0.05. The original and modified series are shown in Figure 4a.

Figure 4.

(a) Artificial data proportional to the SOI (black curve) and with normally distributed white noise and a linear trend added (red curve). (b) Filtered versions (using the MFC09 procedure) of the series in Figure 4a.

[12] The squared correlation between the modified series and the SOI series is only R2 = 0.0171. When both are transformed with the filter used by MFC09 (Figure 4b) the squared correlation between the filtered series is R2 = 0.8295. However, it would be incorrect to claim that variations in the SOI account for 83% of the variation in the original series; in fact the SOI accounts for less than 2% of the variance.

[13] Such hugely inflated correlations do not hold just for the addition of a linear trend, but hold more generally for any low-frequency variability. We also took the artificial signal proportional to the SOI, and added the same noise and a sinusoidal signal with a period of 30 years, defining z = x + N(0, σ) + 0.5 sin(2π(t − 1995)/30) (Figure 5a). Now the squared correlation between the SOI and the artificial signal z is R2 = 0.1928. But after the filtering of MFC09 (Figure 5b) the squared correlation rises to R2 = 0.8821. Again, it is certainly not correct to claim that variations in the SOI account for 88% of the variation of the original data, when in fact these variations account for only 19%.

Figure 5.

(a) Artificial data proportional to the SOI (black curve) and with normally distributed white noise and a sinusoidal signal added (red curve). (b) Filtered versions (using the MFC09 procedure) of the series in Figure 5a.

[14] In spite of the distorting effect of their filter, the correlations and fractions of explained variation derived by MFC09 are consistently presented as being between the SOI and tropospheric temperature, both in the abstract and the conclusions of the paper.

[15] MFC09 further claim that the statistical properties of the time series for the SOI and GTTA, in which the two halves of a time series have different means but similar variability about that mean, are indicative of “a stepwise shift in the base values of each factor.” However, this is not the case. For any time series consisting of a linear trend plus noise, say x(t) = at + ε(t) over the interval −TtT, where ε(t) is any noise function with zero mean, variance s2 and time scale substantially shorter than T, the expected means over the first and second halves of this interval are of course −aT/2 and aT/2 respectively, but the expected variance of each half about their respective mean values will be equal at a2T2/12 + s2. Thus, their analysis here in no way supports their claim of a step change.

5. Trend in GTTA

[16] In Figure 7 of MFC09, the authors plot actual GTTA (not filtered versions) against the SOI, using different axes, to illustrate the quality of the match between them. However, the GTTA signal they plot is a splice of RATPAC-A data through 1979 followed by UAH TLT data since 1980. RATPAC-A data show a pronounced trend over the entire time span, which is visually evident from Figure 4 of MFC09, the temperature line rising away from the SOI line. It is inappropriate simply to append one data set to the other, as there is a zero-point difference between the two. The mean values of RATPAC-A and UAH TLT data during their period of overlap differ by nearly 0.2 K, so splicing them together without compensating for this introduces an artificial 0.2 degree temperature drop at the boundary between the two. Unfortunately this is obscured by the fact that the overlap is not shown, and their graph is split into different panels precisely at the splicing boundary.

6. Conclusion

[17] It has been well known for many years that ENSO is associated with significant variability in global mean temperatures on interannual time scales. However, this relationship (which, contrary to the claim of MFC09, is simulated by global climate models [e.g., Santer et al., 2001]) cannot explain temperature trends on decadal and longer time scales. The analysis of MFC09 overstates the influence of ENSO, primarily by filtering out any signal on decadal and longer time scales. Therefore, their method of analysis is a priori incapable of addressing the question of causes of long-term climate change. In fact, it is widely acknowledged that the general rise in temperatures over the 2nd half of the 20th century is very likely predominantly due to anthropogenic emissions of greenhouse gases, with natural variability playing a much more minor role [Intergovernmental Panel on Climate Change, 2007].


[18] This work was supported by the Global Environment Research Fund (S-5-1) of the Ministry of the Environment, Japan. NCAR is supported by the National Science Foundation. P.D.J. has been supported by the U.S. Department Of Energy (grant DE-FG02-98ER62601). We are grateful to three reviewers for useful comments.