## 1. Introduction

The Walker circulation (WC) is one of the world’s most prominent and important atmospheric systems. It extends across the entire tropical Pacific Ocean, encompassing 1) the trade winds blowing from east to west; 2) air forced to rise over the western Pacific, Southeast Asia, and northern Australia through enhanced convection; 3) winds blowing counter to the trades aloft; and 4) air descending over the eastern Pacific Ocean (see, e.g., Gill 1982).

Changes in the WC are associated with major changes in rainfall (Ropelewski and Halpert 1989; Allan et al. 1996; Power et al. 1999), river flow (Kahya and Dracup 1993; Merendo 1995; Power et al. 11999), agricultural production (Phillips et al. 1998; Hammer et al. 2000; Power et al. 1999), ecosystems (Holmgren et al. 2001), severe weather (e.g., Callaghan and Power 2011), and disease (Nicholls 1993; Bouma and Dye 1997) in many parts of the world.

The WC weakened during the twentieth century and the early-twenty-first century (Tanaka et al. 2004; Vecchi et al. 2006; Meehl et al. 2007a; Power and Smith 2007; Collins et al. 2010; Vecchi and Wittenberg 2010; Nicholls 2008; Power and Kociuba 2011). Vecchi et al. (2006) found that the pattern, sign, and magnitude of observed trends over the tropical Indo-Pacific since the mid-nineteenth century resembled trends in mean sea level pressure (MSLP) in the runs they performed with their climate model when the forcing applied to the model included anthropogenic forcing. Model trends in the same model without anthropogenic forcing did not match the observed trends. Vecchi et al. (2006) also showed that most of the nineteenth-century–twentieth-century climate model runs in the World Climate Research Programme (WCRP) Coupled Model Intercomparison Project phase 3 (CMIP3) climate model database also exhibited weakening trends, and they concluded that the observed trend is largely due to anthropogenic forcing in the Geophysical Fluid Dynamics Laboratory (GFDL) climate model they used. This conclusion was further supported by their finding that the magnitude of 128- and 152-yr trends arising from internal climate variability—assessed using preindustrial runs of the WCRP CMIP3 models—was very small relative to observed trends over such periods. They also concluded that there is a very low likelihood that internally generated variability alone could cause a trend with a magnitude even half as large as the magnitude of the observed trend.

Power and Smith (2007) showed that the dominance of El Niño and the weakening of the WC measured using the Southern Oscillation index (SOI) reached record low levels in 1977–2006. This weakening is thought to be partly due to global warming (Vecchi et al. 2006; Power and Smith 2007; Vecchi and Wittenberg 2010; Collins et al. 2010) and partly due to both a natural increase in the frequency of El Niño and a natural reduction in the frequency of La Niña (Trenberth and Hurrell 1994; Trenberth and Hoar 1997; Folland et al. 2001; Power and Smith 2007). Power and Smith (2007) noted that further research was needed to quantify the extent to which global warming has driven the observed weakening of the Walker circulation.

The purpose of this study is to further clarify the extent to which the observed twentieth-century weakening of the WC has been driven by external forcing and internally generated natural variability. We will examine annual and seasonal trends in the observations and in both twentieth- and twenty-first-century WCRP CMIP3 climate model integrations. We will primarily focus on the twentieth century, as MSLP data coverage is low prior to the twentieth century in part of our region of interest (Allan and Ansell 2006; section 7).

The index used to track changes in the strength of the WC in this study is described in section 2. The climate model database used in this investigation is described in section 3. Trends in all the model simulations for both the twentieth- and twenty-first centuries are presented and are compared with their observational counterparts in section 4. Trends in various subsets of the models [e.g., models that are best able to replicate El Niño–Southern Oscillation (ENSO) variability)] are discussed in section 5. An alternative measure of BoxΔP that takes model bias into account is considered in section 6, and the accuracy of the observational data used is considered in section 7. Results are briefly discussed in section 8.

## 2. Index for the Walker circulation

We follow Vecchi et al. (2006) and use an index for the WC based on the difference between equatorial MSLP in a western box (5°S–5°N, 80°–160°E) and an eastern box (5°S–5°N, 200°–280°E). We will refer to these areal averages of MSLP as BoxW and BoxE, respectively. The arithmetic difference BoxΔP = BoxE − BoxW is used as a proxy for the strength of the WC. The data for these indices are derived from the second Hadley Centre’s Mean Sea Level Pressure Dataset (HadSLP2) from the Met Office (Allan and Ansell 2006). A summary of annual trends, trends in all seasons, and trends for June–December combined will be presented.

## 3. Climate models and analysis method

We analyze both twentieth- and twenty-first-century integrations from numerous different coupled general circulation models (CGCMs) available from the WCRP Climate Variability and Predictability (CLIVAR) Working Group on Coupled Modelling (WGCM) CMIP3 (Meehl et al. 2007b). We will begin by showing the twentieth-century results. We will then examine twenty-first-century changes in runs forced using the Special Report on Emissions Scenarios (SRES; Nakicenovic et al. 2000) A1B and A2. The A1B scenario has a 2100 CO_{2} concentration of approximately 710 ppm, whereas the A2 scenario has a larger 2100 value of approximately 860 ppm. Twenty-three models are available and analyzed for the twentieth century, 21 for the A1B scenario, and 17 for the A2 scenario. Trends are calculated over periods when all the models have output for every year: 1901–99 for the twentieth century, 2004–99 for A1B, and 2002–98 for A2. Choices were made here to maximize the number of available models for the analysis, as the model integrations showed differences in start times.

We will focus on ensemble mean (EM) and multimodel ensemble mean (MMEM) results. The MMEM is our model-based estimate of the externally forced signal in the variable considered, as the internally generated variability will be very largely cancelled out from such large samples. An EM is calculated for each model. The average of these ensemble means is then calculated to form the MMEM.

In the following section, we will examine MMEMs using *all* the models. In section 5 we will examine MMEMs based on various subsets that take the ability of the models to simulate twentieth-century climate into account.

## 4. Twentieth-century trends in observations and all models

The annual (January–December) observed twentieth-century trends for BoxW, BoxE, and BoxΔP are presented toward the left in Fig. 1 as either a green (positive) or purple (negative) vertical bar. The observed trends for BoxW (+0.22 Pa yr^{−1}), BoxE (−0.30 Pa yr^{−1}), and BoxΔP (−0.52 Pa yr^{−1}) are statistically significant at the 95%, 99%, and 99% levels, respectively. This assessment is based on the method described by Power et al. (1998) using the year as one of the time series, in which persistence is taken into account. Corresponding EMs for each model are also depicted in Fig. 1. Positive (model) trends are red; negative (model) trends are blue. The (all models) MMEM is given as a yellow horizontal line, the median value is given as a horizontal gray line, and estimates of the 10th and 90th percentiles for the (all models) MMEM trend are given as horizontal pink lines. These values were estimated using the method outlined in the appendix. The names of the models analyzed are also provided in Fig. 1. The number of runs available for each model is given in brackets.

Sixteen of the 23 models exhibit positive EM BoxW trends. If we use a binomial distribution—assuming that the chance of any individual EM trend being positive and the chance of any EM trend being negative are both equal to 0.5—then this result (i.e., 16 out of 23 models with trends of the same sign) is significant at the 98% level. Fifteen of the 23 models exhibit negative BoxΔP trends, a result that is significant at the 95% level when estimated in a similar fashion. Only 14 of the 23 models have EM trends for BoxE, and so the robust trend in BoxΔP primarily arises from the upward trend in BoxW.

While there is a robust signal in both BoxW and BoxΔP, the MMEM trends are much smaller in magnitude than the observed trends over the same period. For example, the MMEM trend in BoxΔP is −0.10 Pa yr^{−1}, whereas the observed trend is −0.52 Pa yr^{−1}. Because the MMEM provides an estimate of the externally forced component of changes in BoxΔP, the externally forced component would seem to account for only a small fraction of the observed change. Of course there is scatter among the model EMs, as illustrated in Fig. 1. However, only one of the 23 models has a negative EM trend with a magnitude exceeding the magnitude of the observed trend, and 19 models have magnitudes that are less than 50% of the size of the observed trend.

Equivalent results for the A1B and A2 scenarios are given in Figs. 2 and 3, respectively. An increasing MMEM trend in BoxW and a decreasing trend in the MMEM trend of BoxΔP are again evident under both scenarios. Under the A1B scenario, 14 of the 21 models exhibit negative BoxΔP trends (significant at the 95% level) and 13 of 17 models have negative BoxΔP trends under the A2 scenario (significant at the 98% level).

Modeled trends in annual BoxW, BoxE, and BoxΔP under the A1B scenario over the period 2004–99. Units: Pa yr^{−1}.

Citation: Journal of Climate 24, 24; 10.1175/2011JCLI4101.1

Modeled trends in annual BoxW, BoxE, and BoxΔP under the A1B scenario over the period 2004–99. Units: Pa yr^{−1}.

Citation: Journal of Climate 24, 24; 10.1175/2011JCLI4101.1

Modeled trends in annual BoxW, BoxE, and BoxΔP under the A1B scenario over the period 2004–99. Units: Pa yr^{−1}.

Citation: Journal of Climate 24, 24; 10.1175/2011JCLI4101.1

Modeled trends in annual BoxW, BoxE, and BoxΔP under the A2 scenario over the period 2002–98. Units: Pa yr^{−1}.

Citation: Journal of Climate 24, 24; 10.1175/2011JCLI4101.1

Modeled trends in annual BoxW, BoxE, and BoxΔP under the A2 scenario over the period 2002–98. Units: Pa yr^{−1}.

Citation: Journal of Climate 24, 24; 10.1175/2011JCLI4101.1

Modeled trends in annual BoxW, BoxE, and BoxΔP under the A2 scenario over the period 2002–98. Units: Pa yr^{−1}.

Citation: Journal of Climate 24, 24; 10.1175/2011JCLI4101.1

Figures 1–3 provide annual trends. The observed seasonal trends are given in Table 1. Modeled trends for each season and for the period June–December are provided. The statistical significance of the degree of consensus is assessed for each season independently. All of the BoxΔP trends are negative, and the majority of the trends are statistically significant. The majority of the BoxW trends are statistically significant, and all of the statistically significant trends are positive. An exception to this occurs in March–May, when there is no consensus on the sign of the EM trends among the models in either the twentieth or twenty-first centuries. The sign of the trends in BoxE changes from season to season, and there is generally no consensus on the sign of the trends among the models. Results for the period June–December are also presented. These results are consistent with the findings of Power and Kociuba (2011), who examined changes in BoxΔP for June–December only.

MMEM trends for BoxW, BoxE, and BoxΔP for the twentieth-century (C20; 23 models) scenario and the twenty-first-century scenarios A1B (21 models) and A2 (17 models). Values are provided for all four seasons, for June–December and for January–December. The number of models with an EM trend that have the same sign as the MMEM trend is given in parentheses. The statistical significance of the degree of consensus on the sign of the EM among the models is provided. The number of models used for each set of experiments is given in bold parentheses.

MMEM values for the trends in each season and for each scenario are also provided in Table 1 (in brackets). The magnitude of the statistically significant MMEM trends in BoxW and BoxΔP is generally smallest for the twentieth century and, as expected, is generally largest for the A2 scenario, which has the highest late-twenty-first-century CO_{2} concentrations.

The seasonal values of the observed trends in BoxΔP are −0.65, −0.44, −0.41, and −0.69 Pa yr^{−1} for March–May (MAM), June–April (JJA), September–November (SON), and December–February (DJF), respectively. Comparing these figures with the corresponding tabulated figures from the models indicates that the magnitude of the observed changes are larger than the magnitude of the modeled changes in BoxΔP in all seasons in the twentieth century and in the twenty-first century under both the A1B and A2 scenarios. In fact, the magnitude of the observed change is *much* larger than the modeled trends in all seasons in both the twentieth century and twenty-first century under the A1B scenario.

If the observed trend is primarily driven by internally generated natural variability, then we might expect to see trends with magnitudes rivaling the magnitude of the observed trend in individual twentieth-century model runs. The trends in BoxΔP for the individual model runs for the twentieth century are presented in Fig. 4 together with the corresponding observed trend. In fact, only 3 out of the 73 model runs show a trend with a magnitude as large as the magnitude of the observed trend.

Twentieth-century trends in annual BoxW, BoxE, and BoxΔP from individual model runs (i.e., not EMs as for Figs. 1–3), showing 95% confidence intervals for the trend in each model run. Trends are calculated for the period 1901–99. Units: Pa yr^{−1}.

Citation: Journal of Climate 24, 24; 10.1175/2011JCLI4101.1

Twentieth-century trends in annual BoxW, BoxE, and BoxΔP from individual model runs (i.e., not EMs as for Figs. 1–3), showing 95% confidence intervals for the trend in each model run. Trends are calculated for the period 1901–99. Units: Pa yr^{−1}.

Citation: Journal of Climate 24, 24; 10.1175/2011JCLI4101.1

Twentieth-century trends in annual BoxW, BoxE, and BoxΔP from individual model runs (i.e., not EMs as for Figs. 1–3), showing 95% confidence intervals for the trend in each model run. Trends are calculated for the period 1901–99. Units: Pa yr^{−1}.

Citation: Journal of Climate 24, 24; 10.1175/2011JCLI4101.1

As noted above, Vecchi et al. (2006) examined the magnitude of trends over 128- and 152-yr periods expected in the models from internally generated variability alone. They found that the magnitude of the observed trend fell outside the 95% confidence intervals of all the models. In other words, it is very unlikely that internal variability alone can account for the observed trend. We only examined 99-yr trends. The observed trend in BoxΔP over the period 1901–99 (i.e., −0.52 Pa yr^{−1}) has a *t* value of −2.9, which corresponds to a trend that is significant above the 99% level—as noted above. So, if the observed trend is very largely driven by internally generated variability, then the internal variability would have to be unusually large.

Important sources of internal variability in the tropical Pacific are ENSO and the Interdecadal Pacific Oscillation (IPO) (Power et al. 1999, 2006; Arblaster et al. 2002; Meehl et al. 2009), and both drive variability in BoxΔP. For example, the correlation coefficient between the SOI and BoxΔP over the period 1901–99 is 0.83. The corresponding correlation coefficient between the IPO index and decadal changes in BoxΔP is −0.36, indicating that there is a weak tendency for BoxΔP to decline during El Niño–like phases of the IPO and to increase during La Niña–like phases of the IPO. So, if there has been a large change in BoxΔP due to natural variability, then we would expect to see a large change in one or both of the SOI or the IPO index. The annual average SOI exhibits a downward trend during 1901–99, but it is very weak in the sense that the *t* statistic is very low in magnitude (−1.1), indicating that it is not at all unusual. While this weakening trend in the SOI would reduce BoxΔP, it would not drive an unusually large downward trend in BoxΔP. Note that the SOI is also impacted by external forcing (Power and Kociuba 2011). However, twentieth-century trends are very inconsistent across the models, and the MMEM is very small. Thus, the observed downward trend in the SOI seems to be dominated by internal variability, yet it is unexceptional and so a major change in ENSO activity has not driven the larger observed trend in BoxΔP. A similar statement can be made for the IPO: it has trended toward a more El Niño–like state over the period 1901–99 and this would have contributed to the large downward trend in BoxΔP, but the trend in the IPO over the same period is again very weak.

So, while the models taken together (Fig. 4) suggest that large internally generated variability has been very largely responsible for the observed change, the modest trends in ENSO and the IPO suggest that internally generated changes have contributed but have not been large.

In summary, we have an all-model MMEM that is much smaller in magnitude than the magnitude of the observed trend, but the internal variability does not seem large enough in the models or the observations to make up the shortfall.

One possible explanation for this apparent inconsistency is that the models might underestimate the magnitude of internally generated variability or underestimate the degree of persistence in internally generated variability, as either of these deficiencies will lead to an underestimation of the magnitude of possible trends that can arise. To test this we examined the standard deviation and the autocorrelation of BoxΔP in the models and observations. We found that model values for both statistics varied around the observational values, but there is no large generic bias in the standard deviation (Fig. 5a). However, the models tend to underestimate the level of persistence in the annual BoxΔP (Fig. 5b). In fact, in some models, there is a large negative correlation at a 1-yr lag. In such models the trends that can be generated by internal variability will tend to be smaller than the trends that can be generated by internal variability in the observations and in models that exhibit persistence across calendar years.

The (a) standard deviation and (b) autocorrelation (at a 1-yr lag) of annual (January–December) data for the observations (green) and model runs over the period 1901–99.

Citation: Journal of Climate 24, 24; 10.1175/2011JCLI4101.1

The (a) standard deviation and (b) autocorrelation (at a 1-yr lag) of annual (January–December) data for the observations (green) and model runs over the period 1901–99.

Citation: Journal of Climate 24, 24; 10.1175/2011JCLI4101.1

The (a) standard deviation and (b) autocorrelation (at a 1-yr lag) of annual (January–December) data for the observations (green) and model runs over the period 1901–99.

Citation: Journal of Climate 24, 24; 10.1175/2011JCLI4101.1

A second possible explanation for the apparent inconsistency is that some of the models might be underestimating the magnitude of the externally forced response. We will explore this possibility in the following section. The possibility that observational error might result in an overestimate of the observed trend is addressed in section 7.

## 5. A closer examination of model trends

In the previous section, we examined trends from *all* the models and we estimated the MMEM using all the models weighted equally to be −0.1 Pa yr^{−1}, which is much smaller in magnitude than the magnitude of the observed trend (−0.52 Pa yr^{−1}). However, some models do a better job of simulating observed climate in the tropical Pacific than others (e.g., van Oldenborgh et al. 2005; Guilyardi et al. 2009; Brown et al. 2011; Irving et al. 2011), and this might underpin systematic biases in the response of BoxΔP to external forcing in some of the models. If it turns out that the better-performing models produce larger declines in BoxΔP than the less skillful models, then our conclusion regarding the relative importance of internal and external forcing in driving the observed trend in BoxΔP might change and the apparent inconsistency noted above might not persist.

In fact, the observed and modeled changes are inconsistent in some but not all of the models. By “inconsistent” we mean that if uncertainty associated with internal variability is taken into account, then the trends for some of the models do not have 95% confidence intervals that encompass the observed change. This is illustrated in Fig. 4, which shows trends in BoxΔP from individual runs together with the 95% confidence intervals for each model run. It is apparent that only 14 models have at least one run, which is consistent with the observed change (depicted in the same plot), and 9 do not. The MMEM based on the 14 consistent models is increased in magnitude (i.e., changed from −0.1 to −0.17 Pa yr^{−1}). Thus, the estimated relative importance of external forcing to internal variability increases. We will use this figure, that is, −0.17 to −0.52 Pa yr^{−1} or approximately 30%, as an estimate of the lower bound on the fraction of the observed trend explained by external forcing.

This approach is, to a certain extent, circular because the analysis is restricted to models that are closer to the observed change, and so it is inevitable that the agreement between observations and the MMEM of the subset will increase. An alternative approach that circumvents this problem is simply to examine trends in models that are best able to simulate other important aspects of twentieth-century climate. We know, for example, that van Oldenborgh et al. (2005) ranked models according to their ability to simulate ENSO, and that they identified a “best 6” and a “best 4.” If we restrict attention to these two subsets, then the new MMEM becomes −0.26 (best 6) and −0.2 Pa yr^{−1} (best 4). The larger magnitude for the best 6 arises because of the presence of the large downward trend in one particular model {Model for Interdisciplinary Research on Climate 3.2, high-resolution version [MIROC3.2(hires)]}, which is a member of van Oldenborgh et al.’s best 6 but not their best 4. The MMEM was also increased in magnitude for a “best 10” group of models we chose on the basis of correlation maps between Niño-3.4 and MSLP over the Pacific (MMEM = −0.20 Pa yr^{−1}).

The model with the next largest EM trend is the GFDL model version 2.1 (GFDL2.1), which is the model analyzed by Vecchi et al. (2006) and which is a member of the best 4. The EM trend in this model is approximately −0.37 Pa yr^{−1}, which is in much closer agreement with the observed trend (−0.52 Pa yr^{−1}). There are several runs available for this model, so this increases confidence in our estimation of its EM. We will therefore use this figure, that is, −0.37 to −0.52 Pa yr^{−1} or approximately 70%, as an estimate of the upper bound on the fraction of the observed trend caused by external forcing.

In summary, the models that exhibit consistency with the observed changes in BoxΔP and the models that are best able to reproduce ENSO variability tend to produce larger externally forced changes in BoxΔP that are in closer agreement with the observed trend. However, the MMEM of all the models, and 2 of the 3 MMEMs based on the best 4 and best 10 subsets have magnitudes that are less than half of the magnitude of the observed change in BoxΔP. And while the magnitude of the MMEM in the top 6 subset exceeds 50% of the corresponding observed value, the magnitude of the median value for this subset does not. Finally, only 3 runs out of the 73 analyzed have a trend that exceeds the observed trend in magnitude. We therefore conclude that both internal variability and external forcing contribute to the weakening of the WC, but the contribution from internal variability seems more likely than not to be larger than the contribution from external forcing. So, while our estimate of the fraction due to external forcing is estimated to be 30%–70%, an uncertain degree of extra weight should probably be given to the likelihood of values less than 50%. If we use the best 4 estimate as our best estimate, then we obtain an estimate of 40%.

It is interesting to note that the MIROC3.2(hires) has a declining trend that is larger in magnitude than the magnitude of the observed trend. To see if internal variability is contributing to the weakening of the WC, we conducted EOF analyses of sea surface temperature (SST) variability in this model to try to isolate variability linked to ENSO and the IPO. We found that the ENSO EOF (the second EOF of raw SST) exhibited a trend toward more El Niños over the twentieth century. Both the second and third EOFs of decadal changes in SST have spatial structures with a resemblance to the observed IPO (Power et al. 1999; Folland et al. 1999). One of these exhibited very little trend; while the other trended toward an El Niño–like phase of the IPO. Thus, internal variability seems to have contributed to this model’s downward trend in BoxΔP too. A caveat here is that EOF analyses do not necessarily decompose internally and externally forced variability accurately (see, e.g., Meehl et al. 2009) and so the results might be influenced by aliasing of the externally forced signal onto the higher-order EOFs that approximate internal variability.

## 6. Redefining BoxΔP to account for model bias

In the above discussion, we used the same boxes (BoxW and BoxE) for both the observations and the models. However, model SST variability coherent with ENSO in the eastern Pacific tends to extend too far into the western Pacific. It is therefore possible that MSLP variability does the same, so that some of the variability in the models that is coherent with variability in BoxE extends into BoxW in contrast to the observations. This is indeed the case for the vast majority of models. This is illustrated in Fig. 6, which shows the first EOF of MSLP over the tropical Indo-Pacific for the observations (top panel) and four representative models. Only one model captures this aspect of the observed spatial structure of MSLP variability [Canadian Centre for Climate Modelling and Analysis (CCCma) Coupled General Circulation Model, version 3.1 (CGCM3.1)], 17 of the 23 models show variability that is coherent in the east extending too far to the west [e.g., Centre National de Recherches Météorologiques Coupled Global Climate Model, version 3 (CNRM-CM3)], one group of models tends to show variability that is spuriously coherent over both boxes [the three Goddard Institute for Space Studies (GISS) models], and two models show variability in the east that is too weak and spuriously incoherent over BoxE [L’Institut Pierre-Simon Laplace (IPSL) and MIROC(hires)].

The first EOF of twentieth-century MSLP over the tropical Indo-Pacific for (top) the observations and four representative models. The boxes used are also depicted. The alternative BoxW used in section 6 is also shown.

Citation: Journal of Climate 24, 24; 10.1175/2011JCLI4101.1

The first EOF of twentieth-century MSLP over the tropical Indo-Pacific for (top) the observations and four representative models. The boxes used are also depicted. The alternative BoxW used in section 6 is also shown.

Citation: Journal of Climate 24, 24; 10.1175/2011JCLI4101.1

The first EOF of twentieth-century MSLP over the tropical Indo-Pacific for (top) the observations and four representative models. The boxes used are also depicted. The alternative BoxW used in section 6 is also shown.

Citation: Journal of Climate 24, 24; 10.1175/2011JCLI4101.1

It is of interest to know if our earlier conclusions are affected if we redefine BoxW so that all the variability in the box is coherent. We therefore repeated some of the earlier analysis using a new BoxW, which extends 20° less to the east than the original BoxW considered—as illustrated in Fig. 6. We examined trends in individual model runs, EM values, and the MMEM trends in BoxΔP using all the models and the top 4 only. We found very similar values to the values obtained above, indicating that this redefinition of BoxW does not have a major impact on the results.

## 7. A closer look at the observed changes

In previous sections we concentrated on changes over the period 1901–99. It is of interest to examine observed changes over longer and shorter periods to see how trends over our primary period of interest relate to trends over different periods to make sure that there is nothing particularly special about using 1999. Trends in BoxΔP over periods ranging from 1901 to various end dates (from 1990 to 2004) are depicted in Fig. 7a, together with corresponding *t* statistics. Note that more recent data than the data compiled by Allan and Ansell (2006), that is, after 2004, are available, but they are derived from a reanalysis product and are not used here to avoid the possibility of a spurious inhomogeneity in the data.

Observed trends in BoxΔP for (a) periods ranging from 1901 to various end dates (1990–2004), e.g., 1901–90, 1901–99, and so on, and for (b) 1870–2004, 1871–2004, and so on through to the period 1950–2004. Corresponding *t* statistics are also shown.

Citation: Journal of Climate 24, 24; 10.1175/2011JCLI4101.1

Observed trends in BoxΔP for (a) periods ranging from 1901 to various end dates (1990–2004), e.g., 1901–90, 1901–99, and so on, and for (b) 1870–2004, 1871–2004, and so on through to the period 1950–2004. Corresponding *t* statistics are also shown.

Citation: Journal of Climate 24, 24; 10.1175/2011JCLI4101.1

Observed trends in BoxΔP for (a) periods ranging from 1901 to various end dates (1990–2004), e.g., 1901–90, 1901–99, and so on, and for (b) 1870–2004, 1871–2004, and so on through to the period 1950–2004. Corresponding *t* statistics are also shown.

Citation: Journal of Climate 24, 24; 10.1175/2011JCLI4101.1

The plot shows that although the sign of the trend remains negative, the magnitude of the trend varies from −0.57 Pa yr^{−1} with a 1998 end date to −0.44 Pa yr^{−1} with an end date of 2004. These changes are linked to recent ENSO activity—trends increase in magnitude if a large El Niño event is included or decrease if a large La Niña is included. The corresponding *t* statistics vary in a similar manner, though with larger amplitude, around a value of approximately −2.8.

The trend for the period ending in 1999 has a value (−0.52 Pa yr^{−1}) that is smaller in magnitude than other values (e.g., for end dates of 1994 and 1998) but larger in magnitude than later dates, for example, after La Niña events have occurred. The *t* statistics vary between −3.2 (1998) and −2.2 (1990). The *t* statistic for the period ending in 1999 is larger than for most other years. These results do not change our conclusion that both internal variability and external forcing are needed to explain the observed trend. However, they further highlight the fact that we cannot provide an accurate value for the relative importance of external forcing in driving the observed trend.

One final point that needs to be made is that the observed values of trends in BoxΔP quoted above are estimates based on a MSLP dataset (Allan and Ansell 2006). This gridded dataset was carefully assembled using MSLP data from stations and from ships. However, the observational density underpinning the gridded data tends to decline markedly the further back in time one looks (Allan and Ansell 2006). This is especially important for BoxE, where the number of observations available in the late nineteenth century and the early twentieth century is relatively limited. It is therefore of interest to examine trends in BoxΔP over later (and earlier) periods. The trends for periods ranging from 1870 to 2004, from 1871 to 2004, and so on through to the period 1950–2004 are depicted in Fig. 7b. The trends are all negative and range from approximately −0.4 to −0.5 Pa yr^{−1} for start dates 1870–1910 to extremely negative values after 1930. The corresponding *t* statistics, conversely, vary from −3.9 for the 1870 start date and then diminish in magnitude to approximately −1.7 for start dates around 1920. The *t* statistics then increase in magnitude (to approximately −2.3) for start dates between 1930 and 1950. Thus, the possibly less reliable trends before 1910 have the largest *t* values. The possibility therefore exists that the observational estimates for 1901–99 used here and those examined by Vecchi et al. (2006) over longer periods might be in error.

This is supported by the fact that most of the trend in BoxΔP during 1901–99 was primarily driven by a trend in BoxE (−0.3 Pa yr^{−1}), with the trend in BoxW (+0.22 Pa yr^{−1}) contributing a smaller 42%. The possibility that observational error in BoxE is large in the late nineteenth century and in the early twentieth century is further supported by data presented in Fig. 8, which shows the correlation coefficient between year-to-year changes in Tahiti MSLP and BoxE in running 20-yr blocks. The values tend to be reduced before 1940 compared with the values they have after 1940. This is in contrast with the relationship between year-to-year changes in BoxW and Darwin MSLP, which is much more stable. While such features might be genuine, or they might reflect problems in Tahiti rather than in BoxE, the possibility that the trends in BoxΔP are overestimated by the available observations cannot be excluded. If the observed trend in BoxΔP is an overestimate, then the relative importance of external forcing increases.

Correlation coefficients between observed year-to-year changes in both Tahiti MSLP and BoxE in running 20-yr blocks. Equivalent correlation coefficients between Darwin MSLP and BoxW are also shown.

Citation: Journal of Climate 24, 24; 10.1175/2011JCLI4101.1

Correlation coefficients between observed year-to-year changes in both Tahiti MSLP and BoxE in running 20-yr blocks. Equivalent correlation coefficients between Darwin MSLP and BoxW are also shown.

Citation: Journal of Climate 24, 24; 10.1175/2011JCLI4101.1

Correlation coefficients between observed year-to-year changes in both Tahiti MSLP and BoxE in running 20-yr blocks. Equivalent correlation coefficients between Darwin MSLP and BoxW are also shown.

Citation: Journal of Climate 24, 24; 10.1175/2011JCLI4101.1

Fortunately, we can use BoxW alone as an alternative index for the strength of the WC. This is useful because the data density in BoxW is much greater in the late nineteenth and early twentieth centuries than it is in BoxE. It is reassuring to note that results using BoxW are consistent with the results presented in previous sections for BoxΔP: most models show an increase in MSLP in BoxW, the MMEM trend using all models (+0.06 Pa yr^{−1}) is much less than the observed trend (+0.22 Pa yr^{−1}), the observed trend is significant at the 95% level, the MMEM tends to be larger in the models best able to simulate ENSO (e.g., the MMEM of the top 10 models is increased to 0.1 Pa yr^{−1}), and only two models [GFDL2.1 and MIROC3.2(hires)] exhibit an EM trend that exceeds the observed trend. This increases confidence in the conclusions reached in section 5.

## 8. Discussion

We examined trends in an index we called BoxΔP (section 2), which has been used previously to track the strength of the Walker circulation (WC; Vecchi et al. 2006; Power and Kociuba 2011). We found that BoxΔP (and therefore the WC) weakened in the models during the twentieth century, consistent with the earlier studies. However, the magnitude of the multimodel ensemble mean (MMEM) trend (using all models) in the WC driven by external forcing is very small compared with the magnitude of the observed trend over the same period. This is true in all seasons. Even the twenty-first-century MMEM changes were shown to have magnitudes less than the observed trends in all seasons, and they were much smaller in all seasons under the A1B scenario and during December–May under the A2 scenario. The observed trends in BoxW, BoxE, and BoxΔP are +0.22, −0.30, and −0.52 Pa yr^{−1}, respectively—all of which are statistically significant at or above the 95% level. The corresponding MMEM trend in BoxΔP using all the models is −0.1 Pa yr^{−1}, which is much smaller in magnitude than the observed change. As the MMEM is a model-based estimate of the externally forced signal, these results suggest that the observed twentieth-century weakening of the WC, as measured by the index used (BoxΔP), was primarily driven by internally generated natural variability and was reinforced by external forcing—not the other way around. However, this could only occur if the internal variability underpinning the trend is extremely large in terms of modeled and observed interannual variability. For example, only 1 model run out of the 73 analyzed had a trend with a magnitude that rivaled the magnitude of the observed trend. Furthermore, the remaining observed trend—that is, −0.42 Pa yr^{−1}—is significant at the 98% level—that is, it remains unusually large. This is at odds with the fact that trends in indices linked to both ENSO and the IPO are weak. This suggests that the MMEM based on all the models is too small in magnitude.

We therefore examined changes in subsets, taking the ability of the models to replicate features of twentieth-century climate into account. We found that the externally forced signals tended to be larger in magnitude in models with a better representation of twentieth-century climate. For example, among the four “best” models identified by van Oldenborgh et al. (2005) on the basis of their ability to simulate ENSO, the MMEM trend is −0.2 Pa yr^{−1}. The equivalent figures for a top 6 and a top 10 we identified are −0.26 and −0.2 Pa yr^{−1}, respectively.

We therefore conclude that (i) both external forcing and internal variability have contributed to a weakening of the WC; (ii) the magnitude of the external contribution derived from the MMEM of all the models seems too small in magnitude; and (iii) the external contribution is larger for models better able to reproduce twentieth-century ENSO-related variability.

While we cannot be precise, we estimate that approximately 30%–70% of the observed weakening of the WC is due to external forcing, with internal variability making up the rest. Our appraisal of the results suggests that the contribution from internal variability is more likely than not to be larger than the contribution from external forcing, although this is a matter of judgment. The latter is partially driven by a weak trend toward more El Niño–like conditions, as reflected in indices for both ENSO and the interdecadal Pacific oscillation. We also noted that observational MSLP data coverage over the eastern Pacific is much reduced in the early twentieth century (Allan and Ansell 2006). Clearly, our estimate of the relative contribution of external forcing to the observed change depends on the magnitude of the observed change. If the available data overestimate the magnitude of the weakening that has actually occurred, for example, then the fractional contribution from external forcing might be larger than 30%–70%.

While advancement in our ability to simulate the earth’s climate over recent decades has been impressive, the CMIP3 models are not perfect. It will be interesting to see if the WCRP CMIP5 models provide more realistic depictions of tropical Indo-Pacific climate and if internal variability and external forcing make similar relative contributions to the observed weakening of the WC.

## Acknowledgments

The gridded MSLP data were provided by the Met Office. We wish to thank the Climate Variability and Predictability (CLIVAR) Working Group on Coupled Modelling (WGCM) Climate Simulation Panel for devising, initiating, and managing the WCRP CLIVAR WGCM Coupled Model Intercomparison Project phase 3 (CMIP3) experiment; agencies participating in CMIP; the Program for Climate Model Diagnostics and Intercomparison (PCMDI) in the United States for collecting, collating, and making CMIP3 output available; both Aurel Moise and Lawson Hanson for providing ready access to the data here in the Bureau of Meteorology; Francois Delage for ranking the models; and two anonymous reviewers for their constructive and very helpful reviews. This project was supported by the Australian Climate Change Science Program.

## APPENDIX

### Estimating the 10th and 90th Percentiles Presented in Figs. 1–4

The EMs for each scenario (i.e., the twentieth-century runs, the A1B runs, or the A2 runs) were separately ranked from smallest to largest: *R*_{1}, *R*_{2}, *R*_{3}, … , *R _{N}*. For example, Fig. 1 indicates that for the twentieth-century integrations, the smallest (annual average) EM =

*R*

_{1}= −0.61 Pa yr

^{−1}[for the MIROC3.2(hires)] and the largest EM for BoxΔP =

*R*= +0.21 Pa yr

_{N}^{−1}[for the National Center for Atmospheric Research (NCAR) Community Climate System Model, version 3 (CCSM3), run 5].

*p*= 10th and

*p*= 90th percentiles because they do not lie exactly on one of the ranked values

*R*. The 10th and 90th percentile values

_{i}*R*(at

*p*= 10) and

*R*(at

*p*= 90) are estimated using the following weighted mean of the adjacent

*R*and

_{i}*R*

_{i}_{+1}:

*a*=

*p*−

*j**100.0/(

*N*− 1),

*b*=

*k**100.0/(

*N*− 1) −

*p*,

*p*= 10 or 90 (or any other value between 1 and 100),

*j*= integer [(

*N*− 1)*

*p*/100], and

*k*=

*j*+ 1. The formula for

*j*gives the truncated (not rounded) integer part of the expression in [].

The Eq. (A1) works for all percentiles 1–100 even if (*N* − 1)**p*/100 is an integer equal to *j* (i.e., no interpolation is necessary). In this case the resultant percentile is reduced to *R _{i}*.

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