For many generations, models simulate an Indian Ocean dipole (IOD) that is overly large in amplitude. The possible impact of this systematic bias on climate projections, including a projected frequency increase in extreme positive IOD (pIOD) using a rainfall-based definition, has attracted attention. In particular, a recent study suggests that the increased frequency is an artifact of the overly large IOD amplitude. In contrast, here the opposite is found. Through intermodel ensemble regressions, the present study shows that models producing a high frequency in the present-day climate generate a small future frequency increase. The frequency is associated with the mean equatorial west-minus-east sea surface temperature (SST) gradient: the greater the gradient, the greater the frequency because it is easier to shift convection to the west, which characterizes an extreme pIOD. A greater present-day gradient is associated with a present-day shallower thermocline, lower SSTs, and lower rainfall in the eastern equatorial Indian Ocean (EEIO). Because there is an inherent limit for a maximum rainfall reduction and for the impact on surface cooling by a shallowing of an already shallow mean EEIO thermocline, there is a smaller increase in frequency in models with a shallower present-day EEIO thermocline. Given that a bias of overly shallow EEIO thermocline and overly low EEIO SSTs and rainfall is common in models, the future frequency increase should be underestimated, opposite to an implied overestimation resulting from the overly large IOD amplitude bias. Therefore, correcting the projected frequency from a single bias, without considering other biases that are present, is not appropriate and should be avoided.
During austral winter and spring, when easterlies prevail over the eastern equatorial Indian Ocean (EEIO), an initial cooling induces easterly anomalies, which lift the thermocline to a shallow depth. The shallower thermocline promotes an intensified upwelling, which in turn reinforces the initial cooling over the EEIO (Saji et al. 1999; Webster et al. 1999). This atmosphere–ocean positive feedback is referred to as Bjerknes feedback (Bjerknes 1969; Chang et al. 2006). In addition, the easterly wind anomalies transport warm water from the east to the west and shift the convection westward, further contributing to the zonal SST gradient and the wind anomalies. This is defined as a positive IOD event measured by a difference between the western equatorial Indian Ocean (WEIO) and EEIO SST anomalies (average over 10°S–10°N, 50°–70°E minus average over 10°S–0°, 90°–110°E; Saji et al. 1999). A negative IOD (nIOD) event is generally a mirror opposite to a positive IOD (pIOD) event but not symmetric, either in pattern or intensity; for example, a pIOD can reach a greater amplitude and exert a stronger impact than an nIOD (Hong et al. 2008), a feature referred to as the positive IOD skewness.
As the dominant source of interannual variability in the Indian Ocean (IO), a pIOD event, especially an extreme pIOD (Cai et al. 2014), can severely affect the atmosphere circulation in the IO-rim regions, affecting extreme weather, ecosystems, fishery, and agriculture (Emmanuel 2000; Frankenberg et al. 2005). During the extreme pIOD events of 1961, 1994, and 1997 (Cai et al. 2014), the easterly anomalies along the equator are far greater than other events, suppressing the convection over the EEIO with reduced rainfall extending farther westward but concentrating over the WEIO and East African countries, leading to bushfires in East Asia and southern Australia (Cai et al. 2009; Emmanuel 2000; Frankenberg et al. 2005) and coral reef death across western Sumatra (Abram et al. 2003) but devastating floods in East Africa (Behera et al. 2005; Black et al. 2003).
The fast warming since the 1950s induced by an increased level of greenhouse gases, although interrupted by a recent hiatus (Dai et al. 2015; England et al. 2014; Kosaka and Xie 2013; Watanabe et al. 2014), is projected to continue (Frölicher et al. 2014). As such, how the extreme pIOD events will respond to greenhouse warming is one of the most important issues of climate change science. To distinguish an extreme pIOD event from that of a moderate one, Cai et al. (2014) applied an empirical orthogonal function (EOF) analysis on rainfall anomalies over the equatorial IO and found that two EOF modes of rainfall anomalies over the equatorial Indian sectors are required. The EOF1 pattern reflects rainfall anomalies associated with the conventionally defined IOD (Saji et al. 1999), featuring concentrated anomalously low rainfall over the EEIO and anomalously high rainfall over the WEIO. The EOF2 pattern, which is strong during an extreme pIOD event, additionally captures the along-equator westward extension of dry anomalies from the EEIO and anomalously strong convergence and high rainfall anomalies over the East African countries. The future change in the frequency of extreme pIOD events can be quantified by applying EOF to rainfall anomalies referenced to the present-day climatological mean. Cai et al. (2014) found that although the frequency of moderate pIOD decreases (as more moderate events are going to be extreme in the future; see Ng et al. 2015), the frequency of extreme pIOD increases significantly under the representative concentration pathway (RCP) 8.5 in a majority of models participating in phase 5 of the Coupled Model Intercomparison Project (CMIP5; Taylor et al. 2012).
However, a recent study (Li et al. 2016) argued that the projected frequency increase is an artifact of the overly large IOD amplitude seen in most models. Given this bias, Li et al. (2016) went on to apply a statistical correction to the projected frequency, resulting in a nondiscernible projected change. To assess the validity or otherwise of their conclusion, we repeat their analysis and show that a linkage in the present-day climate between the IOD amplitude and frequency of extreme pIOD is absent and that this absence undermines their argument that the projected increase in the frequency of extreme pIOD is due to the present-day overly large IOD amplitude. Further, we show that an overly shallow EEIO thermocline, another common bias in most models (Cai and Cowan 2013), would lead to an opposite conclusion. That is, models with a shallower EEIO thermocline produce a smaller frequency increase, and because the present-day EEIO thermocline is overly shallow, the projected frequency increase would be underestimated.
The rest of our paper is organized as follows. In section 2, we describe the data used, highlight the definition of extreme pIOD, and introduce an approach adopted to examine intermodel relationships, the so-called emergent constraint. In section 3, we illustrate that the IOD amplitude has no influence in the projected frequency increase, and we show that the present-day frequency of extreme pIOD itself provides a constraint for its own future change. In section 4, we explore the associated mechanism, particularly its link to the bias of an overly shallow EEIO thermocline. A summary is given in section 5.
2. Data and methods
To compare with model simulations under present climate, we used the Hadley Centre Sea Ice and Sea Surface Temperature dataset (HadISST; Rayner et al. 2003), focusing on austral spring season [September–October–November (SON)] from 1900 to 1999. We also used thermocline depths, defined by the depth of 20°C isotherm, from the European Centre for Medium-Range Weather Forecasts Ocean Reanalysis System 3 (ECMWF ORA-S3; Balmaseda et al. 2008), covering the period of 1959 to 2009. The observed frequency of extreme pIOD events is estimated as six events per century based on the1950–99 period, in which three extreme pIOD events occurred (1961, 1994, and 1997; Cai et al. 2014). Prior to 1950s, rainfall observations were too rare to facilitate a reliable estimate.
b. Definition of extreme pIOD
As mentioned in section 1, EOF1 and EOF2 rainfall modes are required to define an extreme pIOD. Cai et al. (2014) defined an extreme pIOD as an event with rainfall EOF1 greater than 1.0 standard deviation superimposed on rainfall EOF2 greater than 0.5 standard deviations. The combination of the two EOFs depicts the difference between an extreme pIOD from a moderate one (see Cai et al. 2014, their Fig. 1) and identifies the 1961, 1994, and 1997 events as extreme pIOD. The use of the standard deviation thresholds enhances intermodel comparability in the CMIP5 analysis, as the extremity of the event then becomes relative to the variability magnitude within each model. This makes the projected change less dominated by models that produce large variability.
c. Model selection
We examined a total of 34 CMIP5 coupled general circulation models (CGCMs) forced with historical anthropogenic and natural forcings and future greenhouse gas under the RCP8.5 emission scenario (Taylor et al. 2012), focusing on austral spring season from 1900 to 2099. To gauge the influence of greenhouse warming, we compare the frequency between two periods: 1900–99 representing the present-day climate and 2000–99 representing future climate.
The projection of extreme pIOD frequency relies on the ability of models to simulate such an event. Not all models are able, and this model capability is tested by examining if a model simulated rainfall EOF1 and EOF2 patterns (Cai et al. 2014, their Figs. 2a and 2b) with a nonlinear relationship between them (Cai et al. 2014, their Figs. 2c and 2d). In Cai et al.’s (2014) study, a second condition is applied such that for a model to be selected the model must be able to simulate negative SST skewness in the eastern pole (or positive skewness in the IOD SST index). In the present study, we use only the EOF1–EOF2 nonlinear relationship so as to include as many models as possible. A total of 31 models are selected (GISS-E2-H, GISS-E2-R, and IPSL-CM5A-MR are excluded). Of the 31 models, 3 are excluded in the analysis involving thermocline depth because of a lack in the available ocean temperature data for calculating the thermocline. To be more precise, the simulated thermocline depth is represented by the depth of the maximum vertical temperature gradient (rather than the commonly used 20°C isotherm), which is regarded as more appropriate in a warming climate (Ng et al. 2014a; Vecchi and Soden 2007; Yang and Wang 2009).
d. Intermodel relationship: Framework of emergent constraint
Intermodel relationship can be used to examine the possible impact of a model bias on a projected change. If a statistically significant intermodel relationship emerges between a present-day observable process (trend, variation, or field) and a projected change (same process or another), then the bias associated with this observable process may potentially constrain future projections. This framework is referred to as emergent constraint (Allen and Ingram 2002; Boe et al. 2009; Collins et al. 2012; Cox et al. 2013; Hall and Qu 2006; Wenzel et al. 2014). To ensure that the relationship does not arise out of serendipity, there must be a statistically significant relationship between the two processes in the present-day climate. This is considered as a necessary condition. For instance, in present-day climate, Northern Hemisphere snow cover retreats during boreal summer (Robinson et al. 1993); therefore, reduced snow albedo will in turn increase temperature and snowmelt. Underpinned by this present-day relationship, the observable seasonal cycle can be a constraint for the future projection of snow albedo feedback (Hall and Qu 2006). To enhance intermodel comparability, the raw change (i.e., the difference between future and present day) can be scaled by the global mean temperature trend for each model (unit becoming original unit per °C of global warming). The scaling helps prevent projected changes to be skewed toward models with a high climate sensitivity (Bracegirdle and Stephenson 2013; Weller and Cai 2013). Note that using the raw difference as the projected change does not qualitatively change our conclusions (figures of this version not shown).
3. IOD amplitude is not an appropriate constraint
We find that there is no systematic intermodel relationship between extreme pIOD frequency and IOD amplitude in the present climate (Fig. 1a). This is despite the fact that there is a statistically significant relationship between the present-day IOD amplitude and frequency change; the greater the present-day IOD amplitude, the greater the change in the extreme pIOD frequency (Fig. 1b)—a relationship similar to that shown in Fig. 13a of Li et al. (2016). As noted by many studies, the simulated IOD amplitude is far greater than the observed. However, the absence of a linkage in the present-day climate (Fig. 1a) questions the validity of the relationship in Fig. 1b.
One may question whether the lack of a relationship between the extreme pIOD frequency and IOD amplitude in the present climate is due to the use of normalized anomalies in the definition of extreme pIOD (Cai et al. 2014). The normalization conceivably removes the impact of the overly large IOD amplitude bias because in models with a larger IOD amplitude the rainfall standard deviation is correspondingly greater. This means that in models with a larger IOD amplitude, the rainfall anomalies need to surpass a greater threshold to be considered as an extreme pIOD event. We therefore test this hypothesis by using the observed absolute EOF standard deviation value to define extreme pIOD.
For the observed, the nonscaled standard deviations for EOF1 and EOF2 are 25.3 and 17.30, respectively. We therefore used EOF1 > 25.3 (1.0 standard deviation) and EOF2 > 8.65 (0.5 standard deviations) to define extreme pIOD in all models for the present-day and future frequency (the alternatively defined frequency is indicated by frequency*). However, we found a similar result to Figs. 1a,b in that while the projected change in frequency* appears correlated with present-day IOD amplitude (Fig. 1d), there is no significant correlation between frequency* and IOD amplitude in present-day climate (Fig. 1c).
Reverting to the original definition of extreme pIOD as in Cai et al. (2014), we show that the projected frequency change could be constrained by the present-day frequency itself. Although rare, such self-constraint also exists in other reported cases. For example, simulated Arctic sea ice extent trend in present-day climate is found to be the best constraint for projected Arctic sea ice extent in the future, with an intermodel correlation coefficient of 0.86 (Boe et al. 2009). In our case, this provides another line of evidence that the present-day IOD amplitude is not a constraint for the future change in the extreme pIOD frequency, a point that will be clear later.
There is indeed a strong intermodel relationship between the present-day frequency and its future change (Fig. 2). Models generating more occurrences of extreme pIOD events in the present day produce a smaller frequency increase under greenhouse warming. With a strong correlation coefficient of −0.8, this is one of the strongest relationships identified, suggesting that the present-day frequency of extreme pIOD is one of the best constraints for its own future change. Based on this relationship and using the observed present-day frequency of six events per century (see section 2), given that the models tend to overestimate the present-day frequency, there is a case supporting that the projected increased frequency could actually be underestimated. The relationship shown in Fig. 2 is as strong as, if not stronger than, that of the emergent constraints shown in Li et al. (2016) but is opposite to that argued by Li et al. (2016). As will be shown below, the associated mechanism further undermines their argument.
4. Mechanism behind the present-day frequency as a constraint
As discussed in the introduction, occurrence of extreme pIOD events is linked to the westward shift of convection along the equatorial IO. The zonal movement of convection is in turn governed by a temperature difference between the WEIO and EEIO. We construct a present-day mean zonal west-minus-east SST gradient and examine whether it affects the present-day extreme pIOD frequency and whether it influences the future change in extreme pIOD frequency.
Models with more strongly positive zonal SST gradient tend to generate more extreme pIOD events in both the present-day climate (Fig. 3a) and future climate (Fig. 3b). This positive relationship strengthens between their projected changes (Fig. 3c). The strong relationship in Fig. 3a suggests that the necessary condition for the zonal SST gradient to be a potential constraint for future frequency change is met. However, there is a tendency (though significant only at the 93% significance level) for a relationship between the present-day mean zonal SST gradient and the projected increase in the frequency (Fig. 3d) that is completely opposite to that seen in the present-day climate. That is, models with a greater mean zonal west-minus-east SST gradient in the present-day climate tend to generate a smaller future increase in the frequency of extreme pIOD events.
Such an opposite relationship presents a case for caution when one attempts to correct the impact of a bias associated with a certain variable, for instance, IOD amplitude, as in the case of Li et al. (2016). For the zonal SST gradient, the multimodel ensemble mean is only slightly more positive than the observed, with a large intermodel spread, and thus does not constitute a systematic bias, unlike the IOD amplitude. However, as we will show below, the thermocline depth in the EEIO (i.e., overly shallow) constitutes a systematic bias that would require a correction that is opposite to that for the overly large IOD amplitude. Li et al. (2016) did notice this bias of the overly shallow EEIO thermocline, but they did not assess the impact of this bias on their projection. Our study shows that adjusting the projection based on the thermocline depth bias would result instead in an underestimation of the increased frequency.
A climatologically shallow thermocline in the EEIO facilitates upwelling off the Sumatra–Java region, cooling the EEIO and intensifying mean zonal SST gradient. As such, models with a shallower mean EEIO thermocline systematically produce a greater mean zonal SST gradient (Fig. 4a). Note that, the majority of the models suffer from a bias of an overly shallow mean thermocline in the EEIO. However, there is an opposite relationship, with a statistically significant correlation, between the present-day EEIO mean thermocline depth and the projected change in the mean zonal SST gradient under greenhouse warming (Fig. 4b). That is, models with shallower mean EEIO thermocline in the present day tend to generate a smaller increase in the mean west-minus-east zonal SST gradient under greenhouse warming.
This is because there is a limit to which the shallowing mean thermocline can impact further when it is already shallow to start with (Fig. 4c); as such, there is an inherent limit for the effect on surface cooling by the shallowing of the EEIO thermocline. In the extreme case, in which a mean thermocline is close to outcropping or well within the mixed layer, a further shallowing would induce no further cooling nor increase in the mean west-minus-east zonal SST gradient. Greenhouse warming brings the mean thermocline closer to this limit because an easterly trend over the EEIO associated with weakening of the Walker circulation leads to a shallowing of the mean thermocline (Cai et al. 2013; Ng et al. 2014b). In models with a shallower mean thermocline, this limit is being approached at a greater ease; therefore, the influence in the EEIO SST, the mean zonal SST gradient, and EEIO rainfall is curtailed.
That models with a present-day mean shallower EEIO thermocline systematically produce a smaller increase in the zonal SST gradient under greenhouse warming (Fig. 4b) provides an explanation for the feature shown in Fig. 2, which shows that models with a higher extreme pIOD frequency tend to produce a smaller frequency increase in the future. These models tend to simulate climatologically shallower thermocline and systematically stronger west-minus-east gradient (Fig. 4a), facilitating convection movement to the west, therefore leading to a higher frequency of extreme pIOD events in the present-day climate (Fig. 5a). But as the impact by the shallowing of the present-day shallow mean thermocline is increasingly curtailed under greenhouse warming (Fig. 4c), its influence on the mean SST gradient and on the frequency is also curtailed, leading to a saturation in the frequency increase under greenhouse warming. Consequently, models with a shallower present-day mean EEIO thermocline tend to produce a smaller increase in the extreme pIOD frequency under greenhouse warming (Fig. 5b).
Because a shallow mean thermocline is linked with a low SST in the EEIO, which in turn leads to low rainfall, and vice versa, the relationships between the present-day SST (or present-day rainfall) and the present-day extreme pIOD frequency (Figs. 6a,c) and between the present-day SST (or present-day rainfall) and the future frequency change (Figs. 6b,d) are similar to those discussed in Figs. 5a and 5b, respectively. These relationships in terms of SSTs and rainfall are another expression of, and help to explain, the relationship between the thermocline and the frequency. For example, models with a shallower mean thermocline depth generate colder SSTs and lower mean rainfall. The low mean rainfall is a limit for rainfall reduction associated with the frequency of extreme pIOD, in conjunction with the limit in thermocline-induced cooling.
Figure 7 depicts the mechanism of a shallower present-day EEIO thermocline constraining the increase in the extreme pIOD frequency under greenhouse warming, by comparing two different groups of models: deeper (Fig. 7a) and shallower (Fig. 7b) EEIO thermocline in the present-day climate. A present-day deeper thermocline is associated with a warmer and wetter condition in the EEIO. In the deeper thermocline group (Fig. 7a), a larger greenhouse-induced enhancement in the zonal west-minus-east gradient makes it easier for the convection to shift westward (i.e., requiring a smaller SST anomaly) (indicated by one purple dashed contour), compared to the shallower thermocline group (Fig. 7b), which requires a greater SST anomaly (indicated by two purple dashed contours). Thus, even if variability of zonal west-minus-east gradient does not change, it is easier to generate a larger increase in extreme pIOD frequency in the deeper thermocline group.
Given the overly shallow thermocline bias, which leads to the overly low SSTs and rainfall, one may be tempted to correct the future projection associated with these biases. In this case, the projected frequency would be adjusted to increase (Figs. 5b, 6b, and 6d). However, the adjusted projection due to the IOD amplitude bias would be a reduction (Fig. 1b). Such compensating adjustments illustrated here emphasize the inappropriateness of using only one aspect of model biases (e.g., the overly large IOD amplitude) (Li et al. 2016) to correct the projected frequency increase. If one corrects the impact of the bias associated with the overly large IOD amplitude, another opposite correction would be needed for the impact of the bias associated with overly shallow mean EEIO thermocline.
Although models simulate an IOD mode that features an overly large amplitude, we demonstrate that this systematic bias has no clear impact on the projected increase in the frequency of extreme pIOD, as defined in Cai et al. (2014). Given the positive correlation between present-day IOD amplitude and the projected increase in the frequency of extreme pIOD, there is, at a first impression, a clear need to adjust the projection downward based on the overly strong simulated IOD amplitude, as done by, for instance, Li et al. (2016). However, we present a series of analyses arguing that such bias correction would be naïve and inappropriate.
First, we show that there is no correlation between IOD amplitude and the frequency of extreme pIOD in the present-day climate. This is not surprising given that the extreme pIOD, which is a nonlinear process depicting zonal movement of convection, is not simply a function of IOD amplitude. Second, we find that the present-day frequency of extreme pIOD provides an effective constraint for its own future change. Interestingly, models that produce a higher frequency in present-day climate tend to generate a smaller future increase, as if there was a process that limits such increases under greenhouse warming when the frequency is already large to start with. We found that the root of such a process is the impact of the thermocline depth. A climatologically shallower thermocline in the EEIO is associated with lower EEIO SSTs, a greater west-minus-east equatorial zonal SST gradient, and lower EEIO mean rainfall, facilitating a higher present-day frequency of extreme pIOD events. However, the impact of further shallowing of the already shallower EEIO thermocline is curtailed under greenhouse warming. This is manifested as a smaller projected increase in zonal SST gradient and a smaller reduction in mean rainfall, both limiting the projected frequency increase. In addition to an overly large IOD amplitude, most models also simulate an overly shallow EEIO thermocline and overly low mean SSTs and mean rainfall in the EEIO region. On the basis of the latter biases, the projected frequency increase would be underestimated, opposite to that based on the overly large IOD amplitude alone. Thus, correcting the projected frequency change from a single bias, as carried out by Li et al. (2016), without considering other biases that could result in an opposite correction, should be avoided. Further, given that it is hard to identify all manifestations of all biases, the corrected result is not consistent with dynamics that generate the original projection and may not necessarily be a better projection than the original.
Given that different systematic biases can lead to opposing corrections, and given that it is difficult to identify all biases, it follows that the most appropriate way to improve climate projections is to keep working toward more realistic climate models. In this way, the improved projections would result from a dynamically consistent system owing to improvements in the simulated climate as a whole.
W. C. and G. W. are supported by the Australian Climate Change Science Program and a CSIRO Office of Chief Executive Science Leader award. A.S. is supported by the Australian Research Council.
Pacific Marine Environmental Laboratory Contribution Number 4427.