This study develops a new observational constraint method, called multimodel ensemble pattern regression (EPR), to correct the projections of regional climate change by the conventional unweighted multimodel mean (MMM). The EPR method first extracts leading modes of historical bias using intermodel EOF analysis, then builds up the linear correlated modes between historical bias and change bias using multivariant linear regression, and finally estimates the common change bias induced by common historical bias. Along with correcting common change bias, the EPR method implicitly removes the intermodel uncertainty in the change projection deriving from the intermodel diversity in background simulation.
The EPR method is applied to correct the patterns of tropical Pacific SST changes using the historical and representative concentration pathway 8.5 (RCP8.5) runs in 30 models from phase 5 of CMIP (CMIP5) and observed SSTs. The common bias patterns of the tropical Pacific SSTs in historical runs, including the excessive cold tongue, the southeastern warm bias, and the narrower warm pool, are estimated to induce La Niña–like change biases. After the estimated common change biases are removed, the corrected SST changes display a pronounced El Niño–like pattern and have much greater zonal gradients. The bias correction decreases by around half of the intermodel uncertainties in the MMM SST projections. The patterns of corrected tropical precipitation and circulation change are dominated by the enhanced SST change patterns, displaying a pronounced warmer-get-wetter pattern and a decreased Walker circulation with decreased uncertainties.
Projections of regional climate change under global warming have been a fundamental problem in climate change research, but they often suffer greater uncertainties than the projection of global mean temperature (Meehl et al. 2007; Christensen et al. 2013; Xie et al. 2015). Patterns of change in tropical Pacific sea surface temperature (SST) are one of the most important issues on regional climate change, which has crucial impacts on changes in some other regional climate variables and climate phenomena, such as precipitation, large-scale circulation, and ENSO (Clement et al. 1996; Cane et al. 1997; Liu et al. 2005; Vecchi and Soden 2007b; Deser et al. 2010b; Xie et al. 2010; Tokinaga et al. 2012; Yeh et al. 2012; Huang et al. 2013; Ma and Xie 2013; Ma and Yu 2014).
The zonal-mean tropical Pacific SST changes, displaying an enhanced equatorial warming pattern due to weaker evaporation damping on the equator (Liu et al. 2005; Xie et al. 2010), are quite robust in the projections by models from phases 3 and 5 of the Coupled Model Intercomparison Project (CMIP3 and CMIP5, respectively) (Fig. 1a; the models, experiments, and time periods in Fig. 1 are described in section 2). However, the zonal structure of the tropical equatorial SST changes, displaying an El Niño–like pattern in the multimodel averaged projection, has great intermodel uncertainties (Fig. 1b). The maximum uncertainty is located on the equatorial western and central Pacific, as illustrated by the sign agreement of more than 90% of models in Fig. 1a and by the intermodel standard deviations in Fig. 1b. The intermodel standard deviations of the SST changes are up to 0.2°C for every 1°C of surface warming, which is greater than the weak zonal gradient of the multimodel mean (MMM) SST changes, around 0.15°C for every 1°C of surface warming (Fig. 1a). An El Niño–like pattern, a La Niña–like pattern, or a zonally uniform pattern is still controversial in previous studies, possibly because various processes favoring different zonal gradient changes counterbalance each other (Cane et al. 1997; Liu et al. 2005; DiNezio et al. 2009; Deser et al. 2010b; Xie et al. 2010; Tokinaga et al. 2012; Yeh et al. 2012). For example, the mean upwelling in the eastern Pacific brings up relatively cool subsurface water, decreasing surface warming in the east (Clement et al. 1996; Cane et al. 1997), whereas the weakened atmospheric circulation as a result of energy constraint will enhance surface warming in the east (Held and Soden 2006; Vecchi and Soden 2007a). The sensitivities of these feedbacks are not identical in various models, simulating controversial changes in the zonal gradient of SST (Xie et al. 2015). As shown in Fig. 2, although the majority of the models project SST changes as an El Niño–like pattern, some models, such as BCC_CSM1.1, BCC_CSM1.1(m), CanESM2, GFDL CM3, IPSL-CM5A-LR, and IPSL-CM5A-MR (see Table 1), project SST changes as a zonally uniform pattern. The uncertainties in the tropical Pacific SST changes are a great source of uncertainty in global circulation and precipitation changes (Huang et al. 2013; Ma and Xie 2013; Huang 2014).
A conventional method to improve reliability of climate model projections is to average changes in multiple models, often called the multimodel ensemble mean (Meehl et al. 2007; Knutti et al. 2010; Collins et al. 2012; Christensen et al. 2013). In MMM, the model background, often represented by long-term mean in historical run, is subtracted from a future run [e.g., representative concentration pathways 4.5 and 8.5 (RCP4.5 and RCP8.5)] for each model member before averaging, based on a simple assumption that model bias stays constant in historical and future runs. However, climate change often interacts with background climate, and faulty climatic feedbacks associated with unrealistic background states also play a role in climate change (Whetton et al. 2007; Räisänen et al. 2010; Bracegirdle and Stephenson 2012; Collins et al. 2012; Bracegirdle and Stephenson 2013). The simple MMM method cannot remove all bias from future simulations. In particular, there likely exists common change bias in MMM change induced by common background bias among ensemble members. For example, the simulations of tropical Pacific SST in CMIP5 models have some well-known common bias patterns (Fig. 3), such as the excessive cold tongue, the southeastern warm bias, and the narrower warm pool (Zheng et al. 2011; Li and Xie 2012; Zheng et al. 2012; Li and Xie 2014). In Figs. 1a and 3c, the spatial gradients of the common historical biases are an order of magnitude higher than the gradients of the MMM changes. It is unclear how the common historical biases could influence the spatial structure of the SST changes projected by MMM.
Several bias correction (calibration) methods were proposed to decrease the influence of background bias (Knutti 2010; Ho et al. 2012). A large number of approaches can be categorized as a model weighting method based on a strategy that “better” models are more trusted (Tebaldi and Knutti 2007; Räisänen et al. 2010). However, the strategy of model weighting methods is questionable, and these methods often have some constraints in domain selection, variable dependence, and subjective model metrics (Tebaldi and Knutti 2007; Knutti 2010; Shiogama et al. 2011; Ho et al. 2012).
Another strategy not widely used yet is derived from a concept called “emergent constraint” that believes there exists a relationship between the response of the Earth system to global warming and the observed features of the Earth system (Boé et al. 2009; Bracegirdle and Stephenson 2012; Collins et al. 2012; Bracegirdle and Stephenson 2013; Cox et al. 2013). Methods based on this strategy often construct a historical–future relationship using intermodel diversity and then project future climate based on the historical–future relationship and observations (Whetton et al. 2007; Räisänen et al. 2010; Abe et al. 2011; Shiogama et al. 2011; Bracegirdle and Stephenson 2012). Bracegirdle and Stephenson (2012) developed an ensemble regression method capturing the linear relationship between polar warming response to global warming and present mean state to improve the precision of multimodel projection. The ensemble regression method can improve the robustness of Arctic warming projections (Bracegirdle and Stephenson 2012, 2013). Shiogama et al. (2011) developed a method exploring spatially coupled modes between present and future climate and then constraining projections using the coupled modes and observations. Similar observational constraint was applied to project global surface temperature changes (Abe et al. 2011). Nevertheless, the previous studies argued the present–future relationship in models is not pronounced in low latitudes (Räisänen et al. 2010; Abe et al. 2011), which implies that the observational constraint methods could be inapplicable to project the tropical Pacific SST change patterns. But actually, the tropical Pacific SST change patterns are very sensitive to the tropical air–sea coupled feedbacks (Clement et al. 1996; Vecchi and Soden 2007a; DiNezio et al. 2009; Xie et al. 2010, 2015), which also dominate background SST patterns in models (Zheng et al. 2011; Li and Xie 2012; Zheng et al. 2012; Li and Xie 2014). Therefore, the present–future relationship of tropical Pacific SST could be remarkable, when we focus on the tropical Pacific in which the tropical air–sea coupled feedbacks are dominant.
In the present study, we propose a novel multimodel ensemble pattern regression (EPR) method to estimate common change bias correlated to common background bias and then to correct the MMM change projection based on the “observational constraint” strategy. This method is applied to correct the tropical Pacific SST changes under global warming, and to correct the changes in tropical Pacific precipitation and circulation, which are closely coupled with the SST changes (Xie et al. 2010; Huang et al. 2013; Ma and Xie 2013; Huang 2014). Section 2 describes the CMIP5 outputs and the observational data used in this study. The correction method is introduced in section 3. Section 4 displays the correction result of the simulated tropical Pacific SST changes, and the corrected changes in precipitation and circulation are discussed in section 5. Some conclusions and a discussion are presented in section 6.
2. Models and data
We use the outputs of 30 coupled general circulation models participating CMIP5 including the historical experiment for the period of 1981–2000 and RCP8.5 experiment for 2081–2100 (Taylor et al. 2012). The 30 models are listed in Table 1. The outputs of SST, precipitation, and 1000-hPa wind are used. The observed SST used in this study comes from the NOAA ERSST, version 3b (v3b), for the period of 1981–2000 on a 2° × 2° latitude–longitude grid (Smith et al. 2008). All outputs in the models and observations are interpolated into a 2.5° × 2.5° latitude–longitude grid before all analyses.
a. Correction for common bias
The framework of the EPR correction method is shown in Fig. 4. The MMM change is first calculated using the conventional MMM method, and the change bias in individual model can be obtained (step 0). We represent historical climatology in model i by Hi and future climatology by Fi, and the future change is defined by Ci = Fi − Hi. In the present study, the historical climatology is calculated by the long-term mean for the period of 1981–2000 in historical run, whereas the future climatology is the mean of 2081–2100 in RCP8.5 run. We suggest that the regional Ci should be normalized by the global mean temperature increase in the respective model to remove uncertainties from global mean temperature change, because regional climate change often responds to global mean warming but not directly to carbon dioxide increases. In the present application, the changes in each model are normalized by respective mean surface warming in middle and low latitudes (60°S–60°N). Based on a hypothesis that all “perfect” models will project a same real change Creal, the MMM change must include the real change Creal and a common change bias of all models . The following steps try to estimate the common change bias and then to correct the conventional MMM change . The individual change bias in model i can be represented by , and the total change bias in model i is .
Similarly, the historical climatology Hi in model i can be decomposed into the observed climate HObs, the common historical bias , and the individual historical bias (step 1).
Step 2 explores the spatially correlated modes between historical bias and change bias using the intermodel diversity in H″ and C″ (hereafter notations without subscript i denote values in all models). Various multivariant linear statistic methods can be applied to explore correlated modes between two variables, such as single field principal component analysis (SFPCA), singular value decomposition (SVD), and canonical correlation analysis (e.g., Bretherton et al. 1992; Wilks 2006). In Shiogama et al. (2011) and Abe et al. (2011), the SVD method is used to analyze the historical–future coupled modes. However, historical background can affect climate change in models, but climate change cannot feed back to historical background. Thus, we use SFPCA method to extract the leading modes in multimodel historical bias and their correlated modes in change bias. In SFPCA, principal component analysis (PCA) [i.e., empirical orthogonal function (EOF)] is first performed on one variable, and then the other variable is regressed onto the principal components (PCs) associated with the EOF modes. Each EOF mode and its related regression pattern can be considered as a couple of historical–change correlated modes (e.g., Bretherton et al. 1992). The SFPCA method makes the discussion on the uncertainty in the corrected change more convenient (in the next subsection).
In step 2, H″ is first expended into M spatially orthogonal modes EOFj, j = 1, …, M using EOF analysis, and the related principal coefficients PCij for the models can be obtained. Note that H″ can be represented as . The truncation of M EOFs should be determined based on the representation of EOF modes for H″ and common historical bias . The EOF modes can be further rotated for interpreting spatial patterns more clearly, but EOF rotation does not influence the final result of correction.
Multivariant linear regression analysis is performed on PCs and individual change bias C″, and thus C″ can be estimated by the regression patterns and PCs:
If the EOF modes are not further rotated, the PCs are linearly independent among all modes and thus the multivariant linear regression patterns equal the single-variant linear regression patterns of C″ onto PCs mode by mode. Together EOFj and , for j = 1, …, M, form M couples of historical–change correlated modes.
Historical–change correlated modes are explored in present method as in Bracegirdle and Stephenson (2012), different from the historical–future correlated modes in other studies (Abe et al. 2011; Shiogama et al. 2011). Using change but not future climatology removes the direct influence of individual historical bias on future climatology. This alternation also makes it easier to compare with projections by the conventional MMM method, and to discuss the intermodel uncertainty in corrected change.
The common change bias can be estimated based on an assumption that the common historical bias will produce a common change bias and that their relationship is identical to the relationship represented by the correlated modes of EOFj and (step 3). The bias can be projected onto EOFj and represented by expansion coefficients ej:
Substituting ej into the regression equation [Eq. (1)], we can estimate as
Then, we can correct the conventional MMM change as to give a bias-corrected change (step 4). The present EPR method could be understood as an extension of the ensemble regression method designed for regional-mean change in Bracegirdle and Stephenson (2012), in which the linear regression method and the historical–change relationship are also applied. The EPR method is more effective in correcting changes characterized by obvious regional patterns (e.g., the tropical Pacific SST changes in this study).
b. Correction for change bias in an individual model
Similar to the correction for common bias in MMM, the change bias in an individual model can also be corrected based on the historical–change correlated modes and the total historical bias in the model. In step 3, the total historical bias in model i, which consists of the common bias and individual bias , can be projected onto EOFj and represented by expansion coefficients eij. (The expansion coefficients eij for are different from the principal components PCij in the EOF analysis that are related to the individual historical bias .) The total change bias in model i can be estimated as . Finally, the change in model i can be corrected as in step 4.
Because of the linearity of Eqs. (2) and (3), and , the estimated change bias related to and the estimated common change bias related to , have relationships , , and , where is the estimated individual change bias related to the individual historical bias . As a result, the corrected change for the common historical bias equals the mean of individually corrected changes:
c. Uncertainty in corrected change
The individual changes C″ are often considered as intermodel uncertainty in conventional MMM projections, usually measured by the standard deviations of C″. Similarly, because of Eq. (4), we can use the individual corrected change , the difference between the corrected changes CCi in model i and the corrected common change , to represent the intermodel uncertainty of the EPR corrected change . The uncertainty can be deduced as
The difference is the residual in the regression equation [Eq. (1)]. Equation (5) indicates that the uncertainty in corrected change only is the part that cannot be interpreted by the linear historical–change relationships. In other words, when we remove the estimated common change bias using the historical–change relationships, the intermodel change uncertainty deriving from the intermodel historical diversity is also removed from the uncertainty in the corrected change.
d. Correction for other variables
In this EPR method, the historical variable and the change variable is not necessary to be the same variable or in the same domain. The correction method can be used to investigate the influence of common historical bias in one climate system on the change in another system. Generally, a driving variable is suggested to be the historical variable. For example, SST is often considered as a driving variable in climate variability and climate change in tropical oceans (Ma and Xie 2013; Ma and Yu 2014). Moreover, a variable in a larger domain is often considered as a driving variable while another variable in a smaller domain as a dominated variable (Shiogama et al. 2011). Applying the EPR method to changes in precipitation and surface wind over the tropical Pacific with SST as the background variable, we will estimate the common change biases in precipitation and surface wind correlated to the common background SST biases.
4. Corrected SST change patterns
Figure 5 shows the first eight intermodel EOF modes of historical SST biases in the simulations of 30 CMIP5 models. Percentages of the explained variances are shown at the top-right corner of panels in Fig. 5. The first EOF mode is a regionally uniform pattern, explaining 51% of the total variance; EOF 2 is a west–east oscillation pattern with two poles in the west and one pole in the east, explaining 13.3% of the variance; EOFs 3, 4, and 8 describe three meridional structures in the east with different poles and spatial scales, explaining 11.1%, 6%, and 1.6% of the variance, respectively; and EOFs 5 and 6 describe two meridional structures in the central Pacific, explaining 4.8% and 3.6% of the variance, respectively. The eight EOFs totally explain around 93% of the variance. The total percentage of 51% and high percentages of local variances (contours in Fig. 5a) explained by EOF 1 indicate that the intermodel variance of regional mean biases is a dominant part of the total variance. Because of the importance of regional patterns, we also calculate the percentages of local variances explained by each mode relative to the total local variances in which the regional mean biases are removed (contours in Figs. 5b–h). As shown in Fig. 5, EOFs 2, 3, 4, and 5 represent modes of interbasin oscillation, whereas EOFs 6, 7, and 8 explain relatively large fraction of variances in smaller regions. From this aspect, EOFs 6, 7, and 8, despite explaining less than 4% of the total variance, are meaningful to represent some small-scale patterns. Consequently, the eight EOFs are truncated in this application.
The importance of one EOF mode for the common historical biases can be measured by the expansion coefficient (EC; ei shown at the top-right corner of the panels in Fig. 5) of the common historical biases projected on the EOF mode (Fig. 3c). The sign of each EOF mode is adjusted to make its related EC positive. The large ECs of EOFs 1, 2, 4, 5, 6, and 8 indicate that the related EOF modes are more important for the common historical biases. By comparing Figs. 5 and 3c, it can be seen that the EOFs successfully capture the main properties of the common historical SST biases in the CMIP models (Zheng et al. 2012; Li and Xie 2014). EOF 1 represents the common cool bias, EOF 2 represents the narrower warm pool and the southeast warm bias, EOFs 4 and 8 represent the south–north antisymmetric bias in the eastern Pacific and the southeast warm bias, and EOFs 5 and 6 represent the excessive cold tongue bias.
The individual SST change biases in the models are regressed onto the PCs associated with the EOF modes grid by grid. The patterns of regression coefficients are shown in Fig. 6. The standard deviations of the PCs are multiplied to the regression patterns, respectively, in order to compare the contributions among the PCs. The contribution of each PC can also be measured by the percentage of the explained variance shown at the top-right corner of each panel in Fig. 6. All eight PCs explain around 50% of the total variance of change biases, and the regression equation is significant at 99% confidence level based on the Student’s t test. However, the percentages explained by most of PCs, individually, are less than 10% (insignificant at 90% confidence level), except PC 5 explaining around 15%.
Similar to the EOF modes, the regression patterns are also characterized by regional patterns with different spatial scales. For example, the regression pattern of PC 5 is mainly located over the central Pacific, and the regression pattern of PC 7 is over the eastern Pacific. Thus, the percentages of local variances explained by each PC (contours in Fig. 6) are calculated, and the local regressions that are significant at 90% confidence level are masked by stipple in Fig. 6. The result shows that the PCs can explain more local variances and are significantly correlated with the change biases over some local regions. It is similar to the EOF modes that only explain comparable variances of historical biases in some local regions (Fig. 5).
The product of EC (ei) and root-mean-square (RMS) of regression pattern in one mode is used to roughly assess the influence of common historical biases on change bias by this mode (shown at the top-right corner of each panel in Fig. 5). The common historical biases represented by modes 2, 4, 5, 6, and 8 will induce relatively large change biases. The change biases induced by different historical bias modes could be against each other. For example, mode 5 (mode 2) could induce warm (cold) change biases in the western-central Pacific, whereas modes 6 and 8 (mode 7) could induce cold (warm) change biases in the eastern Pacific. The regression patterns correlated with the excessive cold tongue and the southeast warm bias in historical simulations (Figs. 5e,f,h) both display a La Niña–like pattern (Figs. 6e,f,h), although they are located in different longitudes. The regression pattern correlated with the narrower warm pool bias approaches an El Niño–like pattern (Figs. 5b and 6b).
The historical–change relationships in these mode couples are quite complicated. It cannot be simply explained by a process that historical warm bias in somewhere will induce warm change bias in the same place. The historical and change biases are both associated with the sensitivities of several tropical air–sea feedbacks in models, such as the Bjerknes feedback, the wind–evaporation–SST feedback, and the cloud–radiation–SST feedback (e.g., Wang et al. 2004; Sun et al. 2006; Lin 2007; Sun et al. 2009; Deser et al. 2010a; Zheng et al. 2012; Li and Xie 2014). Some previous studies have discussed the formation mechanisms of some historical bias modes in CMIP models (Zheng et al. 2011; Li and Xie 2012; Zheng et al. 2012; Li and Xie 2014). However, the processes that the unrealistic feedbacks influence change biases could be different from the processes in historical simulations. For example, EOF 5, representing the excessive cold tongue bias, could be enlarged by a deficient cloud–SST negative feedback in models (Sun et al. 2003; Sun et al. 2006; Zheng et al. 2012), and the deficient cloud–SST negative feedback could not sufficiently suppress the surface warming and induce warm bias in the southeastern Pacific (Fig. 6e). Another important systematic bias, the southeastern warm bias in EOFs 2 and 8, was suggested to be associated with a weak stratus–SST positive feedback (Zheng et al. 2010, 2011) and a too strong wind–evaporation–SST feedback (Li and Xie 2014) in models. As a result, the insufficient positive feedback cannot enlarge the surface warming enough, and thus induces cold bias over the eastern Pacific under global warming (Figs. 6f and 6h). The physical processes should be investigated in future studies.
Figure 7a shows the reconstruction of the common historical biases by the eight modes and ECs, and the residuals of the reconstruction are shown in Fig. 7b. The first eight modes almost describe all spatial structures of the common historical biases with small residuals (Figs. 7a and 3c). The modes after the eighth mode display multiple poles, explain very small percentages of the total intermodel variance, and represent small variance of the common historical biases (not shown). It is another reason that we empirically truncate the eight modes to reconstruct the estimation of common change biases in step 3.
Figure 8a shows the SST change biases constructed by the eight regression patterns and ECs of the common historical biases. The estimated SST change biases exhibit a pronounced La Niña–like pattern. This pattern is mainly contributed by the change biases correlated with the historical excessive cold tongue bias and the southeast warm bias (modes 5, 6, and 7). When the estimated common change biases are removed from the MMM SST changes (Fig. 1a), the corrected SST changes exhibit a more pronounced El Niño–like pattern (Fig. 8b). The zonal gradient of the corrected SST changes, defined by the regional-mean difference between the two domains (5°S–5°N, 130°E–170°W and 5°S–5°N, 145°–85°W; shown by the two green dashed-line boxes in Fig. 8a), is around 3 times as large as the gradient of the uncorrected changes in Fig. 1a. The enhanced gradients of SST changes imply greater impacts on global climate changes (Xie et al. 2010).
Leverage for each model is calculated to evaluate whether there exist outlier models dominating the regression results when the model number is limited (Bracegirdle and Stephenson 2012). The leverage of one model is defined by the difference between corrected changes projected by the other 29 models, excluding the selected model, and the corrected changes projected by all 30 models. The result shows that CanESM2, FGOALS-g2, and GISS-E2-R influence the correction larger than the other models (Fig. 9). Even so, the leverages in these three models are much smaller than the final estimation (Fig. 8b), indicating that there is no apparent outlier model in the estimation by the 30 CMIP5 models.
It is worth noting that the three models with relatively large leverages may not be models with distinct uncorrected change patterns (Fig. 2). For example, CanESM2 and GISS-E2-R have an ordinary weak El Niño–like pattern similar to the MMM. On the other hand, the change patterns in CSIRO Mk3.6.0, NorESM1-M, and NorESM1-ME are quite different from the MMM (Fig. 2), but the leverages of these models are very small. It is because the EPR method is based on the historical–change relationship but not only on the change biases. If the change pattern in one model is extraordinary but the historical–change relationship in the model is consistent with the common historical–change coupled modes, the extraordinary change pattern cannot markedly affect the common historical–change modes and the model should not be an outlier model.
b. Uncertainties in the corrected changes
As discussed in section 3c, the intermodel uncertainties in the corrected SST changes can be investigated by individually correcting SST changes for every model (Fig. 10). Unlike the diverse patterns of uncorrected SST changes (Fig. 2), the corrected change patterns are quite consistent among the models, all displaying a pronounced El Niño–like pattern (Fig. 9). The sign agreement of corrected relative SST changes in models with the MMM changes is shown in Fig. 8b (similar to that in Fig. 1a). After correction, the regions with sign agreement of more than 90% of models almost expand to the whole domain (hatching in Fig. 8b). Robust sign agreement in the corrected relative SST changes appears in the equatorial western Pacific and the northeastern (2°–12°N) Pacific, in which the uncorrected relative changes are not robust (Fig. 1a). The positive–negative boundary in the southeastern Pacific is also clearer.
The intermodel uncertainties in the corrected SST changes can be measured by the standard deviations of the individually corrected changes in the models. The maximum uncertainty in the corrected changes is also located over the equatorial central Pacific (Fig. 8c) with similar spatial pattern to that in the uncorrected changes. However, the corrected uncertainties decrease by around 40%–50% relative to the uncorrected uncertainties (dashed contours in Fig. 8c). It indicates that around half of the intermodel uncertainties in SST changes can be explained by the intermodel diversities in SST background bias. This part of uncertainties is not “uncertain” any more when the common change biases that can be attributed to the common background biases have been removed from the MMM changes. The other variances of changes, which are not linearly correlated to the background biases, remain the uncertainties in the corrected SST changes. The processes such as the direct CO2 feedbacks, the internal variability, and the nonlinear interaction between background and change could contribute to the remaining uncertainties in the corrected SST changes (e.g., Deser et al. 2012; Ho et al. 2012; Deser et al. 2014; Monier et al. 2015).
The robustness of the corrected SST change pattern and its high similarity with the El Niño pattern (Fig. 10) imply that the El Niño–like pattern could be an intrinsic mode of the tropical Pacific SST. Different external forcings would induce a similar spatial pattern response, for example in ENSO, Pacific decadal oscillation (PDO), response to spatially uniform CO2 increases, and response to spatially nonuniform aerosol changes (Xie et al. 2013).
5. Correction for the tropical Pacific precipitation and circulation changes
The SST change patterns are one of the most important factors on the changes in regional precipitation and circulation, and are also the main source of their uncertainties (Lu et al. 2008; Xie et al. 2010; Huang et al. 2013; Ma and Xie 2013; Huang 2014; Ma and Yu 2014). The tropical SST change patterns dominate the dynamic component of precipitation changes: the tropical precipitation will increase over regions with greater SST warming but decrease over less-warming regions (i.e., the warmer-get-wetter effect; Xie et al. 2010; Huang et al. 2013; Huang 2014). On the other hand, the thermodynamic component of precipitation changes associated with the increased moisture will enhance precipitation over current wet regions (i.e., the wet-get-wetter effect; Chou and Neelin 2004; Held and Soden 2006; Chou et al. 2009; Seager et al. 2010). In the tropical Pacific, the weak El Niño–like pattern of the uncorrected SST changes leads to positive precipitation changes in the central Pacific and negative changes over the less-warming regions. The dynamic contribution of the SST change patterns and the increased precipitations over the climatological wet regions are comparable with each other in MMM and form a hooklike pattern of precipitation changes over the tropical Pacific (Fig. 11a; Huang 2014).
The tropical overturning circulation should generally slow down to maintain energy balance (Held and Soden 2006; Vecchi and Soden 2007a) because the global total precipitation will increase at a rate of 2%–3% K−1 warming determined by the radiative energy constraint whereas atmospheric moisture will increase at a much higher rate of around 7% K−1 determined by the Clausius–Clapeyron equation. However, the regional circulation changes also depend on the regional air–sea coupling changes (Ma and Xie 2013). The slowdown of the trade winds potentially forces out an El Niño–like SST change pattern, and the El Niño–like SST change pattern will further decrease the trade winds in turn as the Bjerknes feedback. But some slab ocean model experiments suggested that the SST changes could exhibit an El Niño–like pattern without dynamic air–sea coupling (Vecchi and Soden 2007a; Lu and Zhao 2012). Because of the complexity of the processes, the surface (1000 hPa) zonal wind changes in CMIP5 MMM are not pronounced (Fig. 11a), coupling with the weak El Niño–like SST change pattern (Fig. 1a).
The common change biases in precipitation and surface wind correlated with the common historical biases in SST are corrected by the EPR method in section 3c using the intermodel historical biases in SST and the intermodel change biases in precipitation and surface wind. The estimated common change biases in precipitation and surface wind are shown in Fig. 11b. The estimated precipitation change biases are negative over the central and eastern Pacific and positive over the western Pacific. The estimated surface wind biases show pronounced easterly changes. The estimated common change biases in precipitation and surface wind are consistent with the estimated SST change biases, negative (positive) precipitation changes versus decreased (increased) SST changes, and surface winds blowing from greater to smaller SST increases (Figs. 11b and 8a).
The precipitation and surface wind changes can be corrected by removing the estimated common change biases (Fig. 11c). Positive precipitation changes are located over the central and eastern Pacific and negative changes over the western Pacific and out of the equator. The pattern of corrected precipitation changes is closely coupled with the pronounced El Niño–like pattern of the corrected SST changes (Fig. 8b) and displays a dominant warmer-get-wetter effect. This is because the dynamic warmer-get-wetter effect is enhanced by the increased horizontal gradients of corrected SST changes and dominates the thermodynamic wet-get-wetter effect, which constantly depends on the global mean warming and climatological precipitation distribution.
A pronounced convergence and westerly pattern can be observed in the corrected surface wind changes (Fig. 11c), implying a weakened Walker circulation but an enhanced Hadley circulation. This characteristic of surface wind changes can be understood as a result of the Bjerknes feedback with the El Niño–like SST change pattern. This implies that the dynamic air–sea coupling could be underestimated as a result of the background biases (Vecchi and Soden 2007a; DiNezio et al. 2009; Xie et al. 2010).
The uncertainties in the corrected precipitation and surface wind changes can also be discussed by applying the EPR correction to individual models. The intermodel standard deviations of the uncorrected precipitation and surface zonal wind changes are shown in Figs. 12a and 12c. The maximum uncertainty is located over the tropical western Pacific, consistent with the distribution of uncertainties in the SST changes. The intermodel standard deviations of the uncorrected changes are greater than the MMM changes in most of regions, indicating great uncertainties in the MMM change projections. The corrections for precipitation and wind changes also remove the intermodel variances of changes correlated to the historical SST biases. The corrected uncertainties in precipitation and surface wind changes are significantly decreased relative to the uncertainties in the conventional MMM changes (Figs. 12b,d). The decreased percentages are up to 40%–50%, which is comparable with the decreased percentages of uncertainties in the corrected SST changes. This result is consistent with the previous conclusion that the tropical SST change pattern is a major source of uncertainties in the tropical precipitation and circulation changes (Ma and Xie 2013).
6. Conclusions and discussion
Of great importance and uncertainty, the tropical Pacific SST change patterns have been given increasing attention. The zonal structure of SST changes varies among La Niña–like, El Niño–like, and zonally uniform patterns in different studies and models under a delicate balance among various air–sea feedbacks, although the MMM projection displays an ambiguous El Niño–like pattern in CMIP3 and CMIP5.
The unweighted MMM method has been widely used in projecting regional climate change under global warming. It improves our confidence in change projections, but possibly includes some common change biases of multiple models as the existence of common biases in MMM background. In the present study, a linear ensemble pattern regression (EPR) method is developed to estimate the common change bias in multiple models correlated to their common background bias, and then to correct the MMM projection. This method is a development of other “observational constraint” or “emergent constraint” methods (Boé et al. 2009; Räisänen et al. 2010; Shiogama et al. 2011; Bracegirdle and Stephenson 2012; Cox et al. 2013). The EPR method first constructs several historical–change correlated bias modes based on the intermodel diversities in historical simulations and change projections, and then estimates the common change bias correlated to the common historical bias using these correlated modes. While the EPR method is applied to correct MMM projection, the intermodel uncertainty from background diversity is also implicitly removed. The method can also be applied to estimate the common change bias of one variable in one domain induced by the common historical bias of another variable in another domain.
In the present study, the EPR method is applied to correct the MMM tropical Pacific SST change patterns. The EPR method estimates that the common background biases in tropical Pacific SST including the excessive cold tongue bias, the southeastern warm bias, and the narrower warm pool bias will induce common La Niña–like biases under global warming. After the estimated common change biases are removed, the corrected tropical Pacific SST changes display a pronounced El Niño–like pattern. The zonal gradient of the corrected SST changes increases by 3 times as much as that of the uncorrected MMM changes, implying much greater impacts on global climate changes. The corrected SST change patterns in the models are very robust in all models regardless of their inconsistent uncorrected changes, background biases, and estimated change biases because around half of the uncertainties in the uncorrected SST changes linearly correlated to the SST background biases have been removed.
The common change biases in precipitation and circulation over the tropical Pacific are also estimated, which are coupled with the common change biases in SST. The common La Niña–like SST change biases could induce positive (negative) biases in precipitation over the western (central and eastern) Pacific and easterly biases in surface wind. The corrected precipitation changes display a pronounced warmer-get-wetter pattern dominated by the corrected SST changes with enhanced horizontal gradients, and the corrected surface wind changes display a stronger westerly pattern indicating a stronger slowdown of the Walker circulation under global warming. The corrected changes in precipitation and surface wind are more robust than the uncorrected changes because around half of the uncertainties from the historical SST biases are removed.
The newly developed EPR method could depend on various conditions, such as domain, models, time periods, and the truncation of EOF modes. The selection of domain could influence the significance of regression patterns. When a big domain is selected, which means more total variance, the regressions of regional modes, particularly the high-order EOF modes, would not be significant. This could explain why the historical–future bias relationship at low latitudes is not significant when similar methods were applied to global surface temperature in previous studies (Räisänen et al. 2010; Abe et al. 2011). In the present application, the truncation of EOF modes (the first eight modes) is empirically selected based on spatial structure, explained variance, and regression significance. The total regression patterns in some truncated EOF modes are not significant, but they are selected because they can significantly explain some regional variances. The EOF modes should be truncated with care when the EPR method is used elsewhere. More objective criteria for the truncation should be developed in future for applying the EPR method more easily.
In a linear regression model, an outlier model member can contribute more than in the simple mean. Thus, the EPR method is more sensitive for outlier models than MMM (Bracegirdle and Stephenson 2012). In the current application, the leverage test for each model shows that there is no apparent outlier model playing a dominant role on the corrected SST changes. When the EPR method is applied on fewer models, so that outlier models could play more important role, the corrected SST changes also display an enhanced El Niño–like pattern even though different degrees of zonal gradient changes may be obtained (not shown). It implies that the El Niño–like pattern of the corrected SST changes is a robust projection and does not depend on the model selection.
This study provides a statistical connection between historical and change biases in tropical Pacific SST, but it does not deeply investigate the physical mechanisms of the historical–change correlated modes. Reasonable physical mechanisms are as important as the statistical significance test for regional climate change projection (Xie et al. 2015). Two simple mechanisms for the main systematic biases are hypothesized. The deficient cloud–SST negative feedback associated with the excessive cold tongue bias will enlarge the surface warming and induce a warm bias over the central Pacific; on the other hand, the deficient stratus–SST positive feedback associated with the southeastern Pacific warm bias will underestimate the surface warming and induce a cold bias over the eastern Pacific. These hypotheses and the formation mechanisms of other modes will be investigated in future studies.
The work was supported by the National Basic Research Program of China (2012CB955604 and 2014CB953903) and National Natural Science Foundation of China (Grant 41461164005). We acknowledge the World Climate Research Programme’s Working Group on Coupled Modeling, which is responsible for CMIP5, and the climate modeling groups (listed in Table 1) for producing and making available their model output. We wish to thank Prof. Shang-Ping Xie for helpful discussion. We also thank the three anonymous reviewers for their constructive suggestions.