Corresponding author: W. Cai, CSIRO Marine and Atmospheric Research, PMB 1, Aspendale, Vic 3195, Australia. (Wenju.Cai@csiro.au)
 The Indian Ocean Dipole (IOD) affects weather and climate in many parts of the world, but a realistic simulation of the IOD in state-of-the-art climate models remains a challenge. In most models, IOD peak-season amplitudes are systematically larger than that of the observed, a bias that deterministically affects climate projections in IOD-affected regions. Understanding the cause of this bias is therefore essential for alleviating model errors and reducing uncertainty in climate projections. Here it is shown that most Coupled Model Intercomparison Project Phase Three (CMIP3) and CMIP5 models produce too strong a Bjerknes feedback in the equatorial Indian Ocean, leading to the IOD bias. The thermocline-sea surface temperature (SST) feedback exerts the strongest influence on the simulated IOD amplitude; models simulating a stronger thermocline-SST feedback systematically generate a greater IOD amplitude. The strength of the thermocline-SST feedback in most models is predominantly controlled by the climatological west-east slope of the equatorial thermocline, which features an unrealistic mean slope tilting upward toward the eastern Indian Ocean. The unrealistic thermocline structure is accompanied by too strong a mean easterly wind and an overly strong west-minus-east SST gradient. The linkage of the mean climatic conditions, feedback strength, and projected climate highlights the fundamental importance of realistically simulating these components of the climate system for reducing uncertainty in climate change projections in IOD-affected regions.
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 A positive IOD (pIOD) event refers to a pattern of SST variability occurring on inter-annual time scales in the equatorial Indian Ocean [Webster et al., 1999; Saji et al., 1999Murtugudde et al., 2000]. A pIOD event, with anomalously cool SSTs in the eastern Indian Ocean and warm SSTs to the west, induces droughts in East Asia, Australia, and the Arabian Peninsula, and flooding to parts of India and East Africa (short rains) [Ashok et al., 2001; Black et al., 2003; Zubair et al., 2003; Yamagata et al., 2004; Meyers et al., 2007; Cai et al., 2009a, b; Ummenhofer et al., 2011], as well as modulating the El-Niño Southern Oscillation (ENSO)-monsoon relationship [Behera et al.2008]. The IOD has an imprint on ecosystems and human health, including as a precursor to major bushfires in southeast Australia [Cai et al.2009a] and an association with a resurgence of malaria in East Africa [Hashizume et al.2012]. These severe impacts raise the issue as to how the Indian Ocean and the IOD may change under greenhouse warming. Climate model experiments participating in CMIP3 have been used to address such issues, and the consensus that emerges shows a mean state change with a shoaling thermocline and slower subsurface warming in the eastern Indian Ocean compared to the west [Vecchi and Soden, 2007]. However, referenced to such an evolving mean state change, the amplitude of the IOD displays little trends [Zheng et al.2010]. The lack of change in amplitude results from a decreasing coupling strength between wind and SST gradients, which offsets an increase in the strength in the thermocline-SST feedback.
 However, the majority of climate models used for CMIP3 simulate too large an IOD amplitude [Cai et al.2011; Liu et al.2011]. Although this model bias has little implication for a change in the future IOD amplitude [Zheng et al.2010], and although it is not clear how this bias will influence the balance of various feedbacks to greenhouse warming, it has already been shown that the bias has a deterministic impact on projected rainfall changes [Cai et al.2011; Weller and Cai, 2013]; models with a greater IOD amplitude tend to produce a greater rainfall change in IOD-affected regions as greenhouse warming proceeds—this tendency is systematic and statistically significant. For example, over southeast Australia, where a pIOD is associated with anomalously low austral winter and spring rainfall [Ashok et al.2001; Meyers et al.2007; Cai et al.2009b], a far greater rainfall reduction is projected in models that simulate larger IOD amplitudes [Cai et al.2011]. That is, the bias in the amplitude of the IOD propagates into climate projections and must be rectified or taken into account. As a first step, we diagnose the cause for the overly large IOD amplitude. We show that there is a direct link of the amplitude to the strength of IOD feedback processes, which are in turn related to the mean state simulation of zonal winds, the zonal gradient (west minus east) of SST, and zonal slope of the thermocline.
2 Observations, Models, and IOD Definition
 We analyze historical (twentieth century) SST, thermocline ( 20°C isotherm depth, z20), zonal wind, and precipitation outputs from available coupled model experiments that form part of the CMIP5 and CMIP3. In total, 33 CMIP5 and 23 CMIP3 models are used in this study (see list of models in Figure 1). Different numbers of models are utilized for wind, thermocline, and precipitation based on availability of data at the time of writing (refer to Figure 1 legend). The model ocean and atmospheric outputs are interpolated onto a common 1° × 1° grid. We take outputs from a common 50 year period of the twentieth century for CMIP3, i.e., 1950–1999, but 56 years for CMIP5 (1950–2005), to better match the observed period. The output is stratified into four seasons; however, we restrict our analysis to the austral spring season (September–October; SON), when the IOD matures. For observations, we utilize a number of reanalysis products including SST from the Hadley Centre Global Sea Ice and SST reanalysis [HadISST1; Rayner et al., 2003] and from National Oceanic and Atmospheric Administration's Extended Reconstructed Sea Surface Temperature (ERSST) V3b [Smith et al.2008], thermocline data from Simple Ocean Data Assimilation (SODA)-Parallel Ocean Program (POP) V2.2.4 [Carton and Giese, 2008], lower tropospheric (850 mb) zonal wind from ERA-Interim [Dee et al., 2011], and precipitation from National Centers for Environmental Prediction-National Center for Atmospheric Research (NCEP-NCAR) [Kalnay et al., 1996]. Using independent precipitation data sets such as Climate Prediction Center Merged Analysis of Precipitation (CMAP) [Xie and Arkin, 1997] and the Global Precipitation Climatology Project (GPCP) [Adler et al., 2003] produces almost identical results to the NCEP-NCAR reanalysis precipitation, and are therefore not shown in this study.
 For each model, and the reconstructed observations (HadISST1, ERSST), the IOD (for SON) is first described through Empirical Orthogonal Function (EOF) analysis on detrended SST anomalies in the tropical Indian Ocean domain ( 20°S– 20°N, 40°E– 120°E). The IOD index is taken as the time series associated with the first EOF spatial pattern (principal component), with the total variance of the spatial pattern being scaled to unity, that is, with a standard deviation of one. An alternative, the Dipole Mode index (DMI) [Saji et al., 1999] constructed as the SST difference over the western and eastern tropical Indian Ocean, is also used for comparison and testing the robustness of our results. However, several studies have identified a small number of CMIP3 models that do not simulate realistic IOD patterns [e.g., Cai et al., 2009c; Liu et al., 2011]. Tests show that our results are robust to the removal of these unrealistic models; however, we retain all available models in the first part of the analysis.
3 Robustness of Simulated Large IOD Amplitude
 We first test the IOD characteristics in the CMIP3 and CMIP5 models to see if any substantial differences exist in the simulated IOD realism such that models from the two phases can be combined to increase the number of samples in a multi-model statistics analysis. In terms of the simulated IOD amplitude, whether it is calculated using an EOF analysis [Cai et al.2011] or through a difference in SST anomalies between the east and west tropical Indian Ocean [Saji et al.1999], CMIP5 models show similar magnitude biases to their CMIP3 counterparts (Figure 1a). The multi-model ensemble mean using the available CMIP3 and CMIP5 models is around 1.8 times as large as the observations using the DMI definition to describe the IOD. The corresponding ensemble mean DMI amplitude over the CMIP3 and CMIP5 model group for SON are 0.71 and 0.73, respectively (see Figure 1 text box), compared to 0.39 and 0.40 for HadISST and ERSST. However, the spread amongst the two CMIP groups, as measured by the standard deviation of the model amplitudes, is substantially less for CMIP5 than that for CMIP3 for both the DMI and EOF definitions of the IOD.
 The large IOD amplitude is simulated despite a stronger damping effect in the majority of CMIP3 models [Cai et al., 2009c, 2011]. The damping is often described as the SST-cloud radiation negative feedback with anomalously cold SSTs over the eastern Indian Ocean reducing cloud cover and rainfall, leading to an increase in the shortwave radiation into the ocean. This can be measured by a response of rainfall averaged over the eastern pole of the Indian Ocean (IODE; Eq.- 10°S, 90°E- 110°E) to the DMI (Figure 1b). An inter-model relationship shows that the strength of damping increases with modeled IOD amplitude in both CMIP3 and CMIP5 models (Figure 1b). Models with a greater amplitude tend to produce a stronger damping, and the tendency is statistically significant (greater than a value of 0.27 required for the 95% confidence level). In other words, there is no association of a greater amplitude with a weaker damping. Thus, to identify the cause of the overly large amplitude, we need to examine the positive ocean-atmosphere feedbacks associated with the IOD (i.e., the Bjerknes feedback).
4 IOD Amplitude and the Strength of the Bjerknes Feedback
 A statistically significant relationship exists between inter-model variations in model IOD amplitude and inter-model variations in the strength of the elements of the Bjerknes positive feedback loop. These elements include a response of lower tropospheric (850 mb) zonal winds over the equatorial eastern Indian Ocean (EEIO; Eq.- 10°S, 80°E- 100°E) to the DMI (Figure 2a), SST to thermocline in the IODE (the thermocline feedback; Figure 2b), and the IODE thermocline to 850 mb zonal winds over the EEIO (Figure 2c). Previous studies [Zheng et al.2010; Ogata et al.2012] have shown that the IODE thermocline is most sensitive to the equatorial winds, which generate equatorial Kelvin waves propagating into the IODE region. First, models with a stronger thermocline response to zonal wind tend to generate a greater IOD amplitude (Figure 2c). Second, the influence of the thermocline feedback dominates, recording the strongest inter-model correlation with the IOD amplitude, with a correlation of 0.92 (Figure 2b). Removing the five models that show virtually no damping (Figure 1b; these are CSIRO Mk3.0 and Mk3.5, and NCAR PCM1, CCSM4, and CESM1-BGC) strengthens the inter-model relationships shown in Figure 2 (figure not shown), particularly in the feedbacks involving the 850 mb zonal winds. This suggests that these models potentially suffer from biases in the tropical ocean-atmosphere coupling. From the perspective of inter-model statistics, these results strengthen the notion that the thermocline feedback is dominant in the IOD positive feedback process, as seen in the relationship on inter-annual time scales in a model [Zheng et al.2010] and in Argo float observations [Cai and Qiu, 2012].
 The central result in Figure 2 is that these feedbacks are overly strong when compared with that in observations/reanalysis. The large biases in the modeled IOD amplitudes are mainly a direct result of the overly strong thermocline feedback. In the Bjerknes positive feedback loop, a stronger thermocline feedback would lead to a greater strength of other elements in the loop, such as the response of winds to the zonal SST gradient, making them better able to manifest out of the stochastic noise. This explains why the IOD amplitude increases with the strength of all elements of the Bjerknes feedback loop.
5 What Determines the Strength of the Bjerknes Feedback?
 A factor that influences the strength of the thermocline feedback is the climatological west-minus-east (IOD west pole (IODW; 10°S- 10°N, 60°E- 90°E)IODW minus IODE) thermocline slope. Under the same size of a given wind anomaly, a greater thermocline slope should result in a stronger thermocline response, inducing a greater SST anomaly in the IODE region, than a weaker thermocline slope. Thus, we expect models with a greater climatological thermocline slope to exhibit a stronger thermocline feedback. This is indeed the case (Figure 3a), with the inter-model relationship statistically significant at the 99% confidence level.
 Figure 3a also reveals an important bias in the simulated climatological thermocline slope, although models simulate a reasonable thermocline depth in the IODE region (the CMIP3/5 multi-model mean is approximately 106 m compared to 110 m in the observations; Figure 3, schematic loop). The observations, as represented by SODA-POP, shows an almost flat thermocline (or, if anything, a weak slope upward toward the west). The ensemble of CMIP3 and CMIP5 models shows a thermocline slope that tilts downward toward the west with a much deeper thermocline in the western tropical Indian Ocean (represented by the IODW region). Averaged across all models, the western Indian Ocean is deeper than the eastern Indian Ocean by approximately 10–20 m (Figure 3, schematic loop); this is quite an unrealistic feature, considering that the standard deviation of the observed slope is only 11.5 m. It should be noted that two CMIP3 models (giss-model-er and giss-aom, shown as yellow dots in Figure 3) generate a mean thermocline depth in the IODE region more than twice that of the observations ( > 200 m) and are therefore not included in any of the inter-model relationships in Figure 3 due to this unrealistically large bias. What controls this unrealistic tilt in the climatological Indian Ocean thermocline in the climate models?
 It turns out that this unrealistic feature is accompanied by other systematic biases in the mean climate simulation such as SST and wind (as indicated in the Figure 3 schematic loop). The bias of the overly steep thermocline slope tilting upward towards the eastern tropical Indian Ocean is a consequence of the stronger climatological easterly winds (Figure 3b). Similar to variability on inter-annual timescales [Zheng et al.2010; Ogata et al.2012], the equatorial climatological winds, through the equatorial seasonal waveguide, have a strong influence on the climatological thermocline slope. The climatological SST gradients (IODW minus IODE), particularly the contribution by the IODE, are in turn generated by the steeper climatological west-minus-east thermocline slope (Figure 3c).
 Inter-model statistics reveal that there is a slightly stronger climatological zonal SST gradient, which is in turn associated with overly strong climatological easterly winds over the EEIO (Figure 3d); models with a greater SST gradient (warmer in the IODW region) tend to simulate a greater easterly wind. This suggests that the wind is overly sensitive to the SST gradient in the models. In the observations (using HadISST1), the eastern tropical Indian Ocean is warmer than the west. However, more than half the models (27 out of 51) produce an opposite SST gradient to the observations meaning that the IODE region is cooler than the IODW region, conducive to the development of easterlies (Figure 3 schematic loop).
 Thus, the development of these biases in the simulated mean climate involves a positive feedback loop, similar to the Bjerknes feedback, because ocean and atmosphere are closely coupled in the tropical Indian Ocean. In this positive feedback loop, it is difficult to identify the element that initiates the development of biases, because after the initiation, the biases will propagate into all elements of the loop.
6 Discussion and Conclusions
 The amplitude of model IOD is systematically larger than that of the observed. These biases/errors have persisted in several generations of models, and there is no clear improvement from CMIP3 to CMIP5. These biases deterministically affect climate projections in IOD-affected regions. Understanding the cause of these biases is therefore essential for alleviating model errors and reducing uncertainty in climate projections. Our study takes a step forward to address the important question of what gives rise to the overly large amplitude. We show that the majority of models produce too strong a Bjerknes feedback in the equatorial Indian Ocean, involving winds, SST, and the thermocline, leading to the bias. The thermocline-SST feedback exerts the strongest influence on the simulated amplitude; models with a stronger feedback systematically generate a greater amplitude.
 The strength of the thermocline-SST feedback is, in turn, controlled by the climatological ocean-atmosphere mean state, in particular, the climatological west-east (west minus east) slope of the equatorial thermocline (Figure 3a). Most models generate an overly deep western Indian Ocean thermocline (Figure 3 schematic) that results in an unrealistic upward slope toward the eastern tropical Indian Ocean. The unrealistic thermocline structure is associated with too strong a mean easterly wind over the equatorial Indian Ocean, which is in turn supported by a slightly stronger mean west minus east SST gradient, reinforced by the unrealistic thermocline slope. The Figure 3 schematic illustrates the development of the biases, leading to the large IOD amplitude. The linkage of climatology, feedback strength, and projected climate highlights the fundamental importance of getting the mean climate right for a realistic simulation of variability and for a reduction in uncertainty in the projected climate.
 We thank Arnold Sullivan and Evan Weller for reviewing the paper before submission and the two anonymous reviewers for their comments and suggestions. This work is supported by the Australian Climate Change Science Program, The Goyder Institute for Water Research, and the CSIRO Wealth from Oceans National Research Flagship.