Introduction

The Indo-Pacific warm pool (IPWP), the warmest tropical ocean region located in the western Pacific Ocean and the eastern Indian Ocean, acts as the atmospheric heat and moisture sources influencing the global climate system through consistently supporting and maintaining tropical deep convection throughout the year, and its long-term change is an important signal indicating how greenhouse warming affects the Earth’s climate1,2,3. The convections over the IPWP act as the upward branches of both the Hadley and Walker circulations, which determines the global-scale precipitation pattern4,5. It also plays a critical role in affecting tropical cyclones activity6,7,8, the Madden-Julian Oscillation4,9, the El Niño Southern Oscillation5,10,11, Asian-Australian monsoon variability12,13,14, and teleconnections to mid-high latitudes15,16, etc. Because of the IPWP’s importance to the global climate system, changes in the IPWP area have implications for the climate response to greenhouse warming. Researchers have been paying close attention to the changes in the IPWP size in recent decades, and it was reported that the IPWP size has been expanding significantly in the past century as the global sea surface temperature (SST) increases under anthropogenic greenhouse warming1,9,17,18,19. For example, Hoyos and Webster (2012) reported that the observed global oceanic warm pool expanded from about 4.0–7.0 × 107 km2 during 1920–2000, and the climate model-projected warm pool area increases by 2100 were greater than 70% and 90% relatively to the 2000–2004, under the IPCC A1B and A2 scenario, respectively18. Meanwhile, one of the latest published research revealed that the IPWP size was doubled during 1981–2018, in comparison to 1900–19809.

In many early studies about the impacts of IPWP expansion on climate systems, the IPWP is considered as the oceanic region that favors atmospheric deep convection and is identified as the region with SST exceeding a certain threshold (usually between 27.5 and 29.0 °C, and mostly 28 °C), a pre-condition that is necessary to favor tropical deep convection1,3,9. In the following discussion, we refer the region covered with 28 °C SST to as the oceanic warm pool (OWP28)18. However, numerous independent works argued that the SST threshold for deep convection (σconv) has a statistically significant long-term increasing trend in the past few decades, which implies that a higher σconv is needed to favor deep convection in a warmer climate18,20,21,22,23,24,25. For example, an upward trend in σconv from 1980 to 2009 was revealed and linked to tropical mean SST in a study published in 201020. Later in 2012, an independent research, based on the relationship between atmospheric column-integrated heating (CIH) and SST, showed that σconv increased by about 0.5 °C from 1950 to 2004. They also reported that the OWP28 expansion overestimates the area change of positive atmospheric heating (or the dynamic warm pool), which was shown to remain constant, based on reanalysis data and the Coupled Model Intercomparison Project phase 3 (CMIP3) simulations18. These works suggest that the area change of the 28 °C isotherm may be unequal to the area change of atmospheric convection. Furthermore, under different shared socio-economic pathway (SSP) scenarios, numerical climate models projected that the global average SST will increase by 0.86 °C (SSP1-2.6) to 2.89 °C (SSP5-8.5) from 1995–2014 to 2081–210026, which will result in almost the whole tropical ocean being warmer than 28.0 °C by the end of the 21st century under the SSP5-8.5 scenario17,27. In such sense, on one hand, according to the traditional IPWP definition, the OWP28 would cover most of the tropical-wide ocean; on the other hand, the significant tropical ocean warming also indicates the possibility of a further increase in σconv20, implying that some parts of the projected OWP28 may not be featured with deep convection activity or even be covered by atmospheric subsidence, such as the eastern Pacific region17,18,28. This disagrees with the definition of the IPWP (or OWP28) which considers constant SST = 28 °C as the threshold for deep convection.

These prior publications suggested a disagreement of the area changes between OWP28 and atmospheric convection over the Indo-Pacific Ocean. However, despite some discussion on the variability of σconv in a global aspect9,18,20,21,24,25,29, many latest relevant research still stick to the traditional IPWP definition9,17,18,19, giving little care to the significance of the changing σconv. Due to the above reasons, it remains unclear how the changing relationship between SST and deep convection affects the deep convection favoring ocean surface (or deep convection favoring pool, DCFP) over the Indo-Pacific Ocean under greenhouse warming in the past and future, from the view that local SST acts as the heat and moisture sources favoring deep convection thermodynamically. Given the role of IPWP in the global climate system, in terms that deep convection is the key process to transport tropical signals and energy to other parts of the world, it is necessary to consider the variability of SST conditions for deep convection while discussing IPWP expansion. Hence, in this study, using the latest observed data and the state-of-the-art climate model simulations, we aim at exploring the area change of DCFP over the Indo-Pacific Ocean based on the time-varied σconv, by considering the relationship between deep convection and local SST change. Our results show that although the DCFP tends to expand with global warming, its expansion speed is dramatically slower than that of the OWP28 in both past and future climate change, and is more indicative of the deep convection area. The DCFP did not and likely will not expand to a large extent, and will remain within the Indian Ocean and western Pacific Ocean regardless of the anthropogenic emission level in the future climate.

Results

The changing σconv over the Indo-Pacific Ocean

The variability of σconv has been revealed by numerous research in regional- and global-scale aspects, especially for the tropical region18,20,21,29. In this study, we focus on the σconv over Indo-Pacific Ocean region (25°S–25°N, 40°E–220°E). The changing σconv can be estimated by the joint frequency distribution (JFD) of SST and precipitation (P) over the Indo-Pacific Ocean, which reflects the joint probability (i.e., area of grid points) that certain values of SST and P cover (see Methods section). The 42-year average P-SST JFD (Fig. 1a) clearly shows that deep convections, characterized by large monthly precipitation values (e.g., P ≥ 8 mm/day), over the Indo-Pacific Ocean seldom occur when the SST is below 27.5 °C, and are mostly observed when SST ranges from 27.5–30.0 °C (thin vertical dashed lines in Fig. 1a). This is consistent with the current definition of IPWP, i.e., the region enclosed by the 28 °C isotherm1. However, the P-SST JFD exhibits, to first order, a horizontal shift to warmer SST from 1979–2020 (Fig. 1b). The high joint frequency area of P ≥ 8 mm/day is originally observed between 27.5–30.0 °C in 1979 (Fig. 1c), but then shifted to 28.0–30.5 °C in 2020 (Fig. 1d). The long-term shift of the P-SST JFD indicates that there is a consistent increase in σconv over the Indo-Pacific region.

Fig. 1: Increasing SST threshold for IPWP deep convection from 1979–2020.
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a P-SST JFD averaged over 1979–2020 (shading, 0.05 × 105 km2 interval). b Long-term mean (same as (a), contour, 0.1 × 105 km2 interval) and long-term trend (shading, 0.01 × 105 km2 interval, only trends being significant at the 90% confidence level are plotted) of the P-SST JFD from 1979–2020. c, d P-SST JFD (shading, 0.05 × 105 km2 interval) in 1979 (c) and 2020 (d). The thin vertical dashed lines in a–d denote 27.5 °C and 29.0 °C, the common range of IPWP definitions. The thick vertical dashed lines in c, d denote the estimated σconv (28.1 °C for 1979, and 28.7 °C for 2020). e Time series (thin solid lines) of σconv (unit: °C) derived from different precipitation criteria and σtrop (unit: °C) over the Indo-Pacific Ocean. The thick solid lines denote 9-year running mean series, which filter out the interannual variability. The linear trends of all series, marked on the figure legend, are statistically significant at the 99.9% confidence level. Results are based on the ERSSTv5 and GPCP precipitation data. The results show that, under greenhouse warming, the observed σconv of different intensities have been increasing steadily since 1979.

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We further examine the annual time series of σconv over the Indo-Pacific Ocean. The σconv that favors convection of different intensities are estimated based on the P-SST joint cumulative frequency distribution (JCFD, Fig. 2a–b) for each year (see Methods section), which reflects the probability (shaded areas in Fig. 2) that a certain precipitation rate is observed below a σconv. For instance, in 1979, there is 20% (purple shading of Fig. 2a) of convection with P = 10 mm/day occurs when SST is lower than 28.1 °C; in other words, 80% of convection with P = 10 mm/day is observed when SST is higher than 28.1 °C in 1979. As expected, relatively lower SST is enough for supporting weak convection (e.g., P = 4.0 mm/day), and higher SST is needed for stronger convection. Based on the P-SST JCFD, we define σconv as the minimum SST where more than 80% of the area with P = 10 mm/day is observed throughout the year. The choice of 80% is made with the assumption that a small proportion of deep convection is not only triggered purely by warm ocean surface but also induced by other atmospheric systems and dynamic factors. The deep convection criterion of P = 10 mm/day is chosen based on two facts: (1) it is above the minimum requirement of deep convection (P = 8 mm/day), which is shown in Fig. 3 that the σconv almost remains unchanged for P ≥ 8 mm/day but increases with precipitation level for P < 8 mm/day; and (2) the σconv derived from 10 mm/day has an average value (28.2 °C) being consistent with the widely used IPWP definition (28 °C). The choice of P = 10 mm/day is partly arbitrary and one could estimate the SST threshold based on other criteria. We have carried out the analyses with different deep convection criteria and found that the conclusions are not sensitive to the choice of deep convection criteria. For more details about the calculation of σconv, reasons for choosing P = 10 mm/day as the deep convection criterion, and the sensitivity test results, readers are referred to the Methods section. In addition, we also define the SST threshold for deep convection based on the changes in the tropical mean SST, which was shown to be a simple but widely used indicator of σconv20, for comparisons and mark it as σtrop hereafter.

Fig. 2: Changes in the relationship between SST and precipitation over the Indo-Pacific Ocean from 1979 to 2020.
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a, b P-SST JCFD (shading, 10% interval) in 1979 (a) and 2020 (b), in which the shaded area indicates the probability that a certain precipitation rate occurs below an SST value. Thick solid curves are the 20% contour lines of JCFD smoothed by a 21-point running mean filter. Thin solid lines mark the 10 mm/day precipitation level and the estimated σconv. The thin vertical dashed lines denote 27.5 °C and 29.0 °C, the common range of IPWP definitions. The thick vertical dashed vertical lines in denote the estimated σconv. Results are based on ERSSTv5 and GPCP precipitation data. c, d same as (a) and (b), except that the SST data are based on the HadISST dataset. The results show the changing relationship between SST and deep convection, with the P-SST JCFD shifting to the right, which indicates an increase in σconv over the Indo-Pacific Ocean from 1979 to 2020.

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Fig. 3: Relationship between σconv and precipitation over the Indo-Pacific Ocean in the past four decades.
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a, b Curve (thin solid lines) of σconv (unit: °C) against precipitation (unit: mm/day) averaged over 1980–1990 (red), 1990–2000 (blue), 2000–2010 (green), and 2010–2020 (purple), based on a ERSSTv5 and b HadISST datasets. The thick solid lines are the 21-point running mean filtered curve of the thin solid lines, which are equivalent to the 21-point running mean filtered 20% contour lines of JCFD (thick solid lines in Fig. 2). The dashed lines are the slopes (first derivative, unit: °C/(mm/day)) of the 21-point running mean filtered curves. The thin horizontal black dashed lines denote 27.5 °C and 29.0 °C, the common range of IPWP definitions. The results show that while the σconv slightly shifts upward in the past decades, the relationship between σconv and precipitation does not exhibit significant changes.

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The estimated σconv varies year by year, ranging from 27.9 to 28.7 °C during 1979 to 2020, and has an average value of 28.2 °C, being consistent with the current definition of IPWP (Fig. 1e). Time-series analyses show that σconv has a steady increasing trend with obvious interannual variability. σconv increases from 28.1 °C in 1979 to 28.7 °C in 2020 (thick vertical dashed lines in Fig. 1c–d and 2a–b), with a long-term linear trend of 0.09 °C/decade (Fig. 1e, statistically significant at the 99.9% confidence level), being consistent with the results of previous research that focus on global or tropical-wide spatial scale analyses18,20. Similar increasing trends are also obtained for the SST threshold derived based on different precipitation levels (ranging from 0.09 to 0.10 °C/decade for P ≥ 8 mm/day; Fig. 1e) and from another SST dataset (Fig. 2c–d and Supplementary Figs. 1–2). It is interesting to note that the σtrop exhibits a slightly larger increasing trend (0.11 °C/decade, significant at the 99.9% confidence level, red line in Fig. 1e) than the σconv does. This indicates that the increasing rate of tropical mean SST may slightly overestimate the changes in SST threshold for deep convection. The slight difference between the σconv and σtrop is consistent in both ERSSTv5 and HadISST (Fig. 1e and Supplementary Fig. 1e).

It is also important to note that the relationship between σconv and precipitation criterion seems not to change under greenhouse warming in the past decades. As shown in Fig. 3, while the curve of σconv against precipitation slightly shifts upward as a result of the overall increase in σconv over time, the slope (first derivative) of the curve does not exhibit significant changes in the past four decades. While the past and future greenhouse warming may influence the extremeness of precipitation30,31,32,33,34, that the σconv increases with precipitation for P < 8 mm/day and stays steady for P ≥ 8 mm/day implies the consistency of the minimum requirement of deep convection, and hence the validity of the definition of σconv under the context of climate change.

The above results indicate that warmer Indo-Pacific SST is needed to favor deep convection of the same intensity in the present day compared with the past. This is consistent with numerous previous studies which suggested the strong relationship of tropical upper-tropospheric temperature with convective instability and σconv. As the upper troposphere warms faster than the lower troposphere does under greenhouse warming, the atmosphere has been stabilized and the enhanced atmospheric instability due to oceanic warming is partly offset18,20,29. Consequently, the same SST threshold becomes less favorable for deep convection activity over the Indo-Pacific Ocean, suggesting that the static SST = 28 °C threshold will inevitably become infeasible to characterize convective activities as the bar for deep convection rises in a warmer climate. Hence, the changes in σconv should be considered in the analyses on the long-term variability of the IPWP features. The increasing σconv implies that using a time-varied σconv while studying the long-term change of the IPWP may be more physically rational, in terms that the incentive of studying IPWP change is to understand its impacts on atmospheric deep convection activity.

Different expansion speeds between DCFP and OWP28 in the past four decades

Although the increasing trend σconv is not as large as the local SST warming, it has a great impact on our interpretation of the IPWP expansion analyses. Namely, the expansion speed of the OWP28 estimated by the static 28 °C threshold could differ greatly from that of the DCFP defined by the time-varied σconv. In the following analyses, the DCFP is defined as the ocean enclosed by the σconv (or σtrop) isotherm, marked as DCFPconv (DCFPtrop) hereafter, and its area change is compared with that of the OWP28 (see Methods section). Because the σconv is determined from the relationship between precipitation and local SST values, the defined DCFPconv reflects the region where the local SSTs reach the threshold that is favorable to deep convections. Note that although the derivation of σtrop does not involve precipitation, the σtrop also approximates the connection between rainfall and local SST, according to previous studies20,29.

Based on the ERSSTv5 dataset, we find that, from 1979–2020, while both the OWP28 and DCFPconv expanded statistically significantly, the increasing trend of the OWP28 area (25.02 × 105 km2/decade, statistically significant at the 99.9% confidence level) is 2.6 times larger than that of the DCFPconv area (9.50 × 105 km2/decade, statistically significant at the 99.9% confidence level). In comparison, the DCFPtrop area does not exhibit significant changes (trend = −0.31 × 105 km2/decade, statistically insignificant). The difference between changes in areas of DCFPconv and DCFPtrop results from that between σconv and σtrop. Namely, the larger σtrop increasing trend causes the smaller and insignificant trend of the DCFPtrop area. The constancy of the DCFPtrop size compared to the expanding DCFPconv and deep convection area suggests that the SST threshold may not be accurately represented by the tropical mean SST change. It is noted that the OWP28 area trend is greater than the expansion trend of the area with a precipitation rate larger than 10 mm/day (hereafter deep convection area) inside the Indo-Pacific Ocean (7.09 × 105 km2/decade, statistically significant at the 99.9% confidence level; Fig. 4a and Supplementary Fig. 2a). Such difference was suggested to be due to the upper tropospheric warming and insignificant change in SST gradient18,20,35.

Fig. 4: Changes in the DCFP and OWP28 area in the past four decades.
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a Time series of the area change (unit: 107 km2) of OWP28 (red line), DCFPconv (blue line), DCFPtrop (green line), and that of the area with monthly precipitation rate larger than 10 mm/day (i.e., deep convection area, black line) inside the Indo-Pacific Ocean (25°S–25°N, 40°E–220°E; black box in b and c). The linear trends are marked on the figure legend. Trends of all series are statistically significant at the 99.9% confidence level, except that of DCFPtrop is statistically insignificant. b, c Monthly precipitation distribution (shading, 2 mm/day interval) in January 1979 (b) and January 2020 (c), where the red, blue, and green contours respectively indicate the regions covered by the OWP28, DCFPconv (σconv = 28.1 °C for 1979 and 28.7 °C for 2020), and DCFPtrop (σtrop = 28.1 °C for 1979 and 28.6 °C for 2020). Results are based on the ERSSTv5 and GPCP precipitation data. The results show that as σconv and σtrop increase, the traditionally defined IPWP may cover a comparatively large region without deep convection. By taking the increase in σconv into account, the expansion speed of DCFP is ~2.6 times slower than that of IPWP, while the DCFPtrop size does not exhibit a statistically significant change.

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Figures 4b, c visualize the inconsistency between the OWP28 and DCFP expansions. In 1979, σconv and σtrop (28.1 °C) are only 0.1 °C higher than the OWP28 definition (28.0 °C), thus the OWP28 and DCFP nearly cover the same domain where heavy rainfall is mostly observed (Fig. 4b). However, when the relationship between SST and precipitation changes with climate warming, the difference between σconv (28.7 °C) and the traditional IPWP definition increases to 0.7 °C in 2020, and the σtrop increases to 28.6 °C. It implies that compared to the past, a warmer ocean surface is required to favor deep convections and heavy rainfall is less likely to be observed with the same SST value in the present day. This is evident in Fig. 4c where a large precipitation rate is mostly observed inside the DCFPconv (blue contour) and the DCFPtrop (green contour), but not the region with 28.0 °C < SST < 28.7 °C (the region in between the OWP28 and DCFP boundaries). The same conclusion can be drawn based on another independent SST data, the HadISST dataset (Supplementary Fig. 2), as well as based on σconv derived from different deep convection precipitation criteria (Supplementary Figs. 3 and 4).

The above results illustrate that the increasing SST does not lead to a same increase in the area that fulfills conditions favoring deep convection activity. As a result, the large OWP28 area change contradicts the small DCFP area change, implying that the OWP28 expansion speed based on the fixed 28 °C threshold is not equivalent to the increase in potential of deep convection occurrence over the Indo-Pacific Ocean. This suggests, in the context of the IPWP inducing climate responses through favoring atmospheric deep convection, that the impacts of IPWP expansion on the global climate may be overestimated if the changing relationship between SST and deep convection under global warming is not considered9,17,19. The agreement between the changes in DCFP and deep convection area confirms that the DCFP area change acts as a more reasonable measure for studying the climate effects generated by the Indo-Pacific Ocean warming and suggests the necessity of taking the σconv variability into account when studying the long-term variability of the IPWP.

Changes in the DCFP size in future climate projections

Although σconv changes over time, its value generally varied from 27.9 to 28.7 °C in the past four decades, i.e., within the range of traditional definitions of the IPWP (27.5–29.0 °C, Fig. 1e). Thus, its impact on historical IPWP expansion analyses may not be crucial. However, σconv will further increase, reaching 29.0 °C or higher, in the 21st century based on climate model simulations. In this case, the use of a fixed SST threshold is no longer reasonable for defining the IPWP, as also discussed in previous studies18. Based on the future climate projections by 20 Coupled Model Intercomparison Project phase 6 (CMIP6) climate models (see Methods section), which are all able to capture the statistically significant historical increasing trend of σconv (Fig. 5), we further examine the future changes in the σconv and DCFPconv size in the 21st century under different emission scenarios.

Fig. 5: Historical changes in σconv and the area of OWP28 and DCFP simulated by 20 CMIP6 models.
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a–d respectively same as Figs. 1a, b, e and 4a, except based on the ensemble historical simulations of 20 CMIP6 models from 1979–2014. The linear trends of all series in c, marked on the figure legend, are statistically significant at the 99.9% confidence level. In d, the linear trend of the OWP28 area is statistically significant at the 99.9% confidence level but those of the other series are insignificant. The results show that the increase in σconv and the inconsistent expansion speed between OWP28 and DCFP are also captured by current climate models. Note the relatively smaller σconv of the same precipitation level compared to observation, which may be a result of systematic model bias of precipitation simulation.

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We first evaluate the ability of the 20 CMIP6 models’ ability to simulate the historical changes in the relationship between precipitation and SST. All the models could reproduce the horizontal rightward shift of the P-SST JFD from 1979–2014 in their historical runs. As shown in Fig. 5a, the ensemble P-SST JFD has a similar pattern to that obtained from observed data (Fig. 1a), in terms that large precipitation is more likely to occur when SST is in between 27.5 °C and 30.0 °C. The ensemble simulated P-SST JFD exhibits a long-term rightward shifting trend (Fig. 5b), which is consistent with Fig. 1b. The model simulated σconv increases together with the rightward shift of P-SST JFD. All the 20 models could capture the historical increasing σconv trend, with trend values ranging from 0.09 to 0.24 °C/decade. However, the simulated ensemble σconv trend (0.15 °C/decade) overestimates the observed value (0.07 °C/decade based on ERSSTv5) (Fig. 5c and Table 1). Similarly, the model simulated historical σtrop trend, which shows very similar values (ranging from 0.09 to 0.23 °C/decade with an ensemble value of 0.15 °C/decade) to that of σconv, is much higher than observation (0.09 °C/decade based on ERSSTv5) (Fig. 5c and Supplementary Table 1). However, there are underestimations of DCFPconv changes, while the ensemble changes in the simulated OWP28, DCFPtrop size and deep convection area are relatively close to the observations. Most models (15 out of 20) successfully simulated the increasing trend of the DCFPconv area from 1979 to 2014, but with magnitudes smaller than the observed values and only two (ACCESS-CM2 and CMCC-CM2-SR5) of them gives statistically significant trends at the 99.9% confidence level (Table 2). Meanwhile, 19 models could reproduce the insignificant DCFPtrop area trend, except one (MIROC6) gives an statistically insignificant decreasing trend (Supplementary Table 2). It is interesting to note that all the CMIP6 models are unable to reproduce the observed difference between σconv and σtrop (i.e., the difference between σconv and tropical mean SST changes). Also, smaller simulated historical DCFPconv expansion rates, compared to the observation, are found in all CMIP6 models (Table 1); and the models overall overestimate the long-term trends of σconv (Table 2). This may be due to the systematic positive bias of the SST change simulation (Supplementary Table 1). Given that σconv change is approximately the same as the tropical mean SST increase20 (Fig. 1e), the positive bias of SST change may lead to the overestimation of σconv trend and underestimation of DCFPconv expansion rate in model simulations. These may be the reasons for the underestimation of the historical DCFPconv expansion by the CMIP6 models. Based on the evaluation results, 5 models that simulated the DCFPconv area trend mostly consistent with observations are selected as the best models for further investigation of future projections. According to Table 2, the five best models are ACCESS-CM2, CAS-ESM2-0, CESM2-WACCM, CMCC-CM2-SR5, and INM-CM5-0, of which the DCFPconv area trends are 4.23, 3.13, 4.24, 5.74, and 2.74 × 105 km2/decade, respectively.

Table 1 Long-term trends of σconv (unit: °C/decade) in the past and future projected climate change, based on ERSSTv5, HadISST, and 20 CMIP6 models.
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Table 2 Long-term trends of DCFPconv (unit: 105 km2/decade) in the past and future projected climate change, based on ERSSTv5, HadISST, and 20 CMIP6 model simulations.
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As the troposphere continues warming with greenhouse gas concentration increases, the current relationship between SST and convection intensity will further change in the future18. The best CMIP6 models projected a long-term rightward shift of the P-SST JFD from 2015–2100, with a larger shift under higher emission scenarios (Fig. 6), indicating the greatest increase in σconv under the SSP5-8.5 scenario over the Indo-Pacific region. Figure 7a–b give the time series of model-simulated σconv and σtrop from 1979–2100, revealing similar long-term changes in both σconv and σtrop, consistent with that in historical runs. Specifically, under the SSP1-2.6 scenario, where the anthropogenic emission peaks by the mid-21st century and the radiative forcing level returns to 2.6 W m−2 by 2100, σconv (σtrop) will first have a steeper increase followed by a relatively constant stage and reach 29.4 °C (29.3 °C) by the end of the 21st century, with their linear trends of 0.09 °C/decade (statistically significant at the 99.9% confidence level) from 2015–2100. Under the stabilized scenario (SSP2-4.5), with a comparatively larger emission and the total radiative forcing is stabilized before 2100, σconv (σtrop) increases steadily at 0.20 (0.21) °C/decade (statistically significant at the 99.9% confidence level). Both σconv and σtrop exceeds 29 °C in the second half of the 21st century (after 2040). Under the higher emission scenario (SSP5-8.5), σconv (σtrop) rises more rapidly, with their long-term linear trends reaching 0.39 (0.41) °C/decade (statistically significant at the 99.9% confidence level), which means that σconv (σtrop) increases by nearly 4 °C from 1979 and reaches 31.9 °C (31.9 °C) by 2100. No matter under which scenario, both σconv and σtrop will reach 29.0 °C by or before 2040 (Fig. 7a, b). The σconv and σtrop for convection with different precipitation levels grow steadily at similar linear trends under the same emission scenario (Fig. 7), but with trend magnitudes being larger under higher emission scenarios (Supplementary Fig. 5). This implies that simply approximating tropical mean SST change as the SST threshold will still likely be a feasible way under different emission scenarios, according to the model simulations.

Fig. 6: Changes in the relationship between SST and precipitation over the Indo-Pacific Ocean in climate model simulations.
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a–c same as Fig. 1a, except based on future climate simulation of the five best CMIP6 models from 2015 to 2100 under the SSP1-2.6 (a), SSP 2–4.5 (b), and SSP 5-8.5 (c) scenarios. d–f same as Fig. 1b, except based on future climate simulation of the five best CMIP6 models under the SSP1-2.6 (d), SSP 2–4.5 (e), and SSP 5-8.5 (f) scenarios. The results show that, under future greenhouse warming, the σconv increases with emission levels, and will no longer be within the range of current IPWP definitions (27.5–29.0 °C).

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Fig. 7: Variability of SST threshold for deep convection in climate simulations.
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a, b Time series (unit: °C) of σconv (a) and σtrop (b) over the Indo-Pacific Ocean simulated by the five best CMIP6 model under the historical run (black line), SSP1-2.6 (green line), SSP2-4.5 (blue line), and SSP5-8.5 (red line), respectively. Shadings denote the uncertainties of model results. Results show that both the σconv and σtrop for convection with different precipitation levels grow steadily at similar linear trends under the same emission scenario (see also Table 1 and Supplementary Table 1), but with trend magnitudes being larger under higher emission scenarios.

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As a result of the σconv and σtrop increases, the difference of the area changes between the OWP28 and DCFP further increases by the end of the 21st century, with larger differences under higher emission scenarios. The area of OWP28 increases rapidly from 2015–2100 at the rates of 12.6, 25.2, and 39.7 × 105 km2/decade (statistically significant at the 99.9% confidence level) respectively under the SSP1-2.6, SSP2-4.5, and SSP5-8.5 scenarios (Fig. 8). The projected OWP28 expansion is characterized by an eastward extension and meridional expansion of the OWP28 boundaries. This results in an OWP28 further covering part of the eastern Pacific under the SSP1-2.6 projection and covering the whole tropical Indian Ocean and Pacific Ocean under both the SSP2-4.5 and SSP5-8.5 scenarios by 2100, where deep convection less frequently occurs even in the future projection (Fig. 9), which was also reported in a previous study comparing the sizes of OWP28 and dynamic warm pool18. Thus, it is evident that the OWP28 expansion rate based on the constant 28 °C SST threshold does not indicate a change in convection activity supported by the warm ocean surface, and hence does not realistically reflect the influence of IPWP on the global climate system under greenhouse warming.

Fig. 8: Long-term change of the DCFP size in future climate projections.
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a–c Time series of the area change (unit: 107 km2) of the OWP28 (red lines), DCFPconv (blue lines), DCFPtrop (green lines), and deep convection (P ≥ 10 mm/day, black lines) inside the Indo-Pacific Ocean under the SSP1-2.6 (a), SSP2-4.5 (b), and SSP5-8.5 (c) scenarios, respectively. Shadings denote the uncertainties of model results. Results are based on the five best CMIP6 models. Results show that the model-predicted DCFPconv expansion is much smaller than that of the OWP28 and is more consistent with the change in the deep convection area (see also Table 2).

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Fig. 9: Model-projected DCFP in the future climate.
figure 9

a–c Monthly precipitation distribution (shading, 2 mm/day interval) in January 2100 under the SSP1-2.6 (a), SSP2-4.5 (b), and SSP5-8.5 (c) scenarios, respectively, where the red, blue and green contours respectively indicate the regions covered by the OWP28, DCFPconv, and DCFPtrop, respectively. d–i, Region of the OWP28 (d–f) and DCFPconv (g–i) of every 5 years from 2015–2100 under the SSP1-2.6 (d, g), SSP2-4.5 (e, h), and SSP5-8.5 (f, i), respectively. Results are based on the simulation of CESM2-WACCM, one of the five best models, as an example. The results show that in a future warmer climate, the DCFP will remain within the Indian Ocean and western Pacific Ocean while the IPWP expands to the eastern Pacific, where deep convection is less frequently observed. Results of other models can be found in Supplementary Figs. 9–11.

Full size image

Comparatively, the model-predicted DCFP expansion is much smaller than that of the OWP28 and is more consistent with the change in the deep convection area. Compared to the OWP28 area trend, the DCFPconv expansion rate is 12–27 times slower under different emission scenarios. The increasing trends of DCFPconv area are rather insignificant under the SSP1-2.6 (0.46 × 105 km2/ decade) and slow under the SSP2-4.5 (1.45 × 105 km2/decade, statistically significant at the 99.9% confidence level) scenarios, which are respectively 27 and 17 times smaller than that of the OWP28. Although the DCFPconv area under the SSP5-8.5 has a greater increasing trend (3.24 × 105 km2/decade, significant at the 99.9% confidence level) from 2015–2100, it is 12 times smaller than the OWP28 expansion speed (Fig. 8 and Table 2). By the end of the 21st century, the DCFPconv will remain within the Indian Ocean and western Pacific Ocean, instead of extending to the eastern Pacific Ocean as does the OWP28. Similar to the historical observation (Fig. 4b–c), the smaller trend of the projected DCFPconv area is more consistent with that of the deep convection area (Fig. 9). The projected DCFPtrop also shows very similar results. The DCFPtrop size remains almost the same under the three emission scenarios, with statistically insignificant trends (Fig. 8 and Supplementary Table 2), and stays within the Indian Ocean and western Pacific Ocean. The difference in area changes of the OWP28 and DCFP are also shown in the time series (Supplementary Figs. 6–8) and horizontal plots (Supplementary Figs. 9–11) obtained from other CMIP6 models. Both the projected DCFP region is consistent with the position of the Pacific Walker Circulation upper branch which does not expand along with the OWP28 in the future warming climate, despite its weakening trend28,36 (Supplementary Fig. 12). These results indicate that the expansion of DCFP, which considers the long-term variability of σconv (or σtrop), has a more reasonable physical basis that estimates the impacts of changing IPWP area on the global climate system via modulating deep convection activity under past and future climate change.

Discussion

The analyses presented here illustrate from the deep convection view that due to the increasing SST threshold for deep convection (σconv) over the Indo-Pacific Ocean, the traditional IPWP definition (static SST = 28 °C threshold) becomes infeasible to characterize convective activities as the bar for deep convection rises in a warmer climate. We thus propose defining the IPWP and examining its expansion by considering the time-varied σconv, namely the deep convection favoring pool (DCFP), in the context of climate change. Despite the changing of σconv under global warming has been noticed in numerous early publications, many latest studies about the IPWP expansion ignored the σconv change over time, which is not true because the different warming rates between the upper and lower troposphere partly offset the enhanced atmospheric instability caused by sea surface warming18,20,21,29.

Based on the latest observation and the state-of-the-art climate simulations, our results show that such assumption is approximately valid only in a relatively short period (<10 years), but does not hold on a longer timescale (>40 years). Specifically, σconv increased by 0.09 °C/decade in the past four decades. The short-term increase (~10 years) in σconv has unnoticeable effects on the difference between the OWP28 and DCFP area (3.3% of the OWP28 size), but the difference is nonnegligible if one analyzes the long-term changes of the IPWP (comparing blue and black lines in Fig. 4a) and the difference reaches 12.2% of the OWP28 size on a time scale of 40 years, not even mentioning that the σconv trend could be even larger (0.09–0.39 °C/decade) in the future climate projections. Hence, the OWP28 expansion rate calculated based on the static 28 °C IPWP definition overestimates the increase in the warm ocean area that favors deep convection (i.e., DCFP). Consequently, the OWP28 expansion trend is 2.6 times larger than that of the DCFPconv from 1979–2020, and the difference enlarges to 12–27 times in future projections of climate models. No matter under which future emission scenarios, in contrast to the fast-expanding OWP28, the DCFPconv will remain within the Indian Ocean and western Pacific Ocean by the end of the 21st century, with a slightly increasing trend of its area. For comparison, the area changes of the DCFPtrop, which is estimated by assuming the SST threshold changes according to the tropical mean SST variation, is also analyzed and is also shown to stay within the Indian Ocean and western Pacific Ocean both in the past and future. The results are insensitive to models and the definition of σconv. Besides, CMIP6 model evaluation results show that although most models could reproduce the statistically significant increasing trend of the observed σconv, all the 20 models overestimate the historical changes in σconv. Most models failed to capture the slight difference of the linear between σconv and tropical mean SST change, as shown in observed data. These factors affect the model ability to simulate the realistic DCFP and its long-term variability.

It is worth mentioning that numerous research in early years have already revealed the disagreement between the changes in the OWP28 and convection areas. For example, prior research has noted the disagreement between the OWP28 and the dynamic warm pool, which was derived from the quantity of CIH and can be regarded as the area with atmospheric updraft. They also show that the dynamic warm pool area did not change much even in the Mid-Holocene and last glacial maximum period when the SST was 2–3 °C lower than the present value, implying that the existence of a constant SST threshold for deep convection does not stand up to simple scrutiny18. However, as mentioned at the beginning, many latest relevant research still stick to the traditional IPWP definition9,17,18,19. Thus, a target of this study is to emphasize the necessity of considering the response of the relationship between deep convection and SST to climate change, when studying the long-term variability of the IPWP. Based on the latest observation and model simulations, we estimated and reported the long-term change in the DCFP area by determining the local SST threshold favoring deep convection of each year, which shares the same concept of the IPWP definition.

Another important remark is that local SST is not the only factor influencing the atmospheric convection occurring frequency and intensity. The surface temperature gradient serves as the primary force driving the large-scale atmospheric circulation through producing atmospheric pressure gradient and hence air flow and convergence. For example, the Walker circulation is driven by the zonal SST gradient between the Indian Ocean and Pacific Ocean37,38,39. Thus, the DCFP (and also OWP28), which is defined by a local SST threshold, considers solely the effects of local SST on deep convection, without considering other dynamical factors such as SST gradient. Differently, the earlier proposed dynamic warm pool, which is derived based on CIH, can be regarded as defined dynamically by the large-scale coupled ocean–atmosphere system in addition to local SST18. The differences of the long-term changes and the physical meaning between the two should be noted according to their definitions.

The IPWP response to greenhouse warming is an important topic of projecting future changes of the global climate system. This study suggests that in a warmer climate, the relationship between SST and deep convection over the Indo-Pacific Ocean has been changing in the past and will be expected to have further changes in the future. Given that the most direct impact of the IPWP on the global climate system is its role in supporting atmospheric deep convection, it is necessary to take the σconv variability into account when studying how global warming influences the climate system through the IPWP. In this context, we claim that the IPWP expansion estimated based on the fixed σconv may not reflect the direct impacts of Indo-Pacific warming on the climate system, and the DCFP serves as a more reasonable reference for research about IPWP and climate change. Based on observation and climate model analyses, the DCFP did not and will not expand to a large extent, and will remain within the Indian Ocean and western Pacific Ocean regardless of the anthropogenic emission level. This study, on the basis of the early works18,20, proposes a more reasonable and feasible way of defining and estimating the IPWP size and its response to climate change, which is important for understanding the impacts of greenhouse warming on the future global climate through the tropical ocean heat source. The σconv and DCFP data generated in this study can be downloaded from an open repository (see Data availability section).

Methods

Data

Two monthly SST datasets were analyzed in this study to examine the variability of IPWP and change, including the National Oceanic and Atmospheric Administration (NOAA) Extended Reconstructed Sea Surface Temperature V5 (ERSSTv5) with a 2° × 2° grid40 and the Hadley Centre Global Sea Ice and SST (HadISST) with a 1° × 1° horizontal resolution41. The deep convection activity over the Indo-Pacific Ocean is estimated by the monthly-mean precipitation rate obtained from the Global Precipitation Climatology Project (GPCP) Version 2.3 Combined Precipitation Data Set, which has a 2.5° × 2.5° resolution42,43.

Apart from observed data, the simulations of 20 the Coupled Model Intercomparison Project phase 6 (CMIP6) models, with data available at the time of analysis, were used in the analyses of the IPWP expansion in future climate conditions, including ACCESS-CM244, CAMS-CSM1-045, CAS-ESM2-046, CESM2-WACCM47, CMCC-CM2-SR548, CMCC-ESM249, EC-Earth350, EC-Earth3-Veg50, FGOALS-f3-L51, FGOALS-g352, GFDL-ESM453, INM-CM4-854, INM-CM5-055, IPSL-CM6A-LR56, MIROC657, MPI-ESM1-2-HR58, MPI-ESM1-2-LR58, MRI-ESM2-059, NESM360, and TaiESM161 (Table 1). The choices of models depend on their availability of both SST and precipitation data of at the time of analysis. Experiments of the historical run and the future shared socio-economic pathway (SSP) 1–2.662, 2–4.563, and 5-8.564 scenarios were analyzed. Since the GPCP data is available since 1979, the historical analyses presented here start from 1979, and the future climate projections were analyzed over 2015–2100.

Estimation of the changing SST threshold for deep convection (σconv)

To estimate σconv, we examine the relationship between SST and convection activity over the Indo-Pacific Ocean by making use of the frequency distribution method, or the so-called image histogram approach65,66,67,68, which analyzes the probability frequency distribution (PFD) and the cumulative frequency distribution (CFD) of a numerical variable (e.g., SST) to determine the probability at which (i.e., the number of grids or the area in which) particular values appear in an image (or a field). The relationship between SST and precipitation can be visualized in the joint frequency distribution (JFD) and the joint cumulative frequency distribution (JCFD) of precipitation versus SST (P-SST JFD and JCFD). The P-SST JFD reflects the joint probability (i.e., area) that certain values of SST and precipitation cover (e.g., Fig. 1a), and the P-SST JCFD indicates the probability (i.e., area) that a certain precipitation rate occurs below an SST value (e.g., Fig. 2a). The image histograms are calculated for each year based on monthly SST and precipitation data inside the Indo-Pacific Ocean region (25°S–25°N, 40°E–220°E), and were applied to further statistical analyses (such as regression analysis and retrieving σconv etc.).

The detailed procedure for deriving a P-SST JFD is as follows:

  1. (1)

    Extract monthly observed or model-simulated precipitation and SST data inside the Indo-Pacific Ocean region (25°S–25°N, 40°E–220°E);

  2. (2)

    For each month, estimate the frequency of each JFD bin by calculating the area of grid points with SST and precipitation values in the range of each bin. The bin widths of SST and P are set to 0.01 °C and 0.1 mm/day, respectively, in this study;

  3. (3)

    Derive the annual mean P-SST JFDs by averaging the monthly P-SST JFDs of each year;

  4. (4)

    Plot the estimated frequency value in the form of a two-dimensional histogram, where the x-axis and y-axis indicate the SST and precipitation values, respectively;

  5. (5)

    Note that, in this study, the frequency value of the JFD is equivalent to the area of grid points, thus the unit of JFD in this paper is presented as km2;

  6. (6)

    Also note that one should constrain the total summed frequency of each histogram, which represents the total area, to be equal if the study domain does not change over time.

The calculation of the P-SST JCFD is the same as that of the P-SST JFD, except for step 2. The frequency of each JCFD is estimated by calculating the area of grid points that precipitation values are observed below each SST bin. Again, the bin widths of both SST and P are set to 0.01 °C. The P-SST JCFD reflects the probability that a certain precipitation rate occurs below an SST value, thus the unit of JCFD is presented as %. For instance, in 1979, as shown in Fig. 2a, there is 20% (purple shading of Fig. 2a) of convection with P = 10 mm/day occurs when SST is lower than 28.1 °C; in other words, 80% of convection with P = 10 mm/day is observed when SST is higher than 28.1 °C in 1979.

The yearly σconv was derived from the P-SST JCFD (Fig. 2) of each year. Based on the P-SST JCFD, we define σP=P0 for convection with a particular precipitation level (P0) as the minimum SST where more than 80% of the area with P = P0 is observed throughout the year. The choice of 80% is made with the assumption that a small proportion of deep convection is not only triggered purely by warm ocean surface but also induced by other atmospheric systems and dynamic factors, such as tropical waves, tropical cyclones etc. In this study, we take P0 = 10 mm/day as the criterion of deep convection over the Indo-Pacific Ocean, and σconv is defined as the SST threshold for convection with P0 = 10 mm/day (i.e., σP=10). For example, 80% of convection with P = 10 mm/day is observed when SST is higher than 28.1 °C in 1979 (Fig. 2a), so the estimated value of σconv = σP=10 = 28.1 °C in that year. Based on the above approach, σconv over the Indo-Pacific Ocean has an average value of 28.2 °C, ranging from 27.9 to 28.7 °C during 1979–2020 (Fig. 1e).

The choice of P = 10 mm/day as a proxy of deep convection is made based on the variation of σP=P0 against P0. According to early research, atmospheric deep convection is not favored when the SST is lower than a threshold and the continuous rise of SST above the threshold has little effect on increasing the intensity of deep convection3,69. As shown in Fig. 3, σP=P0 increases gradually with P0 with a decelerating rate, from ~25 °C at P0 = 2 mm/day to ~28 °C at P0 = 12 mm/day. The increasing rate of σP=P0 drops to lower than 0.1 °C/(mm/day) nearly at P0 = 8 mm/day, which implies that the rise of SST does not increase the occurring frequency of P0 when P0 ≥ 8 mm/day. P0 = 8 mm/day is set as the minimum criterion of deep convection. And, since the range of σP=10 values (27.9–28.7 °C) is closer to the widely used IPWP definition (28 °C), P0 = 10 mm/day is chosen as the proxy of deep convection in this study. Although the choice of deep convection criterion is partly arbitrary, the conclusions of this manuscript are insensitive to the choice. Analysis results of the σconv variation and the comparisons between the OWP28 and DCFPconv based on different choices of deep convection criteria can be found in Fig. 1 and Supplementary Figs. 3 and 4. It is interesting to point out that, while the extremeness of precipitation may change under the past and future greenhouse warming30,31,32,33,34, the above reasons for determining the P0 = 10 mm/day as the proxy of deep convection seem not to be affected. According to the CMIP6 model simulations, although the σconv increases more quickly with higher degree of warming, the changes in the relationship between σP against P0 is insignificant. As shown in Supplementary Figure 13, the increasing rate of σP=P0 drops to lower than 0.1 °C/(mm/day) nearly at P0 = 9 mm/day, regardless of emission scenarios. Therefore, we believe the P0 = 10 mm/day deep convection proxy likely will be valid in the future climate status, based on CMIP6 simulations.

In addition, we also define the SST threshold for deep convection based on the changes in the tropical mean SST, which was shown to be a simple but widely used indicator of σconv20, for comparisons and mark it as σtrop hereafter. The derivation of σtrop involves three steps:

  1. (1)

    Calculate the annual mean SST time series averaged over the whole tropical region (20°S–20°N, 360°E);

  2. (2)

    Adjust the whole annual mean tropical mean SST by adding the difference between σconv and the tropical mean SST in 1979. This step ensures that both σtrop and σconv have the same initial value in 1979;

  3. (3)

    σtrop is defined as the adjusted tropical mean SST time series.

Indo-Pacific Oceanic warm pool area

Following most previous works, the OWP28 area is estimated by the total area of the Indo-Pacific Ocean (25°S–25°N, 40°E–220°E) enclosed by the 28 °C SST isotherm1.

Indo-Pacific deep convection favoring pool area

The DCFP refers to the ocean that fulfils the SST criterion of favoring atmospheric deep convection, which shares the same concept of the traditional IPWP definition except for considering the time-varied σconv. That is, the DCFP area is defined as the total area of the Indo-Pacific Ocean (25°S–25°N, 40°E–220°E) enclosed by the isotherm of a time-varied SST threshold of deep convection. In this study, two definitions of SST threshold of deep convection were applied: (1) σconv derived based on P = 10 mm/day deep convection criterion, and (2) σtrop derived according to the changes in tropical mean SST. Details of the calculation of σconv and σtrop are given above.

Linear trend analyses

The statistical significance of all linear trend analyses performed in this study was tested by a two-tailed Student’s t-test.