Changes in the SST-precipitation relationship over the Indo-Pacific warm pool under a warming climate

The Indo-Pacific warm pool (IPWP) is a region known for its strong atmospheric convection, which plays a key role in global climate. However, in recent decades, the IPWP has experienced human-induced warming, and it has been observed to have a non-linear relationship between sea surface temperature (SST) and precipitation. Despite the rising SSTs, the increase in precipitation is limited until a specific SST, which is defined as saturation threshold SST (STT). The STT indicates a distinct transition before and after the STT, highlighting the non-linear response of precipitation to SST. Nevertheless, the impact of warmer climates on the SST-precipitation relationship and STT remains uncertain. To investigate future changes in this relationship, we analyzed a joint distribution of SST and precipitation using the historical data and three different Shared Socioeconomic Pathway (SSP) scenarios (SSP2-4.5, SSP3-7.0, and SSP5-8.5). We examined the near future (2041–2060), and far future (2081–2100). Our findings reveal that the STT increases with the shift in mean state due to the involvement of atmospheric stratification. This increase is observed across all three scenarios in both future periods, with the SSP5-8.5 scenario exhibiting the most substantial rise during the far future. The warming climate leads to a more pronounced warming in the upper troposphere than the surface, resulting in tropospheric stabilization. This process contributes to the increase in STT through moist-adiabatic lapse rate adjustment. Additionally, the weakening of vertical motion constrains the increase in precipitation, despite the availability of abundant moisture. This study sheds light on the changing SST-precipitation relationship and provides a possible mechanism for the limited increase in precipitation. Therefore, this study offers a background for a better understanding of the non-monotonic response of precipitation to SST in the context of climate change.


Introduction
As a distinctive region of the tropics, the Indo-Pacific warm pool (IPWP) encompasses the equatorial Indian Ocean, Maritime Continent, and the western Pacific Ocean. With sea surface temperatures (SSTs) exceeding 28 • C throughout the year, the IPWP is the largest and warmest ocean. It provides a favorable condition for atmospheric deep convection (Yan et al 1992, De Deckker 2016. It is also well-known as the most extensive and wettest tropical ocean region on Earth, characterized by vigorous atmospheric deep convection (Oberhuber 1988, Kerns and. The IPWP serves as a significant source of heat energy and water vapor, which are transported to various regions around the globe through surface fluxes and deep convection. As a crucial energy reservoir, deep convection within the IPWP exerts profound influences on global climate by driving large-scale atmospheric circulation (Xie et al 2005, Duan et al 2008. Specifically, the IPWP supports the ascending arm of Walker circulation and has a significant impact on the rainfall distribution across regions spanning from the tropics to the extratropics (Fasullo and Webster 1999, Neale and Slingo 2003, Kim et al 2020. It also plays an outsized role not only in monsoon variability throughout Africa and Asia but also in large-scale climate variability (Hoerling et al 2012, Annamalai et al 2013, Abram et al 2020, Yin et al 2020, Yue et al 2020. Moreover, the IPWP warming can lead to the dryness of the lower-stratosphere (Xie et al 2018). In recent decades, much of the IPWP warming and expansion has been attributed to human-induced climate change (Rao et al 2012, Roxy 2014, Weller et al 2016, Yao et al 2016, Seager et al 2019, Bai et al 2022. Given the importance of the IPWP for the global climate system, future changes in the IPWP are essential to investigate the climate response to global warming. Some studies have shown that the intensity of deep convection is influenced not only by variations in the SST but also by the size of the IPWP (Clement et al 2001, Roxy et al 2019. The convection threshold typically refers to a SST value when deep convection initiates, and it has been studied in many ways including the outgoing longwave radiation, column water vapor, buoyancy, and precipitation (Lau et al 1997, Peters and Neelin 2006, Neelin et al 2009, Johnson and Xie 2010, Ahmed and David Neelin, 2018, Leung et al 2022. According to Graham and Barnett (1987), SST greater than 27.5 • C is necessary for the occurrence of large-scale deep convection. The convection threshold has important implications for regulating the temperature in the tropics and identifying areas of tropical cyclone development and intensified convection (Johnson and Xie 2010). However, despite its importance, it remains unclear how much the convection threshold will change in the future under different levels of greenhouse gas warming during the future period.
Interestingly, note that the relationship between SST and atmospheric deep convection is nonmonotonic. Previous studies have revealed that deep convection can be intensified more strongly by increasing SST over the IPWP (Gill andRasmusson 1983, Fu et al 1994). Although local SST plays a key role in supplying heat and moisture for deep convection, it is worth mentioning that the convection does not increase consistently. In other words, several studies suggested that when a certain threshold value is exceeded, this relationship breaks down, indicating that atmospheric convection is constrained even if SST increases (Waliser et al 1993, Zhang 1993, Roxy 2014. Noteworthy is that this non-linear relationship is not observed everywhere. In certain regions such as the inter-tropical convergence zone and the South Pacific convergence zone, there is a linear increase in atmospheric convection and precipitation with rising SST. However, a non-linear behavior between SST and convection is observed over the IPWP (Sabin et al 2013). The factors responsible for the suppression of deep convection have been discussed in previous studies (Graham and Barnett 1987, Gutzler and Wood 1990, Michelsen 1993, Lau et al 1997. For instance, Graham and Barnett (1987) provided evidence indicating that areas with limited convection are associated with regions of continuous surface wind divergence. Lau et al (1997) investigated that the relationship between deep convection and SST in the tropics is strongly modulated by the upper-level wind divergence. In regions where there is intense rising large-scale motion, atmospheric convection increases with SST and decreases under subsiding conditions. Their findings highlight the importance of large-scale atmospheric circulation in atmospheric convection. While some studies have pointed out that the role of SST gradients in generating strong low-level wind and surface moisture convergence, which in turn promote precipitation and deep convection in the tropics, it has been emphasized that the vertical circulation plays a crucial role in limiting the intensity of deep convection (Lindzen andNigam 1987, Martin andSchumacher 2012). These preceding studies have revealed that the reduction in deep convection is affected by large-scale downward motion induced by nearby or remotely generated deep convection.
Most previous studies have focused on the convection threshold as a starting point of atmospheric deep convection. However, it is also important to understand the non-linear response of precipitation to SST. After a certain point, precipitation responds differently to SST. But the reason for this nonlinear response over the IPWP as well as how SSTprecipitation relationship will change under anthropogenic greenhouse warming remain unexplored. Hence, in this study, we focused on two main objectives. Firstly, we examined the changes in the relationship between SST and precipitation, as well as the SST threshold for deep convection under a warming climate. Secondly, we investigated why precipitation does not increase continuously with SST warming over the IPWP and how much precipitation will increase in the future.

Data and methods
In this study, we employed widely used monthly mean precipitation data, which is based on both satellite and rain gauge measurements provided by the Global Precipitation Climatology Project version 2.3 (GPCPv2.3) with a 2.5 • × 2.5 • horizontal resolution (Adler et al 2003). The monthly data were utilized to obtain averaged atmospheric fields, such as temperature and vertical velocity from the European Center for Medium-Range Weather Forecasts Interim reanalysis dataset (Dee et al 2011). Additionally, monthly mean SST data were acquired from the Hadley Centre Sea Ice and Sea Surface Temperature (HadISST) (Rayner et al 2003).
To investigate the future relationships between SST and precipitation in the IPWP, we analyzed datasets from phase six of the Coupled Model Intercomparison Project (CMIP6) archive. The CMIP6 includes comprehensive climate model simulations under different scenarios to assess the impacts of climate change including adaptation, vulnerability, and mitigation (Riahi et al 2017). In this study, we focused on the four scenarios: the historical run (HIST) from 1995 to 2014 as well as three Shared Socioeconomic Pathway (SSP) scenarios: SSP2-4.5, SSP3-7.0, and SSP5-8.5. The SSP2-4.5 scenario is a developed version of the Representative Concentration Pathways 4.5 (RCP4.5) of the CMIP5 framework, adopting the moderate forcing of greenhouse gas emissions (O'Neill et al 2016). The SSP3-7.0 run assumes relatively strong land-use changes with higher greenhouse gas emissions. On the other hand, the SSP5-8.5 scenario represents a high-emission pathway, comparable to the RCP8.5 pathway, which leads to a radiative forcing of 8.5 Wm −2 at the end of the 21st century (O'Neill et al 2016). For each of the SSP scenarios, we examined two time periods: the near future (2041-2060) and the far future (2081-2100). For our study, we used output from 24 climate models that participated in the CMIP6, which were available for all variables used in this study at the time of analysis (table S1). For the SSP3-7.0 scenario, 23 climate models were employed because one model (NESM3) was not provided. Additionally, one climate model (KACE-1-0-G) is not available for the vertical velocity and temperature in the SSP5-8.5 scenario. Each model was evaluated using a Taylor diagram, against the GPCP and HadISST data to quantify the reliability of 24 climate models in CMIP6 (figure S1). The spatial correlation coefficients between the HadISST and CMIP6 simulations were greater than 0.95. For precipitation, the pattern correlation coefficients between the reanalysis dataset and the CMIP6 dataset ranged from 0.80 to 0.95. In the case of the 24-member multi-model ensemble (24MME), it is well simulated the reanalysis data. The spatial correlation coefficient of SST is greater than 0.99 and that of precipitation is greater than 0.93 (not shown). All datasets were re-gridded with a common 2.5 • latitude × 2.5 • longitude grid using a bilinear interpolation technique.
In this study, the anomaly is calculated as the difference between future emission scenarios and the historical run to investigate future changes in climatic condition. These anomalies stand for the impact of climate change (Anom = Future-HIST). To identify changes in the SST-precipitation relationship, we defined the two variables as follows: (1) deep convection threshold SST (CTT) is derived from the minimum SST which precipitation exceeds 10 mm d −1 , the threshold value that is favorable to deep convection based on (Leung et al 2022); and (2) saturation threshold SST (STT) is defined as the SST value at which the monthly mean precipitation peaks based on the joint probability density distribution. A hypothesis proposes that precipitation initially exhibits a continuous increase until reaching its maximum, after which it begins to decrease. We have identified this point as the STT. In the vicinity of the STT, the hypothesis suggests the presence of a non-monotonic relationship between SST and precipitation.

The recent warming SST and intensified deep convection over the IPWP
For our analysis, the IPWP area was defined as the region where climatological SSTs were above 28 • C between 50 • E to 140 • W and 25 • S to 25 • N (yellow green box in figures 1(a) and (b)) (Weller et al 2016). Figure 1(a) presents the 20 year trend in SST in the tropics during the historical period (1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014). Based on observational data, SSTs significantly decreased in the eastern Pacific but increased in the tropical Atlantic and the IPWP with a 90% significance level. Significant warming trends were observed within the IPWP, with most parts of the Indian Ocean and the warm core region of the western Pacific where SSTs are above 29.5 • C (figure 1(a), gray contour). Figure 1(b) shows the trend in precipitation for 20 years same as in SST. Throughout the historical period, precipitation generally increased across the western Pacific, except for a small region in the southeast and northern parts. A significant increase in precipitation is shown over the regions where climatological precipitation is greater than 6 mm d −1 (figure 1(b), gray contour). Especially, 8 mm d −1 is considered as the minimum requirement of atmospheric deep convection (Leung et al 2022). When it comes to the areas where precipitation is more than 8 mm d −1 , a significant increasing trend of precipitation is displayed over the western Pacific. Moreover, these areas have experienced significant SST warming as well (figures 1(a) and (b)). This result implies that deep convection tends to be intensified during the historical period and SST warming also has an impact on it.

The response of the relationship between SST and precipitation to climate change
To gain a better understanding of the relationship between SST and precipitation, we utilized a joint probability density distribution to determine the probability of events that involve both variables. Several sensitivity tests were conducted. We examined the spatial distribution of climatological SST and precipitation, as well as the areas where the STT was exceeded (figure S2). From a seasonal perspective, autumn exhibited a relatively continuous increase in precipitation with rising SST compared to other seasons. However, excluding autumn, a clear nonlinear relationship was observed (figure S3). Spatially, regions with higher SST tend to show greater precipitation ( figure S4). Additionally, to investigate the influence of large-scale circulation, we examined the geopotential height at 500 hPa and 850 hPa (figures S5 and S6). Considering each season, the IPWP is found to be more associated with low-pressure systems rather than high-pressure systems. Figure 2 displays distributions of SST and precipitation intensity over the IPWP during the period of the historical, near future, and far future, respectively. For the climatological mean value, the observational data suggested that at SST of 28.8 • C, the climatological rainfall value during the historical period is approximately 5.26 mm d −1 (figure 2(a)). Additionally, CTT is 27.9 • C and STT is 29.7 • C from the observation. However, the CMIP6 data suggests that when climatological SST is 28.9 • C, the ensemble mean of climatological precipitation is about 6.49 mm d −1 at the same period ( figure 2(b)). Also, CTT is shown at 28.4 • C and STT is presented at 29.9 • C. These results indicate that the ensemble mean of model simulation tends to overestimate both SST and precipitation compared to the observation. The observational data also exhibits a wider spread in the high probability of precipitation frequency, from 0 to 10 mm d −1 (figure 2(a)), whereas the CMIP6 ensemble mean is more concentrated in rainfall range of 7-11 mm d −1 (figure 2(b)). It shows that the simulated ensemble mean underestimates the frequency of light precipitation compared to the observation.
In comparison with the historical period, future climate projections display a rightward shift of SST-PRCP joint probability distribution (figures 2(c)-(h)). To quantify the changes in mean, CTT, and STT, the change rate is calculated based on each value of the historical period. Across all future scenarios and terms, all variables are expected to rise. Specifically, both mean SST and mean precipitation are projected to increase more under higher emission scenario such as SSP5-8.5 in the far future, with values of 9.69% and 6.78%, respectively (table S2). However, it is noteworthy that mean SST shows further increase than mean precipitation. Similarly, the higher emission scenario is anticipated to result in a larger increase in both the CTT and STT over time (table S2). The increasing rate among future scenarios shows notable differences between the near future and far future.
The sensitivity of precipitation to SST is determined from the slope between the mean precipitation and SST ranging from the CTT to the STT (dP/dT). The multi-model ensemble of CMIP6 denotes that the precipitation sensitivity is 2.12 mm d −1 • C −1 , which exhibits a steeper increase in precipitation with 1 • C SST warming compared to the observed sensitivity of 1.90 mm d −1 • C −1 . Unlike the increasing rate, the precipitation sensitivity does not grow proportionally with greenhouse gas emission. Specifically, in the near future, the precipitation sensitivity is the highest in SSP2-4.5 (2.40 mm d −1 • C −1 ), followed by SSP5-8.5 (2.38 mm d −1 • C −1 ) and SSP3-7.0 (2.36 mm d −1 • C −1 ) (table S3). However, in the far future, the largest precipitation sensitivity is shown in SSP3-7.0 (2.82 mm d −1 • C −1 ), SSP5-8.5 (2.66 mm d −1 • C −1 ), and SSP2-4.5 (2.45 mm d −1 • C −1 ) (table S3). When comparing the precipitation sensitivity to SST between the near future and far future, there is a greater sensitivity in the far future. However, it is worth mentioning that the response of rainfall sensitivity to greenhouse gas warming is non-linear.

Greater upper tropospheric warming and stabilization of the troposphere
To understand the possible causes of changes in the STT in the projected future climates of the IPWP, we examined the changes in the vertical temperature and vertical velocity profiles over the IPWP during the historical and future periods. Climatologically, the temperature decreases with height in the troposphere (figure S7). To examine the difference in temperature structure between the historical and future terms, the vertical distributions of temperature anomalies are presented for two future periods (figures 3(a) and (b)). The temperature increases with height in all three scenarios and the two future periods when compared to the historical period. Greater warming is presented in the upper troposphere with the highest temperature anomalies observed at 200 hPa (figures 3(a) and (b)). During the near future period, the SSP2-4.5, SSP3-7.0, and SSP5-8.5 scenarios display surface temperature anomalies of 0.97, 1.09, and 1.27 • C. These values increase to 2.26, 2.54, and 2.98 • C, respectively, at 200 hPa. The temperature anomalies become even more pronounced in the far future, with surface anomalies of 1.57, 2.37, and 2.97 • C, and 200 hPa anomalies of 3.61, 5.53, and 6.94 • C, for the three scenarios, respectively. These findings indicate that the upper troposphere will experience a more rapid temperature increase in the future compared to the surface. Furthermore, the temperature anomaly increases with the magnitude of radiative forcing, with the SSP2-4.5 and SSP5-8.5 scenarios demonstrating the lowest and highest temperature anomalies, respectively.
The climatology of vertical velocity over the IPWP during the historical period is shown in figure S8. The most active ascending motion over the IPWP usually occurs at the 500 hPa level (figure S8). As one indicator to see the atmospheric stability, we analyzed the vertical velocity anomaly. Figures 3(c) and (d) present positive vertical velocity anomalies, indicating a weakening of the ascending motion in the future, with the most significant weakening observed at 500 hPa. Similar to the temperature anomalies, positive vertical velocity anomalies become larger as the radiative forcing increases (figures 3(c) and (d)). The vertical velocity anomalies at 500 hPa are 0.71, 0.91, and 1.17 hPa d −1 during the near future period, and 0.87, 1.82, and 2.21 hPa d −1 during the far future period in the SSP2-4.5, SSP3-7.0, and SSP5-8.5 scenarios, respectively. While the SSP2-4.5 scenario shows little difference in the vertical velocity anomaly during the two future terms, the decrease in the vertical velocity anomalies almost doubled in the other two scenarios in the far future. This suggests that the troposphere over the IPWP will become more stable in the future, with the reduced rising motion.
Greater warming in the upper troposphere compared to the surface can be attributed to the moist adiabatic lapse rate (MALR) adjustment. When an air parcel becomes saturated, a warmer parcel can contain more water vapor, leading to more condensation. As the warm air parcel ascends through the troposphere, the temperature gradually cools with height, releasing a significant amount of latent heat. This process follows an MALR, resulting in a larger temperature increase in the upper tropospheric relative to the surface in the tropics. To investigate the relationship between the STT and the upper tropospheric temperature, we analyzed individual models and the multi-model ensemble of CMIP6. Note that the MRI-ESM2-0 was excluded from this analysis because the STT could not be defined in this particular model. We selected 200 hPa as a representative level for the upper troposphere, as it consistently showed the largest temperature anomaly among the CMIP6 results (figures 3(a) and (b)). There is a remarkable correspondence between the changes in the STT and the 200 hPa mean temperature for each model ( figure  S9). As shown in Johnson and Xie (2010), the temperature changes in the upper troposphere plays a crucial role in the rapid increase of the convection threshold, along with SST warming. The STT also rises as a result of the MARL adjustment. In other words, a warmer SST is necessary to sustain the same intensity of deep convection in the future because stabilized troposphere makes the IPWP warming effect weakened.

Possible mechanism for a limited increase in precipitation over the IPWP
In this study, we selected two variables that affect precipitation as representatives of dynamic and thermodynamic factors: the vertical velocity at 500 hPa (dynamic factor), and the specific humidity at 850 hPa (thermodynamic factor). With respect to the mean of the vertical velocity at 500 hPa, the However, there is a consistent decrease in ascending motion across all future projections and periods (table S4). According to the SSP5-8.5 scenario, the largest decrease in rising flow is expected by 9.83% in the far future. These results present the upward motion becomes weaker in the future and are in line with the weakened vertical velocity over the IPWP shown in section 3.3. In contrast, the low-level specific humidity becomes larger in the future period. In the historical period, the mean values of specific humidity are 11.31 g kg −1 in the observation and 11.25 g kg −1 in the CMIP6 ensemble mean (figures 5(a) and (b)). Compared to the historical period, average amounts of the low-level specific humidity tend to increase under all future scenarios and terms (table S4). For the SSP5-8.5 scenario, a significant increase in the low-level specific humidity is observed with a value of 24.80% in far future. By increasing the amount of anthropogenic greenhouse gas warming, the low-level specific humidity rises perceptibly, especially in the far future.
We also considered the SST value when each variable reaches its maximum. Comparing those SSTs with STT value, the SST of the maximum vertical velocity corresponds to the STT only except for the observation (figure 4). In the case of observation, STT is 29.7 • C while the maximum vertical velocity occurs at 29.8 • C. On the other hand, the low-level specific humidity reaches its maximum over the STT except for the CMIP6 historical simulation (figure 5). In addition, the mean curve of the low-level specific humidity displays a gradual slope while that of precipitation and vertical velocity at 500 hPa show a steeper slope. These results indicate that abundant moisture is consistently supplied over the STT, but the upward motion is limited at a certain SST which is almost the same as the STT. In other words, the weakened vertical motion is likely to be a limiting factor for rainfall changes in the IPWP, which is more dominant than the increase in moisture supply caused by the rise in specific humidity at low levels.

Conclusion and discussion
Over the IPWP, one of the most important regions of extensive atmospheric convection in the world, warm SSTs furnish a pre-condition for deep convection. The analyses presented in this study illustrate the SST-precipitation relationship in terms of mean state, convection threshold SST, and STT over the IPWP. Although the warmer atmosphere can contain more water vapor, precipitation does not increase commensurately with increasing temperature. Therefore, the STT is an important factor in determining the extent to which precipitation increases with SST warming and in inducing the non-linear response of precipitation to SST. While the deep convection over the IPWP has significant implications for global climate states, changes in its behavior have not been robustly understood under a warming climate. Moreover, our current knowledge of the STT and its relationship with precipitation is insufficient. Hence, it is necessary to investigate how the SST-precipitation relationship might change in the future and comprehend the underlying physical mechanisms for the non-monotonic relationship between SST and precipitation.
Based on the observation and the CMIP6 climate simulations, our results present that SSTprecipitation distribution moves toward higher SSTs in a warmer climate, although the mean SST changes at a slower rate than the STT. These changes become more noticeable in future scenarios towards the end of the century. The increase in STT is closely linked to changes in vertical temperature and atmospheric stability. Our analysis suggests that the troposphere is projected to experience warming in the future, with greater warming in scenarios with higher radiative forcing. Across all three scenarios, there is a pronounced warming towards the end of the century. Furthermore, our findings display that the magnitude of warming will be greater in the upper-troposphere compared to the surface. The vertical velocity anomalies in all three scenarios indicate a weakening of active ascending motion in the troposphere during the mid-century period, with further weakening projected in the end-century period for the SSP3-7.0 and SSP5-8.5 scenarios. The greater warming in the upper troposphere, relative to surface warming, is expected to stabilize the troposphere through a MALR adjustment. It partly offsets the SST warming effect over the IPWP, which means that warmer SSTs will be required to maintain the same intensity of the convection in the future (Hoyos and Webster 2012, Ceppi and Gregory 2017, Williams and Pierrehumbert 2017, Yun et al 2021.
Another important remark is that precipitation responds non-linearly to SST warming. Based on the STT, precipitation responded to SST differently: below the STT, precipitation increases, but above the STT, precipitation decreases again with higher SSTs. Two factors were identified as the key determinants of precipitation. The first factor, the vertical velocity at 500 hPa shows a very similar behavior to precipitation as a dynamic factor. The upward motion increases only up to STT value except for observations and above the STT, the rising motion becomes weaker. The second factor, the specific humidity at 850 hPa, is a thermodynamic factor that increases beyond the STT value. These results suggest that although more moisture is supplied to the atmosphere, precipitation does not increase beyond a certain STT due to the limited vertical motion.
This study highlights future changes in the relationship between SST and precipitation over the IPWP under a warming climate and proposes a possible mechanism for the existence of the STT, which is essential for understanding the non-linear relationship between SST and precipitation. Our findings are expected to improve the understanding of the underlying physical mechanisms of the SSTprecipitation relationship under climate change and aid in the development of more accurate climate models. Further study is necessary to identify the possible impacts of the Pacific and Indian Walker circulation, monsoon gyre, and subtropical convergence zone as dynamic factors more specifically.

Data availability statement
The data that support the findings of this study are openly available. Reanalysis datasets can be accessed on the following websites. ERA-Interim data: http:// apps.ecmwf.int/datasets/. SST data used in this study, is available from the Met Office Hadley Centre observations datasets: www.metoffice.gov.uk/hadobs/ hadisst/data/download.html. Precipitation data is obtained from the GPCP: https://esrl.noaa.gov/psd/ data/gridded/index.html. The CMIP6 model output analyzed in this study is available from the Earth System Grid Federation server (https://esgf-node.llnl. gov/search/cmip6/).
The data that support the findings of this study are openly available at the following URL/DOI: https:// esgf-node.llnl.gov/projects/cmip6/.