Attribution of the August 2022 Extreme Heatwave in Southern China: Role of Dynamical and Thermodynamical Processes

Hainan Gong Center for Monsoon System Research, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China, and Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters (CIC-FEMD), Nanjing University of Information Science & Technology, Nanjing, China;

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Kangjie Ma Center for Monsoon System Research, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China, and Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters (CIC-FEMD), Nanjing University of Information Science & Technology, Nanjing, China;

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Zhiyuan Hu School of Atmospheric Sciences, Key Laboratory for Climate Change and Natural Disaster Studies of Guangdong Province, Sun Yat-sen University, and Southern Marine Science and Engineering Guangdong Laboratory, Zhuhai, China;

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Zizhen Dong Department of Atmospheric Sciences, Yunnan University, Kunming, China;

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Yuanyuan Ma Key Laboratory of Land Surface Process and Climate Change in Cold and Arid Regions, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou, China;

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Wen Chen Department of Atmospheric Sciences, Yunnan University, Kunming, China;

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Renguang Wu School of Earth Sciences, Zhejiang University, Hangzhou, China

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Lin Wang Center for Monsoon System Research, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China, and Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters (CIC-FEMD), Nanjing University of Information Science & Technology, Nanjing, China;

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Abstract

We estimate that anthropogenic forcing caused half of the observed temperature anomaly during the August 2022 heatwave in southern China. Thermodynamical processes, especially soil moisture–SAT feedback, amplified the heatwave.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

CORRESPONDING AUTHOR: Zhiyuan Hu, huzhiyuan@mail.sysu.edu.cn; Lin Wang, wangling@mail.iap.ac.cn

Abstract

We estimate that anthropogenic forcing caused half of the observed temperature anomaly during the August 2022 heatwave in southern China. Thermodynamical processes, especially soil moisture–SAT feedback, amplified the heatwave.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

CORRESPONDING AUTHOR: Zhiyuan Hu, huzhiyuan@mail.sysu.edu.cn; Lin Wang, wangling@mail.iap.ac.cn

In August 2022, an extraordinary and unprecedented heatwave hit southern China with record-breaking high temperatures. This heatwave is the longest-lasting and most intense since 1961 (Lu et al. 2023). Long-persistent heatwaves have serious adverse impacts on social economy and human health. An area of 1.476 million km2 in China experienced moderate or severe drought and about 360 million people suffered from extreme temperature above 40°C (Mallapaty 2022) and the economic losses reached up to ≫51.2 billion yuan as counted by Ministry of Emergency Management of China (www.mem.gov.cn/xw/yjglbgzdt/202301/t20230113_440478.shtml).

With global warming, such extreme events, especially the heatwaves, emerge stronger and more frequently over most of the world (e.g., Wehrli et al. 2019; Dong et al. 2023; Faranda et al. 2023; Zhang et al. 2023). Previous studies have mentioned that the internal variability and external forcing can both contribute to the occurrence of extreme heatwaves. Therefore, a key question is to what extent the record-breaking heatwave of August 2022 in southern China is due to anthropogenic forcing as opposed to internal variability. Here we present an attribution study to quantify the contributions of natural and anthropogenic forcings and internal dynamical and thermodynamical components to the extreme heatwave of August 2022 in southern China based on the large-ensemble simulations in HadGEM3-A attribution model (Ciavarella et al. 2018; Vautard et al. 2019) and the dynamical adjustment method (e.g., Deser et al. 2016). In particular, the atmospheric dynamical and thermodynamical processes responsible for the extreme heatwave are further illustrated.

Data and methods

The monthly surface air temperature (SAT), sea level pressure (SLP), and geopotential height are from the ERA5 dataset, with a 1.0° × 1.0° global grid (Hersbach et al. 2020). The monthly soil moisture (SM) data at 0–28 cm are obtained from ERA5-Land dataset (Munoz-Sabater et al. 2021). The sea surface temperature (SST) data are from the NOAA Extended Reconstructed SST (ERSST) version 5 dataset (Huang et al. 2017). The anomalies of all variables are calculated based on the climatological mean of 1981–2010. The HadGEM3-A-N216 attribution simulations for 2022 (Ciavarella et al. 2018; Vautard et al. 2019) are used, which provide 525 ensemble members for 2022 simulations with or without anthropogenic forcings. The HadGEM3-A-N216 attribution system has a good performance in reproducing the observed climate reported in many previous studies (e.g., Ren et al. 2020; Yu et al. 2022). Here the ensemble mean in available members of the historical simulation for 1981–2010 is used to derive the climatology of the model. We average all 525 members’ anomalies of the variables in August 2022 to derive the forced components of them in August 2022. The internal components are obtained by subtracting the forced components from the observations.

The widely used dynamical adjustment method in attributing climate change (e.g., Deser et al. 2016; Gong et al. 2019a,b; Terray 2021, 2023) is also employed in this study to further separate the contributions of the internal atmospheric circulation and residual internal thermodynamics to the extreme heatwave of August 2022 in southern China. This method is briefly described as follows. First, we search for the 200 internal SLP analogs closest to the observed one in August 2022 using pattern correlation among 525 internal SLP fields in HadGEM3-A-N216 simulations. We then randomly subsample 100 SLP analogs from 200 closest SLP analogs and compute their best linear fit to the observed internal SLP field in August 2022 based on multiple linear regressions. We then use the same set of linear weights to the corresponding internal SAT fields to obtain the internal dynamically induced portion of observed SAT anomaly patterns in the August 2022. This random selection and reconstruction procedure is repeated 100 times to avoid overfitting. Finally, the internal dynamical component of observed SAT is obtained as the average of the 100 internal dynamically induced SAT fields to provide the best estimates. Then the internally thermodynamical induced SAT anomalies in observation are obtained by removing the internally dynamical components from observed internal SAT anomalies (see details in Deser et al. 2016).

Results

In August 2022, widespread extreme warm temperature anomalies were observed in southern China (Fig. 1a). The Sichuan Basin region experienced the highest temperature anomalies and was 5°C higher than the mean of 1981–2010. Such an extreme heatwave event in southern China is unlikely to be solely caused by internal climate variability because the observed temperature anomalies in southern China (25°–35°N, 104°–122°E) fall outside the range by probability density function of 525 ensemble members, which only consider natural forcings according to the HadGEM3-A attribution system (Fig. S1a in the online supplemental material; https://doi.org/10.1175/BAMS-D-23-0175.2). However, if the anthropogenic forcings have been included, the probability distribution of temperature anomalies shifts toward a warmer condition and the observed temperature anomalies of August 2022 in southern China can be within the range of the model simulations (Fig. S1a). This result suggests that the anthropogenic forcings can significantly increase the risk of extreme heatwave of August 2022 in southern China.

Fig. 1.
Fig. 1.

The SAT (shading; °C) and SLP (contours; interval: 0.6 hPa) anomalies in August 2022 for (a) ERA5 data, (b) externally forced component, (c) internal component, (d) internal dynamical component, and (e) internal thermodynamical component. The boxes denote the region of southern China, and the values in the upper-left corner indicate the area-averaged SAT anomalies in southern China.

Citation: Bulletin of the American Meteorological Society 105, 1; 10.1175/BAMS-D-23-0175.1

Here the ensemble mean of 525 members with external forcings from HadGEM3-A-N216 simulations are used to represent the externally forced responses. The externally forced SAT anomalies centered on northern China show a strong amplified warming pattern accompanied by the negative SLP anomalies (Fig. 1b). The externally forced SAT anomalies of August 2022 in southern China reach to 1.13°C, accounting for 40% of observed SAT anomalies (2.81°C) in southern China. The externally forced SAT anomalies can be further divided into components from natural and anthropogenic forcings. The natural forcings induces a slight cooling in southern China (–0.3°C), which may be associated with the cooling effect caused by the volcanic eruption in Tonga in early 2022 (Fig. S1c). Anthropogenic forcings have resulted in a 1.43°C increase in SAT anomalies, contributing approximately 50% to the intensity of August 2022 heatwaves in southern China (Fig. S1d). The internally induced SAT anomalies are 1.68°C, contributing residual 60% of the SAT anomalies in southern China (Fig. 1c). The internal components of the SLP anomalies exhibit a large resemblance to the observations, but with a stronger and wider anomalous anticyclone extended from the western North Pacific to southern China (Fig. 1c). Many studies have demonstrated that the extreme heatwave events can be strongly influenced by the atmospheric dynamics via an anomalous anticyclonic circulation (e.g., Dong et al. 2023; Faranda et al. 2023; Zhang et al. 2023). In August 2022, this internally generated strong anticyclone may play an important role in triggering and maintaining the heatwaves by enhancing subsidence, increasing insolation, and transporting the warm air mass from lower latitudes to southern China (e.g., Zhang et al. 2023). Here we use the dynamical adjustment method (see methods) to further quantify the contribution of internal atmospheric circulation to the extreme heatwave of August 2022. The internal SLP anomalies in August 2022 can be well reconstructed by the dynamical adjustment (Figs. 1c,d). We find that this anomalous anticyclonic circulation could induce widespread warming in southern China, which contributes 34% (0.96°C) to SAT anomalies in southern China. These results suggest that this extreme heatwave may be triggered by the extreme phase of internal circulation and further amplified by the anthropogenic forcings.

Since this anomalous anticyclone is a key dynamical factor for this heatwave in southern China, here we develop a circulation projection method to explore the possible source of this anomalous atmospheric circulation based on the long-term observations. To minimize the potential influence of external forcing on the projection of the circulation pattern, here we employed a detrending process to extract the long-term internal components from the observation during 1960–2022. Note that the detrending and removing the CMIP6 multimodel ensemble average (Table S1) are consistent in minimizing the long-term influence of external forcing (Fig. S3). A circulation projection index (CPI; Fig. 2a) is constructed by projecting the detrended SLP anomalies (10°–50°N, 90°–150°E) during 1960–2022 onto the detrended SLP anomalies of August 2022 (Fig. 1c) to represent the temporal evolution of atmospheric circulation anomalies similar to those in August 2022. When the CPI increases, there is an anomalous western North Pacific subtropical high (WNPSH) with westward extension, causing the widespread warming in southern China (Fig. 2b). The externally forced response of 500 hPa geopotential height (HGT500) in August 2022 also displays a strengthened WNPSH (Fig. S1b), confirming the important effect of external forcing, especially anthropogenic forcing on this heatwave. Xiang et al. (2013) indicated that the cold SST anomalies in the central Pacific can strengthen WNPSH significantly in August via westward emanations of descending Rossby waves. Indeed, there are significant cold SST anomalies in the central Pacific both in July and August accompanied by the increase of CPI (Fig. 2c, Fig. S2a). Here we regress the internal SAT and HGT500 onto the standardized reversed central Pacific SST index (CPSST) defined as the area-averaged SST anomalies over the central Pacific (5°S–5°N, 165°E–172°W). We find that accompanied with the August SST cooling in the central Pacific, an anomalous WNPSH is observed with westward extension from the WNP to southern China, inducing the widespread SAT warming in southern China (Fig. 2d). In fact, the internal SST anomaly in the central Pacific in August 2022 is –1.46°C, which is also the lowest value in the past 63 years and which contributes to about 0.45°C of SAT warming in southern China (Figs. S2b,c). The extreme cold SST anomalies in August 2022 are largely associated with the persistent “triple” La Niña event during 2020–22 (Jones 2022). This result suggests that extreme cold SST anomalies in the central Pacific in August 2022 may be a key factor in the strengthening of the WNPSH and triggering this heatwave in southern China.

Fig. 2.
Fig. 2.

(a) Time series of circulation projection index (CPI) during 1960–2022. (b) Internal SAT (shading; °C) and HGT500 (contours; interval: 1 gpm) anomalies regressed onto the normalized CPI. (c) As in (b), but for SST. (d) Internal SAT (shading; °C) and HGT500 (contours; interval: 1 gpm) anomalies regressed onto the normalized CPSST index. (e) Normalized internal soil moisture (SM; black lines) and SAT (red lines) indices in southern China during 1960–2022. Corresponding solid lines are the decadal components obtained by 9-yr sliding mean. (f) Internal SAT (°C) anomalies regressed onto the normalized SM index. The boxes in (b), (d), and (f) denote the region of southern China. The box in (c) and (f) are the regions to define the CPSST and SM indices, respectively. Stippled regions indicate where the significance exceeds the 90% confidence level.

Citation: Bulletin of the American Meteorological Society 105, 1; 10.1175/BAMS-D-23-0175.1

Except for the atmospheric dynamics, the internal thermodynamical component also contributes about 26% (0.72°C) of SAT warming in southern China in August 2022 (Fig. 1e). The feedback between the SM and SAT may be a key thermodynamical process amplifying the heatwaves (e.g., Fischer et al. 2007; Zhang et al. 2023). Thus, we further calculate correlation coefficient between the internal SM and corresponding SAT in southern China (Fig. 2e) and find a significant negative correlation (–0.66). It indicates that much lower soil moisture tends to correspond to a higher SAT in southern China (Fig. 2f). The lower soil moisture not only leads to weaker evaporative cooling, but also reduces water vapor evaporated into the atmosphere, which suppresses the cloud formation and increasing insolation. Therefore, soil moisture–SAT feedback can amplify the atmospheric circulation induced heatwaves in southern China of August 2022.

Conclusions

Based on the ERA5 and HadGEM3-A-N216 attribution simulations, we demonstrate that this extreme heatwave in southern China is primarily caused by the extreme phase of internal variability and the anthropogenic forcings significantly amplify this heatwave. The internal variability contributes about 60% of SAT anomalies and the external forcings contribute the residual 40% of the SAT anomalies. Anthropogenic forcings have offset the slight cooling effect of natural forcings, contributing approximately 50% to the intensity of August 2022 heatwaves in southern China. We identify that an anomalous anticyclone extended from WNP to southern China is the key dynamical factor driving this heatwave. Using the dynamical adjustment method, we find that this internally generated atmospheric circulation anomaly contributed about 34% of the SAT anomalies in southern China directly. Further analysis indicates that the extreme cold SST anomalies in the central Pacific play an important role in the trigger and formation of this anomalous anticyclone through the Gill-type response. In addition, the internal thermodynamical process, especially the soil moisture–SAT feedback, can further amplify this heatwave, which contributes about 26% (0.72°C) of SAT warming in southern China. Although this study focuses on southern China, the main conclusions also apply to the eastern Tibetan Plateau, including the dominant role of the internal component and the importance of soil moisture–SAT feedback on the magnitude of heatwave in eastern Tibetan Plateau (Figs. 1 and 2).

In addition, although the main trigger factor of this event is the extreme phase of internal variability, the anthropogenic forcings contribute about 50% to this heatwave intensity in the current climate background. This result indicates that if the anthropogenic forced warming cannot be alleviated but further intensifies, more extreme and frequent heatwaves may occur in southern China in the near future.

Acknowledgments.

We thank the Editor Thomas Knutson and two anonymous reviewers for their insightful comments that led to improvements to the manuscript. We thank Dr. F. C. Lott for providing the data of HadGEM3-A-N216 attribution simulations. This study was supported by the National Natural Science Foundation of China (41925020, 42075105, 42075033, and 42275023); the members of the Youth Innovation Promotion Association, Chinese Academy of Sciences; the Guangdong Basic and Applied Basic Research Foundation (2022A1515010585); and the 2022 “Future Earth” Early Career Fellowship from “Future Earth Global Secretariat Hub China.”

References

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    • Search Google Scholar
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
  • Wehrli, K., B. P. Guillod, M. Hauser, M. Leclair, and S. I. Seneviratne, 2019: Identifying key driving processes of major recent heat waves. J. Geophys. Res. Atmos., 124, 11 74611 765, https://doi.org/10.1029/2019JD030635.

    • Search Google Scholar
    • Export Citation
  • Xiang, B., B. Wang, W. Yu, and S. Xu, 2013: How can anomalous western North Pacific subtropical high intensify in late summer? Geophys. Res. Lett., 40, 23492354, https://doi.org/10.1002/grl.50431.

    • Search Google Scholar
    • Export Citation
  • Yu, H., and Coauthors, 2022: Attribution of April 2020 exceptional cold spell over northeast China [in “Explaining Extreme Events of 2020 from a Climate Perspective”]. Bull. Amer. Meteor. Soc., 103, S61S67, https://doi.org/10.1175/BAMS-D-21-0175.1.

    • Search Google Scholar
    • Export Citation
  • Zhang, X., and Coauthors, 2023: Increased impact of heat domes on 2021-like heat extremes in North America under global warming. Nat. Commun., 14, 1690, https://doi.org/10.1038/s41467-023-37309-y.

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Supplementary Materials

Save
  • Ciavarella, A., and Coauthors, 2018: Upgrade of the HadGEM3-A based attribution system to high resolution and a new validation framework for probabilistic event attribution. Wea. Climate Extremes, 20, 932, https://doi.org/10.1016/j.wace.2018.03.003.

    • Search Google Scholar
    • Export Citation
  • Deser, C., L. Terray, and A. S. Phillips, 2016: Forced and internal components of winter air temperature trends over North America during the past 50 years: Mechanisms and implications. J. Climate, 29, 22372258, https://doi.org/10.1175/JCLI-D-15-0304.1.

    • Search Google Scholar
    • Export Citation
  • Dong, Z., L. Wang, P. Xu, J. Cao, and R. Yang, 2023: Heatwaves similar to the unprecedented one in summer 2021 over western North America are projected to become more frequent in a warmer world. Earth’s Future, 11, e2022EF003437, https://doi.org/10.1029/2022EF003437.

    • Search Google Scholar
    • Export Citation
  • Faranda, D., G. Messori, A. Jezequel, M. Vrac, and P. Yiou, 2023: Atmospheric circulation compounds anthropogenic warming and impacts of climate extremes in Europe. Proc. Natl. Acad. Sci. USA, 120, e2214525120, https://doi.org/10.1073/pnas.2214525120.

    • Search Google Scholar
    • Export Citation
  • Fischer, E. M., S. I. Seneviratne, P. L. Vidale, D. Luethi, and C. Schaer, 2007: Soil moisture–atmosphere interactions during the 2003 European summer heat wave. J. Climate, 20, 50815099, https://doi.org/10.1175/JCLI4288.1.

    • Search Google Scholar
    • Export Citation
  • Gong, H., L. Wang, W. Chen, and R. Wu, 2019a: Attribution of the East Asian winter temperature trends during 1979–2018: Role of external forcing and internal variability. Geophys. Res. Lett., 46, 10 87410 881, https://doi.org/10.1029/2019GL084154.

    • Search Google Scholar
    • Export Citation
  • Gong, H., L. Wang, W. Chen, and R. Wu, 2019b: Time-varying contribution of internal dynamics to wintertime land temperature trends over the Northern Hemisphere. Geophys. Res. Lett., 46, 14 67414 682, https://doi.org/10.1029/2019GL086220.

    • Search Google Scholar
    • Export Citation
  • Hersbach, H., and Coauthors, 2020: The ERA5 global reanalysis. Quart. J. Roy. Meteor. Soc., 146, 19992049, https://doi.org/10.1002/qj.3803.

    • Search Google Scholar
    • Export Citation
  • Huang, B. Y., and Coauthors, 2017: Extended Reconstructed Sea Surface Temperature, version 5 (ERSSTv5): Upgrades, validations, and intercomparisons. J. Climate, 30, 81798205, https://doi.org/10.1175/JCLI-D-16-0836.1.

    • Search Google Scholar
    • Export Citation
  • Jones, N., 2022: Rare ‘triple’ La Niña climate event looks likely—What does the future hold? Nature, 607, 21, https://doi.org/10.1038/d41586-022-01668-1.

    • Search Google Scholar
    • Export Citation
  • Lu, R., K. Xu, R. Chen, W. Chen, F. Li, and C. Lv, 2023: Heat waves in summer 2022 and increasing concern regarding heat waves in general. Atmos. Ocean. Sci. Lett., 16, 100290, https://doi.org/10.1016/j.aosl.2022.100290.

    • Search Google Scholar
    • Export Citation
  • Mallapaty, S., 2022: China’s extreme weather challenges scientists trying to study it. Nature, 609, 888, https://doi.org/10.1038/d41586-022-02954-8.

    • Search Google Scholar
    • Export Citation
  • Munoz-Sabater, J., and Coauthors, 2021: ERA5-Land: A state-of-the-art global reanalysis dataset for land applications. Earth Syst. Sci. Data, 13, 43494383, https://doi.org/10.5194/essd-13-4349-2021.

    • Search Google Scholar
    • Export Citation
  • Ren, L., and Coauthors, 2020: Anthropogenic influences on the persistent night-time heat wave in summer 2018 over northeast China [in “Explaining Extreme Events of 2018 from a Climate Perspective”]. Bull. Amer. Meteor. Soc., 101, S83S88, https://doi.org/10.1175/BAMS-D-19-0152.1.

    • Search Google Scholar
    • Export Citation
  • Terray, L., 2021: A dynamical adjustment perspective on extreme event attribution. Wea. Climate Dyn., 2, 971989, https://doi.org/10.5194/wcd-2-971-2021.

    • Search Google Scholar
    • Export Citation
  • Terray, L., 2023: A storyline approach to the June 2021 northwestern North American heatwave. Geophys. Res. Lett., 50, e2022GL101640, https://doi.org/10.1029/2022GL101640.

    • Search Google Scholar
    • Export Citation
  • Vautard, R., and Coauthors, 2019: Evaluation of the HadGEM3-A simulations in view of detection and attribution of human influence on extreme events in Europe. Climate Dyn., 52, 11871210, https://doi.org/10.1007/s00382-018-4183-6.

    • Search Google Scholar
    • Export Citation
  • Wehrli, K., B. P. Guillod, M. Hauser, M. Leclair, and S. I. Seneviratne, 2019: Identifying key driving processes of major recent heat waves. J. Geophys. Res. Atmos., 124, 11 74611 765, https://doi.org/10.1029/2019JD030635.

    • Search Google Scholar
    • Export Citation
  • Xiang, B., B. Wang, W. Yu, and S. Xu, 2013: How can anomalous western North Pacific subtropical high intensify in late summer? Geophys. Res. Lett., 40, 23492354, https://doi.org/10.1002/grl.50431.

    • Search Google Scholar
    • Export Citation
  • Yu, H., and Coauthors, 2022: Attribution of April 2020 exceptional cold spell over northeast China [in “Explaining Extreme Events of 2020 from a Climate Perspective”]. Bull. Amer. Meteor. Soc., 103, S61S67, https://doi.org/10.1175/BAMS-D-21-0175.1.

    • Search Google Scholar
    • Export Citation
  • Zhang, X., and Coauthors, 2023: Increased impact of heat domes on 2021-like heat extremes in North America under global warming. Nat. Commun., 14, 1690, https://doi.org/10.1038/s41467-023-37309-y.

    • Search Google Scholar
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  • Fig. 1.

    The SAT (shading; °C) and SLP (contours; interval: 0.6 hPa) anomalies in August 2022 for (a) ERA5 data, (b) externally forced component, (c) internal component, (d) internal dynamical component, and (e) internal thermodynamical component. The boxes denote the region of southern China, and the values in the upper-left corner indicate the area-averaged SAT anomalies in southern China.

  • Fig. 2.

    (a) Time series of circulation projection index (CPI) during 1960–2022. (b) Internal SAT (shading; °C) and HGT500 (contours; interval: 1 gpm) anomalies regressed onto the normalized CPI. (c) As in (b), but for SST. (d) Internal SAT (shading; °C) and HGT500 (contours; interval: 1 gpm) anomalies regressed onto the normalized CPSST index. (e) Normalized internal soil moisture (SM; black lines) and SAT (red lines) indices in southern China during 1960–2022. Corresponding solid lines are the decadal components obtained by 9-yr sliding mean. (f) Internal SAT (°C) anomalies regressed onto the normalized SM index. The boxes in (b), (d), and (f) denote the region of southern China. The box in (c) and (f) are the regions to define the CPSST and SM indices, respectively. Stippled regions indicate where the significance exceeds the 90% confidence level.

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