Impact of summer Tibetan Plateau snow cover on the variability of concurrent compound heatwaves in the Northern Hemisphere

The weekly climate data record for SC is obtained from the Rutgers University Global Snow Lab, which has a horizontal resolution of 25 km for the period of 1979–2021. Then, we convert the SC data to monthly mean data with a horizontal resolution of 1° × 1°. The SC over the Western TP (SC_WTP) index is the regional average for the Western TP (31°–43° N, 69°–80° E). The SC data is validated by comparing it with ERA5 reanalysis SC data. The strong agreement between the two datasets confirms the accuracy and reliability of the SC over the western TP, bolstering the robustness of our analysis (supplementary figure 3). Monthly mean surface and atmospheric variables are obtained from ERA5 reanalysis data (Hersbach et al 2020) and NCEP-NCAR Reanalysis 1 data (Kalnay et al 1996), including upward shortwave/longwave radiation, mean surface sensible/latent heat flux (LHF), surface temperature, 10 cm soil temperature, geopotential height, temperature, vertical velocity, SC, meridional and zonal wind, with a horizontal resolution of 1° × 1°. The daily UTCI, which combines air temperature, wind, radiation, and humidity for June–August from the ECMWF-ERA5 dataset, has a horizontal resolution of 1° × 1°. The gridded demographic datasets are from the Gridded Population of the World, Version 4 (CIESIN 2020). To mitigate the influence of global warming on our analysis of CCHWs and causality, we initially removed linear trends from all data.

In the current work, the identification of CHWs is based on ERA5 UTCI (Bröde et al 2012), which integrates temperature, humidity, wind and radiation, thus manifesting a substantial health risk (Russo et al 2017, Di Napoli et al 2018). Therefore, this work emphasizes the consideration of climate change and its impact on human health by focusing primarily on multivariate CHWs. Following Bröde et al (2012), the mathematical term of UTCI is expressed as:

$$\begin{align}{\text{UTCI}}\left( {{\text{Ta}},{\text{Tr}},{\text{va}},{\text{pa}}} \right) = {\text{Ta}} + {\text{Offset}}\left({{\text{Ta}},{\text{Tr}},{\text{va}},{\text{pa}}} \right)\end{align} \tag{ 1 }$$

where ${\text{Ta}}$ is the air temperature of the reference condition causing the same model response as the actual condition. The ${\text{Offset}}$ represents the deviation of UTCI depends on the actual values of air and mean radiant temperature (${\text{Tr}}$), wind speed (${\text{va}}$) and water vapor pressure (${\text{pa}}$).

CHWs days are firstly defined when detrended daily UTCI exceeds the 90th percentile of the UTCI index within a centered 15 day window; then, the occurrence of three consecutive days meeting this criterion is needed to define a CHW event (Rousi et al 2022). In addition, we also employed the 95th percentile to identify CHWs for validation purposes, and the results were not sensitive to the thresholds (supplementary figures 1 and 2). This work examines the total number of CHWs days in summer. The time series associated with the first empirical orthogonal function (EOF) of the total days of CHWs in the NH (PC1_CHWs) is used to represent the CCHWs variation in the NH.

• (1)  
  Quasi-stationary wave decomposition: the amplitudes, phase and proportion of quasi-stationary waves of zonal wavenumbers 4–6 are calculated by applying a fast Fourier transform to monthly 200 hPa meridional wind in the NH (10°–90° N) (Petoukhov et al 2013, Riboldi et al 2022).
• (2)  
  Atmospheric energy analysis: The Rossby wave source (RWS) is calculated following Sardeshmukh et al (1988). The barotropic energy conversion (CK) is calculated following Kosaka and Nakamura (2006). The baroclinic energy conversion (CP) is calculated following Kosaka and Nakamura (2010).
• (3)  
  Atmospheric heat analysis: In order to improve the understanding of the forcing of surface snow on the above column atmosphere, the atmospheric heat source (Q₁) is calculated following Yanai et al (1973) and Li et al (2021).

More details of the RWS, CK, CP and Q₁ can be found in the supplementary information.

The long-term trends of summer CHWs in the NH for 1979–2019 have large loading over Southern North America (SNA), North Africa–Europe (NAE) and South Asia-Southeast Asia (SASA) (figure 1(a)). The leading EOF (EOF1) of the summer CHWs variation (with linear trends removed) in the NH, which has a variance contribution of 12.8%, shows a global scale pattern (figure 1(b)), with a similar pattern to figure 1(a). This indicates that the CHWs occurring in SNA, NAE and SASA exist at different time scales and have a close relationship. To further verify the synchronization of CHWs in the above three regions, we calculate the correlation between the area-averaged CHWs in SNA and grid-point CHWs in the NH (figure 1(c)). The correlation coefficients exceed the 95% significance test in all the above three regions. In addition, the correlation coefficients between the time series associated with the EOF1 of the CHWs (PC1_CHWs) (figure 1(f), red line) and the area-averaged CHWs in SNA, NAE and SAS are 0.63, 0.88 and 0.72, respectively, all are significant at the 99% confidence level, indicating that the CHWs are changing synchronously in the three regions. In the following, the PC1_CHWs represents the variation in summer CCHWs in the NH. A high index value of PC1_CHWs indicates that all three regions experienced a higher number of CHWs days during the summer, exceeding the climatology. Notably, the spatial patterns of multivariate CHWs are distinct from the univariate heatwaves studied by previous researchers (Zhang et al 2022, Wang et al 2023), while multivariate CHWs more accurately reflect the risks of human health exposure to climate change, which reinforces the necessity of studying multivariate CHWs and their mechanisms in this work.

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The western TP demonstrates the largest values for both the climatological mean and variation in summer SC (supplementary figure 4). The distribution of the regressed summer SC (with linear trends removed) over the TP onto the PC1_CHWs illustrates a strong relationship between the variation of the SC over the western TP (SC_WTP) and CCHWs in the NH (figure 1(d)). An SC_WTP index is then constructed by averaging the anomalies of summer SC (with linear trends removed) over the region of 26–45° N and 69–90° E (indicated by the gray box in figure 1(d)), which can represent effectively the variation of summer SC over the western TP (figure 1(e)). The contemporaneous correlation coefficient between the SC_WTP and PC1_CHWs indices is 0.44 (p < 0.01). Furthermore, the preceding SC_WTP can have a cross-seasonal impact on the occurrence of CCHWs in the following summer. Firstly, excessive SC_WTP can persist from spring to summer, maintaining the snow-atmosphere coupling effect (supplementary figure 5). Secondly, we evaluate the correlation between the summer PC1_CHWs and the SC_WTP index spanning from spring to summer (table S1). The results consistently demonstrate a significant relationship between SC_WTP and summer CCHWs throughout the spring to summer period. These findings highlight the enduring influence of SC_WTP on the occurrence of summer CCHWs. In addition, the regression map of summer CCHWs in the NH onto the SC_WTP index (figure 1(g)) is similar to figure 1(b), confirming the correlation of SC_WTP with the CHWs while with the most significant correlations over SNA, NAE and SASA. The above results imply that the excessive SC over the western TP from spring to summer is likely to be followed by the occurrence of summer CCHWs in the NH.

Previous work revealed that surface SC can affect local climate by modulating the thermal conditions through the snow albedo effect. Here we show that the surface albedo increased with excessive SC_WTP, which resulted in positive anomalous upward shortwave radiation over the western TP as more shortwave radiation was reflected into space (figure 2(a)). Less solar radiation was absorbed by the surface and the 10 cm soil temperature decreased (figure 2(f)), thereby causing a significant decrease in the upward sensible heat flux (figure 2(b)) and longwave radiation (figure 2(c)). In addition, the excessive SC_WTP led to weak upward LHF from the land to the atmosphere (figure 2(d)). As a result, excessive SC_WTP caused a decrease in skin temperature (figure 2(e)) over the western TP. Furthermore, a significant negative atmospheric heat source (Q₁) anomaly is seen over the western TP with an eastward tilt (figure 2(g)). This indicates a cooling effect of the excessive SC_WTP on the column of the atmosphere from the surface to the upper troposphere. The result suggests that the cooling effect of the excessive SC_WTP was not limited to the lower atmosphere, but extended to the middle and high troposphere. Consequently, the cooling gives rise to a low-pressure anomaly (figure 2(g), contour), accompanied by an upward motion to its eastward while downward motion to its westward.

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Some previous work revealed that the dynamic and thermal effects of the TP favor the formation of Rossby waves, while the friction and heating effects of the TP promote the development of Rossby waves into planetary waves (Lin 1982, Donner et al 1984, Huang 1986), and the TP can then affect the weather in remote areas (He and Li 2015). In this study, the alterations in SC_WTP are associated with anomalous vertical motions and upper-level convergences/divergences that led to considerable vorticity anomalies (supplementary figure 6(a)). The anomalous SC_WTP-related RWS above the TP displays a tripole pattern over the mid-latitude central Eurasian continent (figure 3(a)), with the most prominent positive center over the western TP and two negative anomaly centers situated over the western Caspian Sea and eastern TP. The corresponding upper-level meridional winds and geopotential heights are circumglobal quasi-stationary planetary waves (figure 3(b)). A triple circulation pattern is observed with positive, negative, and positive geopotential height anomalies over the western Caspian Sea, western TP and eastern TP, respectively. In addition, the SC_WTP-related quasi-stationary waves bear many similarities to the PC1_CHW-related circulation anomalies (figure 3(c)). Positive anomalies indicate southerly winds, while negative meridional wind anomalies indicate northerly winds, and troughs and ridges are present in the transitional regions between the positive and negative meridional winds. Figures 3(b) and (c) show a circumglobal quasi-stationary planetary wave with ridges dominating the key CCHW regions of SNA, NAE and SASA, which is a favorable condition for widespread and long-lasting CHWs in the NH (figures 3(b) and (c)).

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Notably, the relationship between the SC_WTP and CCHW persists from spring to summer (table S1). The spring atmospheric response to anomalous SC_WTP is mainly confined to the local area (supplementary figure 7(a)). In contrast, the summer atmospheric response to anomalous SC_WTP exhibits a significant mid-latitude quasi-stationary wave train (supplementary figure 7(b)). Results of energy conversion analysis indicate that the SC_WTP related summer circumglobal circulation pattern can be maintained and enhanced by extracting barotropic (CK) and baroclinic (CP) energy from the basic flow (supplementary figures 6(b) and (c), with CK energy conversion dominating (Wallace and Lau 1985). In addition, the surface anomalous SC and the tropospheric quasi-stationary waves also interact with each other. Excessive TP SC can enhance and sustain the quasi-stationary waves, while the low-pressure anomalies associated with these waves over the TP help maintain the surface anomalous TP SC by mechanisms of snow–atmosphere positive feedback (Henderson et al 2018).

During the boreal summer, quasi-stationary waves in the NH are primarily dominated by zonal wavenumbers 4–6 (supplementary figure 8). Notably, their anomalies frequently act as triggers for simultaneous extreme events across multiple regions. The correlation coefficients between PC1_CHWs and the phase, amplitude, and proportion of quasi-stationary waves, computed for the compositing of wavenumbers 4–6 and averaged over the NH, are 0.43 (p < 0.01), 0.51 (p < 0.01) and 0.30 (p < 0.05), respectively. It suggests a significant correlation between the quasi-stationary waves with wavenumbers 4–6 and CCHWs. Based on the aforementioned analysis, it is possible that the SC_WTP anomaly may influence CCHWs in the NH by changing the thermal conditions of the TP, stimulating hemispheric atmospheric circulation, and modulating quasi-stationary planetary waves.

Figures 4(a)–(c) present the regression of meridional winds for waves 4–6 on the SC_WTP index. These quasi-stationary waves, when combined, give rise to a global-scale quasi-stationary planetary wave, as depicted in figure 3, featuring significant anticyclonic high-pressure anomalies over NAE, SNA and SASA. The meridional wind regressed against PC1_CHWs displays a pattern similar to the regression against the SC_WTP (figures 4(d)–(f)). The SC_WTP-related waves with wavenumbers 4–6 at 500 hPa exhibit a pattern resembling that of figures 4(a)–(c) (supplementary figure 9), indicating a quasi-barotropic structure. The phases of the quasi-stationary waves, associated with the SC_WTP, strongly favor the occurrence of CCHWs. The correlation coefficient between the SC_WTP and the phase of quasi-stationary waves, computed by averaging wavenumbers 4–6 in the NH, is 0.43 (p < 0.01).

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The intensification of quasi-stationary planetary waves can be attributed to multiple climatic factors. Some studies have proposed that the weakening of zonal westerlies, which is a result of the reduced meridional temperature gradient in the NH due to the Arctic warming (Bartusek et al 2022, Kornhuber et al 2017) or eastern Pacific cooling (Baxter et al 2019, Sun et al 2022b), can explain the increase in quasi-stationary planetary waves observed in recent decades. The weakened zonal westerlies lead to higher amplitude trough and ridge systems that propagate more slowly, resulting in more persistent extreme events (Francis and Vavrus 2012, 2015, Coumou et al 2014, 2018). An increasing number of studies have suggested that the increase in quasi-stationary planetary waves of wavenumbers 6–8, is caused by the QRA effect (Mann et al 2018, Teng et al 2019). The QRA can be triggered under the favorable conditions of decelerating zonal westerlies and a 'double jet stream' (enhanced polar and subtropical jet streams) (Rousi et al 2022). Rossby waves with wavenumbers 6–8 can be effectively trapped within the mid-latitude waveguide, and a 'double jet stream' prevents wave energy from escaping to the Arctic and the equator. If the waveguide is circumglobal, the Rossby wave energy is constrained within the extratropics. Furthermore, if some trapped planetary waves are close to the quasi-stationary waves excited by thermal or orographic forcing, the QRA will occur (Mann et al 2018).

The regressions of the 200 hPa zonal wind and meridional temperature gradient in the NH on the SC_WTP index (supplementary figure 10) show that significant negative westerly anomalies dominate the mid-latitude NH, resulting from weakened meridional temperature gradients. This condition would promote the meridional development and deceleration of mid-latitude trough-ridge systems (Francis and Vavrus 2012, 2015), contributing to the formation and amplification of quasi-stationary waves. Furthermore, a strengthened polar jet is also observed, forming a distinctive 'double jet stream' pattern in the NH. The decreasing SC_WTP-associated changes in the upper-level circulations lead to conditions that are favorable for the slow movement of quasi-stationary planetary waves and the QRA of quasi-stationary planetary waves with wavenumber 6.

The quasi-stationary wave with wavenumber 6 associated with SC_WTP and CCHWs, as depicted in figures 4(c) and (f), bears a striking resemblance to the circumglobal Rossby wave with wavenumber 6 identified in a prior investigation on the QRA effect. These results suggest that the excessive SC_WTP can promote the generation and amplification of wavenumber 6-dominated quasi-stationary waves by weakening mid-latitude westerly winds and creating a 'double jet stream' pattern, thereby creating favorable conditions for the simultaneous occurrence of surface heatwaves in various regions.