Introduction

Pakistan lies in the semi-arid to arid belt of western South Asia1,2. The summer monsoon supplies 65–75% of the total annual rainfall in Pakistan, which is of great importance for both natural ecosystems and socio-economic development there3,4. However, dramatic fluctuations in monsoon rainfall frequently result in catastrophic floods. In the summer of 2022, unprecedented extreme rainfall hit Pakistan, particularly the accumulated rainfall amount in August notably surpassing 500% of its climatological mean5,6. During this event, record-breaking rainfall anomalies swept across a large area of southern Pakistan, including southern Baluchistan and Sindh (Fig. 1a). This catastrophic event broke the rainfall record set in 2010, internally displacing about 32 million people, causing 1486 fatalities, with the economic losses up to $30 billion7,8. Therefore, understanding the drivers of this devastating rainfall in Pakistan remains an important question to be addressed, essential for improving the accuracy of extreme precipitation prediction.

Fig. 1: The observed precipitation and maximum surface air temperature anomaly in August 2022.
Fig. 1: The observed precipitation and maximum surface air temperature anomaly in August 2022.The alternative text for this image may have been generated using AI.
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a The precipitation anomaly in 2022 (mm day−1; shading) and precipitation in climatology (mm day−1; contour). The box outlines the region (64°−72°E/24°–32°N) for defining the Southern Pakistan rainfall index (SPRI), while the purple outline represents the border of Pakistan. b The maximum surface air temperature anomaly (°C; shading) and geopotential height anomaly at 200 hPa (gpm; contour). The white dot in (a, b) indicates the largest rainfall/ surface air temperature anomaly since 1979.

It is widely accepted that tropical air-sea interactions, such as El Niño-Southern Oscillation (ENSO) and Indian Ocean dipole (IOD), shape the South Asian summer monsoon (SASM) rainfall by modulating the Walker circulation and local Hadley circulation9,10,11,12. When La Niña occurs, ascending limb of Walker circulation over the Indian sector strengthens, favoring enhanced rainfall over the South Asian monsoon region, whereas El Niño causes drought13,14. Hong et al. (2023) proposed that the observed La Niña in the summer of 2022 could induce anomalous easterly moisture transport and contribute to this extreme Pakistan rainfall15. However, most areas of Pakistan belong to the edge of the South Asian monsoon region. The Pakistan rainfall-ENSO relationship is weaker than the SASM-ENSO relationship, which is supported by both the observations and numerical experiments16. Moreover, La Niña alone cannot explain such catastrophic 2022 Pakistan floods due to its moderate amplitude in this year15,16. In terms of the IOD signal, its linkage with Pakistan rainfall is also tenuous, with their correlation coefficient less than 0.1 during 1958–201017. Collectively, these studies imply that the individual tropical sea surface temperature (SST) is insufficient in explaining the variability of Pakistan precipitation.

Beyond the tropical sea-atmosphere interaction, mid- and high-latitude processes also have potential impacts on Pakistan precipitation. Concurrent with the extreme Pakistan rainfall in August 2022, a severe heatwave swept across Northwestern Russia, coinciding with an exceptionally strong European blocking high (Fig. 1b)15. Similar Russian heatwave-Pakistan flooding configuration also occurred in the summer of 2010, and numerous studies attributed it to a large-scale atmospheric Rossby wave train that emanated from the enhanced European blocking high, crossed the vicinity of Lake Baikal, and reached the north China-Tibetan Plateau region18,19,20,21. Downstream energy dispersion from the European blocking region deepened the trough northwest of Pakistan, triggering anomalous ascending motions and heavy rainfall over northern Pakistan in late July and early August of 201018,20,22. In the summer of 2022, Hong et al. (2023) and Hu et al. (2024) likewise suggested a potential influence of European blocking on Pakistan precipitation through the physical pathway akin to that documented for the 2010 event15,23. Beyond inducing anomalous ascent, whether and how mid-high latitude atmospheric circulations modulate the anomalous moisture transport into Pakistan remain unrevealed. Meanwhile, the extreme rainfall in 2022 mainly confined to southern Pakistan6, hinting that the direct influence of European blocking on the core precipitation region might be weaker than that in 2010.

Geographically, Pakistan lies to the southwest of the Tibetan Plateau (TP). As the highest plateau in the world situated in the subtropics of the Eurasian continent, the TP exerts significant impacts on regional and global climate due to its unique geographical position, altitude, area, and steep slopes in the south and east24,25,26,27,28. On the one hand, the TP and its adjacent regions serve as a huge atmospheric heat source during summer, exerting profound influences on Asian summer monsoon variability27,29,30,31,32. Particularly, condensational heating around the eastern TP is identified as a critical driver of Pakistan rainfall1. On the other hand, TP thermal heating itself is also partly regulated by the mid-latitude westerly systems and SST anomalies over the North Atlantic Ocean33,34. Therefore, the TP could act as a bridge that conveys the mid- and high-latitude forcing into the Asian monsoon region28,34. However, the role of TP in the Pakistan extreme rainfall during the summer of 2022 is still unclear.

In this study, we first attempt to address the possible intermediate role of the TP in linking European blocking to the Pakistan extreme rainfall, based on the observational precipitation and atmospheric reanalysis data. Then, numerical simulations are also conducted with a linear baroclinic model (LBM) to vindicate the underlying physical mechanisms.

Results

The water vapor budget over Southern Pakistan and associated anomalous atmospheric circulations in August 2022

Climatologically, a prevailing south-westerly monsoon in August sweeps from the Arabian Sea across most area of the Indian subcontinent (Fig. 2a), promoting warm and moist air transport from ocean toward South Asia and bringing abundant monsoon rainfall here (Fig. 2b). Pakistan abuts the western TP and consists of plains in the southeast and the mountainous areas in the northwest (Fig. 2a). This region lies on the northwestern margin of the South Asian monsoon domain, which experiences a greatly attenuated direct influence of the south-westerlies with column-integrated moisture fluxes are substantially weaker than those over southern India (Fig. 2b). Consequently, Pakistan receives much less rainfall than areas farther south, with the climatological mean rainfall in August gradually decreasing from ~4 mm day−1 in south-eastern Pakistan to <1 mm day−1 in the north-west (Fig. 2b).

Fig. 2: The moisture transport and associated lower-level atmospheric circulations in August.
Fig. 2: The moisture transport and associated lower-level atmospheric circulations in August.The alternative text for this image may have been generated using AI.
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a The topographic height (m; shading) and horizontal wind at 850 hPa of climatology (m s–1; vector). b The column-integrated moisture flux (from surface to 300 hPa; kg m–1 s–1; vector) and precipitation (mm day–1; shading) of climatology. The numbers denote net water vapor input (positive) or output (negative) (Kg s–1) across four boundaries of the key region. c The anomalies of horizontal wind at 850 hPa (m s–1; vector) and surface pressure (hPa; shading) in 2022, with the dashed box outlines the region for defining the easterly index (EI). d The anomalies of column-integrated moisture flux (kg m–1 s–1; vector) and its divergence (×10–5 kg m–2 s–1; shading) in 2022. The black and red numbers/thick arrow denote net water vapor input (or output) in 2022 and their departure from the climatology, respectively. e The standardized time series of SPRI (black) and EI (red) from 1979 to 2022. f Same as in (d), but for the regressions against the standardized EI during 1979–2022, in which black dots denote significance at p = 0.05 level.

In August 2022, this canonical pattern is reversed. A pronounced anomalous easterly flow exceeding −3 m s−1 at lower-level replaces the climatological mild westerly flow over the northwestern Indian subcontinent (Fig. 2a, c). Guided by this reversed flow, abnormal water vapor originating from Bangladesh and Bay of Bengal migrate zonally along the Himalayan foothills with the maximum flux magnitudes exceeding 260 kg m−1 s−1, and surge into southern Pakistan, where anomalous moisture convergence reached −2 × 10−4 kg m−2 s−1 (Fig. 2d). The water vapor budget for the target region also suggests that the anomalous column-integrated water vapor fluxes at all four boundaries are opposite to their climatological states (Fig. 2b, d). Climatologically, water vapor flows into southern Pakistan through the western and southern boundaries and flows downstream mainly through the eastern boundary (Fig. 2b), while in August 2022, the flux at eastern boundary substantially switches from an export of −431.4 kg s−1 to an import of 156.6 kg s−1 (Fig. 2d). This 588.0 kg s−1 increase in water vapor fluxes through the eastern boundary dominates the moisture surplus in 2022 relative to the climatology (Fig. 2d), and thus fuels the rainfall intensification over the target region (Fig. 1a). These results also corroborate the moisture equation diagnosis of Luo et al. (2023), who identified the dynamic component, namely the humidity advection induced by the anomalous easterly flows, as the primary contributor to this Pakistan extreme rainfall6. Additionally, Hong et al. (2023) reported contributions from both westward moisture transport from the Bay of Bengal and eastward moisture transport from the Arabian Sea to Pakistan extreme rainfall in summer 2022, with the former far exceeding the latter15. It is worth noting that Hong et al. (2023) examined the July-August mean state15, whereas our analysis focuses on the condition in August. Despite this difference, their findings generally align with our conclusion that the westward moisture transport originating around the Bay of Bengal dominates the moisture supplement within southern Pakistan.

Given the role of the anomalous lower-tropospheric easterlies over the northwest Indian subcontinent in triggering Pakistan extreme rainfall in August 2022, we define an easterly index (called the EI) to depict the features of this easterly flow (Fig. 2e). The EI is calculated as the August mean zonal wind anomalies at 850 hPa averaged over 65°E-77°E/24°N-31°N (denoted by the rectangle in Fig. 2c) and multiplied by −1 to be consistent with the situation in 2022, that is, positive values denote strengthened easterlies. Figure 2f shows the regression map of August mean moisture transport relative to the EI during 1979–2022. As the anomalous easterly wind accelerated, a pronounced westward moisture corridor along the southern flank of the Himalayas and moisture convergence over southern Pakistan tend to be strengthened (Fig. 2f), which contributes to enhanced precipitation here. These regressed patterns align closely with the observations in 2022 (Fig. 2d, f). Accordingly, EI shows a significant correlation coefficient up to 0.78 with the Southern Pakistan rainfall index (SPRI; defined in Fig. 1a) during 1979–2022, explaining approximately 60.8% of SPRI variance (Fig. 2e). At the same time, the EI in 2022 reaches 2.3 m s−1, about 2.4 standard deviations above the 1979–2022 mean and the highest value since 1979, corresponding to the record-breaking SPRI (Fig. 2e), which could well explain the extremity of precipitation in southern Pakistan. It is noteworthy that the EI in 2006 is comparable to that in 2022, ranking as the second strongest after 2022 (Fig. 2e). In August 2006, pronounced westerly moisture transport appears from the tropical Arabian Sea to Indian Peninsula (Supplementary Fig. 1a), whereas such transport is invisible in 2022. The strong eastward moisture transport conflicts with westward moisture transport along the Himalayas, causing intense moisture convergence over the central Indian Peninsula (Supplementary Fig. 1a), with the anomalous precipitation center mainly appearing in the regions to the southeast of Pakistan (Supplementary Fig. 1b). Therefore, the SPRI in 2006 exhibits a weaker positive anomaly than that in 2022 (Fig. 2e). Although moisture transport from the tropical Arabian Sea plays a relatively minor role in this 2022 extreme event, it may also exert a certain modulation on Pakistan rainfall variability from a long-term perspective15.

The above results imply that the anomalous lower-level easterly flow over the northwest Indian subcontinent is pivotal to the Pakistan extreme rainfall in August 2022 by channeling excessive moisture into southern Pakistan. We therefore investigate the possible mechanisms of the anomalous easterly flow in the following section.

Direct impact of TP thermal forcing on the anomalous lower-level easterly flow over the northwestern Indian subcontinent

As reviewed in the introduction, the variability of the SASM has been traditionally linked to the remote forcing of slow-varying SST anomalies, especially the tropical Indo-Pacific Ocean. In August 2022, the tropical SST anomalies exhibit a central Pacific type of La Niña and a negative IOD phase (Supplementary Fig. 2a), yet these SST anomalies appear to have played a minor role in this extreme rainfall event. This is because tropical SSTs show limited capacity in modulating the atmospheric circulation anomalies in the higher latitudes of the South Asian monsoon region16. The regression map of anomalous moisture transport onto the Niño 4 index show that the central Pacific type of La Niña drives westward moisture fluxes cross the Bay of Bengal between 10° and 20°N, but this moisture channel weakens markedly as it advances into the northwestern Indian subcontinent (Supplementary Fig. 2b). This is inconsistent with the observed feature in 2022, in which the anomalous westward moisture transport along Himalayan foothills is stronger than that over the lower-latitudes of south Asia (Fig. 2d). Likewise, the westward moisture transport over northwest of India associated with the negative IOD is also invisible (Supplementary Fig. 2c). Obviously, both the Niño 4 and IOD indices present weak correlations with the simultaneous EI and the SPRI during 1979–2022 (Supplementary Table 1). Moreover, anomalies in these tropical Indo-Pacific SST modes manifest moderate amplitudes in August 2022 in comparison with historical years (Supplementary Table 1), which are unable to explain the rarity of this Pakistan extreme rainfall in 2022. These results suggest that tropical SST anomalies alone exert limited impacts on the anomalous easterly flow over the northwest Indian subcontinent as well as the extreme rainfall within southern Pakistan in 2022, implicating the involvement of additional factors.

Besides the remote influences of SST anomalies, the thermal forcing of the TP has long been recognized as a crucial driver for the onset and maintenance of the SASM24,35,36, especially the atmospheric latent heating associated with rainfall anomalies dominates the total diabatic heating around the TP in summer37,38. Concurrent with the excessive rainfall over southern Pakistan, it is also worth noting that extreme rainfall deficiency is witnessed around the southeastern slope of TP in August 2022 (Fig. 3a). This rainfall decrease is accompanied by locally reduced condensational heating, whose magnitude is comparable with the vigorous condensational heat release above Pakistan (Fig. 3a). The corresponding vertical profile of condensational heating over southeastern slope of TP also shows that the entire troposphere basically exhibits a reduction in the release of latent heat, resulting in deep diabatic cooling from lower to upper troposphere (Fig. 3b).

Fig. 3: The precipitation, diabatic heating and associated anomalous atmospheric circulations in August.
Fig. 3: The precipitation, diabatic heating and associated anomalous atmospheric circulations in August.The alternative text for this image may have been generated using AI.
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a The anomalies of both apparent moisture sink (\({{\rm{Q}}}_{2}\); see Methods) vertically integrated from surface to 300 hPa (\(\left\langle {{\rm{Q}}}_{2}\right\rangle\); shading; W m−2) and precipitation (mm day–1; contour; interval: 2; negative values are dashed) in 2022. b Vertical profiles of apparent heat source (\({{\rm{Q}}}_{1}\); see Methods) (W kg−1; blue) and \({{\rm{Q}}}_{2}\) (W kg−1; black) averaged over the southeastern TP as denoted by the box in (a). c The regressions of \(\left\langle {{\rm{Q}}}_{2}\right\rangle\) (W m–2; shading) and horizontal wind at 850 hPa (m s–1; vector) against the standardized STPRI (multiplied by –1) during 1979-2022, in which black dots denote significance at p = 0.05 level. d Same as in (c), but for the column-integrated moisture flux (kg m–1 s–1; vector) and its divergence (×10−5 kg m–2 s–1; shading).

From the statistical perspective, the southeastern TP rainfall index (called the STPRI), defined as the regional mean rainfall over 89°–99°E/24°–30°N in August (Supplementary Table 1), is well coupled with the simultaneous release of latent heat in situ during 1979–2022 (Fig. 3c). When rainfall and associated condensational heating over the southeastern TP weaken, the resulting negative diabatic heating anomalies facilitate a westward acceleration of the airflow, yielding a pronounced low-tropospheric easterly anomaly along the southern foothills of the Himalayas (Fig. 3c). More water vapor is thus transported into southern Pakistan from Bay of Bengal and Bangladesh, and evident convergence of moisture flux appears within southern Pakistan (Fig. 3d), promoting enhanced rainfall in this region. Consequently, the STPRI manifests significant correlation coefficients of −0.70 and −0.40 with EI and SPRI during the historical period, respectively (Supplementary Table 1).

The aforementioned results have illustrated a close link between the anomalous easterlies over the northwestern Indian subcontinent and the rainfall anomalies over southeastern TP, yet the cause-and-effect relationship between them remains unclear. Here, we argue that the thermal forcing tied to southeastern TP rainfall could directly drive this anomalous easterly flow. To verify this hypothesis, a numerical experiment with prescribed heat forcing is conducted in the LBM (see Methods). In the simulation, an idealized elliptic heating sink is imposed onto the southeastern slope of TP throughout the integration period (Supplementary Fig. 3a), with its vertical profile prescribed in accordance with the observations (Fig. 3b, Supplementary Fig. 3b). This anomalous heating cools the surrounding air, causing it to contract, become denser, and sink, which raises near-surface pressure in adjacent regions (Supplementary Fig. 3a). Meanwhile, this anomalous near-surface high is accompanied by a lower-tropospheric anticyclone northwest to the heat forcing, thus enhancing the anomalous easterly flow along the Himalayas (Supplementary Fig. 3a), which resembles the Matsuno–Gill response pattern39,40. The simulated circulation anomalies closely match the observed patterns in August 2022 (Fig. 2c), confirming the important role of thermal forcing around TP in this event. The above results are also supported by previous studies1,41, which identified TP heating as a driver of the zonal moisture transport along the Himalayas and monsoon rainfall variability in Pakistan based on the observations during 1980–2014.

Moreover, the STPRI is basically independent of tropical SST forcing, which shows a weak correlation coefficient of −0.17 (−0.10) with the Niño 4 (IOD) index. In August 2022, the STPRI falls to its lowest value since 1979, coinciding with the simultaneous record-breaking EI and SPRI (Supplementary Table 1). These results demonstrate that the anomalous latent-heat linked to rainfall anomalies near the southeastern slope of the TP could directly drive anomalous easterlies over the northwestern Indian subcontinent and enhance precipitation within southern Pakistan, via a pathway that is independent of both ENSO and IOD. This raises the next question: what governs precipitation over the southeastern TP itself? Beyond tropical SSTs, could mid- and high-latitude processes play a role?

Remote modulation of European blocking on rainfall anomalies over the southeastern slope of the TP and Southern Pakistan

From the perspective of the large-scale circulation anomalies across middle and high latitudes of Eurasia, a strong blocking high is observed in the upper troposphere over northeastern Europe, accompanied downstream by an anomalous low extending from Central Asia to Northeast Asia region and an anomalous high over subtropical East Asia (Fig. 4a). This pattern constitutes a stationary Rossby wave train, with apparent wave activity fluxes originated near the European blocking high and propagating downstream (Fig. 4a). The Rossby-wave energy disperses along two pathways, of which the stronger one propagates eastward across the Caspian Sea and Lake Baikal toward the East Asia (Fig. 4a). This reinforces the anomalous upper-tropospheric high and attendant anticyclone anchored over subtropical East Asia, since the Rossby-wave activity exerts great effects on the formation and maintenance of midlatitudes anomalous highs42.

Fig. 4: The atmospheric teleconnection pattern across Eurasia and vertical motion above the southeastern TP in August.
Fig. 4: The atmospheric teleconnection pattern across Eurasia and vertical motion above the southeastern TP in August.The alternative text for this image may have been generated using AI.
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a The anomalies of geopotential height (gpm; shading) and horizontal wind (m s−1; grey vector), and the T-N wave activity flux at 200 hPa (m2 s−2; purple vector; only the values exceeding 4 are shown) in 2022, in which the dashed box outlines the region for defining European blocking index (EBI). b The pressure-longitude cross section of zonal-vertical circulation (u: m s−1; ω: ×0.01 Pa s−1; vector) and vertical velocity (×0.01 Pa s−1; shading) averaged over 24°–31°N in 2022 with the climatological mean potential temperature (K) superposed by contour, in which the black shaded area is for topography along 30°N. c, d are same as in (a, b), respectively, but for the regressions against the standardized EBI during 1979–2022, in which black dots denote significance at p = 0.05 level.

Along the southern flank of the anomalous anticyclone over subtropical East Asia, upper-tropospheric easterly anomalies dominate the southeastern slope of TP, while zonal wind anomalies over southern Pakistan remain relatively weak (Fig. 4a). Notably, the mid- and upper- tropospheric zonal flow across the TP is crucial for driving local vertical motion in summer, owing to the unique atmospheric thermal structure near the TP43,44,45. In climatology, a tropospheric warm center with high potential temperature is entrenched over the southwestern TP (Supplementary Fig. 4a), establishing a strong longitudinal potential temperature gradient and an upward inclined isentropic surface from southeastern TP toward middle and lower Yangtze River basin, especially in the mid-upper troposphere (Supplementary Fig. 4b). Since air parcels adiabatically move along the isentropic surfaces46, zonal wind anomalies over the southern TP tend to exhibit significant negative correlations with local p-vertical velocity (Supplementary Fig. 4b). Consequently, the pronounced easterly anomalies above the southeastern slope of the TP observed in August 2022 could induce intense descent in situ (Fig. 4b), suppressing the convection and reducing precipitation there (Fig. 3a).

Furthermore, the regressed pattern of upper-tropospheric circulations against the European blocking index (call the EBI; defined in Supplementary Table 1) during 1979–2022 also shows an apparent Rossby wave train across north Europe to subtropical Asia (Fig. 4c), highly consistent with the observed pattern in August 2022 (Fig. 4a). The anomalous easterly flow at the south flank of the enhanced subtropical East Asian anticyclone slides along the isentropic surface favouring significant descent and reduced rainfall over the southeastern TP (Figs. 4d, 5a). With the bridge role of southeastern TP rainfall and associated condensational heating (Fig. 5a), the European blocking could remotely modulate the anomalous lower-tropospheric easterlies over the northwestern Indian subcontinent, facilitate the moisture transport and convergence over the southern Pakistan (Fig. 5b), and thus enhance the precipitation there (Fig. 5a). Further calculations reveal that the EBI is tightly linked to the STPRI, EI, and SPRI, with significant correlation coefficients during 1979–2022 of −0.57, 0.45 and 0.38, respectively (Fig. 5c; Supplementary Table 1). When the influence of southeastern TP rainfall is excluded, the enhanced European blocking high no longer effectively induces anomalous easterly moisture transport over the northwestern Indian subcontinent (Fig. 5d). The partial correlation coefficient between the EBI and SPRI with the variability of STPRI removed becomes statistically insignificant (r = 0.18), underscoring the indispensable intermediate role of the southeastern TP condensational heating.

Fig. 5: The precipitation, diabatic heating and anomalous atmospheric circulations in August associated with enhanced European blocking.
Fig. 5: The precipitation, diabatic heating and anomalous atmospheric circulations in August associated with enhanced European blocking.The alternative text for this image may have been generated using AI.
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a The regressions of \(\left\langle {{\rm{Q}}}_{2}\right\rangle\) (W m−2; shading), precipitation (mm day−1; contour; interval: 0.6) and horizontal wind at 850 hPa (m s−1; vector) against the standardized EBI during 1979−2022, in which dots are significant at the p = 0.05 level. b Same as in (a), but for the column-integrated moisture flux (kg m–1 s–1; vector) and its divergence (×10–5 kg m–2 s–1; shading). c Scatter plot of the standardized STPRI (X-axis), EBI (Y-axis) and SPRI (shading) during 1979−2022, with correlation coefficients between these indices given at the upper right corner. d Same as in (b), but for the partial regressions against the standardized EBI with the variability of STPRI eliminated.

A numerical experiment with the LBM further verifies the downstream influence of the European blocking high. In this experiment, a negative vorticity source is imposed over northeastern Europe (20°E–55°E, 52°N–72°N) throughout the integration, to mimic the observed European high anomaly in August 2022. As shown in Supplementary Fig. 5a, the negative vorticity forcing increases geopotential height and induces an anomalous anticyclone in situ. Meanwhile, this blocking high anomaly further triggers a Rossby wave train that propagates towards East Asia and intensifies the subtropical East Asian anticyclone (Supplementary Fig. 5a), basically reproducing the observed upper-tropospheric teleconnection pattern of August 2022 (Fig. 4a). However, the lower-tropospheric response exhibits a near-surface low pressure around the TP (Supplementary Fig. 5b), which is distinct from the near-surface high pressure in observation (Fig. 2c). This discrepancy likely arises because the dry version of the LBM neglects the release of condensational heating and its feedback on the atmospheric circulation. To address this issue, an additional TP thermal heating forcing is introduced into the European blocking experiment. This combined-forcing experiment not only simulates the observed upper-level wave train crossing Eurasia (Supplementary Fig. 5c), but also reproduces the near-surface high anomaly and a lower-tropospheric anticyclone extending from TP to northwestern India, thus enhancing the anomalous easterly flow over the northwestern Indian subcontinent (Supplementary Fig. 5d). These results closely resemble the observations (Figs. 2c and 4a), which further confirms the indispensable bridge role of TP condensational heating for conveying the remote influence of European blocking to the South Asia monsoon region.

The aforementioned results delineate a clear physical pathway linking intensified European blocking, reduced southeastern TP rainfall, and excessive rainfall over southern Pakistan observed in 2022. Moreover, the European blocking high in August 2022 ranks as the strongest since 1979 (Supplementary Table 1), confirming its important role in producing the Pakistan extreme rainfall by regulating anomalous southeastern TP heating and zonal moisture transport over the northwestern Indian subcontinent.

Discussion

In the present study, the local and remote atmospheric drivers responsible for the unprecedented Pakistan rainfall event in August 2022 are investigated using observational data and LBM numerical simulation. The water vapor budget over southern Pakistan shows that the westward moisture transport regulated by the anomalous lower-level easterly flows over the northwestern Indian subcontinent dominates the increase of moisture and precipitation within southern Pakistan. Compared with moderate tropical SST anomalies, the extreme rainfall deficiency around the southeastern TP associated with local anomalous diabatic cooling directly drives the pronounced anomalous easterly flow over the northwestern Indian subcontinent. Further analysis reveals that the southeastern TP rainfall is, in turn, governed by mid- and high-latitude processes. In mid- and high-latitudes, an unprecedented European blocking high triggers Rossby-wave energy dispersing toward East Asia and bolsters the anomalous anticyclone there. The pronounced easterly anomalies at the south flank of the East Asian anticyclone, combined with the unique thermal structure over the TP, induce intense descent and reduce rainfall around the southeastern TP. Consequently, the enhanced European blocking could remotely modulate the Pakistan extreme rainfall. Furthermore, both the statistical linkage during 1979−2022 and LBM simulations mirror the observations in 2022, supporting the above conclusions. Our findings highlight the TP heating as an indispensable bridge that connects the European blocking to the southern-Pakistan rainfall extreme by driving the lower-tropospheric westward moisture transport. The conclusions provide an essential supplement for the physical pathway of how the European blocking high influences Pakistan rainfall.

It should be noted that the feedback effect of the local diabatic heating linked to the record-breaking Pakistan rainfall on atmospheric circulations is not considered in this work. Our primary aim is to uncover the causes of the precipitation itself, although condensational heating release that occurs after rainfall onset may further enhance adjacent circulation anomalies and precipitation in situ. Furthermore, the present study mainly focuses on the dynamic modulation of the European blocking high on Pakistan rainfall, but the causes of this intensified European blocking have not been covered in our research yet. This positive height anomaly over Europe persisted for more than one month around August 2022, which may be related to some lower-boundary forcings. For example, the SST anomalies over the North Atlantic Ocean could alter the lower-tropospheric baroclinicity, result in a northward shift of the storm track, and facilitate a positive geopotential height tendency above Europe through eddy vorticity forcing47,48. Arctic SST and sea ice anomalies also contribute to the persistence of Eurasian blocking and equatorward Rossby wave train via local air-ocean-sea ice interaction49,50,51. Moreover, soil moisture conditions over the European plain could interact with the above atmosphere through latent and sensible heat fluxes, and drought surface conditions produce an enhanced ridging in the mid- and upper-troposphere52,53. The roles of these slow-varying factors warrant further investigations, which will be ultimately beneficial for improving the prediction skill of both TP and Pakistan summer rainfall.

Methods

Data sources

Monthly-mean precipitation on a 2.5° grid for the period 1979–2022 is provided by the Global Precipitation Climatology Project (GPCP), the widely-used global gridded precipitation dataset that synergistically merges satellite-derived estimates with rain gauge observations54. The daily maximum surface air temperature on a 0.5° grid for the same period is provided by the National Centers for Environmental Prediction/Climate Prediction Center (NCEP/CPC). All atmospheric circulation variables used in this study are derived from the fifth generation of European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (ERA5) with a horizontal resolution of 2.5°55. Monthly-mean sea surface temperature data on a 1° grid comes from the Hadley Centre56. Anomalies are calculated as departures from the climatological mean of 1979–2022.

Statistical analysis

Linear correlation and regression are adopted to analyze the relationship between two variables, with their statistical significance tested by the two-tailed Student’s t-test.

Atmospheric apparent heat source/moisture sink

The atmospheric apparent heat source (\({Q}_{1}\)) and apparent moisture sink (\({Q}_{2}\))57 are estimated from the following Eqs. (1) and (2), respectively:

$${Q}_{1}={Cp}\left(\frac{\partial T}{\partial t}+\vec{V}\cdot {\nabla }_{p}{\rm{T}}+{\left(\frac{p}{{p}_{s}}\right)}^{k}\omega \frac{\partial \theta }{\partial p}\right)$$
(1)
$${Q}_{2}=-L\left(\frac{\partial q}{\partial t}+\vec{V}\cdot {\nabla }_{p}{\rm{q}}+\omega \frac{\partial q}{\partial p}\right)$$
(2)

where \(T\), \(q\), \(\vec{V}\), \(p\),\(\,\omega\) and \(\theta\) indicate air temperature, specific humidity, horizontal wind, pressure, vertical velocity and potential temperature, respectively; \({\nabla }_{p}\) refers to the isobaric gradient operator; \({p}_{s}=1000\,{hPa}\) is the surface pressure; \(k=\frac{R}{{C}_{p}}\), \(R=287{J}{{kg}}^{-1}\,{K}^{-1}\) and \({C}_{p}=1004{J}{{kg}}^{-1}\,{K}^{-1}\) are the gas constant and specific heat of dry air at constant pressure, respectively; \(L=2.5\times {10}^{6}{J}{{kg}}^{-1}\) is the latent heat of condensation.

Wave activity flux

To detect the characteristics of Rossby wave propagation, the two-dimensional T-N wave activity flux based on the quasi-geostrophic framework58 is utilized here:

$${\rm{W}}=\frac{{p}\cos \varphi }{2\left|{\bf{U}}\right|}\left(\begin{array}{ll}{\frac{U}{{a}^{2}\,{\cos }^{2}\varphi }\left[{\left(\frac{\partial {\psi }^{{\prime} }}{\partial \lambda }\right)}^{2}-{\psi }^{{\prime} }\frac{{\partial }^{2}{\psi }^{{\prime} }}{\partial {\lambda }^{2}}\right]+\frac{V}{{a}^{2}\,\cos \varphi }\left[\frac{\partial {\psi }^{{\prime} }}{\partial \lambda }\frac{\partial {\psi }^{{\prime} }}{\partial \varphi }-{\psi }^{{\prime} }\frac{{\partial }^{2}{\psi }^{{\prime} }}{\partial \lambda \partial \varphi }\right]}\\{\frac{U}{{a}^{2}\,\cos \varphi }\left[\frac{\partial {\psi }^{{\prime} }}{\partial \lambda }\frac{\partial {\psi }^{{\prime} }}{\partial \varphi }-{\psi }^{{\prime} }\frac{{\partial }^{2}{\psi }^{{\prime} }}{\partial \lambda \partial \varphi }\right]+\frac{V}{{a}^{2}}\left[{\left(\frac{\partial {\psi }^{{\prime} }}{\partial \varphi }\right)}^{2}-{\psi }^{{\prime} }\frac{{\partial }^{2}{\psi }^{{\prime} }}{\partial {\varphi }^{2}}\right]}\end{array}\right)$$
(3)

where \({\psi }^{{\prime} }=\frac{{\phi }^{{\prime} }}{f}\) denotes the perturbation of geostrophic streamfunction, here \({\phi }^{{\prime} }\) and \(f\) refer to perturbation of geopotential and Coriolis parameter, respectively. Moreover, \(a\) is the earth’s radius, \(p\) is pressure/1000 hPa, and (\(\lambda\), \(\varphi\)) are longitude and latitude, respectively. U = (U, V) represents the basic flow.

Numerical experiments

The dry version of the linear baroclinic model (LBM) is utilized here to verify the atmospheric responses to prescribed heat forcing and vorticity forcing, based on the observed August mean basic state. The LBM could give a response to prescribed external forcing (including vorticity, divergence, temperature, and surface pressure perturbations) via adiabatic processes59. This model simplifies the dynamic framework of the atmospheric general circulation model (AGCM) and excludes complex nonlinear processes and various feedback mechanisms in the atmosphere, making its results much easier to be interpreted in comparison with those in AGCM59,60. In this study, the model with a horizontal resolution of T42 (roughly 2.8° × 2.8°) and vertical 20 levels of sigma (\({\rm{\sigma }}\)) coordinate system is adopted, using a time integration method continued up to 30 days. Given that the atmospheric responses generally approach the quasi-steady state around 30 days, the last 5-day average of the 30-day integration could be considered as an equilibrated response61.