Comparative analysis of characteristics and physical mechanisms for typical summer extreme precipitation in Pakistan

The 2022 floods in Pakistan resulted in severe losses and garnered global attention. This study aims to enhance the understanding of extreme precipitation (EP) events in Pakistan by examining the characteristics and mechanisms behind the persistent EP during summer, utilizing daily precipitation data from the Climate Prediction Center (CPC). Results showed that the monsoon precipitation in 2010, 2020 and 2022 are the highest three years on record. Notably, these peak events in 2010 (concentrating in the north) and 2022 (concentrating in the south) spanned from July through August. Conversely, the extreme precipitation in August 2020 was concentrated in northern Pakistan. For the circulation patterns, the intensification of the South Asian High and the western Pacific subtropical high with a strong Indian monsoon is a unifying feature, but the Iranian high and monsoon low-pressure system on the south of Pakistan was different. Additionally, the EP in July 2010 and August 2022 were also influenced by the teleconnection associated with European Blocking. La Niña events and the negative-phase Indian Ocean Dipole (IOD) also played a role in affecting summer EP, with the strongest La Niña occurring in 2010 and a notable triple-dip La Niña coinciding with a significant negative IOD phase in 2022. La Niña contributed to the formation of an anomalously strong anticyclone over the northwest Pacific and easterly winds along the southern Himalayas, impacting moisture transport to Pakistan. Conversely, the negative IOD phase amplified EP in Pakistan by enhancing the northward movement of convective systems and westerly winds over the Indian Ocean. Furthermore, reduced snow cover on the Tibetan Plateau in the springs of 2010 and 2022 likely induced a stronger thermal dynamical effect, acting as a heat source in summer and increasing precipitation in Pakistan.


Introduction
Pakistan is located in the northwestern corner of the Indian subcontinent and has a typical arid and semi-arid climate.The majority of annual rainfall in this region comes from the monsoon season, which is dominated by the Indian monsoon during the June-September period and accounts for approximately 50% of the total annual rainfall (Ma et al 2023b).Furthermore, the steep terrain of the northern Pakistani-Himalayan foothills receives most of the precipitation.As the impact of climate change, global water vapor is undergoing redistribution, which has escalated the occurrence of extreme weather events across numerous regions (Ghanghas et al 2023).As one of the eight countries most vulnerable to climate change, Pakistan has been witnessing a rising trend in annual precipitation over recent years, coupled with an escalated frequency of extreme rainfall episodes (David et al 2021).However, it is noteworthy that there exist significant spatial disparities in the distribution of extreme precipitation.Within these variations, a prevailing trend of escalated extreme precipitation predominantly manifests in the northeastern sector of Pakistan, whereas a general decline in such occurrences is discernible in the southwestern part of the country (Zahid andRasul 2011, Hussain andLee 2013).
With global warming and the increasing occurrence of extreme precipitation events in the background, Pakistan has repeatedly confronted substantial rainfall events that have led to devastating floods, inflicting extensive human casualties and considerable economic damages across the nation.Among the most characteristic instances of such events is the following: (1) In 2010, unprecedented extreme precipitation precipitated widespread flash flooding across all provinces, resulting in extensive damage to numerous roads, bridges, and flood control structures (Britannica 2023), claiming the lives of 1,985 individuals and impacting approximately 900,000 people across the region (Scott 2011), (2) In 2020, as documented by the Office for the Coordination of Humanitarian Affairs (OCHA 2020), a catastrophic flood event precipitated by historically unprecedented heavy rainfall led to the tragic loss of 409 lives.Notably, the cumulated precipitation that inundated the region within that week was strikingly comparable to Karachi's average annual precipitation levels (Owen et al 2020), (3) the extreme precipitation in 2022 was one of the most impactful catastrophic events with the largest cumulative precipitation in history, resulting in the flooding of one-third of the country, 1,700 deaths, 33 million people affected, and $30 billion in direct economic losses (Nanditha et al 2023).
Owing to the special geographical location, Pakistan's climate is profoundly influenced by the sea surface temperature (SST) of both the Indian Ocean and Pacific Ocean, as well as by the thermodynamic effects of the Tibetan Plateau.In the summer of 2010, La Niña-like SST anomalies and the negative Indian Ocean Dipole (IOD) phase constitute the primary driver of circulation anomalies, which in turn engender rainfall deviations in Pakistan (Di Capua et al 2021).The robustly intensifying La Niña phenomenon exacerbated extreme precipitation in Pakistan by strengthening easterly winds anomalous along the Himalayan foothills and augmenting a downstream energy dispersion from the western Russia blocking region in late July (Hong et al 2011, Galarneau et al 2012, Trenberth and Fasullo 2012).In addition, El Niño and southern oscillation (ENSO) is widely acknowledged as a significant determinant of the interannual variability in the South Asia High (SAH) (Xue et al 2015).Xue et al (2018) revealed that following the winter El Niño (La Niña) state, the SAH typically exhibits a tendency to be stronger in intensity and situated farther southward.When SAH is strong, the Arabian Sea has a significant induction of water vapor, and western Pakistan has a strong convergence of water vapor leading to precipitation (Zahid and Rasul 2013).At the same time, La Niña events are also known to prompt the westward extension of the western Pacific subtropical high (WPSH) and easterly wind anomalies in the lower troposphere.This configuration fosters the development of a north-south oriented parabolic trough within the Indo-Pakistani region by westerly winds from the upper mid-latitudes of the troposphere and contributing to the transport of water vapor from the Arabian Sea southwards to form heavy precipitation events in Pakistan (Mujumdar et al 2012, Yang et al 2022).
Tropical Indian Ocean SST influences anomalous summer precipitation in Pakistan by altering the summer circulation (Hong et al 2015, Priya et al 2015).Previous studies have suggested the IOD affected the development of contemporary ENSO events through the Walker circulation anomalies and ocean fluctuation processes associated with latitudinal wind anomalies (Jiang et al 2021).In recent years, many IOD events have occurred independently of ENSO events and have become more dominant in Pakistan's precipitation (Iqbal and Hassan 2018).During periods of a negative IOD phase, the SST pattern across the Indian Ocean exhibits a characteristic west-low-east-high.In the eastern Indian Ocean sector, intensified vertical upward enhances the Walker circulation, leading to stronger westerly winds.These enhanced westerly winds create favorable conditions for increased precipitation occurrences in Pakistan.
The surface sensible heating over the Tibetan Plateau in summer makes the upper atmosphere a heat source to heat the atmosphere in the middle troposphere, regulating Pakistan's summer monsoon precipitation on an interannual scale (Ye andGao 1979, Wang et al 2019).The anomalous heating over the Tibetan Plateau instigates the Rossby wave responses in the upper atmosphere, thereby triggering substantial downward flow in Pakistan.Concurrently, it also engenders abnormal westerly winds along the Himalayan range in the lower troposphere, which further attenuates water vapor transport from the Bay of Bengal to Pakistan (Wang et al 2019).In the summer of 2010, a strong anomalous southeasterly flow along the Himalayas foothills coupled with an extensive northward moisture transport in the Bay of Bengal driven by the interseasonal oscillation of the Indian Monsoon significantly amplified and sustained the heavy rainfall events in Pakistan (Lau and Kim 2012).The anomaly of Tibetan Plateau snow cover (TPSC), a critical indicator of thermal conditions over the Tibetan Plateau, could instigate atmospheric thermal anomalies by modulating soil moisture and surface temperature through changes in albedo and snowmelt processes, which alterations subsequently influence atmospheric heat fluxes, water vapor fluxes and radiation fluxes (Qian et al 2003, Wu et al 2016).For instance, Ma et al (2023a) demonstrated that extreme summer precipitation in Pakistan in 2022 was closely associated with anomalous late spring snow cover over the western Tibetan Plateau.
This study delves into extreme precipitation events that transpired in Pakistan during the summers of 2010, 2020, and 2022, which led to substantial economic losses.It scrutinizes the characteristics of these extreme precipitations and the direct causes of the formation of precipitation anomalies in Pakistan.Subsequently, the possible impacts of the SST and the TPSC on the extreme precipitation are analyzed.By investigating the characteristics and causative factors pertaining to extreme precipitation, this research is expected to enhance the understanding and knowledge of extreme precipitation in Pakistan and endeavors to furnish valuable reference material for forecasting extreme precipitation in the domain.

Data and method
(1) The dataset utilized in this work includes the CPC Unified Gauge-Based Analysis of Global Daily Precipitation dataset provided by the Climate Prediction Centre (CPC) of the United States of America's NOAA.
(2) Also, the fifth-generation reanalysis product (ERA5) with a spatial resolution of 0.25°× 0.25°provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) is used.We selected the period 1979-2022, and the variables include month-by-month geopotential heights, horizontal winds, and stratified water vapor fluxes and their convergence.(3) The ERA5-Land reanalysis dataset was selected for the snow cover data.ERA5-Land has a higher resolution than ERA5 and uses the laws of physics to combine the modeled data with observations from around the world to form a complete dataset on a global scale (Muñoz-Sabater et al 2021).(4) The SST data are linear optimally interpolated global SST data (OISST-v2) provided by NOAA, USA, with a spatial resolution of 0.25°× 0.25°, and the data are selected for the period from 1981 to 2022.The 30-year average from 1991 to 2020 is chosen as the climatology of SST, snow and precipitation.Unless otherwise specified, winter in this paper refers to the average from December of the previous year to February of the current year, spring refers to the average from March to May of the current year, and summer refers to the average from June to August of the current year.
The Indian Monsoon Index (IMI) is a good indicator of the strength of the monsoon currents in the Indian Ocean and is defined as the difference of the 850 hPa latitudinal winds between the region (5°-15°N, 40°-80°E) and the region (20°-30°N, 70°-90°E) (Wang et al 2001).The tropical Indian Ocean dipole (IOD) index is defined as the difference of SST between the tropical western Indian Ocean (50°-70°E, 10°S-10°N) and the southeastern Indian Ocean (EQ-10°S, 90°-110°E) (Saji et al 1999).The Nino3.4 index is defined as the 3-month running mean SST anomaly in the Nino3.4region (5°S-5°N, 170°-120°W), and the five consecutive months of Nino3.4 has adopted a ±0.5 °C threshold to an El Niño if the Nino3.4exceeded +0.5 °C, and as a La Niña if the Nino3.4dropped below −0.5 °C.
The Silk Road Pattern Index (SRPI) is defined as the leading mode of the empirical orthogonal function (EOF) mode of the 200 hPa meridional wind within the domain (20°-60°N, 0°-150°E) (Yasui and Watanabe 2010).The T-N wave activity flux (WAF) is used to characterize the energy dispersion of a constant Rossby wave and is calculated as follows: Where W stands for the horizontal wave activity flux of the Rossby wave.The overbar signifies the climatological mean value while the prime denotes the corresponding anomaly.y represents the stream function.Furthermore, U = (u, v) is used to denote the horizontal wind (Ma et al 2023b).

Comparison of precipitation characteristics
Annual precipitation in Pakistan is dominated by local monsoon rainfall, spanning from June to September.Notably, the precipitation during July-August accounts for approximately 35% of the local annual precipitation (Ma et al 2023b).Figure 1 illustrates the interannual series of monsoon precipitation and July-August precipitation during 1979-2022 in Pakistan.The monsoon precipitation in Pakistan exhibits an increasing trend with a standard deviation of 64 mm, indicating high interannual variability in monsoon rainfall.The monsoon and July-August precipitation in 2010, 2020, and 2022 ranks among the top three in local precipitation histories since 1979, respectively.For the months of July-August, the average precipitation in 2010 reached 199.5 mm, exceeding the normal average by 106.5% and securing the third position in the historical ranking.Similarly, in 2020, the average precipitation rose to 228.8 mm, representing a remarkable increase of 136.9% above the normal average, and is the second record in historical observations.However, the year 2022 witnessed the most significant precipitation anomaly, with an average of 422.6 mm, which was an astonishing 337.4% above the normal average, thus ranking it first in the historical records (figure 1).
A further comparative analysis was carried out to discern the spatiotemporal variations in extreme precipitation across the monsoon period of 2010, 2020, and 2022 in Pakistan.Figure 2 illustrates the time series and time-latitude variation of daily precipitation in Pakistan during the monsoon period.In 2010, the precipitation activity commenced in June and concluded around mid-September, with its zenith predominantly occurring during July-August.Additionally, the peak precipitation levels were largely concentrated in the northern parts of Pakistan toward late July.In 2020, the precipitation advanced from north to south through late July to the end of August.By late August, nearly the entire expanse of Pakistan was subjected to intensified precipitation.In 2022, less intense extreme precipitation began in mid-June.After approximately a ten-day hiatus, July witnessed the onset of widespread extreme precipitation.In July, the northern region experienced notably larger accumulations of precipitation while the southern part exhibited stronger extremes.By August, the precipitation centre shifted to the south and the accumulated precipitation in the south surpassed in the north.The analysis indicates that in 2010 and 2022, precipitation was mainly concentrated in July-August, while in 2020, precipitation predominantly occurred in August.Figure 3 illustrates the spatial distribution of cumulative precipitation and its anomalies in July and August for the years 2010, 2020, and 2022 in Pakistan.During July and August 2010, an exceptional surplus of precipitation was observed in the north along the Himalayas foothills (31°-36°N), with monthly cumulative precipitation exceeding 400 mm.The significant positive precipitation anomalies were predominantly concentrated north of the 30°N, particularly in the Khyber Pakhtunkhwa and the Gujranwala.In July 2020, cumulative precipitation in Pakistan was below 300 mm.However, in August, the precipitation was not only widely distributed across the northern regions of Pakistan but also manifested as widespread extreme precipitation events in the southeastern parts.Notably, the magnitude of maximum precipitation in the southern areas was comparable to that of the north (exceeding 450 mm, approximately 400 mm more than climatology).The spatial distribution of areas with extreme precipitation anomalies aligned with areas of maximum precipitation.Compared to 2010 and 2020, precipitation in 2022 was significantly stronger and more extensive.The distribution of July precipitation covered the entire country, with the north central region experiencing significantly above-normal precipitation by 200-400 mm.In August, precipitation was concentrated in the southern regions, with precipitation intensity exceeding the climatology by more than 300 mm, leading to unprecedented flooding in the southern regions.

Comparison of atmospheric circulation
The exceptionally positive precipitation anomalies in Pakistan for the years 2010 and 2022 spanned July and August, while in 2020, they primarily occurred in August.Therefore, the subsequent analysis examined the atmospheric circulation anomalies, Indian monsoon, and additional factors influencing the precipitation anomalies in Pakistan over these five months.This comparative analysis aims to deepen our comprehension of the physical mechanisms driving the extreme precipitation events in Pakistan.
Figure 4 shows the spatial distribution of horizontal wind anomalies and geopotential height anomalies spacing at the 200 hPa, 500 hPa and 850 hPa during July and August in 2010, August in 2020, and both July and August in 2022.In July 2010, the geopotential height anomaly at 200 hPa showed a clear 'positive-negativepositive' mode in the high-latitude region.At mid-latitudes, cyclonic circulation anomalies were observed on the northwest of Pakistan, and the South Asia High had exceptionally extended (figure 4(a)).The atmospheric circulation pattern at 500 hPa level over Eurasia mirrored that of the geopotential height distribution at 200 hPa, yet it displayed a more pronounced anomaly in the Europe-Russia region.A deep trough was situated to the northwest of Pakistan, facilitating the ingress of cold air from higher latitudes into the country.Meanwhile, In August 2020, the characteristics of the SAH at 200 hPa bore a resemblance to those in August 2010, manifesting as an eastward intensification and a more pronounced southward expansion (figure 4(g)).Similar anomalous cyclone with greater intensity was also observed on the northwest of Pakistan.At 500 hPa, WPSH exhibited a pronounced northward and westward displacement compared to the climatology, while the Iranian In August, the 'positive-negative-positive' structure in the high-latitude region at 200 hPa bore a resemblance to its configuration in July 2010 but with a more pronounced manifestation.However, the anomalous anticyclone over the Tibetan Plateau and the anomalous cyclone over North Asia/East Russia were stronger (figure 4

Remotely related features at middle and high latitude
In addition to the Indian monsoon, the mid-high-latitude circulation had a potential influence on extreme precipitation in Pakistan.The geopotential height at 500 hPa and the temperature anomaly at 850 hPa demonstrate that in July 2010 and August 2022 the circulation fields have an 'Ω' anticyclonic circulation and significant high-temperature anomaly in Europe (figures 7(a) and (e)).The lasting and deep blocking high in the Europe-Russia region corresponded to the development of the southern part of the anomalous cyclone.The upper trough extends from West Asia to southern Pakistan and directs the downward passage of cold air, favoring the development of updrafts and convection.The T-N wave fluxes revealed that Rossby waves originating from the region of the North Atlantic jet propagate along the Asian jet in bands from Europe to northern Pakistan (figures 8(a) and (e)).Two distinct paths of wave energy propagation were observed, each exhibiting distinct northern and southern wave structures, respectively.The southern wave structure propagates to northern Pakistan along the wave energy propagation path, showing the well-known SRP-like teleconnection pattern over Eurasia in summer (Hong et al 2011).
In July 2022, Europe also experienced an 'Ω' type anticyclonic circulation and significant heat anomalies, but the intensity of the circulation anomaly was weaker and occurred at higher latitudes (figure 8(d)).There was no formation of a blocking high-pressure system, and the northwestern region of Pakistan did not experience a trough similar to July 2010 and August 2022 (figure 7).In August 2010 and 2020, the high-latitude circulation was not obviously anomalous in Europe and the results of wave fluxes also showed that there was no significant

Comparative analysis of external forcing factors
The above analysis indicates that extreme precipitation events in Pakistan for 2010, 2020 and 2022 were accompanied by obvious general circulation anomalies.However, the similarities and differences in the typical external forcing factors responsible for this general circulation anomaly are not clear and need further exploration.Prior research has highlighted the substantial influence exerted by the Pacific Ocean SST, Indian Ocean SST, and TPSC on such extreme precipitation occurrences within Pakistan (Hong et al 2011, Wang et al 2019).Consequently, the following will be analyzed in terms of SST anomalies and TPSC.

Tropical SST
The years 2010, 2020 and 2022, all exhibited La Niña abnormal development years with cold SST anomalies in the middle eastern equatorial Pacific Ocean.The most intense La Niña development occurred in the summer of 2010, followed by 2022, with the weakest occurrence in 2020 (figures 9(a)-(c)).The centre of the largest anomalous cold SST was located off the west coast of South America in both 2010 and 2022, which was a centraltype La Niña.However, the equatorial eastern Pacific Ocean was cooler in 2010 compared to 2022, while the equatorial western Pacific Ocean was warmer in 2022 compared with 2010.In 2020, the largest cold SST  The negative phases of IOD during the respective months in the three years were observed in figure 9(e) and the Indian Ocean SST showed a west-low-east-high pattern in the summers (figures 9(a)-(c)).Specifically, the exceptionally negative IOD in the summer of 2022 manifested an extraordinary cooling of SST in the western equatorial Indian Ocean (figure 9(c)), thereby increasing the meridional SST gradient across the equator.The enhanced gradient led to intensified ascending air currents over the eastern Indian Ocean, strengthening the Walker circulation in the Indian Ocean.Consequently, this amplified the westerlies blowing over the Indian Ocean, intensifying the moisture transport towards Pakistan.In addition, the strong negative phase IOD in summer moderated the precipitation over southeastern Pakistan by enhancing the northward propagation of the convective system over the Indian subcontinent (Ajayamohan et al 2008).
Studies have shown that ENSO controlled both IOD and Indian monsoon precipitation before the 1980s, whereas IOD tended to influence Indian monsoon precipitation independently of ENSO in the post-1980 period (Li et al 2016).Although simultaneous La Niña events did not always lead to a negative IOD, multi-year La

Tibetan plateau snow cover
The surface thermal anomalies over the Tibetan Plateau created and maintained the atmospheric circulation in the Asian monsoon region during summer, and the surface adiabatic heating depended mainly on surface processes (Wu 1984, Wang et al 2008).A prominent characteristic of the Tibetan Plateau's surface was the large amount of snow cover which variations in spring could cause changes in energy and water exchange between the land surface and the atmosphere to affect the thermal forcing of surface adiabatic heating on the atmosphere and significantly alter the thermal anomalies of the Tibetan Plateau (Zhang andTao 2001, Yang andWang 2019).In 2010, a negligible (−2.4%) anomaly appeared in TPSC across the majority of the Tibetan Plateau.It was 16.2% higher in 2020 and 24.5% lower than climatology in 2022, when the negative TPSC anomaly was much more noticeable (figure 10(a)).In accordance with radiation-snow feedback theory, the occurrence of a negative snow cover anomaly prompts a decline in land surface albedo, thereby augmenting the net solar radiation absorbed by the Tibetan Plateau.This heightened solar radiation intake amplifies the thermal heating effect exerted by the plateau, which, during summer, functions as a substantial heat source within the Asian region.The increased land-sea thermal contrast instigated a more robust Indian monsoon system, thereby predisposing to elevated precipitation levels across the Indian subcontinent (Ma et al 2023a).
The product of spring TPSC and regression of the spring TPSC to the 200 hPa geopotential height field and wind field were used to estimate the effect of the spring TPSC on the circulation field during extreme summer precipitation in Pakistan (figures 10(b)-(f)).The results showed that the minute TPSC anomalies in the spring of 2010 had an insignificant effect on the circulation associated with precipitation in Pakistan (figures 10(a)-(c)).In 2020, the positive TPSC anomaly brought anomalous low pressure over the Tibetan Plateau with nearby regions and the northern regions of Pakistan (figure 10(d)).In 2022, an unprecedented negative TPSC anomaly brought strong anticyclones on both sides of Pakistan in July (figure 10(e)).Compared to August 2020, a more significant anticyclone due to the negative TPSC anomaly appeared over the Tibetan Plateau in August (figure 10(f)).The negative spring TPSC anomaly also enhanced the extreme precipitation in July by further enhancing SAH and the southeast jet (figure 10(e)) and extreme precipitation in August by strengthening the Europe-Russia blocking and the WPSH (figure 10(f)) (Ma et al 2023a).Thus, the weaker role of the Tibetan Plateau heat source due to the smaller negative spring TPSC anomaly in 2010 than in 2022 may be an essential factor for the larger positive precipitation anomaly in Pakistan in 2022.

Conclusion and discussion
This study conducts a meticulous comparative analysis of the characteristic features and atmospheric circulation disparities, along with their influencing factors, about typical summer extreme precipitation events in Pakistan.The monsoon precipitation in 2010, 2020 and 2022 are the top three in history, with 264.7 mm, 289.9 mm and 502.0 mm, respectively.These figures represent substantial deviations from the climatology at 106.5%, 136.9% and 337.4%.In 2010, significant precipitation fell primarily in July and August and was concentrated in northern Pakistan.Precipitation in 2020 occurred primarily in August with widespread heavy rainfall falling in the southern coastal areas of Pakistan as well as northern Pakistan.In 2022, longer and more widespread precipitation occurred in July and August, and heavy precipitation occurred across the entire country, with northern centres in July and mainly in southern Pakistan in August.
Extreme precipitation events in July and August 2010, August 2020, and July and August 2022 were selected to explore the differences in atmospheric circulation anomalies and possible external forcing signals that contributed to the precipitation anomalies.In July 2010 and August 2022, a warm blocking over Europe-Russia region resulted in a deep cold trough on the west of Pakistan which brought cold air from the high latitudes to the subtropics.The prominent Rossby waves excited by the blocking travelled to the subtropics along the SRPlike teleconnection pattern and enhanced precipitation in Pakistan, but no similar mid-high latitude teleconnection appeared in the other three precipitation months.During August 2020, anomalous monsoon low-pressure systems prevailing to the south of Pakistan augmented water vapor transport from the Arabian Sea into the nation.Similarly, in August 2010 and July 2022, peculiar monsoon depressions positioned to the southern flank of Pakistan intensified moisture flux from both the Bay of Bengal and the Arabian Sea into the country.In addition, the strong Indian monsoon during all three years positively affects the extreme precipitation in Pakistan.
The 2010, 2020 and 2022 were La Niña development years, under whose influence anomalous anticyclonic circulation emerged in the northwestern Pacific Ocean with strong easterly anomalies, which augmented the westward moisture transport from the Indian Ocean towards the Indo-subcontinent.Particularly, 2022 was triple-dip La Niña and the tropical Pacific SST also led to the strongly westward extension of WPSH to the western Tibetan Plateau in August, which further influenced easterly wind anomalies on the southern flank of the Plateau and the enhanced extreme precipitation.The negative-phase IOD in the Tropical Indian Ocean strengthened the Walker circulation with strong westerly winds over the Indian Ocean, and the northward propagation of the convective system over the Indian Ocean, through increasing the meridional SST gradient in the equatorial Indian Ocean.This ultimately affected precipitation in Pakistan during the three years, especially in 2022.It is clear that the combined influence of the La Niña phenomenon and negative IOD phase has affected Pakistan's precipitation.The negative anomaly of spring TPSC in both 2010 and 2022, resulted in a stronger thermodynamic effect during summer to enhance the Indian monsoon during the extreme precipitation in Pakistan.
This research thoroughly investigates the characteristics of extreme precipitation for Pakistan's summer of 2010, 2020 and 2022, as well as its associated large-scale circulation patterns and possible external forcing factors.This analysis serves to furnish insights that can be referenced for forecasting such extreme precipitation events in Pakistan.However, the nonlinear effects of atmospheric dynamics are also important.For example, La Niña can affect blocking in the Europe-Russia region and spring TPSC (Schneidereit et al 2012, Wang et al 2022), and spring TPSC anomalies may be influenced by Indian Ocean SST (Zhang et al 2019).Therefore, further exploration is required to understand how multi-factor interactions impact extreme precipitation in Pakistan.In addition, extreme precipitation events in Pakistan during the summer of 2020 and 2022 were notably influenced by intense weather systems like cyclones in the Bay of Bengal, hence highlighting the need for deeper study into the effects of extreme weather-scale circulations on precipitation extremes and short-term climate projections.

Figure 1 .
Figure 1.Interannual series of accumulative precipitation (the curve line, units: mm) during the monsoon period (from June to September), accumulative precipitation series during July-August (the solid bar, units: mm) and its trend (the black dashed line, units: mm) over Pakistan from 1979 to 2022.

Figure 2 .
Figure 2. (a) Time series of daily precipitation (units: mm day −1 ) over Pakistan during the monsoon period in 2010 (solid red line), 2020 (solid purple line), 2022 (solid blue line) and climatological mean from 1991 to 2020 (black bars).The black dotted line indicates 1 std dev from the climatological mean.(b)-(d) Time-latitude distribution (shading, units: mm day −1 ) of the precipitation in Pakistan during the monsoon period in 2010 (b), 2020 (c) and 2022 (d).The red dotted lines indicate month boundaries.

Figure 3 .
Figure 3. Spatial distribution of cumulative precipitation (shading, units: mm) and its anomaly (the red contour: >200 mm, units: mm) in Pakistan for July (a) and August (b) in 2010, July (c) and August (d) in 2020, and July (e) and August (f) in 2022.

Figure 4 .
Figure 4. Spatial distribution of the horizontal wind anomalies (vectors, units: m s-l) and geopotential height (H) anomalies (shading: units: gpm) in July and August 2010 (a)-(f), August 2020 (g)-(i) and July and August 2022 (j)-(o).The left column is 200 hPa, the center column is 500 hPa and the right column is 850 hPa.The blue solid (dashed line) line on the 200 hPa circulation field indicates the monthly average of 12500 gpm at the corresponding time (monthly average during 1991-2020 of 1250 gpm).The eddy geopotential height is calculated as the difference between H and zonal mean H (0°N-40°N, 180°W-180°E) (Zhou et al 2009).The purple solid (dashed line) line in the center column indicates the monthly average eddy geopotential height of 0-gpm at the corresponding time (monthly average during 1991-2020 of 0-gpm).
(m)).At 500 hPa, Pakistan was situated on the southwest of the anomalous anticyclone over China.Similar to July 2010, a deep blocking high in the Europe-Russia region and a vertical trough along the western edge of the Tibetan Plateau extending southward to the northern Arabian Sea were observed (figure 4(n)).In addition, owing to the synergistic interaction between the anomalous anticyclone in the northwestern Pacific Ocean and the eastward shift of SAH (Zhang et al 2023), the Iranian high retreated westward to its climatological position and WPSH extended westward to the western part of the Tibetan Plateau (figure 4(n)).At 850 hPa, the monsoon low-pressure system on the south of Pakistan collaborated with a notably extended West Pacific Subtropical High (WPSH) and anomalous easterlies to the south of the Tibetan Plateau, which intensified the moisture transport from the Bay of Bengal to Pakistan (figures 4(o) and 5(e)).In addition to supplying more water vapor, the easterly anomaly has the primary effect of stimulating vertical motion over Pakistan through isentropic gliding (He et al 2023).The strong upward motion and abundant moisture coverage over much of southern Pakistan below 30°N had led to the occurrence of persistent heavy rainfall in the region (figure 5(e)).

3. 3 .
Indian monsoon and mid-high latitude remotely related features 3.3.1.Indian monsoon There existed a significant positive correlation between IMI and precipitation over Pakistan in both July and August (Ma et al 2023b).The standardized interannual series of the IMI shows the Indian monsoon is strong during the five extreme precipitation events.The IMI values were 1.19, 1.33, and 0.97 in July 2010, August 2010, and August 2020, respectively.The index could reach up to 2.0 in July 2022, which was the only month since 1979 to exceed 2.0 and the highest value ever recorded in the same period.Additionally, the IMI in August 2022 continues to be anomalously strong with a magnitude of up to 1.8, and the IMI values above 1.5 were observed in July and August 2022, unprecedented since 1979 (figure 6(a)).In July, a significant positive correlation between IMI and precipitation was obserived in the northern Pakistan-Himalayan foothills, southeastern regions, and central areas (figure 6(b)).The stronger correlation in August further expanded and intensified the impact on southern and central precipitation (figure 6(c)).The analysis based on the relationship between precipitation and IMI shows that it was the persistent strong Indian summer monsoon in July and August of 2010, 2020 and 2022 that partly contributed to the extreme floods in July and August in the Pakistan during the same period.

Figure 6 .
Figure 6.Standardized interannual series of the IMI for July (red) and August (blue) (solid bars) during 1979-2022.The regression of precipitation in Pakistan (shading, unit: mm) onto IMI in July (b) and August (c) during 1979-2022.In b and c, the dotted regions denote statistical significance at the 95% confidence interval, as established through the application of the student's t-test (uncontrol for false discovery rate).

Figure 7 .
Figure 7.The geopotential height at 500 hPa (black contours with an interval of 50 gpm, units: gpm) and temperature anomalies at 850 hPa (shading, units: °C) for July (a) and August (b) in 2010, Aug (c) in 2020, and July (d) and August (e) in 2022.

Figure 9 .
Figure 9.The SST anomalies in summer for 2010 (a), 2020 (b), and 2022 (c).The monthly series of Nino3.4(d) and IOD index (e) (red for September 2009-August 2010, green for September 2019-August 2020, blue for September 2021-August 2022).(f) Interannual relationship between Niño 3.4 and IOD in summer 1982-2022 (The linear trends of SST have been removed before correlation analysis).Red, green and blue points represent the summers of 2010, 2020 and 2022, respectively.

Figure 10 .
Figure 10.Interannual series of spring snow cover anomalies indices on the Tibetan Plateau (a).Regressions of the 200 hPa horizontal wind anomalies (vectors, units: m s −1 ) and geopotential height anomalies (shading, unit: gpm) onto the spring snow cover anomalies indices on the Tibetan Plateau in July and August of 2010 (b)-(c), August of 2020 (d) and July and August of 2022 (e)-(f), with the stippling indicating the significant value above 95% confidence level.