Analysis of the water‐vapor sources in rainstorm processes in Tianjin city based on the trajectory method

Tianjin, one of the four municipalities in China, is the eastern gate of the capital city of Beijing and is of great socioeconomic importance. When rainstorms attack Tianjin, urban flooding often occurs due to the dense river network, well‐developed water system and flat terrain. In this study, the source analysis of water vapor in rainstorm processes in Tianjin during 2012–2020 is conducted based on the moisture source attribution method, and the PyTrajector and HYSPLIT softwares. Then, the evolution characteristics of rainstorms in Tianjin are investigated. The results show that the rainstorm water‐vapor sources in Tianjin city can be roughly divided into four directions. The west and southwest directions are the main source, which contribute about 89% of the water vapor to the rainstorms. For heavy rainstorm, the water vapor from the southwest direction contributes about 60%, which is larger than that of rainstorm. The southwest direction is the main water vapor source of heavy rainstorm in Tianjin and has the main effect on the water vapor fluctuations during heavy rainstorm. For the more hazardous extraordinary rainstorm, the water vapor from the southwest direction occupies an even larger proportion (74.3%). The annual total rainstorm precipitation in Tianjin city in 2012 was more than that in common years, and this is mainly due to the anomalous increase of water vapor from the southwest direction. This result further indicates that the annual total rainstorm precipitation in Tianjin is mainly influenced by the water vapor from the southwest direction. This study reveals that the majority of rainstorm in Tianjin originates from the western and southwestern directions, but significant heavy rainstorm events in Tianjin are particularly influenced by moisture from the southwestern direction. This research holds crucial implications not only for meteorological and water resource management in Tianjin but also provides valuable insights for global urban flood risk studies.


| INTRODUCTION
Water vapor transport, as an important component of the global water cycle, is the major way of transferring ocean water to land.The studies of water vapor transport mainly include the water vapor content, transport paths and water vapor sources (Li et al., 2018).The related studies are favorable for a deeper understanding of the basin water cycle and water resource characteristics, as well as the macrocontrol of water resources (Oki & Kanae, 2016).
With the improvement of numerical weather prediction skills, data assimilation algorithms and computational power in recent years, there have been more comprehensive atmospheric parameter datasets.In particular, the reanalysis datasets issued by the European Centre for Medium-Range Weather Forecasts are widely used in hydrometeorological studies (Meng et al., 2018).Many studies on water vapor transport and its sources are based on the Eulerian method.For example, Huang et al. (1998) found that the water vapor transport characteristics in the East Asian summer monsoon region are significantly different from those in the Indian monsoon region.In terms of the former, the meridional water vapor transport is larger than the zonal water vapor transport.However, the zonal water vapor transport is dominant in the Indian monsoon region.Jiang et al. (2017) studied the effects of water vapor source variations on the interdecadal variability of precipitation in North China.They found that the rainfall decrease in North China is mainly attributed to the reduction of water vapor sources in the Indian Ocean, Bay of Bengal and South China Sea.The transient variation characteristics of the wind field often lead to the transient variation of the water vapor flux presented by the Eulerian method.As a result, only a simple water vapor transport path can be obtained, the quantitative relationship of source-sink relationships cannot be acquired, and the contribution of every water vapor source to rainfall cannot be distinguished (Stohl & James, 2004).However, the studies on the water vapor trajectory based on the Lagrangian method can address the issues.The three-dimensional trajectories of water vapor masses calculated by the Lagrangian method can more clearly reveal the source of water vapor transport.There are some related methods such as the E-P diagnostic method (Stohl & James, 2004;Stohl & James, 2005) and moisture source attribution method (MSAM), and the related common-used models include the Flexible Particle dispersion model (FLEXPART) (Pisso et al., 2019) and the Hybrid Single-Particle Lagrangian Integrated Trajectory model (HYSPLIT) (Stein et al., 2015).The HYSPLIT is a computer model for aerosol and gas transport and dispersion simulations, which is based on the fused method of the single-particle Lagrangian method and the accompanying Eulerian grid method.It is developed by the National Oceanic and Atmospheric Administration, and is widely applied in the simulation of atmospheric transport in the environment and the solution of water vapor trajectories.
The MSAM is the dominant method in analyzing the source of water vapor, which can more accurately reflect the water-vapor transport routes and the water-vapor sources.Previous researchers have conducted abundant related studies.For example, Zhu et al. (2019) used the MSAM to study the water vapor source and transport characteristics of the anomalous rainfall in mid-summer in Tianjin city.Shi et al. (2022) investigated the vertical characteristics of water vapor transport during the rainy season in the eastern China based on the Lagrangian method.Fu (2019) designed the trajectory-solving equation with an efficient design architecture, which significantly improves the speed of trajectory solving and introduces the graph theory into the trajectory-based water vapor transport path analysis.
Tianjin city, one of the four major municipalities in China, is an important economic region in China.Tianjin city is located in the north temperate zone and situated on the east coast of the Eurasian continent.It is mainly controlled by the East Asian monsoon circulation.Besides, Tianjin city neighbors Bohai Bay and is affected by the marine climate.Under the influence of the monsoon climate, the rainstorms in Tianjin city mainly occur from June to August.Due to the concentrated rainfall and the low-flat terrain, water-logging and flooding often occur, which have a great effect on the environment and economy of Tianjin city and its surrounding regions.Therefore, analyzing the water-vapor sources and transport conditions during the rainstorms is of great significance to the designment of rainstorm prevention measures in Tianjin city.
Currently, few studies are based on the Lagrangian trajectory method to conduct the water-vapor tracing analysis in the rainstorm processes in Tianjin.Therefore, this study is conducted with the topic in mind.

| Moisture source attribution method
The principle of the Lagrangian-trajectory-based MSAM method is as follows.The rainfall-producing air mass with a certain scale is regarded as a mass point.By tracing the trajectory and specific-humidity variation along the trajectory of air mass, the water vapor content of air mass along the trajectory can be obtained after the rainfall amount at the terminus is allocated inversely.Then, the distribution of water-vapor source at the terminus can be obtained (Sodemann et al., 2008;Su et al., 2022).
The source trajectories of air masses at different levels are different due to the differences of specific humidity and wind field at different levels in the atmosphere.In the rainfall processes, the contribution of specific humidity at different levels to surface precipitation should be calculated separately due to the differences in specific humidity and its variation at different levels.
The water-vapor transport trajectories are solved by the numerical solution of the ordinary differential equation.For an air mass, its three-dimensional position X (t = t 0 ) at a certain moment corresponds to a threedimensional wind field V = V (X, t).Based on the data above, the motion trajectory of this air mass is obtained by the numerical solution of the ordinary differential equation.The trajectory is also the transport trajectory of water vapor within this air mass, and the equation is R = X (t).After deriving the water-vapor transport trajectory, the specific humidity at any point on the trajectory can be calculated based on the specific humidity field q = q (X, t).
In the MSAM, the rainfall region is taken as the end point of the water vapor trajectories, and then we trace backward along the trajectories.The air mass quality (m w ) contains two components.One is the part that is converted into rainfall at the endpoint (m p ), and the other is the remaining part.The step is to calculate the value of m p at the endpoint before being converted into rainfall (m p0 ), that is, the contribution of air mass to the precipitation at the endpoint.
The specific-humidity-gradient allocation method is used to allocate the rainfall at the endpoint (m p0 ) to every air mass.Specifically, an air column over a grid with area A is divided into several levels of air masses according to the standard pressure altitude.The time step of the calculation is denoted as Δt.The rainfall that occurs between is provided by the air mass over the grid at time t.If the rainfall intensity of the grid in the Δt period is P and the density of water is known to be ρ, the quality of the total rainfall is ρPΔtA.If the quality of every air mass is m, the variation of specific humidity during the Δt period is Δq i (the superscript i indicates the different levels) and N is the total number of levels, see Formula 1: Because the quality of every air mass is equal, the contribution to the whole layer of rainfall should be proportional to the reduction of specific humidity for the air mass with a negative change of specific humidity over the grid.For the air mass with a positive change of specific humidity, its contribution to the whole layer of rainfall is 0 and the allocation weight is defined as k i , see Formula 2: Then, the rainfall contributed by every air mass is m i p0 (Fu, 2019), see Formula 3: Thus, the water vapor trajectories and sources of rainfall for a given period and a given region can be derived grid-by-grid and time-by-time if the wind, rainfall and specific humidity fields are given and the spatiotemporal resolutions are known.By conducting moisture source attribution analysis for all grids in a region with numerous rainfall events in a certain period, the distribution of water-vapor sources of rainfall in the region can be statistically obtained, and the spatial and temporal statistical analysis can also be further performed.

| Spectral clustering algorithm
Spectral clustering is one of the most popular clustering algorithms, which is simple to implement and often outperforms the traditional clustering algorithms.Its main idea is to consider all data as the points in a certain space, which are connected by edges with weights.The edge weights between points that are farther away are lower and vice versa.The purpose of clustering is achieved by cutting the graph composed of all data points and edges.The sum of edge weights between different subgraphs should be as low as possible after the cutting, and the sum of edge weights within the subgraphs should be as high as possible.Spectral clustering can be understood as mapping data from higher dimension to lower dimension, followed by clustering in lower dimensional space with other clustering algorithms (such as k-means clustering).
In this study, all points on the trajectory, namely the large set X = {X 1 , X 2 , …, X n }, are the input data.Every single sample point contains three elements of longitude, latitude and elevation.For clustering, the number of categories to be clustered needs to be entered in advance.Then, different water-vapor sources can be obtained by using the scikit-learn (sklearn) module of Python.

| Study area and input data
As shown in Figure 1a, the whole Tianjin city (surrounded by the red solid line) is chosen as the study area.It is divided into five parts that are represented by five 0.5 Â 0.5 grids (Figure 2b).The average rainfall within every grid is regarded as the representative rainfall for that grid, which is used as the input data for retracing the source of rainfall.
The atmospheric data used in this study include the wind and specific humidity fields of the ERA-5 reanalysis dataset.They are used as the input data to solve the trajectories and the specific humidity variation on the trajectories.The horizontal resolution is 0.75 Â 0.75 , and the temporal resolution is 1 h.In the vertical direction, there are 17 levels from 1000 to 200 hPa with an interval of 50 hPa (Hersbach et al., 2020).Accessible URL: www.ecmwf.int.
The nationwide rainfall data are provided by the China Meteorological Administration (CMA).China Meteorological Administration Precipitation Analysis (CMPA) data are a product maintained by the CMA.It integrates various data sources, including observation stations, radar, satellite and model data, to provide highresolution precipitation information within China.These data are widely used in meteorological monitoring, water resource management, disaster monitoring, agriculture and other fields.They contribute to decision support for flood warnings, drought monitoring, agricultural management and more (Yan et al., 2010).The time period is from June to September and from 2012 to 2020.The temporal resolution is 1 h.The horizontal spatial resolution is 0.1 for 2012-2015 and 0.01 for 2016-2020.
According to the related regulations of CMA, the rainfall larger than 50 mm/h is called rainstorm, the rainfall larger than 100 mm/h is termed heavy rainstorm, and the rainfall over 250 mm/h is termed extraordinary rainstorm.If the rainfall in one or more of the five grids in Tianjin exceeds the rainstorm threshold in a certain day, then it is deemed as a rainstorm day.It is similar to heavy rainstorm day and extraordinary rainstorm day (CMA, 2012).
The air masses at different levels over the rainfall grids are divided with an interval of 50 hPa.Based on the rainfall events in Tianjin city from 2012 to 2020, the trajectories of the air mass participating in the rainfall at different levels are retraced, which are defined as rainfall trajectories.As the meantime of moisture retention in the air is 10 days, the maximum retracing period of rainfall source trajectories is defined as 10 days with a temporal resolution of 1 h.

| The calculation model of rainfall trajectory
In this study, the PyTrajector model developed by Su et al. (2022) is used to solve the rainfall trajectories, which is based on the efficient parallel computing architecture designed by Fu (2019).The PyTrajector model is developed in Python language with a parallel solver architecture.The PyTrajector model has a built-in water vapor source attribution calculation process.It outperforms the existing HYSPLIT and FLEXPART models in terms of trajectory-solving efficiency.
To verify the accuracy of the simulation results of the pyTrajector model, the trajectories are simultaneously solved by using the HYSPLIT model based on the same input data, and then the results are compared.

| Statistics of heavy rainfall events in Tianjin city
According to statistics, there are 82 days with rainstorm, heavy rainstorm or extraordinary rainstorm in Tianjin city during 2012-2020.As shown in Figure 2a, the rainstorm day is the most in 2016 and 2017 (14 days), and the least in 2019 (5 days).The daily rainfall averaged over the five grids in Tianjin in rainstorm days is 27.7 mm. Figure 2b shows that the annual average accumulated rainfall in rainstorm days is the highest in 2012 (387.8 mm), whereas the least in 2015 (107.2 mm).
According to statistics, there are 24 days with heavy rainstorm and 3 days with extraordinary rainstorm (2 days in 2012 and 1 day in 2019) in Tianjin during 2012-2020.As shown in Figure 3a, the heavy rainstorm days are the most in 2017 (5 days), and there are no heavy rainstorm days in 2014.The daily rainfall averaged over the five grids in Tianjin in heavy rainstorm days is 50.1 mm.The annual accumulated rainfall in heavy rainstorm days is shown in Figure 3b, with the highest being 293.1 mm in 2012.

| Spatiotemporal distribution of rainfall sources
There are both 147,600 water-vapor trajectories of rainstorms (namely the trajectories of air masses in the specific-humidity decreasing level over the effective rainfall region) in Tianjin city calculated by the PyTrajector and HYSPLIT models.The calculation time is 21 h for the PyTrajector model and 43 h for the HYSPLIT model.Compared with the HYSPLIT model, the computational performance of the PyTrajector model is improved by 104.8%.
The density distribution of rainfall trajectories in Tianjin is shown in Figure 4.As can be seen, the results of the PyTrajector and HYSPLIT models are basically the same.The trajectories mainly concentrate on the area around Tianjin city and extend westwards and southwards, basically covering the area from 15 N to 60 N and 30 E to 140 E. The water vapor of rainstorms in Tianjin is from southern China to the Indo-China Peninsula in the south and from Central Asia to the Mediterranean in the west.Furthermore, there is also a part of water vapor from the Pacific Ocean.
There are some differences between the PyTrajector model and the HYSPLIT model in terms of the spatial distribution of trajectories.For example, the distribution range of trajectories with low-to-medium density (below 5 thousand lines [1 Â 1 ] À1 ) by the PyTrajector is larger and extends further compared with that by the HYSPLIT model.Moreover, there may be local region with highdensity trajectories calculated by the HYSPLIT model.The results indicate that the spatial range of rainfall trajectories by the PyTrajector model extends relatively further and more uniformly compared with those by the HYSPLIT model.

| Classification of rainfall moisture sources
The trajectories are colored according to the different pressure levels where the trajectories are located.Figure 5 shows that the distributions of the trajectories provided by PyTrajector and HYSPLIT are more consistent at the pressure levels.Regarding the pressure-level distribution of trajectories, the pressure of the trajectories from the east and south is relatively low, and a part of the trajectories from the west is in a higher pressure level, indicating that the water vapor is transported from upper levels.
To facilitate comparison and analysis, the rainfall moisture trajectories given by PyTrajector and HYSPLIT are clustered by using the spectral clustering algorithm based on the latitude, longitude and elevation of the trajectories.As shown in Figure 6, the moisture trajectories from 2012 to 2020 can be roughly divided into four regions, including the due west region (W) extending from Tianjin to the west, the southwest (SW) region extending southwestwards from Tianjin to the Bay of Bengal, the southeast (SE) region extending southeastwards to the Pacific Ocean, and the high-level region of the low pressure in Central Asia (H).According to the clustering results, the classification of rainfall moisture trajectories is greatly related to the pressure levels.The water vapor originating from the west and west is mainly transported by low pressure.However, the water vapor trajectories originating from the east and south are at higher pressure levels.
The comparison of the clustering results by the two models shows that the pressure levels of trajectories by the PyTrajector are higher than those by the HYSPLIT in the west area.The results are approximately the same in other regions.

| Moisture contribution of each region
Table 1 shows the moisture contribution of each region to the rainstorms in Tianjin from 2012 to 2020.For the PyTrajector model, the moisture contributed by the SW region is the most (46.5%)among all four regions, followed by the W region (42.8%).The H region and the SE region contribute 4.8% and 5.9% of moisture to the rainstorms in Tianjin, respectively.For the HYSPLIT model, the moisture from the SW region still has the largest proportion (44.5%), followed by the W region (44.3%).The results are consistent with those of the PyTrajector model.The moisture contribution from the H region and the SE region accounts for 3.1% and 8.1%, respectively.Compared with the results of the PyTrajector model, the proportion of moisture from the SE region is larger.The above results show that the main moisture sources of rainstorm processes in Tianjin are the west (W) and SE regions, with a total contribution of 89.3%.
The correlations between the annual moisture contribution and the annual rainstorm rainfall amount in each region from 2012 to 2020 in Tianjin are analyzed (Table 1).In Table 1, r (V x , V total ) indicates the correlation coefficients between the annual moisture contribution F I G U R E 6 Zoning of rainfall moisture trajectories.Shading indicates the pressure level with the scale at the bottom (unit: kPa).The left is the result of PyTrajector, and the right is the result of HYSPLIT (W stands for the western region, SE stands for the southeast region, SW stands for the southwest region and H stands for the highaltitude region).show that the rainstorms in Tianjin are the most closely related to the moisture from the SW region, indicating that the rainstorm situation in Tianjin is greatly determined by the moisture contribution in the SW region in that year.
The contribution value and its ratio of each region to the interannual variation of rainstorm amount from 2012 to 2020 are also shown in Table 1.The contribution value is defined as sign (V total ) ΔV x .In Table 1, and ΔV total is the difference in rainfall in Tianjin.The difference between year n and year n À 1 is regarded as the difference of year n.ΔV x is the difference of the moisture contribution in region x, which can quantitatively describe the dominant factor of rainfall fluctuation in Tianjin.The PyTrajector model shows that the interannual variation of the moisture contribution in the SW region has the largest contribution to the interannual variation of rainstorm rainfall amount (65%), indicating that the interannual variation of rainstorm rainfall in Tianjin is mainly influenced by the moisture contribution variation in the SW region, followed by the W region (27%).The interannual variation of the moisture in the SE region to the interannual variation of rainstorm rainfall amount is relatively low with the proportion of nearly 0. For the HYSPLIT model, the moisture contribution of the SW and W regions is the same as those given by the PyTraject model.However, the proportion in the H region is only half of that given by the PyTraject.It is noteworthy that the proportion is only 2% in the SW region.The above results indicate that the dominant factor of rainfall interannual variations in Tianjin is the moisture variation in the SW region.
In addition, the correlations of the moisture contribution interannual variation in each region to the interannual variation of rainstorm rainfall amount from 2012 to 2020 are analyzed.In Table 1, the r (ΔV x , ΔV total ) indicates the correlation coefficient between the difference of annual moisture contribution in region x and the difference of annual rainstorm amount in Tianjin city.Here, the difference between year n and year n À 1 is regarded as the difference of year n.For the PyTrajector model, the correlation coefficient is the highest in the SW region (0.90), followed by the W region (0.35) and H region (0.22).There is a weak negative correlation in the SE region.For the HYSPLIT model, the correlation coefficient is the highest in the SW region (0.94), followed by the W region (0.46) and the H region (0.34), which have been increased when compared with those in the PyTrajector model.The negative correlation for the SE region is weaker (À0.08) than the results of the PyTrajector.Overall, the correlation between the moisture contribution interannual variation and the interannual variation of rainstorm rainfall amount in Tianjin is relatively stronger in the SW and W regions.In contrast, the correlation is relatively weaker in the SE region.
The moisture contribution in each region to the heavy rainstorms in Tianjin from 2012 to 2020 is analyzed (Table 2).As can be seen, for the PyTrajector model, the SW region contributes the most water vapor (61.8%), followed by the W region (27.7%).The H region and SE region contribute 2.7% and 7.8% of the water vapor, respectively.For the HYSPLIT model, the moisture from the SW region still accounts for the largest proportion (60%), followed by the W region (28.7%), which is consistent with the results of the PyTrajector model.The moisture contribution from the H region and SE region accounts for 2.3% and 7.7%, respectively.The above analysis shows that the moisture contribution of the SW region to heavy rainstorms is much larger than that to rainstorms.The moisture from the SW region is the main source of water vapor for the heavy rainstorm events in Tianjin.
In Table 2, the correlations between the annual moisture contribution of each region and the heavy rainstorm rainfall amount in Tianjin from 2012 to 2020 are analyzed.As can be seen, for the PyTrajector model, the correlation coefficient in the SW region is the highest (0.98), whereas the correlation coefficient in the SE region is the lowest (0.11).For the HYSPLIT model, the results of r (V x , V total ) in each region are consistent with those of the PyTrajector model.The moisture from the SW region is the dominant factor influencing the rainfall of heavy rainstorm in Tianjin.The above analysis shows that the heavy rainstorm in Tianjin is the most closely related to the water vapor from the SW region, and the heavy rainstorm situation in Tianjin is greatly determined by the moisture contribution in the SW region in that year.
The contribution value and its ratio of each region to the interannual variation of heavy rainstorm amount from 2012 to 2020 are also shown in Table 2.As can be seen, for the PyTrajector model, the interannual variation of the moisture contribution in the SW region to the interannual variation of heavy rainstorm rainfall amount is the largest (73.3%), followed by the W region (31.0%).For the HYSPLIT model, the results in the SW and W regions are the same to those of the PyTraject model.Therefore, we can see that the dominant factor of heavyrainstorm rainfall amount fluctuation in Tianjin is the moisture fluctuation in the SW region.
The correlations of the moisture contribution interannual variation in each region to the interannual variation of heavy-rainstorm rainfall amount in Tianjin from 2012 to 2020 are analyzed.As shown in Table 2, for the PyTrajector model, the correlation coefficient in the SW region is the largest (0.99), followed by the W region (0.88) and the H region (0.43).There is weak negative correlation in the SE region.The results of the HYSPLIT model are consistent with those of the PyTrajector model.

| Interannual variation of moisture contribution in each region
The annual moisture contribution of each region to the rainstorms in Tianjin from 2012 to 2020 is analyzed in Figure 7.The annual average moisture contribution in the other two regions is relatively small, but it has interannual variations.The statistics in 2012 show that the moisture from the SW region in 2012 is more, leading to more rainfall amount of rainstorms in Tianjin in 2012.From the statistical results of 2016 and 2017, we find that when the rainstorm rainfall amount is more the moisture contribution of the SW region is larger.The interannual variation of the moisture contribution of the W region, which accounts for a large proportion of moisture contribution, is relatively stable, and the variation amplitude is small except for 2017 and 2019.The proportions of moisture contribution from the H region and the SE region are relatively small in all years.Note that, there is a sharp increase of moisture contribution from the SE region in 2019, which provide the most moisture for the rainstorms in Tianjin in 2019.The results of the HYSPLIT model are similar to those of the PyTraject model, and the moist contribution in the SW region is less than that of the PyTraject model.

| Moisture source analysis in 2012
Because of the unique rainfall characteristics in 2012, the moisture sources of rainstorms in this year are analyzed separately.As shown in Figure 8, the moisture originating from the Indian Ocean enters the central China via the southern part of the Tibetan Plateau, which is the main moisture source of the rainstorms in Tianjin in 2012.Statistics show that the total water vapor volume during the rainstorm period in 2012 is 1077 Â 10 7 m 3 , in which the water vapor contribution from the SW region is 849.8Â 10 7 m 3 , accounting for 78.9%, and it is much higher than the multiyear average.Based on the specific humidity distribution, as depicted in Figure 9, when moving from north to south, the moisture content carried by air masses gradually increases.Air masses originating from the western region of Tianjin exhibit the lowest moisture content during their movement, with specific humidity generally below 5 gÁkg À1 .Conversely, air masses originating from the SW direction over the Indian Ocean carry the highest moisture content during their transit, with specific humidity consistently exceeding 15 gÁkg À1 for the majority of trajectories, and reaching up to 20 gÁkg À1 .Liao et al. (2013) found that the extraordinary heavy rainstorm in North China in 2012 was produced by the joint effect of the West Pacific subtropical high, typhoons, SW monsoon, north-south lowpressure zone in the lower troposphere and mesoscale low vortex.Specifically, the typhoons provided a southto-north impetus to the moisture transportation in the Bay of Bengal, and caused a strong water vapor convergence over North China, resulting in the appearance of extraordinary rainstorm.Thus, the abnormal increase of moisture provided by the SW region is the main reason for the increased accumulated rainstorm rainfall in Tianjin in 2012.

| Effect of changes in water vapor contribution on rainstorm
To analyze the feasibility of reducing rainstorm disasters in Tianjin through artificial intervention, the annual average water vapor contribution of each region was quantitatively reduced by 50%.The average precipitation of rainstorms and heavy rainstorms in Tianjin was considered.It should be noted that the average precipitation mentioned in this section refers to the average precipitation across Tianjin city when a rainstorm or heavy rainstorm occurs in any region (i.e., any grid within the five grids defined in this study).
Regarding rainstorm precipitation, as shown in Figure 10a, the reduction of water vapor contribution in the W region and SW region has the most significant impact on the precipitation.When the water vapor contribution in these two regions is reduced by 50%, the average precipitation decreases by 6.15 mm (22.2%) and 6.17 mm (22.3%), respectively.The reduction in water vapor contribution in the H region and SE region has a relatively smaller impact on rainstorm precipitation.In comparison to rainstorm precipitation, in the case of heavy rainstorm precipitation, the influence of water vapor contribution in the SW region on the average precipitation increases.As shown in Figure 10b, when the water vapor contribution in this region decreases by 50%, the average precipitation decreases by 15.34 mm (31.7%).The proportion of water vapor contribution in the W region decreases, and when the water vapor contribution in this region decreases by 50%, the average precipitation decreases by 7.18 mm (14.4%).The influence of water vapor contribution in the H region and SE region on precipitation remains almost unchanged.Therefore, if the focus is on rainstorms and above, it is advisable to strengthen artificial weather infrastructure on the western and SW sides of Tianjin.This can intercept water vapor through artificial means, reducing the amount of water vapor entering Tianjin from those directions, and thus minimizing the precipitation of rainstorms and above in Tianjin, mitigating the adverse effects of extreme rainstorms.If the focus is solely on heavy rainstorms and above, it is recommended to enhance artificial rain enhancement infrastructure primarily on the SW side.

| Effect of different proportional water vapor contribution changes on rainstorm
Analyzing the specific impact of reducing water vapor contribution at different proportions on rainstorms in Tianjin, we can examine the changes in precipitation occurrences for rainstorms, heavy rainstorms and extraordinary rainstorms when the water vapor contribution of each region is reduced by 50%, 20% and 10% respectively.As shown in Figure 11a-c, when it comes to rainstorm and above precipitation, the reduction of water vapor contribution from the W region has the greatest impact on the occurrence of precipitation events.A 50% reduction in water vapor contribution from the W region would result in a 41% decrease in rainstorm and above events, a 20% reduction would lead to a 15% decrease, and a 10% reduction would result in a 9% decrease.The SW region follows, with a 50% reduction in water vapor contribution from the SW region leading to a 17% decrease in rainstorm and above events, a 20% reduction resulting in a 7% decrease, and a 10% reduction causing a 6% decrease.The reduction in water vapor contribution from the SE and H regions has a smaller impact on rainstorm events.Therefore, reducing the water vapor contribution from the W region can significantly decrease the probability of rainstorm and above precipitation occurrences.
When it comes to heavy rainstorm and above precipitation, As shown in Figure 11a-c, the reduction of water vapor contribution from the SW region and the W region has the greatest impact on the occurrence of precipitation events.A 50% reduction in water vapor contribution from the SW region would result in a 43% decrease in heavy rainstorm and above events, a 20% reduction would lead to an 18% decrease, and a 10% reduction would result in an 11% decrease.Similarly, for the W region, a 50% reduction in water vapor contribution would lead to a 36% decrease in heavy rainstorm and above events, a 20% reduction would result in an 18% decrease, and a 10% reduction would cause a 14% decrease.The reduction in water vapor contribution from the SE and H regions has a smaller impact on heavy rainstorm events.
When it comes to heavy rainstorm and above precipitation, As shown in Figure 11a-c, the reduction of water vapor contribution from the SW and W regions has the greatest impact on precipitation events, and the influence becomes more significant as the proportion of reduced water vapor from the SW region increases.When it comes to extraordinary rainstorm and above precipitation, the reduction of water vapor contribution from the SW region has the greatest impact on the occurrence of precipitation events.A 20% reduction in water vapor contribution from the SW region would result in a 100% decrease in extraordinary rainstorm and above events, whereas a 10% reduction would lead to a 67% decrease.The impact of reducing water vapor contribution from the W region on extraordinary rainstorm events is limited, as even a reduction of 10% to 50% in water vapor contribution from the W region only results in a 33% decrease in extraordinary rainstorm and above precipitation events.The reduction in water vapor contribution from the SE and H regions has a smaller impact on extraordinary rainstorm events.Therefore, reducing the water vapor contribution from the SW region can effectively prevent the occurrence of extraordinary rainstorms.

| CONCLUSIONS
In this study, the traceability analysis of rainstorms (more than 50 mm day À1 ) in Tianjin city during 2012-2020 is conducted based on the Lagrangian trajectory method by using the MSAM.The moisture sources and the evolution patterns of rainstorms are studied.Moisture trajectory solving and analysis are conducted by using the selfdeveloped PyTrajector and the commonly used HYSPLIT model.The main conclusions are as follows.
The moisture sources of the rainstorms in Tianjin can be roughly divided into four regions.The W and SW regions are the main moisture sources, and they contribute about 89% of the moisture to the rainstorms.For heavy rainstorms, the proportion of moisture contribution by the SW region (60%) is larger than that of rainstorms.The SW region is the main moisture source for heavy rainstorms in Tianjin and plays a dominant role in moisture fluctuation during heavy rainstorm period.For the extraordinary rainstorm, the moisture contribution of the SW region is even larger (74.3%).The annual rainstorm rainfall amount in Tianjin in 2012 was higher than in common years due to the anomalous increase of moisture contribution from the SW region.The result further indicates that the annual precipitation of rainstorm in Tianjin is mainly influenced by the moisture contribution from the SW region.Reducing water vapor from the SW region by 50% can significantly decrease rainstorms in Tianjin city by 22.3% and up to 31.7% for heavy rainstorms.Decreasing the contribution of water vapor from the west region effectively reduces the likelihood of rainstorm occurrences.For heavy rainstorms, the most influential factors are the reduction of water vapor from both the SW and west regions.Increasing the proportion of reduced water vapor from the SW region intensifies its impact on heavy rainstorms.In summary, mitigating water vapor from the SW direction can effectively prevent extraordinary rainstorms and reduce their associated damages in Tianjin city.
Based on the above results, we conclude that the SW region is the main moisture source of rainstorms, heavy rainstorms and extraordinary rainstorms in Tianjin.If the water vapor entering Tianjin from the SW region is reduced by artificial intervention during the rainstorm processes, the rainstorm rainfall amount can be reduced to the greatest extent, and the loss caused by rainstorms and secondary disasters can be further decreased.
In terms of methodology, this study explores the water vapor source of rainstorm in the study area, but the trajectory analysis method can further quantitatively analyze the evaporation-transport-rainfall cycle, and the related studies need to be carried out in depth.It should be noted that the data used in this study are from the ERA-5 reanalysis dataset, which has its own uncertainty and greatly impacts the accuracy and reliability of the conclusions.More datasets need to be used in future studies.

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I G U R E 1 The Tianjin geographic map.(a) The geographical location of Tianjin city and (b) the land cover type in Tianjin and its five sub-regions.F I G U R E 2 Long-term rainstorm information for Tianjin.(a) Annual frequency of rainstorm and above days in Tianjin city, and (b) annual average accumulated rainfall (in millimeters) of rainstorm and above days averaged over the five grids in Tianjin.

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I G U R E 3 Long-term heavy rainstorm information for Tianjin.(a) Annual frequency of heavy rainstorm and above days, and (b) annual average accumulated rainfall (in millimeters) of heavy rainstorm and above days averaged across the five regions in Tianjin.F I G U R E 4 Density distribution of rainfall trajectories (unit: 10 4 lines [1 Â 1 ] À1 ).F I G U R E 5 Pressure distribution of rainfall moisture trajectories.Shading indicates the pressure level with the scale at the bottom (unit: kPa).The left is the result of PyTrajector, and the right is the result of HYSPLIT.
T A B L E 1 Statistical indicators of moisture contribution in each region to the rainstorms in Tianjin.

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I G U R E 1 0 Average precipitation amount after a 50% reduction in water vapor contribution from various regions.(a) Rainstorm and above.(b) Heavy rainstorm and above.

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I G U R E 1 1 Number of different types of precipitation events after a 50%, 20% and 10% reduction in water vapor contribution from various regions.(a) The number of precipitation events of different types when the contribution of water vapor from each source is reduced by 50%.(b) The number of precipitation events of different types when the contribution of water vapor from each source is reduced by 20%.(c) The number of precipitation events of different types when the contribution of water vapor from each source is reduced by 10%.
) in region x and the annual rainstorm rainfall amount (V total ) in Tianjin city.For the PyTrajector model, the correlation coefficient between the moisture contribution and the rainstorm amount in the SW region is the highest (0.87), and the correlation coefficient in the SE region is the lowest (only 0.05).The results of the HYSPLIT model are quite similar to those of the PyTraject model.The moisture of the SW region is dominant.The above results T A B L E 2 Statistical indicators of moisture contribution in each region to heavy rainstorms in Tianjin.Annual moisture contribution of each region to the rainstorms in Tianjin from 2012 to 2020 (unit: 10 7 m 3 ).