The Roles of Low-level Jets in “21·7” Henan Extremely Persistent Heavy Rainfall Event※

Yuhan LUO and Yu DU*

1School of Atmospheric Sciences, Sun Yat-sen University, and Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai 519082, China

2Guangdong Province Key Laboratory for Climate Change and Natural Disaster Studies,Sun Yat-sen University, Zhuhai 519082, China

3Key Laboratory of Tropical Atmosphere-Ocean System (Sun Yat-sen University),Ministry of Education, Zhuhai 519082, China

ABSTRACT An extremely heavy rainfall event lasting from 17 to 22 July 2021 occurred in Henan Province of China, with accumulated precipitation of more than 1000 mm over a 6-day period that exceeded its mean annual precipitation. The present study examines the roles of persistent low-level jets (LLJs) in maintaining the precipitation using surface station observations and reanalysis datasets. The LLJs triggered strong ascending motions and carried moisture mainly from the outflow of Typhoon In-fa (2021). The varying directions of the LLJs well corresponded to the meridional shifts of the rainfall. The precipitation rate reached a maximum during 20-21 July as the LLJs strengthened and expanded vertically into double LLJs, including synoptic-weather-system-related LLJs (SLLJs) at 850—700 hPa and boundary-layer jets (BLJs)at ～950 hPa. The coupling of the SLLJ and BLJ provided strong mid- and low-level convergence on 20 July, whereas the SLLJ produced mid-level divergence at its entrance that coupled with low-level convergence at the terminus of the BLJ on 21 July. The formation mechanisms of the two types of LLJs are further examined. The SLLJs and the low-pressure vortex(or inverted trough) varied synchronously as a whole and were affected by the southwestward movement of the WPSH in the rainiest period. The persistent large total pressure gradient force at low levels also maintained the strength of low-level geostrophic winds, thus sustaining the BLJs on the synoptic scale. The results based on a Du-Rotunno 1D model show that the Blackadar and Holton mechanisms jointly governed the BLJ dynamics on the diurnal scale.

Key words: extremely persistent heavy rainfall, low-level jet, dynamic and thermodynamic effect, diurnal cycle

1. Introduction

Heavy rainfall events frequently occur during the warm season in Henan province, commonly affected by complex terrain and the East Asia summer monsoon (Tang et al., 2006;Ke and Guan, 2014; He et al., 2016; Fu et al., 2019). Henan province is located in central North China, with the Taihang Mountains in the northwest, the Funiu Mountains in the southwest, and the North China Plain to the east (Fig. 1a). Compared to short-lived heavy rainfall, persistent heavy rainfall events cause more severe geological disasters such as floods and landslides, economic losses, and casualties. As such,they have garnered more attention in recent decades.

Extremely persistent heavy rainfall events in Henan province included “75·8”, “96·8” and “18·8” (named by“year·month”), which had great societal impacts. For instance, the “75·8” event that featured extremely persistent heavy rainfall accompanied by the landfall of Typhoon Nina (1975) was one of the most influential events that promoted the research on heavy rainfall in China. The collective interaction between the westerlies and tropical circulations,together with the typhoon and a strong easterly low-level jet(LLJ), jointly contributed to the heavy rainfall (Special Research Team for the “75·8” Heavy Rainstorm, 1977a, b).Typhoon Nina (1975) continuously supplied sufficient moisture because of its slow movement due, in part, to blocking highs (Yang et al., 2017). In addition to the factors mentioned above, the persistent rainfall events in central North China are closely related to the Western Pacific Subtropical High(WPSH) (Ding and Wang, 2008; Wang et al., 2019, 2021),low-pressure vortex (Lei et al., 2017; Wang and Liu, 2017),orography (Sun and Zhang, 2012; Xia and Zhang, 2019),and low-level jets (Xue et al., 2018; Xia et al., 2022).

The LLJ plays a vital role in enhancing rainfall by providing favorable dynamic and thermodynamic conditions,which has been widely investigated in previous studies (e.g.,Stensrud, 1996; Monaghan et al., 2010). The LLJ produces low-level convergence at its terminus to trigger strong ascending motions (Chen et al., 2017; Du and Chen, 2019a;Hodges and Pu, 2019; Du et al., 2022). In addition, the LLJ acts as an important transportation carrier of warm-moist air to supply sufficient moisture and destabilize the environment(Trier and Parsons, 1993; Higgins et al., 1997; Gimeno et al., 2016; Algarra et al., 2019). Typically, LLJs can be classified into two types based on their characteristics and formation mechanisms (Chen et al., 1994; Du et al., 2012; Du and Chen, 2018, 2019b; Li and Du, 2021): 1) a boundary-layer jet (BLJ) below 1 km characterized by a profound diurnal variation, and 2) a synoptic-weather-system related LLJ(SLLJ) with a higher jet core (～850—700 hPa) that is often affected by synoptic weather systems. Recent studies have shown that the coupling of the two types of LLJs (double LLJs) produces low-level convergence and mid-level divergence, thus, greatly affecting convective initiation and the growth of heavy rainfall in South China (Du and Chen,2019a; Liu et al., 2020).

It has been widely recognized that the nocturnal intensification of the BLJ contributes to the rainfall peak at midnight or early morning in central North China (Chen et al., 2009,2010; Fu et al., 2019; Zeng et al., 2019). The diurnal variation of the BLJ can be explained by an inertial oscillation in the boundary layer (Blackadar, 1957; hereafter the Blackadar mechanism), the diurnally varying pressure gradient force driven by the thermal contrast of sloping terrain (Holton,1967; hereafter the Holton mechanism), and their combination (Du and Rotunno, 2014; Du et al., 2015; Shapiro et al.,2016). Du and Rotunno (2014) proposed a simple analytical 1D model of the BLJ (hereafter the Du-Rotunno 1D model)that could not only separate but also combine the Blackadar and Holton mechanisms by setting a diurnal periodic frictional effect for the Blackadar mechanism, a diurnally varying pressure gradient force for the Holton mechanism, and considering both for a combined mechanism.

On 17—22 July 2021, an extremely persistent heavy rain-fall event inflicted extensive damage in Henan province(“21·7” for short). Most significantly, the Hebi station observed 1122.6 mm of accumulated precipitation over these six days, a total that exceeded its mean annual precipitation. The 3-day accumulated precipitation at 32 national surface stations in Henan province broke their historical records in this event. This persistent heavy rainfall event caused severe economic losses and casualties and has received extensive attention. Recent studies suggested that a lasting southeasterly LLJ provided upward motion and transported abundant moisture from the outflow of Typhoon Infa (2021) in the west Pacific (Ran et al., 2021; Shi et al.,2021). Su et al. (2021) and Zhang et al. (2021) comprehensively analyzed the characteristics and extremes of the largescale circulation in this lasting rainfall event and cited the LLJs as one of the factors but did not examine the detailed characteristics of the LLJs, including their type, horizontal and vertical structure, and temporal evolution. Additionally,recent studies have analyzed the influential mechanisms of the extremely heavy rainfall, including orography (Wang et al., 2022), meso-γ-scale convective systems (Yin et al.,2022), and binary typhoons (Xu et al., 2022) rather than LLJs. The formation mechanisms of the LLJs and their relationship with rainfall in this event remain poorly understood.Thus, two questions arise. 1) How is the varying strength and direction of the LLJs related to the varying rainfall intensity and location? 2) What are the formation and maintenance mechanisms of the persistent LLJs?

Therefore, the objective of the present study is to examine the impacts and mechanisms of the LLJs on the “21·7”heavy rainfall event. The next section introduces the data and methodology, including an overview of the Du-Rotunno 1D analytical model of the LLJ. Section 3 briefly reviews this torrential rainfall event. The temporal and spatial relationship between the LLJs and heavy rainfall is described in section 4 to elaborate upon the dynamic and thermodynamic effects of the LLJs. Section 5 further elucidates the formation and maintenance mechanisms of the persistent LLJs from the perspectives of the synoptic scale and the diurnal variation. Finally, the last section summarizes the results.

2. Data and methodology

Hourly surface station observations are utilized to reveal the precipitation distribution for this event. The locations of about 21 763 stations in central and northern China are shown in Fig. 1b. The natural neighbor interpolation method is used to interpolate the station data into grid data with a spatial resolution of 0.1° × 0.1° to calculate the spatially- averaged precipitation. To investigate the characteristics of the LLJ in this extremely heavy rainfall event and associated atmospheric environmental conditions, the fifth generation of the European Centre for Medium-Range Forecasts(ECMWF) atmospheric hourly reanalysis data (ERA5, Hersbach et al., 2018), with a horizontal resolution of 0.25° ×0.25° and a time interval of 1 hour, is used in the present study. Considering the 12-hour windows used in the 4D-Var data assimilation of ERA5 from 0900 UTC to 2100 UTC and 2100 UTC to 0900 UTC (the following day) (Hersbach et al., 2020), the diurnal variation shows sudden, artificial changes at 0900 UTC (1700 LST, LST = UTC + 8), near a key turning point commensurate with sunset in central North China, strongly affecting the analysis of diurnal cycle(Chen et al., 2021). To overcome this defect, the Modern-Era Retrospective analysis for Research and Applications,Version 2 (MERRA-2), is additionally introduced to examine the diurnal cycle of the pressure gradient force input from the Du-Rotunno 1D model.

Fig. 1. (a) The terrain height (units: m) in North China and (b) the horizontal distribution of accumulated precipitation (units: mm) from 0800 LST 17 July to 0700 LST 23 July. The black triangle in (a) presents the position of the Funiu Mountains. The grey shading in (b) denotes terrain higher than 700 m. Henan Province is outlined by the purple line in (b). Zhengzhou and Hebi cities are marked by a star and square, respectively. The cities of Xuzhou and Fuyang are marked by blue and red stars in (a). The region between the grey dashed lines is used in Fig. 2. The pink parallelogram refers to the heavy rainfall region (i.e., the downstream region) used in Fig. 6.

Following Du et al. (2014, 2019b), the LLJ is defined so that the following conditions are met. 1) The maximum wind speed below 700 hPa exceeds 10 m s—1; 2) there is a strong vertical wind shear with a at least 3 m s—1wind speed decrease from the wind speed maximum upward to the next wind speed minimum at or below the 600 hPa level. Based on the definition of an LLJ above, the definition of a BLJ is further refined to require the level of the maximum wind to be below 900 hPa. The SLLJ is defined similarly, but the level of the maximum wind is required to be above 900 hPa.

To reveal the roles of the LLJs in moisture transport,the moisture flux [g (s hPa cm)—1] is calculated as

where g, q, and vnare the gravitational acceleration (9.8 m s—2),specific humidity, and wind component perpendicular to the given plane, respectively.

To elucidate the moisture transport associated with the LLJs, the mass-weighted, vertically integrated, horizontal moisture flux [units: g (m s)—1] is further defined as:

where psmeans the pressure at the bottom level in the reanalysis dataset; | V| indicates the total wind speed.

The vertically integrated moisture flux convergence[units: g (m2s)—1] is calculated by the following formula(Banacos and Schultz, 2005; Ranalkar et al., 2016),

Positive (negative) VIMFC suggests moisture convergence(divergence) in the whole column.

The momentum budget analysis is conducted to investigate the maintenance mechanisms of the BLJs. Following Du et al. (2014, 2015) and Zeng et al. (2019), the momentum budget equation can be written as

where the term on the left-hand-side of Eq. (4) represents the tendency of winds (illustrated as TD); the terms on the right-hand-side denote the horizontal advection (HAD), vertical advection (VAD), pressure gradient force (PGF), Coriolis force (CF) and the friction force (Fr), respectively, the latter of which is calculated by the residual of the other terms.The Coriolis force on the ageostrophic wind term is calculated by adding the PGF and CF (PGF+CF=-▽?duì)?f k×V=f k×Vg-f k×V=-f k×Va).

To estimate the dynamic response of BLJs to the topography in North China Plain, the unsaturated moist Froude number is calculated following Chen and Lin (2005) as

where u is the horizontal wind perpendicular to the southwest-northeast-oriented terrain (the wind component of 135°); N represents Brunt-V?is?l? frequency as calculated by the virtual potential temperature as; h is the terrain height, assumed to be 1500 m according to the terrain distribution. The parameters, u and N, are calculated by spatially averaging over the core region of the BLJ and vertically below 950 hPa based on the height of BLJ. When Froude number is less than (greater than) 1, the flow tends to be blocked(unblocked).

A Du-Rotunno 1D model (Du and Rotunno,2014; Du et al., 2015), which allows the Blackadar and Holton mechanisms to be separated and combined, is applied to investigate the mechanisms governing the diurnal variation of the BLJs in this heavy rainfall event. The one-dimensional linear motion equations of frictional flow on an f plane can be written as:

where ( u,v) are wind components in the ( x,y) direction, φ is the geopotential, α (t) is the frictional coefficient with diurnal variation, and ω is the diurnal frequency (2 π d-1). A mean() component and a diurnally varying (cosωt) component make up the pressure gradient force in the x-direction, while a constant () component is considered in the y-direction.Following Du et al. (2015), we set α(t)=α0sin(t-t0)ω to reflect the diurnally varying friction force (maximum at 1300 LST, minimum at 0100 LST), where α0is the daily mean frictional coefficient and t0is set to 1 hour, later than the minimum pressure gradient force in the x-direction. It is noted that the Coriolis force is an indispensable factor for the formation of LLJs due to its meso- to synoptic-scale nature. The equations in the Du-Rotunno 1D model contain only the time dimension. The variables (e.g., geopotential height gradient, friction coefficient) are also simplified to be time-dependent. Though the equations are simplified, the amplitude and phase of the modeled LLJs were in good agreement with observations over the Great Plains of the United States and eastern China (Du and Rotunno, 2014; Du et al.,2015).

The following numerical method is used to obtain the diurnally periodic solutions for the pure Blackadar mechanism scenario (holding the pressure gradient force constant in both the x- and y-directions and diurnally varying the friction coefficient), the pure Holton mechanism scenario (timeindependent friction coefficient, diurnally varying pressure gradient in the x-direction) and their combination scenario(diurnally varying frictional coefficient and pressure gradient in the x-direction) derived after 20-day integration:

and

where the subscript t refers to time; Δt is taken as 60 s.

3. Case overview

In this section, the characteristics of the persistent heavy rainfall event and relevant large-scale environmental conditions are overviewed based on the hourly surface observations and ERA5 reanalysis.

The extremely heavy rainfall occurred in central North China, with mountains in the west and a flat plain in the east(Fig. 1). The spatial pattern of accumulated precipitation (in mm) from 0800 LST 17 July to 0700 LST 23 July was closely related to the orography (Taihang Mountains) for the similar southwest-northeast orientation with terrain(Fig. 1b). The multiple stations observing accumulated precipitation of more than 300 mm were distributed in Hebei and Henan provinces while those recording over 600 mm precipitation were mainly located in Henan province. Twenty-five stations even observed precipitation greater than 800 mm.This was especially true for the accumulated precipitation at the Hebi station (indicated by a square in Fig. 1), located in northern Henan province, which recorded 1122.6 mm, easily exceeding its mean annual precipitation of 625 mm (Zhang et al., 2021).

Figure 2 displays the temporal evolution of the zonallyaveraged precipitation rate (mm h—1) between the dashed gray lines in Fig. 1b to demonstrate the meridional shifts of rainfall. The rainfall gradually intensified from 17 to 19 July and exhibited an evident southward shift from 40°N to 35°N. The average precipitation rate rapidly intensified to more than 8 mm h—1and became quasi-stationary at about 35oN on 20-21 July. The precipitation rate on 20-21 July reached a maximum during the 6-day rainfall process, with 19 national surface stations breaking their historical records for daily accumulated precipitation. The rainfall then started to decrease after 21 July and moved northward to the south of Hebei province. The evolution of rainfall in the present study is consistent with that of Zhang et al. (2021).

Fig. 2. Temporal variation of hourly precipitation rate(shading; units: mm h—1) zonally averaged in the region between the grey dashed lines in Fig. 1. The orange hollow arrows indicate the southward and northward propagations of rainfall. The grey dashed line shows the latitude of Zhengzhou city.

The corresponding large-scale atmospheric circulations at the three stages (18, 20, and 22 July) are further illustrated in Fig. 3. The 500 hPa environmental conditions on 18 July(Fig. 3a) showed that Typhoon In-fa (2021) was distant from the east coast of China while Typhoon Cempaka (2021)reached the coastal area of South China. With the weakening of the cold-core cyclone in the East China Sea (marked with the letter “C” in Fig. 3a), the WPSH extended southwestward to the eastern coast of China and connected with the continental high (CH), while Typhoon In-fa (2021) moved westward along the southern edge of the WPSH on 20 July (Fig. 3b).Afterwards, the WPSH retreated eastward to the Korean Peninsula while the outflow of In-fa (2021) covered the southeastern coast of China on 22 July (Fig. 3c). The evolution of atmospheric circulations at 700 hPa (Figs. 3d—f) showed similar processes as that at 500 hPa in that the high pressure shifted southwestward and then moved eastward. A lowpressure vortex, marked by the letter “L” in Figs. 3d—e was associated with positive relative vorticity and low geopotential height at 700 hPa. It was located in southern Henan province on 18 July, accompanied by southeasterly winds of over 10 m s—1on its northeast side (Fig. 3d), which was considered to be an SLLJ associated with the low-pressure vortex(the vertical wind shear is shown later in Fig. 6). The SLLJ then moved northward to cover the entirety of Henan province and intensified between the westward moving high pressure, associated with the WPSH, and the low-pressure vortex on 20 July (Fig. 3e). When the rainfall began to decrease and move northward on 22 July (Fig. 2), both the positive relative vorticity and its accompanying SLLJ shifted out of Henan province (Fig. 3f). Strong southeasterly BLJs (over 10 m s—1) occurred at 950 hPa with vertical wind shears greater than 3 m s—1(shown later in Fig. 6) in eastern Henan, which were nearly perpendicular to the orientation of the Taihang Mountains (Figs. 3g—i). The daily mean 950 hPa wind speed exceeded 12 m s—1near Zhengzhou city on 20 July, along with the intensification and expansion of warm advection, which is favorable for heavy rainfall(Fig. 3h).

It is necessary to validate the reliability of reanalysis datasets describing LLJs before the relationship between LLJs and rainfall is investigated. Figure 4 compares the verti-cal profiles of wind speed and direction in the ERA5 and MERRA2 reanalysis products with the observational soundings at Xuzhou, Fuyang, and Zhengzhou stations (Fig. 4, the positions of the stations are indicated by stars in Fig. 1),which are located near the core of LLJs. The wind profiles presented a major peak below 900 hPa and a weaker subpeak near 700 hPa in the observations except at 0800 LST at Zhengzhou city (Fig. 4c), where the wind speed at the higher-level peak was stronger than the lower-level peak. At lower levels, the prevailing southeasterlies at the Xuzhou and Fuyang stations were in good agreement with the reanalysis datasets (Figs. 4a-b and 4d-e), as were the southerlies at the Zhengzhou station (Figs. 4c and 4f). The ERA5 and MERRA2 datasets both overestimated the wind speeds but only with biases and root mean square errors (RMSEs) less than 1.5 m s—1and 2.5 m s—1, respectively (Figs. 4a—f). The validation of wind directions varied with time and location,but the wind direction errors from the ERA5 and MERRA2 datasets were less than 15° and 25°, respectively. The results indicate that the wind velocities and directions in ERA5 and MERRA2 were generally consistent with observations.

4. The relationship between LLJs and rainfall

As shown in section 3, the rainfall intensification was accompanied by the enhancement of LLJs. The spatial and temporal relationship between the LLJs and precipitation is further examined in detail. The dynamic and thermodynamic roles of the persistent LLJ in promoting heavy rainfall are also discussed in this section.

Figure 5 shows the daily accumulated precipitation from 0800 LST to 0700 LST on the following day and the corresponding BLJs represented by the daily mean wind speeds over 10 m s—1at 950 hPa. From 17 to 18 July, the horizontal range of the BLJs generally narrowed with a decrease in its southerly wind component, which was accompanied by the southward shift of precipitation (Figs. 5a-b). The daily accumulated precipitation exceeded 400 mm near the Funiu Mountains, while the relatively weak BLJ was directed westward on 19 July (Fig. 5c). The easterly component of the BLJ further intensified and impinged upon the terrain to promote the heavy rainfall near Zhengzhou city on 20 July, where the daily rainfall was measured at 630.7 mm; meanwhile over 30 automated weather stations observed daily precipitation exceeding 400 mm (Fig. 5d). With the enhancement of the southerlies on 21 July, the precipitation moved northward along the Taihang Mountains and maintained its intensity as evidenced by recorded daily accumulations of rainfall exceeding 500 mm at more than 20 stations (Fig. 5e). On the last day of the rainfall process (22 July), the BLJ weakened, and the rainfall decreased correspondingly. Therefore, the rainfall locations were closely related to the varying directions and exit regions of the BLJs. We also investigated the daily evolution of nocturnal BLJs (2000—0700 LST) and found similar spatiotemporal distributions but with stronger intensities and similar relationships between their configuration and precipitation (not shown).

Fig. 3. Horizontal distributions of (a—c) geopotential height (shading; units: gpm) and temperature (contours; units: K) at 500 hPa, (d—f) geopotential height (shading; units: gpm), positive relative vorticity (black contours; units: 10—4 s—1), and 700 hPa winds greater than 8 m s—1 (red vectors), (g—i) warm temperature advection, calculated as u(?T/?x)+v(?T/?y), (red contours; units: 10—4 K s—1), wind speed (shading; units: m s—1), and wind vectors (black vectors) at 950 hPa. The right,middle, and left columns show the daily means of atmospheric conditions on 18, 20, and 22 July, respectively.

Figure 6 displays the temporal evolution in the vertical profile of wind speeds averaged over the core region of the BLJs (red box in Fig. 5f), corresponding average precipitation rate (mm h—1), and VIMFC [g (m2s)—1] in the heavy rainfall region (pink box in Fig. 1b). During the entire period(17—22 July), six persistent nocturnal BLJs with cores at 950 hPa and vertical wind shears over 3 m s—1below 600 hPa were conducive for the continuous precipitation. The temporal evolution of precipitation was closely related to the VIMFC that was strongly affected by moisture transport and dynamic convergence driven by the LLJs. During 20-21 July, the rainfall peaked at the same time that the BLJs and the corresponding moisture convergence became strongest. From 20 July, strong southeasterly winds began to deepen and expand vertically to 700 hPa, and even higher,with strong vertical wind shear. Meanwhile, another jet core at around 700 hPa (regarded as an SLLJ) appeared on the evening of 20 July, similar to the double LLJ pattern proposed by Du and Chen (2019a). With the low-pressure vortex moving to the north of Henan province, the SLLJ moved northward to the north of the BLJ on 21 July (shown in Fig. 9b later). In addition to the daily variation, the LLJs and the corresponding moisture convergence exhibited evident diurnal variations with peaks at night approximately four hours before the diurnal precipitation peak. In particular, the stronger LLJs on 19—21 July enhanced both the daily precipitation and its corresponding nighttime peak.

Fig. 4. Vertical profiles of wind speed (black lines) and direction (brown lines) based on soundings (solid lines), ERA5(dashed lines), and MARRA2 (dotted lines) reanalysis at (a, d) Xuzhou, (b, e) Fuyang, and (c, f) Zhengzhou indicated as stars in Fig. 1a at (a—c) 0800 LST and (d—f) 2000 LST. The RMSEs in wind speed and direction are listed in the figures.

Fig. 5. Horizontal distributions of daily accumulated precipitation (mm) and daily mean of winds at 950 hPa (vectors; units:m s—1) during 17—22 July. The orange shading indicates regions where the 950-hPa wind speed is larger than 10 m s—1. The black triangle denotes the Funiu Mountains. The red line, A—B, in (a) is used in Figs. 7 and 10. The red box in (f) indicates the core region of the BLJ (i.e., the upstream region).

Fig. 6. Temporal evolution of the vertical cross-section of the horizontal full wind speed (shading; units: m s—1) and horizontal wind vectors (black vectors)averaged over the red box of Fig. 5f. The red and black lines denote the corresponding temporal evolutions of rain rate (units: mm h—1) and VIMFC[units: 10—5 g (m2 s)—1], respectively, averaged in the heavy rainfall region(pink parallelogram in Fig. 1b).

Next, the contribution of LLJs to the extremes of the rainfall event is investigated through the statistics of the LLJs in the history of July from 1979 to 2018 (Fig. 7). The daily maximum southeasterly wind components at 950 hPa in the upstream region of Henan province (the red box in Fig. 5f) on 17—22 July all exceeded 90 percent of the days in July over 40 years, especially on 20 and 21 July when they exceeded the 99th percentile (Fig. 7a). The range and occurrence of BLJs in the upstream region of Henan province (a total of 289 grids) is further examined based on the definition of the BLJ. The maximum daily numbers of grids reaching the BLJ criterion on 18—22 July were more than 90% of the days in the history indicating wider ranges,especially on 20-21 July when they exceeded 98% (Fig. 7b).When over 20% of the grids meet the BLJ standard in one hour, the day is defined as a BLJ day. In the current precipitation event, seven consecutive days from 17 to 23 July satisfied the BLJ criterion, which represents one of the longest consecutive number of days in the climate history (Fig. 7c). The lasting BLJs contributed to the persistence of the rainfall event to a certain extent. In addition, the extremes of moisture transport associated with BLJs were examined by the daily maximum of length-averaged moisture fluxes (MF) at 950 hPa across A—B in Fig. 5a. Figure 7d shows that strong moisture transport, exceeding the 70th percentile value, occurred during the six consecutive days to provide extremely abundant moisture to the rainfall region. This was especially the case on 20-21 July, when extremely strong moisture transport occurred, exceeding the 99th percentile value.

4.1. Dynamic effect of LLJs

The horizontal range of the BLJs, vertical motions, and divergence are shown in Fig. 8 to elucidate their relationships in location and intensity. Generally, the locations of strong upward motions and convergence were connected to the exit region (downstream) of the BLJs and the terrain obstacles, and the intensity of vertical motion and convergence was also closely associated with the strength of the BLJs(Fig. 8). From the beginning of the rainfall processes on 17 July, two branches of the BLJ drove two pronounced rising motion (or convergence) centers along the Taihang Mountains where the branches of BLJ impinged the upon the terrain(Fig. 8a), which is favorable for initiating the rainfall process. The convergence and updraft zones moved southwestward into the trumpet-shaped topography between the Taihang Mountains and Funiu Mountains, with the wind shifting from southeasterly to easterly, consistent with the decrease in the southerly wind component from 17 to 19 July (Figs.8a—c). The expansion of the convergence zone that exceeded —5 ×10—5s—1and the intensification of the vertical velocity to over 4 cm s—1at the terminus of the BLJ (Fig. 8d)contributed to the extremely heavy rainfall in Henan province on 20 July (Fig. 5d). The daily mean wind speed exceeded 12 m s—1on 21 July with stronger mesoscale ascent along the Taihang Mountains (Fig. 8e), which partially contributed to the largest daily mean precipitation in Hebei province (Fig. 5e). The precipitation decreased on 22 July when the BLJ weakened with the wind speeds generally smaller than 8 m s—1, resulting in the convergence decreasing to weaker than —5 ×10—5s—1and vertical motions weakening to much less than 2.8 cm s—1(Fig. 8f). The BLJs were stronger at night than in the day and exhibited more intense convergence and ascending motions. Still, they had similar daily variations with the daily mean scenario (not shown).

Fig. 7. The cumulative distribution functions (CDF) of the (a) southeasterly wind speed at 950 hPa, (b) number of grids reaching the BLJ criterion, (c) lasting BLJ days, and (d) average moisture flux along A—B in Fig. 5a. The colored vertical lines indicate the value of 17—22 July respective to their labels given in bottom of the panel.

Next, we concentrate on the heaviest rainfall days(20-21 July) to investigate the dynamic effects of the double LLJs and their vertical configurations. As shown in Fig. 6,the vertical range of the LLJ expanded to 700 hPa, causing and a higher jet core (～750 hPa) to formed at night on 20 July. Figure 9 compares the horizontal distributions of winds and divergence at different levels at 2200 LST on 20-21 July. The ranges of wind speeds greater than 10 m s—1at 950 hPa (contours in warm colors) and 700 hPa (contours in cold colors) represent the locations of the BLJs and the SLLJs, respectively (Figs. 9a-b). The position of the SLLJ generally overlapped with that of the BLJ on 20 July(Fig. 9a), while the SLLJ was located to the north of the BLJ on 21 July (Fig. 9b), which exhibited similarity with the pattern of double LLJs found in Du and Chen (2019a).Du and Chen (2019a) demonstrated that double LLJs were conducive to promoting precipitation due to the low-level convergence at the terminus of the BLJ and the mid-level divergence at the entrance region (upstream) of the SLLJ.

Fig. 8. Daily mean values of upward vertical velocity (shading; units: m s—1), divergence (—5 × 10—5 s—1 indicated by a yellow contour), and horizontal wind speeds (orange, pink and red contours correspond to 8, 10 and 12 m s—1, respectively) at 950 hPa on (a—f) 17—22 July. Grey shading denotes topography higher than 700 m.

To verify the configurations of the double LLJs in this extremely heavy rainfall event, we further examine the horizontal distributions of divergence at 950 hPa (Figs. 9c-d)and 700 hPa (Figs. 9e-f) as well as the vertical cross-section of divergence along plane C—D and C′—D′ in Figs. 9a, b(Figs. 9g, h). The convergence at the exit of the BLJ was stronger than —12 × 10—5s—1on both 20 July and 21 July(Figs. 9c-d), which is consistent with Figs. 8d-e. However,the convergence/divergence at 700 hPa on 20 July differed from that on 21 July (Figs. 9e-f). On 20 July, a broad area of convergence at 700 hPa covered the precipitation center area near Zhengzhou city due to the strengthening positive vorticity driven by the horizontal wind shear in the left sector of the SLLJ (Fig. 9e). The vertical cross-section of divergence along plane C—D on 20 July (Fig. 9g) indicates that deep and thick convergence of about —9 × 10—5s—1on the windward slope of the terrain was attributed to the exit of the BLJ (at about 950 hPa) and the positive vorticity in the left sector of the SLLJ (at about 700 hPa). The vertical extension of the upward motion induced by low- and mid-level convergence partly contributed to the nighttime torrential rainfall on 20 July. In contrast, divergence greater than 12 × 10—5s—1at 700 hPa on 21 July occurred near the rainfall area due to the entrance region of the SLLJ (Fig. 9f). Therefore, the coupling of low-level convergence and mid-level divergence triggered strong upward motions to maintain the heavy rainfall on 21 July (Fig. 9h), which was consistent with the double LLJ pattern proposed by Du and Chen (2019a).

4.2. Thermodynamic effect of LLJs

Previous studies have documented that continuous water vapor transport is a necessary condition for persistent precipitation (Li et al., 2016; Chen and Luo, 2018). In addition to the dynamic roles of the LLJs illustrated above, the moistwarm air transported by the LLJs is favorable for enhancing precipitation as well. The thermodynamic effect of the LLJs in this extremely persistent heavy rainfall event is further discussed.

Figure 10 shows the evolution of the moisture transport related to the LLJs. According to the averaged vertical integration of moisture fluxes (VIMF) calculated by Eq. (2) (Fig.10a), relatively large moisture transport [＞500 g (m s)—1] was distributed near the location of the BLJ in addition to locations near the Typhoon In-fa (2021). The mean VIMFC during the six days is further shown in Fig. 10b. The most intense moisture divergence (source) with negative VIMFC was located along the outflow in the northwest quadrant of Typhoon In-fa (2021), consistent with the southeasterly flow. In addition, moisture divergence also occurred near Typhoon Cempaka (2021) and the West Pacific Subtropical High, but their magnitudes were significantly smaller than that associated with Typhoon In-fa (2021), and the airflow trajectory was not conducive to the transporting moisture into Henan province, implying a relatively smaller contribution to the moisture transport. Trajectory analysis using the Hybrid Single-Particle Lagrangian Integrated Trajectory(HYSPLIT) was further conducted to investigate the moisture sources and sinks by releasing air particles and tracing them for 10 days (not shown). The results suggest that the air parcels obtained abundant moisture from the western Pacific and the outflow of Typhoon In-fa (2021) (including southern China) over the whole period, consistent with the findings of Nie and Sun (2022). After gaining moisture in the SCS on 17-18 July, the water vapor was lost along the path rather than being transported further downstream into Henan province. The strong southeasterly LLJs mainly loaded water vapor from Typhoon In-fa (2021) into central North China and concentrated its moisture on the windward side of the Taihang Mountains, which greatly affected this persistent heavy rainfall event. The daily evolution of moisture fluxes, calculated by Eq. (1) along the plane A—B, is illustrated in Figs. 10c—h to examine the varying intensity and shifting moisture transport. The positive moisture fluxes were mainly located below 700 hPa, with a maximum in the 925—850 hPa layer that was slightly lower than the height of the LLJ core (Figs. 10c—h). The cores of positive moisture fluxes moved southward from 17 to 19 July (Figs. 10c—g), corresponding to the southward rainfall shift. Meanwhile, the moisture fluxes in the 950—850 hPa layer intensified to over 15 kg m—2s—1from 17 to 19 July, accompanied by a strengthening of the LLJs with cores at 850—700 hPa (SLLJs)(Figs. 10c—e). On 20-21 July, the height of the LLJ cores generally coincided with the maximum moisture fluxes below 850 hPa associated with the intensification of the lower BLJs (Figs. 10f-g). Different from 20 July, the moisture fluxes exceeding 20 kg m—2s—1on 21 July moved to the north with a larger range (Fig. 10g). The LLJ weakened,and the related moisture fluxes decreased on 22 July with weaker precipitation (Fig. 10h). Though the maximum moisture fluxes were concentrated below 850 hPa, the positive and relatively larger moisture fluxes (over 9 kg m—2s—1)were distributed upward to near 600 hPa, signaling the midlevel moisture transport of SLLJs. The results suggest that the high moisture fluxes were mainly associated with transport by both the BLJs and SLLJs. The moisture transport by the SLLJs is further confirmed by a Lagrangian method using the HYSPLIT model (not shown). The moisture carried by the SLLJs was obtained not only from the west Pacific and the East China Sea but also from south China, which is different from that of the BLJs.

Fig. 9. Horizontal distributions of horizontal wind speed at 950 hPa (yellow and orange contours; 10 and 12 m s—1) and 700 hPa (blue and purple contours; 10 and 12 m s—1) at 2200 LST on (a) 20 and (b) 21 July. Horizontal distributions of horizontal divergence (units: 10—5 s—1, shading), wind speeds (black contour of 11 m s—1), and vectors (grey vectors, m s—1)at (c and d) 950 hPa, (e and f) 700 hPa, and (g and h) their cross sections along the green lines C—D and C?—D? at 2200 LST on (c, e, g) 20 July and (d, f, h) 21 July, respectively. The black vectors in (g) and (h) denote the horizontal winds(m s—1) along the transect and vertical velocity (cm s—1).

Next, the roles of the LLJs in the transportation of unstable energy and warm-moist air are further examined (Fig. 11).Figure 11a shows that high convective available potential energies (CAPE) of over 1300 J kg—1on 18 July (indicated by green contour) were distant from Henan province while high CAPE values on 20 July (indicated by the blue contour)expanded significantly to approach Henan province. The unstable air was conveyed from the southeastern coast of China to Henan province from 18 July to 20 July by strong low-level southeasterly winds exceeding 10 m s—1. The transportation of unstable air supplemented the potential energy for the heavy rainfall downstream of the LLJs. The largest hourly-averaged CAPE, over 17—22 July, was situated to the south of Henan province instead of near the site of torrential rainfall due to the consumption of CAPE by precipitation processes.

To clearly display the temporal evolution of the warmmoist air transport, Figs. 11b—c show the distance (longitude)—time Hovm?ller diagrams of CAPE, specific humidity at 950 hPa, and equivalent potential temperature at 950 hPa(θe) along the dashed black line (E—F) averaged in the black rectangle in Fig. 11a. Generally, the high CAPE and high specific humidity propagated towards the point, indicated by E,near the precipitation area from 17 to 22 July on a daily timescale (Fig. 11b). The CAPE and specific humidity reached their maximums, exceeding 2400 J kg—1and 18 g kg—1on 20—21 July, respectively. The results suggest that the moist-warm air was transported to the precipitation area from the southeastern coast of China due to the persistent and strong southeasterly LLJs, which were conducive to heavy rainfall by moistening and destabilizing the atmo-sphere.

We further focus on the rainiest days on 20—21 July to demonstrate the detailed transport of warm moist air on the diurnal scale. The 950 hPa θeexhibited a maximum of more than 352 K at noon associated with the solar radiative heating as well as a northward-delayed sub-peak exceeding 349 K at midnight, around 34°N near the rainfall region, on both 20 and 21 July (Fig. 11c). The nocturnal peak of θeto the north might be related to the nocturnal intensification of the low-level winds parallel with E—F and directed towards E(Fig. 11c). The nocturnal peak of θeprovided favorable thermodynamic conditions for nocturnal rainfall, as shown in Fig. 6.

5. The formation mechanisms of LLJs

The significance of the persistent LLJs in this extremely persistent torrential rainfall event has been illustrated from the dynamic and thermodynamic perspectives in the previous sections. It is necessary to investigate the formation mechanisms of the LLJs (including SLLJs and BLJs)on the synoptic and diurnal scales.

5.1. The formation mechanisms of SLLJs

Figure 12 shows the horizontal distributions of the streamlines at 700 hPa, geopotential height at 500 hPa, and wind speeds at 700 hPa to present the low-pressure vortex(dense cyclonic streamlines), the WPSH (light blue shading), and the SLLJ (warm color shading), respectively.Early in the episode (17 July), the low-pressure vortex remained strong and moved slowly to around 32°N, 115°E with a profound SLLJ on its eastern side, meanwhile the WPSH was situated over the Northwest Pacific Ocean away from Henan province (Fig. 12a). With a slight weakening of the low-pressure vortex and an almost static WPSH, the SLLJ became weaker (Fig. 12b). The WPSH moved westward on 19 July when the low-pressure vortex evolved to an inverted trough, as indicated by the brown line (Fig. 12c).The pressure gradient forces increased responding to the rapid-approach of the WPSH and the sustained inverted trough and this interaction significantly accelerated the SLLJ (＞12 m s—1) on 20 July (Fig. 12d). The transformation and northward shift of the WPSH enhanced the southerly wind component (Fig. 12e), leading to the corresponding northward movement of precipitation (Fig. 5e). When the WPSH retreated eastward and the inverted trough diminished on 22 July, the SLLJ moved northward and became parallel to the Taihang Mountains. This dynamic was accompanied by the termination of this persistent rainfall event (Fig. 12f).

Fig. 11. (a) Horizontal distributions of CAPE (shading; units: J kg—1) averaged from 0800 LST 17 July to 0700 LST 22 July, and the daily means of CAPE on 18(green contour of 1300 J kg—1) and 20 July (blue contour of 1300 J kg—1) and BLJ velocity (green and blue vectors indicate daily mean wind speeds over 10 m s—1 on 18 and 20 July). Distance (longitude)-time Hovm?ller diagrams of (b) CAPE(shading; units: J kg—1) and water vapor mixing ratio at 950 hPa (units: g kg—1;blue contours = 16, 17, and 18 g kg—1) and (c) equivalent potential temperature at 950 hPa (units: K, shaded) together with horizontal wind speeds at 950 hPa(black contours = 6, 8, and 10 m s—1) along the black dashed line E—F averaged in the black rectangle in Fig. 10a.

Fig. 12. Daily mean horizontal streamlines at 700 hPa (black contours), wind speed at 700 hPa (orange, red and purple shading indicate 8, 10, and 12 m s—1, respectively), and geopotential height at 500 hPa (blue shading ＞ 5880 gpm) on (a—f)17—22 July. The brown lines in Figs. 11c—e indicates the inverted trough.

The relationship between the SLLJs and the low-pressure vortex was further investigated from the perspective of their varying position and strength (Fig. 13). Based on the position and movement of the SLLJs and low-pressure vortex, the SLLJs were always synchronously located on the east or northeast side of the vortex (Fig. 13a). The left region of the SLLJ is conducive to increased positive vorticity due to the horizontal wind shear. In turn, the strengthening vorticity favors the enhancement of the SLLJ. Furthermore, the strength of SLLJs and vortex were largely consistent in their temporal evolution (Fig. 13b). The maximum vorticity decreased from 17—19 July due to the evolution of the lowpressure vortex into an inverted trough, and the maximum wind speeds related to the SLLJs became correspondingly smaller. Accompanying the enhanced precipitation, copious latent heat was released to strengthen the low-pressure system, further accelerating the SLLJs from 19—21 July. Meanwhile, the southwestward movement of the WPSH increased the high pressure to the east, thus enhancing the pressure gradient force during 19—21 July. On the diurnal scale, the SLLJ and low-pressure vortex also exhibited similar diurnal variations with a peak in the daytime (not shown).As a result, the SLLJs and the low-pressure vortex (or inverted trough) varied jointly as a system, which were affected by the southwestward movement of the WPSH in the rainiest period.

5.2. The formation mechanisms of BLJs

In addition to synoptic forcing, the LLJ in the boundary layer (BLJ) can also be influenced by boundary processes.The momentum budget analysis of winds at 950 hPa based on Eq. (4) from 14 to 22 July is further conducted to examine the mechanisms of a lasting BLJ. The Coriolis force on the ageostrophic wind term is calculated by adding up the PGF and CF as represented by green shading in Fig. 14. Figure 14 shows the time series for each term in the momentum budget equation for the zonal wind (u) and meridional wind (v) at 950 hPa in the core area of the BLJs (red box in Fig. 5f).

Since the magnitudes of the HAD and VAD terms were significantly small and could be neglected, we mainly focus on other terms in the following analysis.

Considering the prevailing easterly wind, the acceleration of the zonal wind corresponded to the negative TD(black line). From the synoptic scale perspective, the rapid increase in the u-component from 16-17 July (red dashed line in Fig. 14a) was responsible for the acceleration of the full wind speed. The total PGF (blue lines in Figs. 14a-b)was a key factor in accelerating the wind, maintaining a value of about —2 m s—1h—1during 17—22 July. The meridional pressure gradient force (blue line in Fig. 14b) played an essential role in enhancing the zonal geostrophic wind. The sustaining decrease of negative meridional PGF to —2 m s—1h—1(blue line in Fig. 14b) continuously strengthened the easterly wind (red dashed line in Fig. 14a), which resulted in the directional change of the low-level winds from southeasterly to nearly easterly with a corresponding southward movement of the rainfall (Fig. 5). An evident enhancement of the winds at midnight of 20 July (Fig. 6) could be attributed to an augmentation of the v-component of the wind (dashed red line in Fig. 14b) driven by the increased absolute value of the zonal PGF (blue line in Fig. 14a). Therefore, the persistently large total value of PGF at 950 hPa maintained the strong geostrophic wind in the boundary layer and thus contributed the most to the sustenance of the BLJ on the synoptic scale.

Fig. 13. (a) The varying positions of the SLLJ (green markers) and lowpressure vortex (orange markers) at 0800 LST from 17 to 22 July and the averaged wind speed at 700 hPa (shading; units: m s—1). (b) The temporal evolution of maximum wind speed at 700 hPa related to the SLLJ (black line),maximum vorticity at 700 hPa related to the low-pressure vortex (orange line)over the region in Fig. 13a, and the spatial average of 700-hPa geopotential height over the blue box in Fig. 12a related to the WPSH (blue line).

In addition to synoptic-scale variations, the BLJ exhibited a profound diurnal cycle. As shown in Fig. 14, the wind tendency terms in both the meridional and zonal directions had a diurnal cycle with maximum accelerations in the afternoon and at night, respectively. The diurnally varying friction force was reinforced in the daytime and weakened at night.The Coriolis force on the ageostrophic wind term was consistent with the diurnal variation of the wind tendency term.

The diurnal variations of precipitation and wind on 17—22 July are correlated, as shown in Fig. 15a. The ERA5 and MERRA2 were in good agreement in representing the diurnal variation of winds, with a peak at 2300 LST for the u-component and the total wind speed, while the peak v-component occurred at 0200 LST. It is noted that a sudden artificial change occurred at 1700 LST in ERA5. The diurnal variation of precipitation exhibited double peaks, including a major peak at 1400 LST corresponding to solar radiative heating and a sub-peak at 0200—0500 LST that occurred several hours after the maximum winds. To further investigate the role of BLJs in the diurnal variation of precipitation, the diur-nal variation of moisture convergence and dynamic convergence is shown in Fig. 15b. Though the BLJ was enhanced at night, the Froude number was much smaller than 1, due to the strong nocturnal stratification, thus implying that the stronger blocking effect of the terrain at night was more conducive to dynamic and moisture convergence compared to the daytime. Therefore, the VIMFC and dynamic convergence presented similar variations to the wind speed with a nocturnal peak at 0000-0100 LST, about four hours before the nocturnal peak of the precipitation, suggesting that the enhanced BLJs at night reinforced the moisture convergence and caused the nocturnal peak of precipitation four hours later (Xue et al., 2018). Consequently, the nocturnal peak in rainfall was attributed to the nocturnal intensification of the dynamic and moisture convergence driven by the strengthened nocturnal BLJs. The nocturnal northward propagation of warm and moist air (Fig. 11b), in addition to the findings of related previous studies (Xue et al., 2018; Fu et al., 2019),highlight and further support the role of nocturnal BLJ.

Fig. 14. Temporal evolution of individual terms in the momentum budget equation at 950 hPa for the (a) meridional and (b) zonal winds averaged over the red box of Fig. 4f. The tendency term (TD), horizontal advection (HAD),vertical advection (VAD), pressure gradient force (PGF), Coriolis force (CF),and the residual (friction, Fr) are shown by black, orange, green, blue, purple and grey lines, respectively. The green shading denotes the sum of the PGF and CF (Coriolis force on ageostrophic wind). The red dashed lines indicate the zonal and meridional wind components in (a) and (b).

Next, we examine the nocturnal enhancement mechanisms of the BLJ. Previous studies have documented that the Blackadar mechanism, Holton mechanism, and their combination are the main factors affecting the diurnal cycle of the BLJ (Shapiro et al., 2016; Fedorovich et al., 2017). The Blackadar mechanism (i.e., the inertial oscillation) (Blackadar, 1957) is characterized by a clockwise rotation of lowlevel perturbation winds in the Northern Hemisphere (Fig. 16).Clockwise rotating perturbation winds indeed occur near the core region of BLJs with a northwesterly perturbation during the daytime (Fig. 16i) due to turbulence mixing and a southeasterly perturbation during the nighttime (Fig. 16a) due to the inertial oscillation. The hodograph of the wind perturbations (Fig. 16e) presented a complete circle consistent with the Blackadar mechanism.

Based on the Holton mechanism (1967), the diurnal oscillation of thermal forcing by terrain causes an oscillation in the southerly component of geostrophic wind along the terrain(Bonner and Peagle, 1970). To better highlight the diurnal variation of geostrophic winds and remove the effect of the synoptic weather systems, a low-pass Barnes filter, following Xue et al. (2018), was applied before calculating the geostrophic wind components. Figures 17a-b show that the opposite directions of geostrophic wind deviations at 1700 and 0500 LST were nearly parallel to the topography corresponding to a downslope pressure gradient force in the early morning and an upslope pressure gradient force in the late afternoon. The diurnal deviations of vertical motions and wind components along the G—H direction (Figs. 17c-d)exhibited a thermodynamic circulation consistent with a mountain-plains solenoid, with downslope winds in the morning and upslope winds in the afternoon, which was also consistent with the Holton mechanism. At 1700 LST, the westward pressure gradient corresponding to the thermodynamic circulation driven by the nearly north-south oriented terrain(indicated by the nearly southerly geostrophic winds along the mountains in Fig. 17a) induced easterly ageostrophic winds (Figs. 17c). The easterly ageostrophic winds rotated clockwise under the Coriolis force to southeasterly winds several hours later to accelerate the background southeasterly winds at night, thus contributing to the nocturnal strengthening of the BLJ.

Fig. 15. (a) Diurnal variations of total wind speed (black lines), u- (blue lines), and v- (red lines) wind components averaged over 17—22 July from MERRA2 (dashed lines) and ERA5 (solid lines), and precipitation averaged over 17—22 July (green line). (b) Diurnal variations of VIMFC (green line) and convergence (blue line) averaged in the heavy rainfall region (pink parallelogram in Fig. 1b), and the Froude number averaged in the core region of the BLJ(red box in Fig. 5f) over 17—22 July. (c—d) Diurnal variations of (c) meridional and (d) zonal pressure gradient forces averaged in the red box of Fig. 4f on 17—21 July from MERRA2. The thick red and purple lines denote the 5-day and monthly means of the diurnal pressure gradient force, respectively, while the black line represents the diurnal variation of the pressure gradient force set in the Du-Rotunno model.

Fig. 16. Average 950-hPa perturbation wind speed (shading; units: m s—1) calculated by subtracting the daily mean wind speed with the actual wind in time intervals of 3 hours over 17—22 July. (i) Hodograph of wind perturbations at 950 hPa averaged in the core area of BLJ (red box in Fig. 5f). The blue hollow vector indicates the general direction of the perturbation winds.

A Du-Rotunno 1D model is applied to examine the relative contribution of these two mechanisms. As the driver of the Holton mechanism, the diurnal variations of pressure gradient forces input in the model were based on the diurnally varying PGF averaged during these precipitation days in addi-tion to the entire month of July (Figs. 15b-c). The ideal mean states of the PGF were calculated by the average of these precipitation days, but the ideal diurnal components of the PGF were derived from the monthly mean to avoid the impacts of synoptic weather systems on the diurnal variation. Under such a PGF, the prevailing geostrophic wind was southeasterly.

The results of the Du-Rotunno 1D model in the present case are presented in Fig. 18. For the pure Holton mechanism scenario, the u- (v-) component of the wind reached a minimum (maximum) at about 1700 (2100) LST, which was before observed real diurnal winds (Figs. 14a-b). As for the pure Blackadar mechanism scenario, the period of clockwise rotation of the ageostrophic wind at this latitude (35°N)was about 20 hours (T =2π/f). Given the southeasterly geostrophic wind, the ageostrophic wind rotated more than a semi-period to accelerate the v-component to its maximum.The v-component in the Blackadar mechanism approached a maximum at about 0400 LST (Fig. 18b), which was delayed compared to observations. The combination of Holton and Blackadar mechanisms was also derived by considering both the diurnal cycle of the pressure gradient force due to the thermal effects of the terrain and the diurnal cycle of frictional effect. The results show that this combined scenario could well simulate the diurnal cycle of winds in both directions. However, the simulated minimum u-component of the wind occurred an hour prior to observations, and the winds during the daytime were slightly underestimated.

We further validate the momentum budget in the combined model compared to reality. The TD in the combined scenario agreed with reality in that the zonal (meridional) wind accelerated in the afternoon (evening) (Figs. 18c-f). The CF exhibited consistency in diurnal variations in addition to the slight underestimate during the daytime in the zonal direction(Fig. 18e). The model well captured the reduction of the RES (the residual terms represent friction) at night in the xdirection but slightly underestimated the RES in the y-direction (Fig. 18f). Accordingly, the Holton and Blackadar mechanisms both played important roles in the diurnal variation of the BLJ, indicated by the results in the combined scenario that seized upon the major diurnal variations of each term in the momentum budget analysis.

Fig. 17. (a-b) Horizontal distributions of the averaged geostrophic wind deviations at 950 hPa (shading and vectors;units: m s—1) at (a) 1700 LST and (b) 0500 LST averaged during 17—22 July. (c-d) Vertical cross sections of vertical motion deviations (shading; units: cm s—1) and perturbation vertical circulation vectors (100 times the vertical velocity) along transect G—H, spatially-averaged in the blue dashed box at (c) 1700 LST and (d) 0500 LST and averaged over 17—22 July. Grey shading denotes terrain higher than 500 m in (a-b) and terrain height along G—H(c-d).

6. Summary and discussion

An extremely persistent heavy rainfall event during 17—22 July 2021 inflicted heavy losses and casualties in Henan province of central North China. The present study examines the roles of persistent low-level jets (LLJs) in maintaining the rainfall using hourly surface observations and reanalysis datasets, including ERA5 and MERRA2.

The accumulated precipitation in this event was mainly distributed along the southwest-northeast-oriented Taihang Mountains. The rainfall processes underwent an evident southward shift on 17-19 July, a rapid intensification when becoming quasi-stationary near Zhengzhou city in Henan, with the maximum precipitation occurring on 20-21 July, prior to a northward shift after 21 July. A conceptual diagram is proposed to summarize the related rainfall processes [Fig S1 in the Electronic Supplementary Material (ESM)].Correspondingly, the large-scale environmental conditions in this event involved the southwestward advance followed by the eastward retreat of the West Pacific Subtropical High (WPSH),a slow westward approach of Typhoon In-fa (2021) in the west Pacific, and a long-lived low-pressure vortex near Henan accompanied by the synoptic-weather-system related LLJs (SLLJs).

The north-south shifts of rainfall well corresponded to the varying directions of boundary-layer jets (BLJs) from southeasterly to easterly and then to southeasterly (Figs.S1a—c in the ESM). The convergence driven by the BLJs,along with terrain interaction, facilitated upward motion on the windward side of the Taihang Mountains. In addition,the BLJs carried moisture, mainly from the outflow of Typhoon In-fa (2021), resulting in the transport of warmmoist air, which served to continuously moisten and destabilize the environment. The precipitation rate in Henan province reached a maximum during 20-21 July as the BLJs became strongest with the simultaneous appearance of an SLLJ. The low- and mid-level convergence at the exit region of the BLJ and the positive vorticity region of the SLLJ contributed to the extremely heavy rainfall on 20 July(Fig. S1b in the ESM). In contrast, the coupling of low-level convergence at the terminus of the BLJ and mid-level divergence at the entrance of the SLLJ triggered strong upward motions to maintain the heavy rainfall on 21 July (Fig. S1c in the ESM).

Fig. 18. Diurnal variations of the (a) meridional wind and (b) zonal wind from ERA5 (red lines), MERRA2(purple lines), pure Blackadar mechanism (blue lines), pure Holton mechanism (yellow line), and combined model (green line). Diurnal variations of each term in the momentum budget equation from (c, d) MERRA2 and(e, f) the Du-Rotunno 1D model. The TD, PGF, CF, and RES terms are indicated by the black, blue, red, and yellow lines, respectively.

The SLLJs and the low-pressure vortex (or inverted trough) varied synchronously as a whole. The southwestward movement of the WPSH enhanced the pressure gradient between the inverted trough and the WPSH and thus accelerated the SLLJs in the rainiest period. The momentum budget analysis of the BLJs is conducted to examine the formation mechanisms of the lasting BLJs. The lasting large PGF associated with WPSH and inverted trough maintained the geostrophic wind in the boundary layer, thus sustaining the BLJs on the synoptic scale. In addition to the synoptic scale,evident diurnal varying signals of the BLJs were found in its zonal and meridional wind components, Coriolis forces,and frictional forces. The low-level perturbation winds rotated clockwise due to the inertial oscillation (Blackadar mechanism). The opposite geostrophic wind deviations parallel to the orography during the daytime and nighttime reflected the effect of the Holton mechanism on the nocturnal BLJs. The Du-Rotunno 1D model further verified the combined effects of the Holton and Blackadar mechanisms in the diurnal variation of the BLJs in this event. The nocturnal intensification of the BLJs yielded the nocturnal rainfall peaks during the persistent heavy rainfall event via the nocturnal strengthening dynamics and moisture convergence.

This paper is our first attempt to specifically investigate the role of LLJs in this extremely persistent heavy rainfall event. The detailed characteristics of the LLJs and their spatial and temporal relationship with heavy rainfall have been specified in the present study. Two types of LLJs, including BLJs and SLLJs, were found simultaneously but played different roles with different formation mechanisms in the lasting heavy rainfall. In addition to the similar double-LLJ pattern with that in South China on 21 July (i.e., low-level convergence at the exit region of the BLJ and mid-level divergence at the entrance region of the SLLJ), the coupling of double LLJs provided low- and mid-level convergence at the exit region of the BLJ, and owing to horizontal shear, a positive vorticity region on the left side of the SLLJ on 20 July,which was different from the vertical structures of the double LLJs in South China.

The present study examines the roles of the LLJs in the“21·7” persistent heavy rainfall and the formation mechanisms of the lasting LLJs based on surface observations and reanalysis datasets. However, high-resolution numerical simulations are further required to investigate the more detailed structures of the LLJs and other associated factors, including terrain, cold pooling, and the presence of mesoscale vortices.Besides, the quantitative comparisons of this extreme rainfall event with other similar historical extreme events in Henan,from the perspective of LLJs, need to be explored in the future.

Acknowledgements.This study was supported by Guangdong Major Project of Basic and Applied Basic Research(2020B0301030004), the National Natural Science Foundation of China (Grant Nos. 42122033, 41875055, and 42075006),Guangzhou Science and Technology Plan Projects (202002030346 and 202002030196).

Electronic supplementary material:Supplementary material is available in the online version of this article at https://doi.org/10.1007/s00376-022-2026-1.