1 Introduction

Extreme precipitation events lead to huge economic losses and fatalities globally every year (Mirza 2002; Jonkman 2005; Gemmer et al. 2008). North China (NC; 35°–42° N, 110°–120° E) is a key political and economic region of China with high population density and substantial agriculture production. However, the socioeconomic conditions in NC are especially vulnerable to extreme precipitation, which cost thousands of millions of dollars in damage every year (Gao and Wang 2017). In recent years, extreme precipitation events over NC have occurred frequently. For example, NC witnessed five extreme precipitation events in August 2010 (Orsolini et al. 2015). On 21–22 July 2012, a disastrous rainstorm hit Beijing with a maximum daily precipitation reaching 460 mm (Liu and Wang 2013; Zhou et al. 2013). Researching on extreme precipitation over NC is a crucial issue in terms of regional disaster prevention and mitigation, and the management of water resources and agricultural irrigation.

One necessary condition for extreme precipitation’s occurrence is sufficient moisture supply (Zhou and Yu 2005; Holman and Vavrus 2012). NC is located on the north margin of the East Asian summer monsoon and receives the bulk of its precipitation during the summer season (Guo et al. 2012). Moisture transport plays an essential role in extreme precipitation during summer (Zhang 1999). Jiang et al. (2014) demonstrated that the southeast and southwest monsoon flows into Beijing with abundant moisture continuously enhanced the low-layer moisture flux and convergence during the Beijing “7.21” heavy-rain case. Zhong et al. (2015) also captured that this heavy rainfall event occurred under the low-level warm and moist southeasterly flows.

Numerous studies have been devoted to studying the roles played by moisture supply for summer extreme precipitation over NC. Zhang and Li (2014) estimated the moisture contributions to a rainstorm over Shandong province in the southern NC, indicating that the moisture supply was originated mainly from neighboring southwest China, whereas little moisture came from the nearby western Pacific. Chen et al. (2018) analyzed the relative contributions of moisture from the Arabian Sea, the Bay of Bengal, and the South China Sea to summer precipitation over mainland China, and found that these three oceanic sources make diverse contributions on different time scales.

Previous works have identified the water vapor path contributing to summer extreme precipitation over NC. Liang et al. (2007) reported that moisture from the western Pacific carried by mid-latitude westerlies has a great impact on the occurrence of summer extreme precipitation over NC, while moisture from the Bay of Bengal intensifies torrential rain to some extent. Zhang et al. (2013) pointed out that it is the convective cells along a quasi-stationary linear convective system and a deep layer of southerly moisture supply that were responsible for the heavy rainfall on 21 July 2012. Jiang et al. (2014) also discussed this “7.21” rainstorm event in Beijing and claimed that strong southwest monsoon stream transport water vapor to Beijing continuously, with remarkable water vapor convergence into the rainstorm system. Wang and Liu (2017) documented that the strong moisture transport path from the Bay of Bengal was one key factor related to the rainstorm over Central China. However, these results did not investigate extreme precipitation over NC and related water vapour transport in a quantitative way. Also, they have not considered the effect of surrounding terrain on extreme precipitation over NC. This study intends to fill this knowledge gap.

Quantitative analysis of moisture transport is useful for identifying relative contributions of diverse moisture sources to extreme precipitation in a region. Moisture flux convergence (MFC) has been considered to directly characterize the behavior of extreme precipitation (Fankhauser 1965; Cook et al. 2008; Chou et al. 2009; Zhou et al. 2017). MFC includes two terms: wind convergence and moisture advection. Some studies have been devoted to quantifying the moisture budget of summer extreme precipitation over NC. Freychet et al. (2015) demonstrated that increased MFC accompanied by northward winds provides a favorable background for torrential rainfall intensification over NC. Wang et al. (2014) simulated the net budget of water vapour of a rainstorm over NC in the summer of 2011, and indicated that the net budget was always positive during this rainstorms process and the contribution of the two terms of MFC was diverse during different state of this rainstorm event. The torrential rainfall over NC during the summer of 2007 was attributable to reinforced MFC as a result of small variations in the vertical advection term (Chen and Tomassiniand 2015). Zhao et al. (2019a) reported that the wind convergence component (accounting for 79.1% of the MFC) had a critical effect on strengthening MFC at 925 hPa relative to the moisture advection part (accounting for 20.9% of the MFC) in seven historical summer rainstorm cases over NC. These studies have quantified how the moisture budget and corresponding MFC at a specific level are associated with a summer extreme precipitation over NC.

NC experiences the second- and third-largest landforms with complex topography in China; i.e., the Loess Plateau with elevations from 500 to 2000 m situated west of the NC region, and the eastern flat plain to its east (Wang et al. 2013). The remarkable Taihang and Yanshan Mountains, with altitudes of 800–2000 m, are located along the western and northern margins of NC, respectively (He and Zhang 2010). Sun et al. (2015) inferred that the complex terrain surrounding NC interferes with circulation patterns, giving rise to conditions that are conducive to extreme summer precipitation over the region. Li et al. (2017) obtained that higher-(lower) frequency hourly heavy rainfall events, along with more (less) accumulated rainfall amounts, occur over Beijing’s northeast mountains (west and northwest mountains), and identified the positive effect of mountain-plain circulation on the generation of the hourly heavy rainfall event in warm season. Wang et al. (2014) indicated that the simulated moisture transport for a summer torrential rain case over NC was mainly influenced by the Taihang Mountain. Liao et al. (2009) used numerical simulations over the Taihang Mountains to demonstrate that the elevated topography favors convection and summer precipitation over NC from a cloud physics perspective. While the existing literature has identified the significant impact of surrounding terrains on summer extreme precipitation over NC, the effect of terrains on modulating moisture budget to further induce summer extreme precipitation over NC deserves to be better understood and quantified.

Given the above considerations, this study aims to quantify and simulate the whole column moisture budget for summer extreme precipitation events over NC under the influence of the topography. Such a research could enhance our understanding of the atmospheric hydrological cycle during periods of extreme precipitation over NC, and has the potential to improve the accuracy of regional forecasts of extremes.

2 Data and methods

2.1 Data

A daily precipitation dataset containing data from more than 2400 rain gauge stations over China during 1979–2016 has been released by the National Meteorological Information Center (NMIC) of the China Meteorological Administration (CMA) (http://nmic.cn/web/index.htm/). This dataset has undergone quality control processes (Zhang et al. 2016; Zhong et al. 2016). We selected 139 fairly evenly distributed surface meteorological stations in the region 35°–42.0° N and 110°–120° E defined as NC (Fig. 1a). A gauge was included if it had less than 15% missing values.

Fig. 1
figure 1

a WRF model simulation domain setup. The blue dashed box denotes the NC region. b Spatial distribution of the 139 observational stations (blue dots) over North China (NC; red box; 35°–42° N, 110°–120° E). Color shading denotes terrain height (m). c Spatial distribution of the 95th percentile threshold daily mean extreme precipitation amount (color shading; mm) over NC in summers during 1979–2016. d Zonal and e is the meridional vertical cross-section of terrain height (m) over NC

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Gridded horizontal and vertical winds, specific humidity at 6-h intervals with a horizontal resolution of 0.75° × 0.75° during 1979–2016 were obtained from the ERA-Interim reanalysis data (http://apps.ecmwf.int/datasets/) produced by the European Centre for Medium-Range Weather Forecasts (ECMWF; Dee et al. 2011). The 6-h precipitation data from the reanalysis were converted to 24-h precipitation amount from 2000 Beijing time (BJT) of the previous day to 2000 BJT of the current day. Because BJT is 8 h ahead of Coordinated Universal Time (UTC), the moisture fluxes were calculated by averaging five 6-h times of the ERA-Interim reanalysis data: 1200 (2000) and 1800 (0200) UTC (BJT) of the previous day and 0000 (0800), 0600 (1400), and 1200 (2000) UTC (BJT) of the current day. Summer over NC is defined as June–July–August (JJA).

2.2 Methodology

2.2.1 Extreme precipitation days

The widely used percentile threshold value is considered to be more appropriate for studying extreme precipitation over mainland China than a fixed criterion (Zhai et al. 2005; Luo et al. 2016). This method supports direct comparison of extreme precipitations in different regions (Tian and Fan 2013). In the present study, the 95th percentile of each station in NC was first calculated. The mean of all the 95th percentiles was then taken as the threshold to select extreme precipitation days for NC, based on the average daily precipitation for NC.

2.2.2 Moisture flux

The zonal (qu) and meridional (qv) components of the column-integrated moisture flux are described as follows (Zhao et al. 2018a, b):

$$ {\text{qu}}(x,y,t) = \frac{1}{g}\int\limits_{{p_{t} }}^{{p_{s} }} {q(x,y,p,t)u(x,y,p,t)dp} , $$
(1)
$$ {\text{qv}}(x,y,t) = \frac{1}{g}\int\limits_{{p_{t} }}^{{p_{s} }} {q(x,y,p,t)v(x,y,p,t)dp} , $$
(2)

where u and v are the zonal and meridional winds, respectively, g is gravitational acceleration, and q is specific humidity. Pt is the pressure at the top of the troposphere. Because most atmospheric water vapor resides below 300 hPa, herein 300 hPa is regarded as the level of top pressure, and hence the specific humidity q at top pressure pt is near zero (Zhang et al. 2010; Zhao et al. 2013; Sahin et al. 2015). Considering that the complex topography over NC can interfere with the moisture transport of extreme precipitation (Sun et al. 2015), ps is defined as surface pressure.

2.2.3 Moisture budget

To identify the most relevant moisture transport processes that contribute to extreme precipitation occurrence, each term in the moisture budget equation is computed (Yoon and Chen 2005; Chen and Tomassiniand 2015):

$$ - \left\langle {\overline{{\frac{\partial q}{\partial t}}} } \right\rangle - \left\langle {\overline{{\nabla \cdot (\vec{v}q)}} } \right\rangle - \left\langle {\overline{{\frac{\partial }{\partial p}(\omega q)}} } \right\rangle = \bar{P} - \bar{E}, $$
(3)

where P is precipitation, E is evaporation, q is specific humidity, \( {\vec{\text{v}}} \) is horizontal vector, and \( \nabla = \vec{i}\frac{\partial }{\partial x} + \vec{j}\frac{\partial }{\partial y} \) is the horizontal gradient operator. Bars denote the temporal mean, and \( \left\langle \cdot \right\rangle \) indicates vertical integrals \( \int_{{p_{t} }}^{{p_{s} }} {( \cdot )dp/g} \). The first item on the left side \( - \left\langle {\overline{{\frac{\partial q}{\partial t}}} } \right\rangle \) denotes the local rate of change in specific humidity. The second item on the left side of the equation \( - \left\langle {\overline{{\nabla \cdot (\vec{v}q)}} } \right\rangle \) denotes horizontal moisture flux convergence (MFC), which is the net moisture transport gain or loss caused by inflow and outflow of an atmospheric column. The third item on the left side of the equation \( - \left\langle {\overline{{\frac{\partial }{\partial p}(\omega q)}} } \right\rangle \) represents vertically integrated MFC. Pressure velocity \( \omega \) is assumed to be zero at the surface ps and at the moisture upper boundary pt.

2.2.4 Moisture flux convergence (MFC)

Assuming zero values of q at the top level pt and of \( \omega \) at ps and pt, the third term on the left side \( - \left\langle {\overline{{\frac{\partial }{\partial p}(\omega q)}} } \right\rangle \) of Eq. (3) is taken to be zero (Chou and Lan 2012). As \( - \left\langle {\overline{{\frac{\partial q}{\partial t}}} } \right\rangle \) contributes little to precipitation, this term can also be neglected (Zhu 2007). Therefore, the moisture budget of summer extreme precipitation over NC depends mainly on the change in horizontal MFC, which is proportional to the vertically integrated product of specific humidity and horizontal mass convergence through the troposphere.

The horizontal MFC is often simply referred to as MFC (Banacos and Schultz 2005). From now on, MFC is defined as the horizontal moisture flux convergence integrated between the surface ps and upper boundary pt at 300 hPa. To further quantify the aggregation and convergence of moisture over NC, MFC is decomposed as follows (Zomeren and Delden 2007):

$$ - \frac{ 1}{\text{g}}\int\limits_{{p_{t} }}^{{p_{s} }} {\nabla \cdot (q\vec{v}} )dp = - \frac{1}{g}\int\limits_{{p_{t} }}^{{p_{s} }} {q\nabla \cdot \vec{v}dp - \frac{1}{g}} \int\limits_{{p_{t} }}^{{p_{s} }} {\vec{v} \cdot \nabla qdp} , $$
(4)

where \( - \frac{1}{g}\int\nolimits_{{p_{t} }}^{{p_{s} }} {q\nabla \cdot \vec{v}} dp \) is the moisture convergence term representing the vertically integrated product of horizontal wind convergence, which is related to forced lifting. The second term \( - \int\nolimits_{{p_{t} }}^{{p_{s} }} {\vec{v} \cdot \nabla qdp} \) is proportional to the moisture advection term, and referred to as “moisture pooling”.

2.2.5 Design of numerical simulations

The weather and research forecasting (WRF) model version 3.4.1 (Skamarock and Klemp 2008; Yu 2013; Zhong and Yang 2015) is a fully compressible and non-hydrostatic atmospheric model, and was used to examine MFC changes due to a change in topography, forcing on the orographic effect on extreme precipitation over NC. Six historical extreme precipitation days over NC were randomly selected from the summer of 1979–2016 (Table 1) for the simulations.

Table 1 Six selected extreme precipitation days over NC in summers from 1979 to 2016 and their mean 24-h precipitation based on all the available station data
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The domain configuration uses one-way interactive nested inner grids of D01 (Fig. 1a). The central point of the simulation is located at 35° N and 100° E. The horizontal grid resolution is 30 km with 201 × 141 grid points. There are 38 unevenly spaced full sigma levels in the vertical dimension with the top level at 50 hPa. A sensitivity test is designed by removing the topography within the NC area of 110°–120° E, 35°–42° N, predominantly covering the Yanshan–Taihang Mountains. Both the control and sensitivity simulations used a time step of 60 s. The output interval of the WRF model is 1 h. Initial conditions and boundary data every 6 h were taken from the ERA-Interim reanalysis data, which have a horizontal resolution of 0.75° × 0.75°. The simulations begin 12 h before the occurrence of extreme precipitation on each of the six selected days.

The performance of different physical schemes employed in the WRF simulation for extreme precipitation events over NC has been documented in the literature. The Kain–Fritsch (KF) cumulus scheme includes convection as well as relevant ascending and downward motions, which hold a large amount of mass, thermal energy, and moisture (Kain and Fritsch 1993). Ma et al. (2012) reported that the WRF Single-Moment 6-Class Microphysics Scheme (WSM6) performed satisfactorily in simulations of the location and intensity of a rainstorm event over NC during 18–19 August 2010 when the horizontal resolution was set to 4 km. Zhao et al. (2010) suggested that parameterizations of the KF cumulus scheme, the Yonsei University planetary boundary layer (PBL) scheme, and the Dudhia shortwave radiative scheme could simulate extreme precipitation over NC well. The KF cumulus parameterization scheme, Yonsei University PBL, Rapid Radiative Transfer Model (RRTM) scheme for long wave radiation, Dudhia scheme for shortwave radiation, and Noah land-surface scheme were also chosen to capture a summer rainstorm and its related moisture transport over NC during 2010 (Wang et al. 2014). Tian et al. (2017) simulated precipitation in the northern China with the Noah land-surface model (LSM) scheme. Based on these previous studies, the WRF model physics packages used in this work are decided and listed in Table 2.

Table 2 Physical parameterization options chosen for the WRF model
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2.2.6 Atmospheric apparent heat source

To further explore terrain effect on moisture transport and precipitation, the atmospheric apparent heat source (Q1) was calculated. By comparing Q1 in the control and sensitivity tests, we try to quantify the atmospheric heating affected by terrain. The equation for Q1 is as follows:

$$ {\text{Q}}_{ 1} = {\text{C}}_{\text{p}} \left( {\frac{\partial T}{\partial t} + \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}}{\text{V}} \cdot \nabla {\text{T}} + \omega \left( {\frac{\text{P}}{{{\text{P}}_{0} }}^{\text{k}} } \right)\frac{\partial \theta }{{\partial {\text{P}}}}} \right) $$
(5)

where \( {\vec{\text{V}}} \) and \( \omega \) represent the horizontal wind fields and vertical motion. The T denotes the temperature.\( {\text{p}}_{0} \) is set to be 850 hPa at here. \( \theta \) is the potential temperature and Cp represents the specific heat constant. The constant k = 0.286. The vertically integrated Q1 equation can be written as:

$$ \langle Q_{1} \rangle = LP + S + \langle Q_{R} \rangle $$
(6)

where L means the latent heat of condensation and q denotes the specific humidity. P represents the precipitation and S denotes the surface sensible heat flux. The radiative heating is denoted as \( \langle Q_{R} \rangle \). The Q1 in whole column represents the sum of latent heat and surface sensible heat fluxes as well as the radiative heating.

3 Results and discussion

3.1 Extreme precipitation over NC and related moisture transport

NC is surrounded by the Yanshan and Taihang Mountains along the eastern margins of the Mongolian Plateau and the Loess Plateau to the north and west, respectively. This region faces the Bohai Sea to the east (Fig. 1b), and is mainly subject to the influence of humid monsoon climate (Ding et al. 2010). The summer mean value of the 95th percentile threshold daily extreme precipitation across the entire NC is estimated to be 22.7 mm. Thus, an extreme precipitation day over NC is defined when the regional mean of daily precipitation over NC is greater than 22.7 mm. With this definition, totally 38 extreme precipitation days over NC were selected from the summers during 1979 and 2016.

The Taihang and Yanshan Mountains, with altitudes above about 1000 m, divide daily mean extreme precipitation across NC in summer into intense precipitation over the eastern coastal areas and relatively weak precipitation over the inland western areas (Fig. 1c). In particular, daily mean extreme precipitation is most intense over the southeastern NC, with values up to ~ 55 mm. This result is consistent with the spatial pattern documented by Zhao et al. (2019b). This feature may have been caused by the foehn effect along the foot of the Taihang and Yanshan mountains and the humid airflow over eastern NC from the ocean (Fig. 1d, e). This spatial pattern of daily mean extreme precipitation over NC indicates the linkage between extreme precipitation and the surrounding topography, which implies that the most intense extreme precipitation is likely to occur over the eastern part of NC, along the steepest slopes in the region.

Moisture transport plays a key role in summer extreme precipitation (Zhao et al. 2016). We first present the climatological mean moisture fluxes in summer during 1979–2016 to illustrate the general moisture transport background over NC (Fig. 2a). South-westerly winds bring moisture to NC, derived mainly from the Bay of Bengal and the South China Sea. The composite column-integrated moisture transport for the 38 extreme precipitation days is then explored. There are two moisture transport pathways for the summer extreme precipitation: the westerly pathway along the northern periphery of the Tibetan Plateau (TP), and the southerly pathway east of the TP that transports abundant moisture primarily from the Bay of Bengal, the South China Sea, and the tropical western Pacific (Fig. 2b).

Fig. 2
figure 2

a Climatologically column-integrated moisture flux (vectors; 102 kg m−1 s−1) in summer during 1979–2016. b Composite column-integrated moisture flux (vectors; 102 kg m−1 s−1) for the 38 summer extreme precipitation days during 1979–2016. c The difference of the column-integrated moisture flux (vectors; 102 kg m−1 s−1) between summer extreme precipitation and climate state. The purple rectangle indicates the NC region and the grey shading represents terrain height (m). Red dots denote the anomalous column-integrated moisture flux exceeding the 90% confidence level of t test. The green line is the 3000 m elevation contour

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Comparisons of moisture transport between the climatological mean and extreme precipitation days over NC reveal some interesting differences. Due to the prevailing anticyclone over the western North Pacific, moisture transport from the tropical western Pacific towards NC during summer extreme precipitation days is more evident than in the climatological mean. The westerly pathway prevails over NC during extreme precipitation days. Most extreme precipitation events were caused by atmospheric circulation anomalies (Tian and Fan 2013). In fact, Hu et al. (2018) reported that summer extremes over mainland China are driven primarily by anomalous circulations, which prompts us to analyze the composite anomalies of column-integrated moisture transport favoring extreme precipitation over NC. A large amount of moisture originates mainly from the westerlies, the South China Sea, and the tropical western Pacific under the combined effects of the anomalous anticyclone over the western North Pacific and the cyclonic anomaly over the South China Sea. It becomes clear that the westerly pathway and the southerly moisture transport pathway are critical to summer extreme precipitation in the region (Fig. 2c).

Moisture transport towards NC during extreme precipitation days is much stronger than in the climatological summer mean. Notably, extreme precipitation days witness that the confluent moisture over NC tends to be transported over the relatively flat plains rather than the neighboring elevated terrains of the Yanshan and Taihang Mountains.

To quantify the effect of moisture transport that facilitates extreme precipitation over NC, we calculate the column-integrated moisture flux across each boundary of NC. During the extreme precipitation days, NC is under the control of westerlies and the southerly moisture transport pathway with moisture sources from the Bay of Bengal, South China Sea, and the western North Pacific. Four boundaries of NC were set to investigate the quantitative features of moisture transport. There is a predominant southerly moisture influx of 311.8 kg m−1 s−1 into NC along the southern boundary and a secondary influx of 107.9 kg m−1 s−1 across the western boundary due to mid-latitude westerlies. In addition, the outward moisture flux across the eastern boundary is 206.9 kg m−1 s−1 and across the northern boundary is 76.0 kg m−1 s−1, as shown in Fig. 3a. The moisture influx across the southern boundary is stronger than that across the western boundary, while the outgoing moisture flux is larger at the eastern boundary than at the northern boundary than at the northern boundary. The zonal budget of moisture flux is negative as the influx along the western boundary is less than the outgoing flux via the eastern boundary. On the contrary, meridional flow evidently brings moisture into NC because the influx across the southern boundary is much stronger than the outflow through the northern boundary. The meridional surplus is distinctly higher than the zonal deficit, consistent with previous literature (Wang et al. 2014). Therefore, NC has a conspicuous maximum of MFC exceeding approximately 4 × 10−5 kg m−2 s−1 (red shading in Fig. 3a) and the corresponding net moisture budget is a gain of 136.8 kg m−1 s−1. The positive net moisture flux certainly favors the generation of extreme precipitation.

Fig. 3
figure 3

a Composite moisture budget for the 38 summer extreme precipitation days over NC for 1979–2016. The purple box denotes the NC region. b Climatological summer mean moisture budget over NC for 1979–2016. The red shading denotes MFC and the blue shading represents moisture flux divergence (10−5 kg m−2 s−1). The dashed contour line denotes the value of MFC exceeding 1.0 × 10−5 kg m−2 s−1. The thick colored arrows and associated values represent the direction and intensity of moisture flux at each boundary (kg m−1 s−1). “Net” denotes the net moisture supply to the box. The grey shading denotes part of the Tibetan Plateau (TP)

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In the summer climatology of MFC during 1979–2016, there are two moisture influx channels at the southern (62.0 kg m−1 s−1) and western (70.0 kg m−1 s−1) boundaries, and both the eastern (124.0 kg m−1 s−1) and northern (8.0 kg m−1 s−1) boundaries are export channels (Fig. 3b). The incoming moisture transport at the southern and western boundaries shares similar intensity, whereas the outgoing moisture transport along the eastern boundary is much stronger than that at the northern boundary. At the same time, the zonal budget of moisture remains negative while the meridional surplus remains significant, broadly consistent with the zonal and meridional net budgets of moisture during extreme precipitation days. Consequently, the climatological meridional surplus just balances the zonal deficit and the net budget of climatological summer mean moisture over NC tends to approach zero.

The above analysis indicates that NC is a prominent moisture sink during summer extreme precipitation days, unlike in the climatological summer mean. In addition, the MFC maximum core, the pronounced moisture fluxes and the striking extreme precipitation zone over NC are all anchored to the east of the surrounding steep slopes of the Yanshan and Taihang Mountains.

As a crucial term in the moisture budget, the vertically integrated MFC is a useful predictor of precipitation connected with synoptic-scale systems. Further, it has been used to forecast convective initiation at mid-latitudes in recent decades (e.g., Banacos and Schultz 2005). Previous studies inferred that the changes in MFC could be divided into two contributions from (1) wind convergence as a result of changes in circulation (Seo et al. 2013; Freychet et al. 2015), and (2) advection due to changes in humidity gradients. Figure 4 shows the two terms of the vertically integrated MFC in Eq. (4) for extreme precipitation days and the climatological summer mean. During the extreme precipitation days, the enhanced moisture transport brought more water vapor to NC from the tropical oceans and via westerlies (Fig. 2b), forming the maximum MFC core inside NC (Fig. 3a). The significant increase in MFC over the entire NC region is mainly attributable to enhancements in wind convergence, and the advection term is only effective over the eastern NC plain (Fig. 4a, c). Quantitative analysis shows that 90% in the increase of 1.54 × 10−5 kg m−2 s−1 in MFC comes from an enhancement of 1.39 × 10−5 kg m−2 s−1 in wind convergence and only 10% from an increase of 1.5 × 10−6 kg m−2 s−1 in advection (Table 3). Thus, the intensified extreme precipitation over NC is mainly caused by reinforced convergence of horizontal winds.

Fig. 4
figure 4

Wind convergence term (color shading, unit: 10−5 kg m−2 s−1) of the MFC over NC for a the 38 summer extreme precipitation days and b the climatological summer mean. c, d As for a and b, but for the moisture advection term. The purple box denotes the NC region. The grey shading indicates the part of the TP

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Table 3 Contributions of wind convergence and advection to the MFC over the whole NC (unit: 10−5 kg m−2 s−1)
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Note that the climatological summer mean MFC is slightly negative over NC. Compared with the case for the extreme precipitation days, and both the climatological wind convergence and advection terms are small. The reduction of the climatological summer mean MFC to 1.3 × 10−6 kg m−2 s−1 in this region corresponds primarily to the sharply decreased convergence term 1.2 × 10−6 kg m−2 s−1 accounting for 92.3% and the slightly reduced advection term 1.0 × 10−7kg m−2 s−1 only accounting for 7.7% (Table 3), demonstrating the dominance of wind convergence term in terms of the MFC that links with the summer mean precipitation over NC.

The summer precipitation over NC on both extreme precipitation days and other days heavily rely on horizontal wind convergence. The intensified convergence leads to greater MFC and consequently heavy summer precipitation over NC.

The above results provide a quantitative understanding of the spatial pattern of extreme precipitation over NC and associated moisture transport, and imply a role of the adjacent elevated terrain on extreme precipitation and associated moisture transport. Many studies have discussed possible mechanism by which the adjacent topography affects summer precipitation in NC and beyond. He and Zhang (2010) attributed warm-season precipitation over NC to the upward and downward branches of a solenoidal circulation between mountain ranges and plains. Liu et al. (2009) proposed that the distinct precipitation contrast between the central TP and the periphery is caused by orographic effects on regional convection, implying a convergence–divergence pattern near the edge of the TP. To visualize the influence of the neighboring elevated terrain on extreme precipitation and related moisture transport, vertical cross-sections of moisture and vertical velocity for summer extreme precipitation days and the climatological summer mean are shown in Fig. 5.

Fig. 5
figure 5

Vertical cross-sections of av (vectors; m s−1), \( \omega \) (vectors; − 10−2 Pa s−1), and humidity (color shading; kg kg−1) showing the meridional average over NC for the 38 extreme precipitation days and bu (vectors; m s−1), \( \omega \) (vectors; − 10−2 Pa s−1), and humidity (color shading; kg kg−1) showing the zonal average over NC for the 38 extreme precipitation days. c, d As for a and b, but for climatological summer mean during 1979–2016. The black shading shows the terrain. NC lies within the grey dashed lines. The meridional and zonal section-cross along the average longitude (110°–120° E) and average latitude (35°–42° N) of NC region

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Comparing the vertical cross-sections for extreme precipitation days with that for climatological mean days, the upward airflow during extreme precipitation days is more vigorous than that of the climatological state in both meridional and zonal directions. An obvious humidity tongue is observed over NC during extreme precipitation days (Fig. 5a, b), with higher humidity than in the climatological summer mean (Fig. 5c, d) at the same level. Note that the remarkable humidity tongue and strong ascending motion conducive to extreme precipitation tend to occur near the steep slopes of terrain over NC, which confirms the important role of the adjacent elevated terrain in enhancing extreme precipitation over NC.

3.2 Difference in moisture transport associated with summer extreme precipitation between the control and sensitivity tests

The above analysis has revealed the important effect of the surrounding topography on extreme precipitation over NC. However, the exact contribution of elevated terrain to extreme precipitation and the details of the associated processes require deeper insight and clarification. To examine the influence of the adjacent elevated terrain on extreme precipitation over NC, the control simulation retains the terrain heights over NC (Fig. 6a), whereas the terrain height is removed over NC in the sensitivity test (Fig. 6b). To reduce the sudden change of the elevation on the boundaries of NC in the sensitivity test, the boundary height was set to be half of those from the control run. Within the boundaries, the elevations were all set to zero.

Fig. 6
figure 6

Terrain height (grey shading; m) over mainland China in the a control and b sensitivity tests. The purple dashed rectangle denotes the NC region. c, d Composite daily mean precipitation amount (color shading, mm) over mainland China for the six extreme precipitation days in the control and sensitivity tests, respectively. e Observed daily mean precipitation (color shading, mm) over mainland China on the six extreme precipitation days. The red rectangle in (c–e) indicates the NC region and the grey shading represent terrain height (unit: m)

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Figure 6 shows the composites of the control and sensitivity tests for the six selected extreme precipitation days (Table 1). Precipitation intensity and spatial distribution over NC in the control simulation have similar patterns to the observed precipitation. The largest precipitation amount is anchored over the Taihang Mountains in both control and observations, but the precipitation peak in the control simulation is slightly weaker than that observed (Fig. 6c, e). Moreover, compared with the observed, the location of central precipitation region in the control test is in higher latitude (Fig. 6c, e). In contrast, precipitation intensity in the sensitivity test is significantly weaker than that observed, especially over the Taihang Mountains. Compared with the control test, the largest value center in the sensitivity test is missing (Fig. 6d). The rain band in the sensitivity is located in the plain area, which is basically along the Taihang mountains (as shown in Fig. 1). The neighboring elevated terrain is found to favor summer extreme precipitation over NC. Without the terrain, precipitation intensity over NC would be weakened dramatically.

We next assess the composites of column-integrated moisture transport for summer extreme precipitation days with and without the orographic effect. In the control and sensitivity tests, the composite column-integrated moisture is transported along the eastern region of the TP from the tropical oceans including the western Pacific, the South China Sea, and the Bay of Bengal, and by the westerlies along the north margin of the TP. In the control simulation, inflows of moisture cross the southern (377.3 kg m−1 s−1) and western (87.4 kg m−1 s−1) boundaries of the NC region, and moisture flows out through the eastern (249.8 kg m−1 s−1) and northern (51.8 kg m−1 s−1) boundaries. The incoming moisture transport at the southern boundary is much larger than that at the western boundary, while the outgoing moisture transport is larger at the eastern boundary, consistent with our diagnosed results from the reanalysis. The corresponding net moisture transport in the control simulation is a gain of 163.1 kg m−1 s−1 (Fig. 7a). In the sensitivity test, the moisture influx over NC includes one channel across the southern boundary of 356.9 kg m−1 s−1 and another across the western boundary of 70.9 kg m−1 s−1. The moisture influx across both the two boundaries in the sensitivity test is weaker than in the control simulation. The outgoing moisture flux across the eastern boundary is 235.4 kg m−1 s−1 and that across the northern boundary is 55.4 kg m−1 s−1. The net surplus of moisture transport in the sensitivity test is 137.0 kg m−1 s−1 (Fig. 7b).

Fig. 7
figure 7

Composite column-integrated moisture flux (vectors; kg m−1 s−1) for the six extreme precipitation days in the control test (a) and sensitivity test (b). The purple shading denotes MFC and the green shading represents moisture flux divergence (10−5 kg m−2 s−1). The thick colored arrows and associated values represent the direction and intensity of moisture flux at each boundary (kg m−1 s−1). The blue dashed rectangle indicates the NC region and the grey shading denotes part of the TP. “Net” denotes the net moisture supply to NC. The black dots indicate the statistically significant results above the 90% confidence level for magnitude of column-integrated moisture flux

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The entire NC has a remarkable maximum of MFC above 4 × 10−5 kg m−2 s−1 (purple shading in Fig. 7a) in the control simulation which is much larger than that in the sensitivity test, especially over the steep slopes of elevated terrain to the west. This indicates that the neighboring Taihang and Yanshan Mountains reinforce the moisture transport and the MFC of enhancing extreme precipitation over NC.

Figure 8 separates the wind convergence and advection terms of the vertically integrated MFC for the six extreme precipitation days in the control and sensitivity tests. In the control simulation, the increased MFC (2.0 × 10−5 kg m−2 s−1) over NC is attributable to the gain of wind convergence (1.73 × 10−5 kg m−2 s−1) and the increased advection (2.7 × 10−6 kg m−2 s−1). For the whole NC, the wind convergence and advection term account for 86.5% and 13.5% of the increased MFC, respectively (Table 4). In the sensitivity test, the enhanced MFC over NC is 1.68 × 10−5 kg m−2 s−1, less than that in the control simulation. After removing the terrain, the convergence and advection term correspond to gains of 1.42 × 10−5 and 2.6 × 10−6 kg m−2 s−1 (84.5% and 15.5% of the total MFC), respectively.

Fig. 8
figure 8

a Composite wind convergence term and b moisture advection term (color shading; 10−5 kg m−2 s−1) of MFC for the six extreme precipitation days in the control simulation. c, d As for a and b, but for the sensitivity test. The grey shading indicates part of the TP. The black dots indicate the statistically significant differences above the 90% confidence level for the wind convergence term and moisture advection term

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Table 4 Contributions of wind convergence and advection to the MFC (unit: 10−5 kg m−2 s−1) for the whole NC in the control and sensitivity tests
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The comparison between the control and sensitivity tests demonstrates that the surrounding elevated terrain significantly enhances wind convergence, leading to the MFC 16% higher than the case without terrain. Moreover, the most significant difference for wind convergence term between the control and sensitivity test lies in the western complex terrain region of NC. This means that the surrounding terrain plays a considerable role for creating extreme precipitation over NC.

3.3 The circulation effects in the control and sensitivity tests

Moisture supply, air instability and vertical motion of the air which depends on diabatic heating all play a role for cloud formation and precipitation. Here we calculated and compared the atmospheric apparent heat Q1 and wind fields in the control and sensitivity tests, to explore the terrain effect for the extreme precipitation in NC.

As shown in Fig. 9, the whole column Q1 in the control test is obviously larger than in the sensitivity test. Especially, relatively large values of whole column Q1 is found over the complex terrain region of NC in the control test, while the sensitivity test shows overall small values (Fig. 9a, b). This is mainly due to the increased precipitation and associated latent heat release.

Fig. 9
figure 9

The distributions of the whole layer atmospheric apparent heat Q1 (color contour; unit: w m−2) a in the control test; b in the sensitivity test. The wind difference at 300 hPa between control and sensitivity test is shown in c. The grey shade is the terrain height (unit: m). The red box represents the NC region. The blue dash line shows the terrain staircase transitional region as shown in Fig. 1c

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The diabatic heating is helpful to make the warm moisture to rise. Moreover, at the 300 hPa level there is a divergence structure in the western part of NC as shown in Fig. 9c. Over this region, it is thus more favourable for the upper winds to diverge, which help pump the moisture from lower level to upper level in the control test. To further explore the terrain effect for the vertical motion, we calculated the meridional and zonal cross sections of Q1 along with wind vectors, and the results are shown in Fig. 10. The heating effect caused by the terrain is obviously stronger than in the sensitivity without the terrain. In the meridional cross section, the largest Q1 is located around 400–200 hPa (Fig. 10a). Compared with the sensitivity test (Fig. 10b), the vertical motion in the control test is much stronger than in the sensitivity test (Fig. 10b). Moreover, the strongest vertical motion is located over the steepest slope of the terrain region in the west. As for the zonal section (Fig. 10c, d), it shows similar results as those in the meridional section. Especially, the vertical motion in the control test is stronger than in the sensitivity test.

Fig. 10
figure 10

The composite latitudinal and meridional cross sections of atmospheric apparent heat source Q1 (contour; unit: 10−4 m2 s−3) and wind fields for the six extreme precipitation days in the control test (a, c) and sensitivity test (b, d). The black color represents the terrain. The meridional cross section along the 113° E and the zonal cross section along the 37° N

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The warm moisture is lifted more strongly when encountering the terrain over NC. This means a higher latent heat and more heating, resulting stronger instability of the air. At the same time, the stronger vertical motion results in that the air in the upper level will be stocked, promoting the divergence structure at the upper level. With help of the thermodynamic and dynamic effects, the pumping of the moisture from the lower levels outside NC will be strengthened, feeding the needed moisture supply for the extreme precipitation.

4 Conclusions and discussions

Based on the ERA-Interim reanalysis data and rain gauge observations, this work has quantified moisture budget for the 38 selected summer extreme precipitation days over NC during 1979–2016 and that of climatology. To improve our understanding of the role played by the orographic effect for the extreme precipitations, numerical modeling was carried for six out of the 38 extreme precipitation days. The results are summarized as follows.

  1. 1.

    During the 38 extreme precipitation days, there is a dominant moisture influx of 311.8 kg m−1 s−1 into NC along the southern boundary from the tropical oceans and a secondary influx of 107.9 kg m−1 s−1 across the western boundary carried by mid-latitude westerlies. In contrast, moisture flows out across the eastern boundary at 206.9 kg m−1 s−1 and across the northern boundary at 76.0 kg m−1 s−1. The corresponding net moisture budget over NC is a gain of 136.8 kg m−1 s−1.

  2. 2.

    Compared to the climatological summer mean, NC during the extreme precipitation days represents a strong moisture sink linked with intensive moisture transport, with the MFC maximum exceeding approximately 4 × 10−5 kg m−2 s−1. The enhanced MFC that facilitates the extreme precipitations over NC is mainly driven by the convergence of horizontal winds rather than moisture advection.

  3. 3.

    The MFC maximum core, the pronounced moisture transport, and the intense extreme precipitation zone over NC are anchored to the east of the steep slopes of the surrounding elevated terrain. Moreover, the remarkable humidity “tongue” and active upward motion that are conducive to extreme precipitation also occur near the steep slope of terrain over NC, indicating the important influence of the adjacent elevated terrain on extreme precipitation over NC.

  4. 4.

    The WRF simulations for the six selected extreme precipitation days confirm the diagnosed results. Additionally, using the WRF simulations, the elevated terrain in the western NC is found to intensify MFC by 16% relative to the case without the terrain.

  5. 5.

    The terrain is found to be able to enhance upward vertical motion driven by precipitation and associated diabatic heating of the atmosphere. The vertically integrated diabatic heating and divergence at the upper level under the influence of the topography are favourable to the occurrence of extreme precipitation. Without terrain, upward motion of warm moisture air at low level would be weakened. Therefore, the western terrain of NC is considered important for the intensive extreme precipitations over the western of NC.

Apart from topography and wind convergence considered in this study, there are still other factors affecting for rainstorms over NC. The impact of ENSO on precipitation changes has been well documented (Zhang et al. 1999; Wang et al. 2016). Extreme precipitation days over NC are significantly less frequent in El Nino phases than in La Nina phases (Li et al. 2011). Large-scale circulation is found to maintain and favour the development of rainstorms over NC (Orsolini et al. 2015). When the Indian monsoon is stronger than normal state, a westward location of South Asian High corresponds to more rainfall over NC (Wei et al. 2014). Likewise, Zhang et al. (2017) found that the strength and location of western North Pacific subtropical high (WNPSH) are closely related to the changes of summer extreme precipitation in eastern China. Additionally, Wen et al. (2015) documented that the WNPSH interacting with typhoons of different intensities may contribute to the development of a southeasterly moisture channel, resulting in a change in rainstorm over NC. Further, a recent study on extreme precipitation events in eastern China also indicated a possibly important role of air pollution and urbanization (Shi et al. 2017).

Since the diagnostic analyses of this study were based on dynamics and thermodynamic processes relevant for precipitation, the impacts of the influencing factors discussed above are to a large extent imbedded into the processes analyzed. However, it should be kept in mind that only six out of the 38 extreme precipitation days were subject to numerical simulation due to limited computing resources. Although the results are in line with the diagnostic analyzed for the 38 days in principle, there can be some details that deserve more in-depth analyses. Future studies building on the findings of this study are thus desirable to systematically understand the dynamics of and causes behind the extreme events.