J. Meteor. Res.  2019, Vol. 33 Issue (3): 416-432 PDF
http://dx.doi.org/10.1007/s13351-019-8606-z
The Chinese Meteorological Society
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#### Article Information

YU, Jiahui, Yimin LIU, Tingting MA, et al., 2019.
Impact of Surface Potential Vorticity Density Forcing over the Tibetan Plateau on the South China Extreme Precipitation in January 2008. Part ll: Numerical Simulation. 2019.
J. Meteor. Res., 33(3): 416-432
http://dx.doi.org/10.1007/s13351-019-8606-z

### Article History

in final form April 2, 2019
Impact of Surface Potential Vorticity Density Forcing over the Tibetan Plateau on the South China Extreme Precipitation in January 2008. Part ll: Numerical Simulation
Jiahui YU1,2, Yimin LIU1,3, Tingting MA1, Guoxiong WU1,3
1. State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), Institute of Atmospheric Physics (IAP), Chinese Academy of Sciences, Beijing 100029;
2. Tianjin Meteorological Service Center, Tianjin 300074;
3. College of Earth Science, University of Chinese Academy of Sciences, Beijing 100049
ABSTRACT: The surface air convergence on the eastern flank of the Tibetan Plateau (TP) can increase the in situ surface potential vorticity density (PVD). Since the elevated TP intersects with the isentropic surfaces in the lower troposphere, the increased PVD on the eastern flank of TP thus forms a PVD forcing to the intersected isentropic surface in the boundary layer. The influence of surface PVD forcing over the TP on the extreme freezing rain/snow over South China in January 2008 is investigated by using numerical experiments based on the Finite-volume Atmospheric Model of the IAP/LASG (FAMIL). Compared with observations, the simulation results show that, by using a nudging method for assimilating observation data in the initial flow, this model can reasonably reproduce the distribution of precipitation, atmospheric circulation, and PVD propagation over and downstream of the TP during the extreme winter precipitation period. In order to investigate the impact of the increased surface PVD over the TP on the extreme precipitation in South China, a sensitivity experiment with surface PVD reduced over the TP region was performed. Compared with the control experiment, it is found that the precipitation in the TP downstream area, especially in Southeast China, is reduced. The rainband from Guangxi Region to Shandong Province has almost disappeared. In the lower troposphere, the increase of surface PVD over the TP region has generated an anomalous cyclonic circulation over southern China, which plays an important role in increasing southerly wind and the water vapor transport in this area; it also increases the northward negative absolute vorticity advection. In the upper troposphere, the surface PVD generated in eastern TP propagates on isentropic surface along westerly wind and results in positive absolute vorticity advection in the downstream areas. Consequently, due to the development of both ascending motion and water vapor transport in the downstream place of the TP, extremely heavy precipitation occurs over southern China. Thereby, a new mechanism concerning the influence of the increased surface PVD over the eastern TP slopes on the extreme weather event occurring over southern China is revealed.
Key words: extreme weather event     Tibetan Plateau     potential vorticity density (PVD)     surface PVD forcing     numerical simulation
1 Introduction

In recent years, under the global warming, extreme weather and climate events have occurred frequently, and their long duration or high intensity often causes major meteorological disasters, bringing in adverse impacts on people’s lives. From 10 January to 5 February 2008, a cascade of extremely strong freezing rain/snow episodes occurred over large areas of southern China, causing serious casualties and property losses (Wang L. et al., 2008; Wang Z. Y. et al., 2008). Understanding the physical processes of this extreme event can help improve the weather forecasting and short-term prediction of such events in the future.

Studies on variations of the climatology (Ding et al., 2008; Gao et al., 2008), anomalies of large-scale circulation systems such as the anomalous blocking high, jet, and polar vortex (Liu et al., 2008; Wang Y. F. et al., 2008; Yang et al., 2008; Wen et al., 2009; Li and Gu 2010), and the impacts of the Tibetan Plateau (TP) (Tao and Wei, 2008; Bao et al., 2010; Li et al., 2011) on downstream weather and climate, have been carried out to analyze the causes of this extreme winter precipitation disaster. Ding et al. (2008) explored the causes of this extreme event from the perspective of global warming and found that global warming may have increased the frequency of extreme weather events through enhancing the circulation and climate anomalies. Gu et al. (2008) discussed this extreme winter precipitation event from the perspective of the East Asian monsoon system (EASM) anomaly, and indicated that occurrence of the extreme freezing rain/snow episodes is the combined result of multiple components of the EASM. Tan et al. (2010) analyzed the climatological background of the disaster. They found that in the winter of strong La Niña event, due to strengthening of the meridional component of the atmospheric circulation in the midlatitudes, frequent outbreaks of cold air could easily result in large-scale low temperatures in China. Based on the reanalysis data from 1953 to 2008, Nan and Zhao (2012) found that in the year with more snowy days in January over central and eastern China, the anomalous low pressure below 500 hPa in the middle and low latitudes was located over the Asian continent and TP, and the anomalous high pressure was located over the east coast of East Asia, making the anomalous southerly wind prevail over southern China, transporting water vapor to central and eastern China. The prevailing near-surface northerly wind is conducive to the development of ascending motion. They also pointed out that the thermal change over the Asian continent in winter exerted a more significant effect than that of the El Niño/Southern Oscillation (ENSO) and the Arctic Oscillation during this extreme winter precipitation and low temperature disaster in China.

By analyzing the characteristics of this weather process, Tao and Wei (2008) concluded that the anomalies of the large-scale circulation (e.g., the continuous maintenance of the blocking high over the Ural Mountains) during this period are important causes of this extreme event. They proposed that the anomalous circulations in the lower troposphere, such as the strengthening of the jet stream and the westward extension and northward shift of the western Pacific subtropical high, have enhanced the water vapor transport through the low-level southwesterly wind. The occurrence of the event is also closely related to the cooperation between the in situ meso- and small-scale circulation systems and dynamic conditions (Tao et al., 2008; Wang D. H. et al., 2008; Zeng et al., 2008; Gao et al., 2011; Gu, 2011). During this process, the anomalous heating effect of the TP also plays an important role. Bao et al. (2010) and Li et al. (2011) used numerical models to analyze the relationship between the TP warming and this extreme event, and found that the TP warming can strengthen the development of the southern branch trough and further enhance its water vapor transport to southern China, which is conducive to the downstream precipitation. The TP warming is somehow associated with the surface forcing conditions of the TP. However, the physical process involved in the TP near-surface effect on the precipitation in the TP downstream area has not yet been explored, and the mechanism is still unclear. This will be discussed in the present study from the perspective of surface potential vorticity density forcing over the TP.

Based on the potential vorticity (PV) theory of Ertel (1942) and Hoskins et al. (1985), PV analysis has been widely used in the study of weather systems development. Tao and Wei (2008) analyzed the PV on the 320-K isentropic surface and found that during the 2008 persistent winter precipitation process, the high-level strong PV disturbances moved eastward from central Asia, via TP, to the region where the southern China stationary front stayed. Due to the constraint of the atmospheric specific volume distribution, PV was amplified in the upper troposphere but reduced in the lower layer; therefore, PV analysis is generally applied to the dynamic analysis in the mid–upper troposphere. Further studies (Held and Schneider, 1999; Schneider et al., 2003) showed that the PV changes in the free atmosphere are affected by changes in the surface PV. Haynes and McIntyre (1987, 1990) introduced the definition of PV density (W = ρP, where ρ is the mass density of the air parcel, and P represents PV), and proved based on Gauss’s theorem that the total PV density (PVD) change on the isentropic surface is determined by the convergence of the PVD flux along its boundary (see Section 2.1). Shaw (1930) and Hoskins (1991) divided the atmosphere into the upper, middle, and lower spaces according to the distribution of isentropic surfaces in the atmosphere. Among them, the isentropic surfaces above the tropical tropopause constitute the upper space, the isentropic surfaces below the tropical tropopause but not intersecting with the ground constitute the middle space, and the lower space is composed of all isentropic surfaces intersecting with the ground. According to the definition of Haynes and McIntyre (1987), the isentropic surfaces in the upper and middle spaces do not intersect with the ground. They surround the earth and have no boundaries, so there is no total change of the PVD. In the lower space, however, as the isentropic surfaces intersect with the ground, and form the boundary, the change or generation of the surface PVD occurs. The PVD can be transported inside along the isentropic surface, and affect local weather changes. In summary, the surface PVD generation is the source of the PVD forcing on the relevant isentropic surfaces.

Since PVD is not affected by the atmospheric specific volume distribution, its signal in the lower atmosphere is significant. Therefore, it should be a useful quantity in diagnosing weather and climate. However, because the isentropic surface is tilted with height in the lower atmosphere, with certain static instability, application of the isentropic surface PVD analysis is limited. It is noted that the TP is a key area for the generation and variation of surface PVD (Liu et al., 2006). The TP top is located in the middle troposphere. In different seasons, the large terrain of the TP intersects with the quasi-horizontal isentropic surface in the free atmosphere to form the boundary. In addition, because the TP is located in the upstream of southern China, the anomaly of surface PVD over the TP region may propagate downstream along the quasi-horizontal isentropic surface, which in turn affects the downstream weather.

Based on the above analysis, the first part of the study (Ma et al., 2019) used the Modern-Era Retrospective Analysis for Research and Applications-2 (MERRA2) reanalysis data to investigate the extreme winter precipitation process over southern China in January 2008, and found that there was a significant PVD increase over eastern TP during this month. During the PVD’s eastward propagation, it induced simultaneous development of low-level southerly wind in southern China and the ascending motion over the middle and lower reaches of the Yangtze River, resulting in heavy local precipitation. Nonetheless, the cause of a meteorological disaster is complicated. The diagnostic analysis in the first part of the study (Ma et al., 2019) may not be enough to identify the impacts of the TP surface PVD forcing.

The current study aims to verify the above hypothesis and results by numerical simulations. The freezing rain and snow event over southern China from 24 to 27 January 2008 is selected for this study. First, the MERRA2 reanalysis data are simply analyzed to reveal the general pattern of PVD and atmospheric circulation features during the study period. Then, the atmospheric general circulation model (AGCM) developed by the State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG) of Institute of Atmospheric Physics, Chinese Academy of Sciences, is used to simulate this winter precipitation event. Finally, a sensitivity experiment with varied increase of PVD on the eastern flank of the TP is performed and the contribution of the surface PVD and its eastward propagation to the extreme winter precipitation in the TP downstream region (southern China) is investigated and identified.

2 PV theory, data processing, and numerical experiment design 2.1 PV theory

The PV equation that describes the atmospheric motion can be expressed as (Ertel, 1942; Hoskins et al., 1985; Hoskins, 1991, 1997, 2015)

 $\frac{{{\rm d}P}}{{{\rm d}t}} = \alpha [{{\zeta _{\rm a}}} \cdot \nabla \dot \theta + \nabla \times {{F}} \cdot \nabla \theta ],$ (1)

where θ is the potential temperature, $\dot \theta = Q$ is the diabatic heating, F is the momentum friction, and P is the potential vorticity (PV). PV is defined as the product between the potential temperature gradient and the projected three-dimensional absolute vorticity (ξa) of a unit mass air parcel in the direction of potential temperature gradient,

 $P = \alpha {{\zeta _{\rm a}}} \cdot \nabla \theta,$ (2)

where α is the specific volume of the air parcel. By introducing a variable W,

 $W = {{\zeta _{\rm a}}} \cdot \nabla \theta,$ (3)

we have P = αW, or

 $W = \rho P = \frac{M}{V}P,$ (4)

where ρ = 1/α is the mass density of the air parcel, which is equal to the ratio of air parcel mass (M) to the volume (V). For an air parcel of unit mass (|M| = 1), W = P/V based on Eq. (4). Thus, W represents the potential vorticity density per unit mass of the air parcel, abbreviated as potential vorticity density (PVD). By comparison of Eqs. (2) and (3), it is known that PV (P) is affected by the specific volume α, so PV is much larger in the upper atmosphere than that in the lower atmosphere, but PVD (W) is not affected by the specific volume, and its magnitude in the upper and lower atmosphere is comparable. Because

 $\frac{{{\rm{d}}P}}{{{\rm{d}}t}} = \alpha \frac{{{\rm{d}}W}}{{{\rm{d}}t}} + W\frac{{{\rm{d}}\alpha }}{{{\rm{d}}t}} = \alpha (\frac{{{\rm{d}}W}}{{{\rm{d}}t}} + W\nabla \cdot {{V}} ),$ (5)

the equation for PVD variation can be obtained from Eqs. (1) and (5) as follows,

 $\frac{{{\rm d}W}}{{{\rm d}t}} = - W\nabla \cdot {{V}} + {{\zeta _{\rm a}}} \cdot \nabla \dot \theta + \nabla \times {{F}} \cdot \nabla \theta .$ (6)

The above equation shows that the convergence, heating, and friction can affect the change of atmospheric PVD. In the case of an adiabatic and frictionless atmosphere

 $\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\frac{{{\rm d}P}}{{{\rm d}t}} = 0,$ (7)
 $\frac{{{\rm d}W}}{{{\rm d}t}} = - W\nabla \cdot {{V}} .$ (8)

Therefore, from Eqs. (7) and (8), for an adiabatic and frictionless case, we have

 $\left\{ \begin{gathered} \!\!\!\!\!\!\!\!\!\! \frac{{\partial P}}{{\partial t}} = - {{V}} \cdot \nabla P \\ \frac{{\partial W}}{{\partial t}} = - \nabla \cdot ({{V}} W) \\ \end{gathered} \right..$ (9)

Equations (7) and (8) show that in the adiabatic frictionless atmosphere, the potential vorticity (P) is conserved but the potential vorticity density (W) is not conserved. In other words, the internal convergence of the atmospheric motion can change the PVD. Therefore, the atmospheric PVD change can be diagnosed by analyzing the spatial distribution of the atmospheric convergence. Equation (9) shows that in the adiabatic and frictionless atmosphere, the local variation of PV is determined by the PV advection, while the local variation of PVD is determined by the convergence of PVD flux (VW). It can be noted from Eq. (3) that in isentropic coordinates, PVD is actually the absolute vorticity: $W = f + {{\rm{\xi }}_{\rm{\theta }}}.$

Therefore, the PVD flux on the isentropic surface is the absolute vorticity flux, and the PVD advection on the isentropic surface is the absolute vorticity advection. This brings great convenience to the following dynamic analysis.

Another advantage of the PVD equation [i.e., Eq. (6)] is that it can be written as a divergence form of the PVD flux (Haynes and McIntyre, 1987, 1990),

 $\left\{ \begin{gathered} \!\! \!\! \!\!\!\! \! \!\! \!\! \!\!\!\!\!\! \!\! \!\! \!\! \!\!\!\!\!\! \!\! \!\! \!\! \!\!\!\!\!\! \!\! \frac{{\partial W}}{{\partial t}} = - \nabla \cdot {{ H} _{{\rm PVD}}} \\ {{ H} _{{\rm PVD}}} = - W{{V}} + \dot \theta {{\zeta _{\rm a}}} + \theta \nabla \times {{F}} \\ \end{gathered} \right.,$ (10)

where HPVD is the total PVD flux (Schneider, 2005). Assume that the area of the isentropic surface θl is S, and the boundary line that the surface intersects with the ground is Γ, by using Gauss’s theorem, the total PVD change on the isentropic surface θl from Eq. (10) is

 $\int\limits_{S} {\frac{{\partial W}}{{\partial t}}} {\rm d}s = - \oint\limits_\varGamma {{{{H} }_{{\rm PVD}}} \cdot {{n}} } {\rm d}l,$ (11)

where dl is the unit length of the boundary line and is positive in the counter clockwise direction, and n is a unit vector perpendicular to dl and oriented to its right side. Equation (11) shows that the change of the total PVD on the isentropic surface θl is determined by the convergence or divergence of the total PVD flux along the surface boundary line Γ; and the surface PVD change can be diffused inside the isentropic surface by the convergence of PVD flux, which then affects the circulation and thermal structure of the atmosphere. Different from the traditional mechanism that the high PV advection in the upper layer can stimulate weather development in the lower layer (Hoskins et al., 1985), the surface PVD analysis focuses on the influences of surface PVD change and its movement on local and remote weather and climate.

This study investigates the effects of surface PVD forcing and its eastward propagation over the TP on the January 2008 precipitation process over southern China, based on a simple data analysis and a detailed numerical simulation as well as a sensitivity experiment. Because the near-surface heating of the atmosphere is mainly the sensible heat heating but the surface sensible heat heating over the TP in winter is weak, the contribution of diabatic heating to the PVD change in the near-surface layer is small (figure omitted) and neglected. Only the contribution of the divergence term [ $- \nabla \cdot \left({{V}W} \right)$ ] in the PVD equation is analyzed in this study.

2.2 Data processing

The data used in this study cover the period from 1 to 31 January 2008, including (1) TRMM (Tropical Rainfall Measuring Mission) daily precipitation on a spatial resolution of 0.25 km × 0.25 km (Huffman et al., 2007); (2) the high-quality precipitation dataset of China (http://cdc.cma.gov.cn) and the 0.5° × 0.5° surface precipitation data over China, provided by the National Meteorological Information Center of China Meteorological Administration; (3) ERA-Interim (Dee et al., 2011) reanalysis data from the ECMWF on a spatial resolution of 0.75 km × 0.75 km and a temporal resolution of 6 h, including basic atmospheric fields such as wind and temperature; and (4) MERRA2 data in the σp coordinate from NASA (Atmospheric Data Service Center at Nanjing University of Information Science & Technology, 2010; Rienecker et al., 2011; Lucchesi, 2012), at 3-h temporal intervals. Since the near-surface MERRA2 data are stored in the σ-coordinate, and there is a relationship between the z- and σ-coordinates

 $\delta z = -\frac{\pi }{{\rho g}}\delta \sigma ,$ (12)

where $\pi$ is surface pressure. Then, the three-dimensional divergence can be calculated from the data in the σ-coordinate

 $\nabla \cdot {{V}} = {\nabla _{\sigma {\rm h}}} \cdot {{ V}_{\rm h}} - \frac{{\rho g}}{\pi }\frac{{\partial \dot \sigma }}{{\partial \sigma }}.$ (13)

In Eq. (13), the first term on the right hand side is the horizontal component of the divergence, and the second term is the vertical component of the divergence. The vertical velocity on the σ-plane in the above equation is

 $\pi \dot \sigma = - \int_0^\sigma {\nabla \cdot (\pi {{V}}){\rm{d}}\sigma - } \frac{{\partial \pi }}{{\partial t}}\sigma .$ (14)

Figure 1 shows the spatial distribution of PVD variation and atmospheric divergence at the near-surface level (σ = 0.985), averaged over 24–27 January 2008 and calculated based on Eqs. (8), (13), and (14) by using the MERRA2 data. During this period, there was a significant increase in surface PVD over the eastern flank of TP at a terrain height of more than 1500 m ( $- \nabla \cdot \left({{V}W} \right)$ > 1.5 × 10 –7 K s–2) (Fig. 1a). The area corresponding to the eastern flank of the TP had atmospheric convergence stronger than –1.0 × 10–5s–1 (Fig. 1b). The horizontal convergence along the topographical surface (Fig. 1c) was dominant, and the vertical convergence was small (Fig. 1d). The result shows that the convergence of the near-surface atmospheric circulation over eastern flank of TP can make an important contribution to the increase of the surface PVD over the eastern flank of the TP.

 Figure 1 Distributions of (a) potential vorticity density − $\nabla \cdot \left({{V}W} \right)$ change (10–7K s–2); (b) divergence and (c) its horizontal component and (d) vertical component (10–5s–1), averaged over 24–27 January 2008 in the surface layer of the TP. Red and blue lines indicate the 1500- and 3000-m contours of the TP topography, respectively.
2.3 Numerical experiment design

The atmospheric component of the global air–sea coupled model developed by the State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG) of Institute of Atmospheric Physics (IAP), Chinese Academy of Sciences, is used to simulate the persistent winter precipitation case over southern China from 24 to 27 January 2008. In brief, this model is called the Finite-volume Atmospheric Model of the IAP/LASG (FAMIL). The horizontal resolution of FAMIL is 100 km, and the σ–p coordinates are adopted in the vertical direction, which is divided into 32 layers. Li et al. (2017) evaluated the performance of FAMIL and showed that it has good computational capability on the supercomputer platform. During the model integration, the sea surface temperature is updated daily. Two experiments are designed (Table 1):

Table 1 Experiment design (CON: control experiment; SEN: sensitivity experiment)
 Experiment name Spatial resolution Nudging scheme Sensitivity experiment design CON 100 km Nudge: 1–17 January; free integration: 18–31 January No SEN Reduce the near-surface wind speed to half in area A of the plateau. See text for wind speed change in areas B and C.

(1) Control experiment (CON). The integration period is from 1 to 27 January 2008. The experiment is driven by daily observed sea surface temperature. For the atmospheric variables from 1 to 17 January, the 6-h wind, temperature, and pressure fields from ERA-Interim are assimilated into FAMIL by using the global nudging method. The atmospheric assimilation process is switched off on 18 January, and the model is self-integrated for 10 days to 27 January. The purpose of the CON is to examine and validate the simulated results over the extended timescale.

(2) Sensitivity experiment (SEN). This experiment is designed to investigate the effect of reduced PVD forcing over the eastern flank of the TP on the downstream precipitation. From the reanalysis data and the control experiment, it is found that the strongest near-surface convergence over eastern TP occurs on the TP slope of 1500 m above sea level from 24 to 27 January (Figs. 6b, c, e, f). For this reason, in the sensitivity experiment, the wind field in the lowest three model layers (σ = 0.976–1.0) over areas A, B, and C of the TP shown in Fig. 2 are modified as follows: in area A (higher than 1500 m) where near-surface convergence is the strongest over eastern TP, the wind speed is reduced to half of the original wind speed. Due to the prevalence of the westerly wind over the TP in winter, only changing the surface wind speed in area A will cause severe discontinuity in the wind field, resulting in false convergence and divergence in the boundary layer. In order to reduce the discontinuity effect, the wind speed is reduced by 40% in area B (above 3000 m) west of area A; and in area C east of area A (1500-m contour line; 25°–40°N, 110°E), a sponge boundary layer is adopted, where the wind speed changes linearly from 1/2 of the original wind speed to 0. The configuration and integration scheme for other variables in the sensitivity experiment are the same as those in the control experiment.

 Figure 2 Location of the areas with surface wind speed altered in the sensitivity experiment (SEN). A represents the area to the south of 40°N and east of 95°E, where the altitude is equal or larger than 1500 m; B denotes the area to the west of 95°E, where the altitude is higher than 3000 m; and C denotes the area to the east of A, to the west of 25°–40°N, 110°E, where the altitude is less than 1500 m. Blue and red lines indicate the 1500- and 3000-m contours of the TP topography, respectively.
 Figure 6 The 24–27 January mean distributions of (a, d, g, j) near-surface wind (m s–1), (b, e, h, k) divergence (10–6 s–1), and (c, f, i, l) velocity potential (shading; 10–6 m2s–1) and divergent wind (vector; m s–1), calculated from the (a–c) MERRA2 data, (d–f) control run, (g–i) sensitivity run. Panels (j–l) show the difference between control and sensitivity runs. Blue and red contours indicate the 1500- and 3000-m contours of the TP, respectively.
3 Simulations of atmospheric circulation and precipitation

The control experiment is performed to numerically simulate the extreme precipitation process over southern China in January 2008. Here, the simulation results are compared with the observation data in terms of total precipitation, high and low-level circulation, and PVD transport; and the performance of the model simulation is examined.

3.1 Precipitation field

Figures 3a and 3b show distributions of the daily-average precipitation based on station observation and TRMM satellite observation over 24–27 January 2008, respectively. Most areas of southern Yangtze River in China had above 10-mm day–1 precipitation. The rainbands were mainly concentrated in the coastal areas of southern China, and the large-value centers were located near Fujian and Guangdong provinces. Another weaker precipitation center appeared in the south of southeastern TP, with rainfall intensity of 5–10 mm day–1. Figure 3c shows the simulation result. Compared with the observations, the model has captured the precipitation in the coastal areas of southern China well, and has reproduced a good rainband distribution and rainfall amount in the Guangdong–Fujian area. In addition, the simulation of precipitation intensity and location on the southeastern side of the TP is also consistent with observations. However, the simulated range of the overall precipitation is larger than that in the observation. For example, the intensity over the North China Plain is significantly large, and a heavy rainband appears from southern Guangxi to central North China Plain, which only shows weak intensity in the observation. Overall, the model can reasonably reproduce the main distribution of strong precipitation observed in this process.

 Figure 3 Precipitation (mm day–1) during 24–27 January 2008 from (a) station observation, (b) TRMM retrieval, and (c) FAMIL simulation. The thick blue line indicates the 3000-m contour of terrain height.
3.2 High- and low-level circulation fields

This extreme winter precipitation process is caused by the combined effect of various systems under the large-scale circulation background. Therefore, the performance of the model in capturing the large-scale systems and background fields needs to be analyzed first. Figure 4 demonstrates the mean circulation during the rainfall period from MERRA2 reanalysis data (Figs. 4a, c, e) and FAMIL control simulation (Figs. 4b, d, f).

 Figure 4 Distributions of temperature (shading; °C) and wind (vector; m s–1) averaged over 24–27 January 2008 at (a, b) 200, (c, d) 500, and (e, f) 700 hPa. Left columns are from MERRA2 reanalysis data, and right columns are from FAMIL control simulation. The thick blue line indicates the 3000-m contour of TP topography.

As revealed by the MERRA2 data, in the 200-hPa wind field (Fig. 4a), there are two westerly jets near TP, one is in the south and the other is in the north. The south jet is strong and extends to the east of Japan to meet with the north jet. In the temperature field, there is a warm center in the western TP and another one in the eastern part of the Sea of Japan, and they are located on the left side of the jet inlet and outlet areas, respectively. At 500 hPa (Fig. 4c), the southern branch trough is located on the west side of the TP, and a center of the subtropical high is located near 16°N, 135°E; thus, warm and humid southwesterly wind ahead of the trough and northwest of the subtropical high prevail over southwestern and southern China. Meanwhile, the northwesterly wind behind the East Asian trough transports cold air to the south. The situation at the low level (700 hPa, Fig. 4e) is basically similar to that at the high level. The southwesterly wind transports warm and humid air from the Bay of Bengal and the South China Sea to southern China, where it meets the cold air from the north. The middle and lower layers over southern China are all located in front of the southern branch trough, which is conducive to the development of ascending motion and provides necessary conditions for the occurrence of precipitation.

Compared with MERRA2 (taken as observation hereinafter), the simulated warm center at 200 hPa has a smaller range (Fig. 4b) and is weaker. The cold center over western Siberia is also weaker in the simulation, and the blocking is not significant. At 500 hPa (Fig. 4d), the position of the East Asian trough is more eastward and the subtropical high is more northward than the observation, which cause the southwesterly wind to advance further northward. The position of the system at 700 hPa (Fig. 4f) also has a similar shift. However, the simulated circulation exhibits a distinct barotropic structure, which is basically consistent with the observation. In general, the high-level atmosphere above southern China is located ahead of the southern branch trough, which is conducive to the development of ascending motion. The lower layer is affected by the southwesterly wind, and the warm and humid air currents transported from the northwest side of subtropical high and from the front area of the southern branch trough provide favorable water vapor conditions for precipitation. The simulated configuration and strength of the high- and low-level systems are basically consistent with the observations. The model can reproduce the high- and low-level circulation fields of this precipitation process reasonably.

3.3 Plateau surface PVD forcing and transport

It is necessary to investigate if the model can reproduce the observed increase and transport of the surface PVD over TP during the winter precipitation process in January 2008. Figure 5 shows daily distributions of the PVD, pressure, and wind fields on the isentropic surface during 24–27 January from the MERRA2 reanalysis data and FAMIL control experiment. Since the simulated temperature has a cold bias compared with the observation (Fig. 4), corresponding to the variables on the 295-K isentropic surface in reanalysis, the simulated fields on the 290-K isentropic surface are used.

 Figure 5 Evolutions of the distributions of PVD (W) (shading; 10–4s–1), wind (vector; m s–1), and pressure (contour; interval of 50 hPa) from 24 to 27 January 2008. (a–d) are from MERRA2 data at 295-K isentropic surface; (e–h) are from the FAMIL simulation at 290-K isentropic surface.

Figures 5ad show the PVD distribution on the 295-K isentropic surface from the reanalysis data. It can be seen that during the event, there is significant transport of large-value PVD from the TP region to the downstream area. For example, on 24 January (Fig. 5a), the large PVD was located near 105°E over the eastern flank of the plateau. Under the steering effect of westerly wind, the large PVD generated in the TP region was transported downstream along the isentropic surface. In addition, southern China was controlled by an anticyclone on 24 and 25 January. On the northwest side of the anticyclone, the low-level wind field passed through the isobar from the high pressure to the low pressure, implying existence of upward air movement in this area.

Figures 5eh show the distributions of PVD on 290-K isentropic surface in the control experiment. Compared with the observation, the model can reproduce the PVD transport over the TP to the downstream area, but the range is smaller, with weaker strength. The moving speed of the large-value PVD center to the downstream area corresponds with the observation. However, because the intensity of the anticyclone over southern China on 24 and 25 January was stronger than the observation, the southerly wind transport was stronger, the ascending motion was more intense, and the area with large PVD was relatively northward.

By comparing the precipitation, the high and low-level circulation fields, and the PVD transport to the downstream area in the control experiment with the observations, it is found that the model can reasonably simulate the extreme winter precipitation process from 24 to 27 January 2008, and has a good simulation of the location and intensity of the precipitation over southern China and the eastern TP, but the rainbands over some areas are slightly stronger than the observation. Meanwhile, the model can reasonably reproduce the configuration of high- and low-level weather systems, and the low-level southerly wind and water vapor transport are well simulated, which is one of the necessary conditions for precipitation. The model can also simulate the surface PVD increase over the TP region and its downstream transport along the isentropic surface. Because the model has a reasonable simulation of this process, a sensitivity experiment is conducted to further explore the impact of the dynamic forcing produced by the surface PVD change over the TP and its downstream transport on the precipitation.

4 TP surface PVD forcing and its effect in the simulations

The above analysis shows that during the extreme winter precipitation over South China in early 2008, the PVD increased over the TP surface and migrated into the downstream southern China. The TP surface PVD forcing and its downstream propagation have played a significant role in causing the extreme weather and climate. Furthermore, a comparative analysis between the results of the control experiment and those of the sensitivity experiment is conducted below to verify the impact of PVD dynamic forcing over the TP region on the change of downstream precipitation.

4.1 Changes in wind and divergence fields

In the sensitivity experiment, in order to weaken the surface convergence on the eastern flank of the TP, the near-surface wind field is reduced in this area. The MERRA2 reanalysis data (Figs. 6ac) show that during the precipitation period, there is an obvious convergence zone near the surface in area A on the eastern flank of TP, and the velocity potential is represented by two large-value centers located on the eastern flank of the TP and over the oceanic area on the southeast side of the southern China coast. In the control experiment (Figs. 6df), the convergence zone over the eastern plateau has a good correspondence with the observation, and the intensities of the two velocity potential centers are also comparable to the observations, which results in the surface PVD increase mainly in area A on the eastern flank of the TP. In the sensitivity experiment (Figs. 6gi), the wind speed is significantly weakened in the TP region, the convergence center in area A over the eastern TP is not seen, and the large-value area of the velocity potential over the TP also weakens/disappears. These indicate that the design of reducing surface convergence by changing the surface wind speed is effective in the sensitivity experiment. During the study period, northerly wind was prevailing in central and eastern China (Figs. 6a, d), and the PVD forcing over the TP also led to convergence of anomalous northerly and southerly wind near the Yangtze River basin (Figs. 6j1), which is conducive to the development of ascending motion in this area. This matches with the fact derived from historical data that increased rainy and snowy days usually occur in central and eastern China in January (Nan and Zhao, 2012).

4.2 TP surface PVD forcing and its downstream transport

In the sensitivity experiment, the surface convergence over TP is obviously weakened by halving the surface wind speed. In particular, the near-surface convergence area on the eastern flank of the TP is basically indiscernible. What effect does this have on the surface PVD forcing over the TP region and its downstream transport? Figure 7 shows the time–longitude cross-sections of the PVD on the 295-K isentropic surface from control and sensitivity experiments and the difference between them. In the control experiment, there are two significant downstream transports of large-value PVD over the TP during 22–26 January, with stronger intensity appearing over 24–26 January. Among them, the large-value area of PVD is located near 105°E on the eastern flank of the plateau on 24 January, and moved eastward to 115°E in the downstream area on 26 January (Fig. 7a), which corresponds well to the precipitation area. In the sensitivity experiment, there occurs no significant downstream transport of PVD during this period, and only a weaker center of PVD appears near 105°E on 21 and 26 January (Fig. 7b). Compared with the control experiment, the intensity and transport of the PVD are significantly weakened in the sensitivity experiment, which can be clearly seen from the difference between the two experiments (Fig. 7c).

 Figure 7 Time–longitude cross-sections averaged over 30°–35°N for 20–27 January 2008 of the PVD (10–4s–1) at 295-K isentropic surface from (a) control run, (b) sensitivity run, and (c) their difference (control run minus sensitivity run).

The above results indicate that in the early stage of the strong precipitation over southern China, the near-surface convergence over eastern TP leads to a significant PVD increase in this area, and then the PVD moves eastward along the westerly wind on the isentropic surface. The large-value area of ​​PVD is located over southern China during the precipitation period. According to Eqs. (3) and (10), the PVD on the isentropic surface is equal to the absolute vorticity. Therefore, the aforementioned eastward propagation of the PVD on the isentropic surface means that there is an eastward transport of strong absolute vorticity along the westerly belt.

4.3 Low-level water vapor transport

Figure 4 shows that the FAMIL model can reproduce the high and low-level circulation fields of this precipitation process reasonably. Figures 8a, 8b, 8d, 8e, 8g, and 8h show the distributions of geopotential height at 500 and 850 hPa from the control and sensitivity experiment, respectively, as well as the differences between the two. For the geopotential height differences in the middle and low latitudes (Figs. 8g, h), the low pressure is located over the Asian continent, the high pressure is on the eastern coast of East Asia, and the southerly wind is prevalent over southern China. These are very similar to the circulation demonstrated in the years when there are more snowy days in central and eastern China in January in the reanalysis (Figs. 2a, b; Nan and Zhao 2012), indicating that the PVD forcing on the eastern flank of TP in winter can strengthen the southerly wind over southern China, which is conducive to the transport of water vapor to central and eastern China. Figures 8c, 8f, and 8i are the distributions of water vapor flux divergence, relative humidity, and wind field at 700 hPa in control and sensitivity experiments, and the difference between the two. In the control experiment (Fig. 8c), the southwesterly airflow brings a large amount of water vapor from the South China Sea and the Bay of Bengal to southern China. The large-value area of relative humidity extends to the northern part of the North China Plain, accompanied by the convergence of water vapor, and there is an obvious large-value center in the coastal area of southern China. This provides sufficient water vapor for the precipitation. In the sensitivity experiment (Fig. 8f), the southerly wind is much weakened, and the large-value area of relative humidity is more southward and westward. The large-value center of water vapor convergence over the coast of southern China has almost disappeared. Comparing this two experiments (Fig. 8i) finds that the dynamic forcing of the surface PVD increase over the plateau can generate a low-level cyclonic circulation over the eastern TP and enhance the southerly wind on the west side of the northwestern Pacific subtropical high. The enhanced southerly wind brings more water vapor from the South China Sea and the western Pacific to the coastal areas of southern China, with strengthened northward water vapor transport, causing the large-value center of relative humidity to expand northward, thereby expanding the precipitation range and providing sufficient water vapor conditions for the precipitation.

 Figure 8 The 24–27 January mean distributions of (a, d, g) geopotential height at 500 hPa, (b, e, h) geopotential height at 850 hPa, and (c, f, i) relative humidity (contour; interval of 10%) and divergence of water vapor flux (shaded; 10–7 g s–1 cm–1 hPa–1) at 700 hPa. Vector represents wind (m s–1); geopotential height unit is dagpm. (a–c) Control experiment, (d–f) sensitivity experiment, (g–i) their difference (control minus sensitivity). Blue solid curve indicates the 3000-m contour of terrain height.
4.4 Development of ascending motion

In the quasi-geostrophic dynamic framework, as the absolute vorticity advection [ $- { V} \cdot \nabla \left({f + {\rm{\xi }}} \right)$ ] increases with height, the ascending motion (w) develops, and vice versa (Hoskins et al., 1978; Holton, 1992; Zhu et al., 2007), that is, $w \propto \dfrac{\partial }{{\partial z}}\left[ { - { V} \cdot \nabla \left({f + {\rm{\xi }}} \right)} \right] > 0$ .

Figure 9 shows the variation of the PVD advection on the isentropic surface, which is essentially the absolute vorticity advection, at the upper and lower levels in the two experiments during the precipitation period (23–27 January). Figures 9a, 9c, and 9e show the time–longitude cross-sections of the absolute vorticity advection (shading) and its zonal component (contour) averaged along 20°–40°N on the 310-K isentropic surface from the two experiments and the differences between the two. It can be seen that the high-level absolute vorticity advection agrees well with its zonal component, indicating that under the control of the high-level westerly wind, the absolute vorticity advection is dominated by the zonal component. In the control experiment (Fig. 9a), starting from 23 January, there occurs positive absolute vorticity advection near 105°–110°E on the eastern flank of the TP, and it moves eastward during the precipitation period. In the sensitivity experiment (Fig. 9c), the upper layer exhibits negative absolute vorticity advection, which is significantly different from that in the control experiment (Fig. 9e).

 Figure 9 Spatiotemporal evolutions of absolute vorticity advection (shading; 10–9 s–2) and its components (contour; interval: 0.2×10–9 s–2) during 23–27 January 2008: (a, b) control experiment, (c, d) sensitivity experiment, and (e, f) their difference. (a, c, e) Time–longitude cross-sections of absolute vorticity advection and its zonal component averaged over 20°–40°N on the 310-K isentropic surface. (b, d, f) Time–latitude cross-section of absolute vorticity advection and its meridional component averaged within100°–120°E on the 285-K isentropic surface.

Figures 9b, 9d, and 9f are the time–latitude cross-sections of the absolute vorticity advection (shading) and its meridional component (contour) on the low-level 285-K isentropic surface during the same period. In the control experiment (Fig. 9b), distributions of the low-level absolute vorticity advection and its meridional component are basically consistent, indicating that the absolute vorticity advection is dominated by the meridional component. It can be seen that the area south of 35°N over southern China is controlled by negative absolute vorticity advection during the precipitation period, because the southerly wind on the low-level isentropic surface has transported the small-value planetary vorticity from low latitude to high latitude, resulting in negative absolute vorticity advection. In the sensitivity experiment (Fig. 9d), the negative absolute vorticity advection is weaker than that in the control experiment due to the weakening of the southerly wind (Fig. 9f). In general, the dynamic forcing of the TP surface PVD increase in the control experiment can enhance the transport of the upper-level absolute vorticity advection; meanwhile, a low-level cyclone is excited to develop, which causes the strengthening of the southerly wind, and thus enhances the low-level negative absolute vorticity advection. Therefore, the absolute vorticity advection over southern China increases with height and promotes the enhancement of the ascending motion. In the sensitivity experiment, this process is obviously weakened, and the ascending motion attenuates or even disappears.

The above analysis shows that during this period of heavy precipitation in southern China, as a stimulating factor, the near-surface atmospheric convergence on the eastern flank of TP can lead to an increase of the surface PVD. Its downstream propagation along the westerly belt causes an enhancement of the high-level positive absolute vorticity advection and also stimulates the low-level cyclone. The cyclonic circulation enhances the low-level southerly wind over southern China, which is conducive to the northward transport of warm and humid airflow, providing water vapor for the generation of precipitation. On the other hand, by strengthening the low-level negative absolute vorticity advection in southern China, a dynamic background that the absolute vorticity advection increases with height in southern China is formed. It is this cooperative mechanism between the high and low-level absolute vorticity advection that promotes the development and enhancement of the ascending motion in southern China during the precipitation period.

4.5 Occurrence and development of the heavy precipitation

The distributions of daily precipitation and vertical velocity at 500 hPa from the two experiments over 24–27 January are shown in Fig. 10. Figures 10ad show the ascending motion and precipitation distributions from the control experiment on each day from 24 to 27 January, respectively. It can be seen that the precipitation area corresponds well with the ascending motion area. At the low latitude (23°N, 110°E) on 24 January, the vertical velocity center (Fig. 10a) is formed due to the forcing generated between the high-level positive absolute vorticity advection (Fig. 9a) and the low-level negative absolute vorticity advection (Fig. 9b) in this area; in the meantime, precipitation is concentrated over southern China. On 25 January, the high-level positive absolute vorticity advection and the low-level negative absolute vorticity advection move to the north of 33°N and east of 110°E respectively, and the corresponding vertical velocity center and rainband also move northeastward to the area of Hunan Province and the North China Plain to form two large-value centers (Fig. 10b). On 26 January, with the continuous eastward movement of the high-level positive absolute vorticity advection and the northward extension of the low-level negative absolute vorticity advection, the vertical velocity center and precipitation center also extend from southern China to the North China Plain and the Bohai Sea (Fig. 10c). On 27 January, the rainband and the large-value center move basically into the sea (Fig. 10d).

 Figure 10 Daily evolutions of the distributions of precipitation (shaded; mm day–1) and vertical velocity at 500 hPa (contour; interval: 2 Pa s–1) during 24–27 January 2008 from (a–d) control experiment, (e–h) sensitivity experiment, and (i–l) their difference. Red contour indicates the 3000-m contour of terrain height.

In the sensitivity experiment (Figs. 10eh), the absolute vorticity advection in southern China decreases with height (Figs. 9c, d), southern China is in general controlled by subsidence and no precipitation occurs on 24 and 25 January. On 26 January, there is only weak ascending motion and precipitation over Yunnan, Sichuan provinces and the eastern flank of the TP, and the large-scale precipitation in the coastal areas of southern China and the Guangxi Region to Shanghai area that occurs in the control experiment is not seen. This is more apparent in the difference plots (Figs. 10i1). The above results indicate that the surface PVD increase on the eastern flank of the TP and its eastward propagation have a very important influence on the precipitation in the downstream area during this whole period.

5 Conclusions and discussion

Based on the potential vorticity theory, a numerical simulation and a sensitivity experiment are performed to study causes of the extreme precipitation over southern China in early 2008. The results demonstrate that the increasing of surface PVD forcing resulted from the surface atmospheric convergence on the eastern flank of the TP, together with the PVD downstream transport, leads to a dynamic forcing effect on the occurrence and deve-lopment of the extreme precipitation over southern China in January 2008. The following conclusions have been obtained.

Based on the FAMIL atmospheric model forced by daily observed sea surface temperature, we have applied the sponge nudging method to assimilate ERA-Interim (taken as observation) data into the initial fields over 1–17 January 2008, and carried out a 10-day control simulation and a sensitivity experiment starting from 18 January for the extreme winter precipitation case. The simulation results show that although the rainbands over the North China Plain and the Guangxi–Shandong area are slightly strong, the model has simulated the precipitation location and intensity in the coastal areas of southern China and the eastern part of the TP well. This means that it has in general reproduced the extreme precipitation process over southern China in early 2008. In the circulation field, the high- and low-level weather systems and the downstream transport of the near-surface PVD over the eastern TP are also well reproduced. On the basis of these, a sensitivity experiment is performed to verify and ascertain the influences of the increased TP surface PVD and its downstream transport on the extreme precipitation event and the new mechanism of the TP impact on the extreme weather process.

The near-surface convergence on the eastern flank of TP can increase the surface PVD. Since the elevated TP intersects with the isentropic surfaces in the lower troposphere, the increased PVD on the TP’s eastern flank thus forms a PVD forcing source in the boundary layer. This PVD source propagates eastward along the westerly belt on the isentropic surface, providing a positive absolute vorticity advection for the downstream region in the middle and upper troposphere, thus creating a dynamic background for the upper-level divergent pumping, favoring the development of ascending motion and precipitation in the downstream regions.

In the lower troposphere, the surface PVD forcing over the TP region can also generate a cyclonic circulation, which strengthens the southerly wind in southern China. On the one hand, it promotes the transport of warm and humid air from the ocean to southern China, providing water vapor conditions for the generation of precipitation. On the other hand, the enhancement of the southerly wind also strengthens the transport of the negative absolute vorticity advection in the lower layer. In combination with the enhancement of the positive absolute vorticity advection in the upper layer, the coupling of absolute vorticity advections in both high and low layers is conducive to the development and strengthening of the ascending motion, thereby promoting the occurrence of precipitation in the downstream areas.

This study has explored the influences of the dynamic forcing due to the surface PVD increase over the TP region and its advection on the extreme winter precipitation over southern China in early 2008. We thus propose a new mechanism about the TP impact on the extreme weather process. However, this is only one case study, and the conclusions have yet to be confirmed by more case studies. Due to the weak surface sensible heating over the TP in winter, the contribution of the diabatic heating to the PVD in the near-surface layer is small and neglected. The analysis in this study only deals with the contribution of the divergence term in the PVD equation. For the summer half-year, the surface sensible heating over the TP is very strong, the contribution of the diabatic heating to PVD in the near-surface layer is not negligible, and the impact of the diabatic heating and friction on the surface PVD change needs to be further investigated in future work.

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