Budget Analyses of Precipitation and Energetics Associated with Torrential Rainfall Events over Zhejiang, Fujian and Jiangxi

Four cases of heavy rainfall over Zhejiang, Fujian and Jiangxi during mid-June are simulated by the two-dimensional (2D) cloud-resolving model using the large-scale forcing data derived from the 6-hourly ERA-Interim data set. The simulations are used to conduct budget analysis of precipitation and energetics associated with the development of torrential rainfall. Surface rainfall is dominated by water vapor convergence (QWVF) in water vapor related surface rainfall budget and heat divergence (SHF) in thermally related surface rain budget. The high linear correlation coefficients between water vapor related precipitation efficiency (PEWV) and heat related precipitation efficiency (PEH) stem from the statistical similarities between QWVF and SHF . The diurnal variations of surface rainfall correspond to the upward motions. An energy conversion efficiency is defined as the ratio of perturbation kinetic-energy to convective available potential energy to measure how efficiently the secondary circulations develop under the consumption of the convective available potential energy. The diurnal variations of energy conversion efficiency generally are in phase with the rainfall, indicating importance of interaction between dynamics and water vapor in build-up of rainfall peaks. (Citation: Yang, X., and X. Li, 2018: Budget analyses of precipitation and energetics associated with torrential rainfall events over Zhejiang, Fujian and Jiangxi. SOLA, 14, 185−191, doi: 10.2151/sola.2018-033.)


Introduction
Rainfall is a key component in understanding atmospheric circulations and hydrological cycles of the Earth system. Ding et al. (2006) summarized the rainy season in China generally begins with the onset of the summer monsoon in the South China Sea then ends with its withdrawal. It is widely recognized that a heavy-rain band moves northward from South China to eastern China with the northward advance of summer east-Asian monsoon (Feng et al. 2001;Chen 2004;Ramage 1971;Tao and Chen 1987;Gao and Xu 1962).
The structure of jet streams is favorable to the development of convection (Ding 1992). Main rain-bearing systems during monsoon period are the mesoscale vortices near the meiyu front (Gao and Xu 2001;Dong and Zhao 2004). Chen and Yu (1988) and Sampe and Xie (2010) argued that low-level westerly jet is important to the development of meiyu rainfall. Matsumoto et al. (1971) and Ninomiya (2000) revealed that meiyu frontal rainfalls reach their maxima at the south of the upper level jet stream. The development of eddies near the front zone are also related to the cold incursion in the upper levels and convergence in the lower levels (Ni and Zhou 2004). Zhai et al. (2014) found a relationship between rainfall peak and moisture convergence in a meiyu event during mid-June in 2011.
East Asian rainy season starts from April-June over Southern China (pre-summer heavy rainfall) and over Jiang-Huai areas during June-July (meiyu torrential rainfall) (Ding and Chan 2005). Many studies argued that this rain band jumps suddenly into Yangtze River Valley from south China (Wang and Fan 1999;Ding and Wang 2008). However, Huang et al. (2016) found an intensive rainfall center over Zhejiang-Fujian-Jiangxi region (ZFJ; see Fig. 1 in this study) when the rain band moves northward into Yangtze River Valley from south China in mid-June (pentad 33−34), filling the gap between pre-summer rainy season over south China and meiyu torrential rainfall. According to the official statistics, heavy rain during this period causes landslides and floods, leading to sever economic losses and casualties in this region. The rainfall in most part of ZFJ over 200 mm during 12 June to 15 June in 1998 (Jiang and Ni 2003). The surge in river systems due to persistent heavy rain caused 103 deaths and economic losses over 1,700 million dollars in June 1998. In June 2010, the daily rainfall of over 100 mm led to landslides, floods and power outages over southern Jiangxi. Hence, quantitative analysis and accurate forecasting for the heavy rain events over ZFJ are very important for governmental decision making for the disaster prevention.
Compared to studies of meiyu torrential rainfall, heavy rain events over ZFJ during mid-June have been seldom studied. Shen and Zhu (2007) analyzed a heavy rain event in 2005 over ZFJ using MM5. Zhang et al. (2012) analyzed the large-scale circulation of the heavy rain events over ZFJ in June 2011.
The objective of this study is to analyze the torrential rainfall events in ZFJ from the view of surface rainfall budget, precipitation efficiency and energy conversion. Four rainfall cases are simulated by a two-dimensional cloud-resolving model and the simulations are validated with the observational data and used for the analysis of rainfall in ZFJ. The model setups and large-scale forcing data are briefly discussed in the next section. The results are presented in Section 3. A summary will be given in Section 4. 121°E; Fig. 1). Observed data of daily precipitation amount is provided by China International Ground Exchange Station, which is assessable at http://cdc.nmic.cn/ including information of quality control. The large-scale forcing data were linearly interpolated into the 12-s interval and imposed horizontally uniformly in the entire model domain at each time step. The simulated rain rates generally follow the observed rain rates (right panel in Fig. 2). The root mean square differences in rain rate between simulations and observations show 23. 2%, 24.9%, 31.1% and 26.7% of standard deviation in 1994, 1998, 2000 and 2002, respectively. The phrases of simulation and observation generally match each other. Thus, the model simulations basically capture the observed evolution of surface precipitation.

Results
From Appendix, the water vapor related surface rainfall budget can be written as Here, the surface rain rate (P S ) is determined by local atmospheric drying (Q WVT > 0)/moistening (Q WVT < 0), water vapor convergence (Q WVF > 0)/divergence (Q WVF < 0), surface evaporation (Q WVE ), and hydrometeor loss/convergence (Q CM > 0) or hydrometeor gain/divergence (Q CM < 0). Model domain mean of Q CM denotes hydrometeor change because hydrometeor convergence/divergence vanishes as a result of lateral periodic boundaries.
Thermally related surface rainfall budget can be expressed by Here, the surface rain rate (P S ) is determined by local atmospheric warming (S HT > 0)/cooling (S HT < 0), heat divergence (S HF > 0)/convergence (S HF < 0), surface sensible heat (S HS ), latent heat due to ice-related progress (S LHLF ), radiative cooling (S RAD > 0)/ anelastic approximation uses periodic lateral boundaries. Free-slip conditions are applied in the upper boundary. The model contains prognostic equations for heat, water vapor, cloud hydrometeor, perturbation zonal and vertical momentum over a horizontal domain of 768 km. There are thirty-three vertical levels stretched from the surface to 42 hPa. The horizontal grid resolution is 1.5 km while vertical grid resolution is 200 m near the surface and 1 km near 100 hPa. A 12-second time step is used for stable computations of the model dynamics. The cloud microphysical parameterization schemes are from Lin et al. (1983), Hobbs (1983, 1984), Tao et al. (1989) and Krueger et al. (1995). Radiative parameterization schemes from Chou et al. (1991Chou et al. ( , 1994Chou et al. ( , and 1998) are furnished. Sub-grid scale turbulence closures derived from Klemp and Wilhelmson (1978). Huang et al. (2016) analyzed the observational precipitation data from 1971 to 2013 and found 7 strong precipitation years (1982, 1994, 1998, 2000, 2002, 2005 and 2010). Among 7 years, four years (1994, 1998, 2000 and 2002) reveal consistencies between observed rainfall and upward motions from the reanalysis data, whereas three years (1982, 2005 and 2010) show inconsistencies between observed rainfall and upward motions (not shown). Since the cloud-resolving model simulations require large-scale forcing (vertical velocity) due to limited model domain (e.g., 768 km in this study), the inconsistencies imply that the model with the large-scale forcing is not capable of simulating rainfall properly. Thus, only four precipitation events in 1994, 1998, 2000 and 2002 were simulated in this study. The twodimensional cloud-resolving model can be used in this study because the previous studies have showed the similarities in the collective thermodynamic feedback effects and vertical transports and rainfall between the two-dimensional and three-dimensional cloud-resolving model simulations (e.g., Tao and Soong 1986;. The recent results from the two-dimensional cloudresolving model simulations can be found in Li and Gao (2016).
The large-scale forcing data required in this model is derived from the 6-hourly ERA-Interim data set. The vertical velocity prescribed for model integrations is shown in Fig. 2  heating (S RAD < 0), and hydrometeor loss/convergence (Q CM > 0) or hydrometeor gain/divergence (Q CM < 0). S LHLF is significantly smaller than other terms (see Appendix) and we thus will not discuss it in this study. The model domain mean surface rainfall budgets in 4 cases are shown in Fig. 3 (water vapor related budget) and Fig. 4 (thermally related budget). The four rainfall cases reveal that the mean rainfall corresponds mainly to the mean water vapor convergence (Q WVF > 0) in water vapor related surface rainfall budget (Fig. 2) and heat divergence (S HF > 0) in thermally related surface rainfall budget. The means of surface evaporation (Q WVE ), surface sensible heat flux (S HS ), radiation (S RAD ) and local hydrometeor change (Q CM ) are negligibly small, compared to Q WVF and S HF . The changes in P S are also associated with those of Q WVT and S HT . For example, the additional surface rainfall significantly corresponds to local atmospheric drying during 19−21 June 1994 (Fig. 3a), 9−14 June 1998 (Fig. 3b) The relationship between water vapor related precipitation efficiency (PEWV) and thermally related precipitation efficiency (PEH) is shown in Fig. 5a. Statistically, PEH nearly equals to PEWV in 1998, whereas PEWV is larger than PEH in the other three years because S HF contributes more to precipitation source comparing with Q WVF (Fig. 5b). The linear correlation coefficients are 0.84 for 1994, 09.7 for 1998, 0.96 for 2000 and 0.86 for 2002. The high linear correlation coefficients between PEWV and PEH stem from the statistical similarities between Q WVF and S HF in 4 cases (Fig. 5b). Figure 5c shows that the other rainfall sources excluding Q WVF and S HF contribute more to precipitation source in 2000 and 1998 than in 1994 and 2002, displaying larger scattered distributions than water vapor convergence versus heat divergence.
Precipitation is intimately associated with secondary circulations, which can be measured by perturbation kinetic energy (K¢). The source of K¢ can be convective available potential energy (CAPE), which is calculated in pseudo-adiabatic process following Li et al. (2002). Thus, efficiency of potential energy conversion (EPEC) can be written as, where,  In Eq. (3a), u and w are zonal and vertical components of wind, respectively; overbar stands for model domain mean; prime stands for a perturbation from model domain mean; Z b and Z t stand for the heights of the top and the bottom of the model atmosphere. The EPEC ranges generally from 0 to 10% with occasions of over 20−30% (Fig. 6), which is consistent with the efficiency of atmosphere thermodynamic engine in tropical natural convection of 10% estimated by Rennó and Ingersoll (1996). The EPEC of over 30% on 19 June 2000 may result from prevailed downward motions before upward motions were restored. The downward motions reduce atmospheric water vapor and thus CAPE. The restored upward motions increase K¢ significantly, while they do not produce large precipitation in a dry atmosphere.
Considering the similarity of PEWV and PEH, we only discuss PEWV in the latter sections. Figure 6 shows the evolution of P S , PEWV and EPEC in the 4 cases. On the onset stage of the rainfall events, PEWV and Epec increases as P S increases on 8−9 June 1994, 12−14 June 1998, 4−5 and 18−19 June 2000, 10−11 and 13−14 June 2002. In this stage, the secondary circulations grow rapidly when CAPE is consumed. As a result, EPEC increases rapidly.
We also notice some abnormal EPECs. The EPEC on 19 June 1994 increases to 5% while P S and PEWV decrease. The downward motions occur below 800 hPa (Fig. 2a1), which leads to atmospheric drying and reduces CAPE. The dry atmosphere reduces precipitation as well as its efficiency, while it increases EPEC. Figure 7 shows the diurnal variations of P S , rainfall source (sum of local atmospheric drying, water vapor convergence, surface evaporation and hydrometeor loss), PEWV and EPEC and the imposed large-scale vertical velocity in the 4 cases. As the trend of energy conversion in rainy period is opposite to rainfree period, main rainy parts of the simulations of 2000 and 2002 are analyzed in this section. The diurnal cycle of rainfall generally corresponds to that of large-scale upward motions. PEWV does not show strong diurnal signals in 1994, 1998 and 2002, while it reveals a strong diurnal cycle in 2000. The diurnal variation of P S is consistent with the satellite observations with a peak in the afternoon (Chen et al. 2012).
Both rainfall and its source increase in the morning and reaches peak in the afternoon, which causes less regular diurnal variation of PEWV. But the diurnal variation of rainfall is intimately associated with EPEC because the rainfall is dynamically controlled by growth of the secondary circulations. We also notice the shifting of P S and EPEC during 1400−2000 Local Standard Time (LST) in Fig. 7c1. In 2000, the K¢ reaches its maximum around 1800 LST after the rainfall peak at 1400 LST 9 June. The rainfall is little despite the large EPEC because rainfall source decays ahead.
Actually, a rainfall event cannot develop without enough rainfall source or the active secondary circulations. Weak water vapor convergence with high EPEC produces little rainfall. But this process can be very efficient, such as the early morning in 2002. If the rainfall source develops ahead of EPEC, the addition of rainfall is minimal, causing the change of PE. The fluctuation of PEWV mainly stems from the phrase difference between EPEC  and rainfall source. There are four asynchronous scenes: rainfall source develops ahead of EPEC; the source stays large when EPEC starts to decay; EPEC develops ahead of rainfall source; EPEC stays large when EPEC starts to decay. The first two scenes show the decrease of PEWV, whereas the latter two show the relatively large PEWV. When rainfall source increases before EPEC does, the water vapor from the influx could not be consumed for the production of rainfall. For instance, P S is maintained small because of the low-level EPEC, while rainfall source increases during 0600− 0800 LST in 1994. PEWV restarts to increase when EPEC grows after 0800 LST as rainfall source keeping increasing. The same scene happens during 0800−1000 LST in 2002. With a decrease in EPEC during 0500−0700 LST, the diurnal variation of PE in 2000 tells similar scenario. When EPEC decays before rainfall source does, PEWV drops significantly during 1200−1500 LST in 1994. The same scenario occurs during 1400−1900 LST in 2002 and 1300−1500 LST in 1998. These two kinds of asynchrony produce a tiny addition even a decrease of P S while rainfall source increases largely, which leads to a sudden decrease of PEWV during this period.
When EPEC develops ahead of rainfall source, the addition of rainfall is ignorable despite the high EPEC and the increasing PEWV, as mentioned previously during the early morning in 2002. When rainfall source decays before EPEC does during 1400− 2000 LST in 2000, PEWV sustains high while P S reduces. With these two kinds of asynchrony, high PEWV can be maintained because the active secondary circulations can consume nearly all the water vapor supply for the production of rainfall.
On the other hand, P S and PEWV augment significantly when rainfall source and EPEC grow synchronously from 0800 LST or so until noon (e.g. from 0800 LSTto 1200 LST in 1994, 0700 LST to 1300LST in 1998, 0800 LST to 1300LST in 2000. During this period, rainfall source increases rapidly and the growing secondary circulation is strong enough to transport the water vapor into rainfall. Thus, P S increases with increasing PE.
From the view of rainfall budget, high PEWV means nearly all the terms in the rainfall budget contribute to the production of rainfall. And the decrease in PEWV is related with hydrometeor divergence and local atmospheric moistening. The significant decrease in water vapor convergence also causes the significant decrease in PEWV. Local atmospheric drying, water vapor convergence and hydrometeor convergence decrease when EPEC and rainfall source reduce synchronously.

Summary
The budgets of water vapor, heat and energe associated with torrential rainfall events during mid June in the four strong rainfall years (1994, 1998, 2000 and 2002) are investigated by analyzing simulation data from the two-dimensional cloud-resolving model. The mean rainfall is largely associated with the mean water vapor convergence in water vapor related surface rainfall budget and heat divergence in thermally related surface rain budget for all the rainfall events. The additional rainfall corresponds to local atmospheric drying in water vapor related surface rainfall budget and to local atmospheric warming in thermally related surface rainfall budget in 1994, 1998 and 2000. In contrast, the water vapor convergence and heat divergence are respectively used to moisten and cool local atmosphere in 2002, which decreases rainfall.
The precipitation efficiencies defined in water vapor related surface rainfall budget (PEWV) and defined in thermally related surface rainfall budget (PEH) in 1998 are similar, whereas PEWV is larger than PEH because heat divergence (S HF ) contributes more to precipitation source compared to water vapor convergence (Q WVF ) in the other years. The statistical analysis with daily simulation data reveals the high linear correlation between PEWV and PEH, steming from the strong statistical similarities between Q WVF and S HF . 60 (0) 70 (1) 80 (2) 90 (3) 100 (4 Precipitation is associated with the secondary circulations measured by perturbation kinetic energy (K¢). CAPE is converted into K¢ to develop the precipitation systems. The ratio of K¢ to CAPE can be defined as the efficiency of potential energy conversion (EPEC). The relationship between PE and EPEC is pertinent with the stage of rainfall. On the onset stage of the rainfall event, PEWV increases as P S increases. EPEC can increases rapidly during this period because secondary circulations grow rapidly when CAPE is consumed. On the mature stage of the rainfall event, PEWV sustains high. EPEC is relatively stable during this period probably due to the fact that the consumption of CAPE by K¢ is compensated by water vapor convergence.
The diurnal variation of surface rainfall is associated with that of upward motions. PEWV generally does not show any strong diurnal signals because both rainfall and rainfall source reveal strong diurnal cycles, while it shows a diurnal cycle in 2000. Unlike PEWV, EPEC reveals strong diurnal signals. The peaks of EPEC are in phase with rainfall in 1998 and 2002, but the peaks of EPEC lag the rainfall in 1994 and 2000 probably because the growth of the secondary circulations with the consumption of water vapor by rainfall peak fails to build up the peak of rainfall sources.