Budget analysis of mesoscale available potential energy in a heavy rainfall event over the eastern Tibetan Plateau

Kuo Zhou ,Lingkun Ran ,?,Yi Liu ,Xiuxia Tian

a Laboratory of Cloud-Precipitation Physics and Severe Storms, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China

b College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing, China

c Key Laboratory of Middle Atmosphere and Global Environment Observation, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China

d Handan Meteorological Bureau, Handan, China

Keywords:Heavy rainfall Available potential energy Budget analysis Vertical motion

ABSTRACT Using model simulated data, the distribution characteristics, genesis, and impacts on precipitation of available potential energy (APE) are analyzed for a heavy rainfall event that took place over the eastern Tibetan Plateau during 10–11 July 2018.Results show that APE was mainly distributed below 4 km and within 8–14 km.The APE distribution in the upper level had a better correspondence with precipitation.Northwestern cold advection and evaporation of falling raindrops were primary factors leading to positive anomalies of APE in the lower level,while positive anomalies of APE in the upper level were caused by a combination of thermal disturbances driven by latent heat and potential temperature perturbations resulting from the orography of the Tibetan Plateau.Budget analysis of APE indicated that APE fluxes and conversion between APE and kinetic energy (KE) were the main source and sink terms.Meridional fluxes of APE and conversion of KE to APE fed the dissipation of APE in the lower level.Vertical motion enhanced by conversion of APE to KE in the upper level was the major factor that promoted precipitation evolution.A positive feedback between APE and vertical motion in the upper level generated a powerful correlation between them.Conversion of KE to APE lasted longer in the lower level,which weakened vertical motion; whereas, northwestern cold advection brought an enhanced trend to the APE,resulting in a weak correlation between APE and vertical motion.

1.Introduction

Atmospheric energetics analysis is conducive to studying the evolution of synoptic systems and energy conversion among systems ( Gao and Li, 2007 ).Gao et al.(2005) found that the storage and conversion of atmospheric energy has an important impact on weather change at middle latitudes.A study of heavy rainfall in Sichuan by Ge et al.(2013) indicated that kinetic energy (KE) converted to eddy potential energy during the development stage of the heavy rainfall, and the conversion tended to slow in the maintenance and dissipation stage.Lorenz (1955) defined available potential energy (APE) as the difference between the total potential energy and minimum total potential energy.After APE was proposed, works around energy budget analysis on the generation, conversion, and dissipation of APE and KE developed rapidly ( Price, 1975 ;Demott and Randall, 2004 ).Derivation of energy equations under nonhydrostatic conditions was proposed by Dutton and Johnson (1967) .Iwasaki and Toshiki (2001) deduced rate equations of KE and APE under isentropic coordinates.Energy diagnostic equations raised by Murakami and Shigenori (2011) consisted of mean energy equations,eddy energy equations, and an extra interaction equation.Diabatic processes are equally important to APE ( Lorenz, 1955 ; Lin and Smith,1980 ).Vincent et al.(1977) suggested that longwave radiation is the primary factor for APE formation during the initial stage of an extratropical cyclone, but latent heat release becomes the main factor during the mature stage.A study of energy analysis within a mesoscale vortex by Li et al.(2017) showed latent heat from condensation led to an increase of eddy APE at the middle tropopause, and then the eddy APE was transported upwards by vertical motion, resulting in an accumulation of APE in the upper level.The concept of moist APE was proposed by Lorenz (1978),based on which Mchall (1990) redefined APE with equivalent potential temperature.Peng et al.(2014) mentioned that APE defined with equivalent potential temperature might enhance the effect of latent heat to some extent, and therefore they modified the budget equation of moist APE and found that the main source of moist APE is the conversion from horizontal KE.The KE equations and potential energy equations of three scales were derived by Shen et al.(2018) through dividing physical quantities into the large-scale background field, meso-

α

scale, and meso-micro-

β

scale.

APE converts to KE, which further promotes the development of the rainfall.In other words, the analyses of APE are treated as a precursor of the rainfall.Thus, the derivation of the APE equation is specified based on former studies in this paper.Then, the primary factors affecting mesoscale APE and effects of APE on precipitation evolution are discussed through a heavy rainfall case in eastern Tibetan Plateau.

2.Data and methods

2.1. Rainfall case

A heavy rainfall occurred in eastern Tibetan Plateau during 9–11 July 2018, leading to a flood disaster and great losses to Sichuan and Shanxi provinces.The precipitation was generated over the southeastern Tibetan Plateau, Sichuan Basin, and southern Shanxi Province at 0000 UTC 9 July.The rainfall gradually developed over eastern Sichuan Province at 0300 UTC 10 July.Scattered precipitation merged into a rain belt that extended from southwest to northeast at 1300 UTC 10 July when the precipitation reached its mature stage, lasting until 2200 UTC 10 July.Then, the rainfall started to fade, dissipating at 1200 UTC 11 July.

The precipitation was generated under favorable conditions of lower and upper systems.The 200-hPa jet stream center was over central Inner Mongolia at 0000 UTC 8 July (Fig.S1a), and the rainfall area lay on the right of the upper jet stream entrance, which led to divergence flow.The 500-hPa trough at Lake Baikal deepened and extended to the southwest forming an enclosed low vortex (Fig.S1b).The subtropical high extended westwards and reached the Asian mainland at 0600 UTC 9 July.Northwestern flow brought by the low vortex and southeastern flow from the subtropical high were favorable for the generation of rainfall.Affected by the low vortex and subtropical high, a convergence belt was formed by the northwestern flow and southern flow from the South China Sea at 700 hPa (Fig.S1c).Divergence in the upper level and convergence in the lower level offered a favorable environment for the heavy rainfall.

2.2. Numerical simulation

The rainfall process was simulated using the WRF model.The model’s initial and lateral conditions were provided by NCEP GFS (resolution: 0.5° × 0.5°).WRF’s horizontal spacing was 3 km (801 × 711 grid points) with a total of 51 vertical levels and the model top fixed at 50 hPa.The numerical simulation was initialized at 0000 UTC 9 July 2018 and the results were output every 30 min with a total simulation length of 72 h.The parameterization schemes used in the model setup are listed in Table 1 .

The simulated and observed hourly precipitation distributions are given in Figure S1(d-g).The observed data were from national automatic weather stations and the CMORPH hourly merged precipitation grid dataset.Precipitation centers located at Guangyuan and Mianyang City of Sichuan Province were simulated successfully.Hourly precipitation near (32.5°N, 106°E) reached 70 mm.The simulated rain belt extended from northeast to southwest (Figure S1(f, g)), which was essentially in agreement with the observation except for much more precipitation in Ziyang City.In short, the numerical simulation successfully presented the generation, development, movement and dissipation processes of the observed rain belt.Therefore, based on the simulated results, analyses of APE were performed to reveal the variation characteristics of APE during the heavy rainfall event and the effects of APE on the precipitation evolution.

Table 1 Configuration of model parameterization schemes.

2.3. Mesoscale APE and its budget equation

For mesoscale systems triggering heavy rainfall, any physical quantity can be divided into large- and mesoscale fields.Mesoscale APE is defined as follows:

Table 2 Physical meanings of the source and sink terms of the mesoscale APE tendency equation.

Mesoscale APE and the terms of the mesoscale APE tendency equation were calculated to analyze the spatial and temporal distribution of mesoscale APE together with its budget analyses.All discussions of APE below refer to mesoscale APE.

3.Spatial and temporal distribution characteristics of mesoscale APE

3.1. Structural features of mesoscale APE

The APE distribution at 2 km is presented in Fig.1 (a, b).As is shown,APE accumulates in northern Sichuan Province at 1200 UTC 10 July.Precipitation strengthens gradually and stays in the development stage at this time ( Fig.1 (a)).Positive anomalies of APE lie along the eastern Tibetan Plateau at 1600 UTC 10 July, with the associated rain belt extending from the northeast to southwest ( Fig.1 (b)).In the late rainfall period, the precipitation dissipates along with the fading of APE.It is shown that, to some extent, precipitation has a correspondence with the horizontal distribution of APE positive anomalies.

From the vertical distribution ( Fig.1 (c, d), positive anomalies of APE mainly distribute below 4 km and within 8–14 km.Relatively speaking,positive anomalies in the lower level are stronger than those in the upper level, while positive anomalies in the upper level have a better correspondence with precipitation.Positive anomalies of APE in the lower level are located at 105°–106°E ( Fig.1 (c)).Vertical motion over the rain area is stronger.Precipitation develops over the lower APE anomalies at 1600 UTC, and upper-level APE accumulates rapidly ( Fig.1 (d)).Vertical motion develops fast under the effects of APE in the upper and lower level.APE positive anomalies in the upper level are obvious in the whole precipitation mature stage.APE positive anomalies in the lower level are still stronger in the precipitation dissipation stage, but upper level anomalies almost disappear accompanied by weak vertical motion.

Comparing the integral average value of APE with hourly accumulated precipitation in terms of time series, precipitation is generated after APE has accumulated for a while ( Fig.1 (e)).They have a similar evolution trend and the correlation coefficient (0330 UTC 10 to 0330 UTC 11 July 2018) reaches 0.575.Precipitation systems cannot develop without vertical motion.Comparing APE with vertical velocity in terms of time series, they have a larger phase difference in the lower level( Fig.1 (f)).Before precipitation, APE develops vigorously in the lower level, while the upper level APE is weak during 0000–0300 UTC 10 July( Fig.1 (g)).The phase distribution of APE and vertical velocity in the upper level is relatively close ( Fig.1 (g)), both of which have stronger positive anomalies in the developing and mature stage of precipitation.Correlation coefficients between APE and vertical velocity below 6 km are relatively small or even negative.Higher correlations occur within 6–14 km.Maximum values of correlation coefficient are at 14 km (Table S1), reaching up to 0.658.

Thus, APE in the lower level already exists before precipitation and stays strong throughout the whole rainfall period.Close relationships between the evolution of APE and precipitation present in the upper level.Causes of the origin of APE are further discussed below.

3.2. Origin of mesoscale APE positive anomalies

Further analysis is carried out to determine the factors responsible for the formation of the APE positive anomalies.Wind and temperature fields at 2 km are shown in Fig.2 (a).The Sichuan and Chongqing areas are dominated by southern warm and moist currents, leading to a higher temperature.Northwestern flow gradually strengthening to the south has a cooling impact on the northwestern precipitation area.From the aspect of the circulation field, the temperature drop resulting from northwestern cold advection arouses the potential temperature perturbations, further leading to APE positive anomalies in the lower level.

As shown in Fig.2 (b), negative anomalies of potential temperature perturbations caused by northwestern cold advection exist between 105°E and 106°E at 1200 UTC 10 July, which correspond with APE positive anomalies in the lower level.Meanwhile, a downdraft between 105°E and 107°E exists over the precipitation area ( Fig.1 (c)).Evaporation effects from dropping precipitation particles enhance negative potential temperature perturbations in the lower level.Upper air is heated by latent heat release and the released latent heat can reach up to 14 km ( Fig.2 (c)).The potential temperature profile shows that potential temperature perturbations aroused by the orography propagate upwards and superpose upon thermal disturbances caused by latent heat( Fig.2 (d)), leading to potential temperature perturbations strengthening over the precipitation area ( Fig.2 b)), also corresponding with APE positive anomalies in the upper level.

4.Budget analyses of mesoscale APE

when an air parcel moves upwards, the vertical velocity of the air parcel will be strengthened by the upward buoyancy, indicating the conversion of APE to vertical KE is significant and the upward motion is enhanced.Positive anomalies of P6 exist below 5 km and the magnitude is comparable to P2, indicating the conversion of vertical KE to APE.Thus,vertical motion is weakened in the lower level.The intensities of P4,P5, P7, and P8 are relatively weak during the rainfall process.

Fig.3 (e and f) shows time series of the source and sink terms in the lower and upper levels.All terms are small at 2 km before precipitation during 0000–0300 UTC 10 July.P6 presents slight negative anomalies,implying the conversion of APE to KE, which is favorable for the generation and development of precipitation.Positive anomalies of P2 are gradually intensified to supplement APE in the lower level during 0800 UTC 10 to 0400 UTC 11 July.P6 converts to positive anomalies after 0800 UTC 10 July and the positive anomalies are dominant until 1600 UTC 10 July.Thus, KE converts to APE.Positive anomalies of P6 alternate with negative anomalies after 1600 UTC 10 July, but negative anomalies occur more frequently.It is obvious that P2 presents positive anomalies during 1600 UTC 10 to 0800 UTC 11 July, while the phases of P1 and P3 are almost contrary to P2, implying the negative effects of zonal and vertical fluxes of APE that bring APE upwards through strengthened updrafts.All terms decrease closely to 0 during 0800 UTC to 1200 UTC 11 July.

P6 presents strong negative anomalies in the upper level during the most precipitation stage ( Fig.3 (f)).The phase of the total source and sink term almost synchronizes with P6, indicating the dominant position of the conversion process of APE to KE.All terms are close to 0 before 0700 UTC 10 July and in the dissipation stage after 2200 UTC 10 July.The distribution characteristics in the upper level show that the development and evolution processes of precipitation are determined by P6 promoting the conversion of APE to vertical motion.

Latent heat release in the middle and high levels improves the accumulation of APE.The release of APE promotes the intensification of vertical motion, and the intensified vertical motion in turn improves the latent heat release during precipitation.In other words, there is a positive feedback mechanism between APE and vertical motion in the middle and upper levels.Thus, correlation coefficients between them are relatively large.

The buoyancy and vertical velocity of air particles in the lower level are not necessarily oriented in the same direction.Actually, they are mostly in reverse directions, causing a decrease in vertical velocity,whereas APE has an increasing trend under the effects of northwestern cold advection ( Fig.1 (f)).These factors lead to weak correlation coefficients between APE and vertical velocity in the lower level.

5.Conclusion and discussion

A heavy rainfall process that occurred in eastern Tibetan Plateau during 10–11 July 2018 was simulated with the WRF model.The precipitation area and intensity were well captured by the model output.Based on that, the structural characteristics and origin of APE were analyzed.In addition, the APE budget and the effects of the primary terms on precipitation were analyzed using the mesoscale APE tendency equation.The main conclusions are as follows:

(1) APE mainly distributed under 4 km and within 8–14 km during precipitation.APE in the lower level was stronger than that in the upper level.The correlations between precipitation and APE in the upper level were better than those in the lower level.

(2) The negative potential temperature perturbations above the precipitation area were aroused by the intensive northwestern cold flow in the lower level where APE displayed positive anomalies.Meanwhile,evaporation effects caused by downward precipitation particles intensified the negative potential temperature perturbations.The latent heat led to stronger thermal disturbances.In addition, potential temperature perturbations caused by the Tibetan Plateau orography propagated to the precipitation area and superposed on thermal disturbances.Thus, potential temperature perturbations showed positive anomalies in the upper level that were related to positive anomalies of APE.

Fig.4.Schematic diagram for the development and evolution of mesoscale APE and precipitation during heavy rainfall over the eastern Tibetan Plateau.“A ”denotes the spatial distribution of mesoscale APE.

(3) The mesoscale APE tendency equation was derived using the thermodynamic equation under adiabatic conditions and the anelastic mass continuity equation.Calculation results showed that the flux transfer terms of APE and conversion term between APE and KE were the dominant terms.The meridional flux transfer term of APE presented positive anomalies in the lower level, indicating the effects of northwestern cold advection.The conversion term between APE and KE showed stronger negative anomalies in the middle and upper levels,reflecting the conversion of APE to vertical KE, while the reverse conversion occurred in the lower level.The conversion of APE to KE appeared before the precipitation, which facilitated the generation of heavy rainfall.The phase of the APE and KE conversion term was roughly in agreement with the phase of the total source and sink term in the upper level, indicating that the conversion of APE to vertical KE was the major factor influencing the precipitation.

From a comprehensive consideration of the factors influencing APE,a conceptual model is shown in Fig.4.Negative potential temperature perturbations caused by northwestern cold advection and downdrafts over the rainfall area lead to the accumulation of APE in the lower level.Potential temperature perturbations governed by the Tibetan Plateau orography together with thermal disturbances above the precipitation area result in the accumulation of APE in the upper level.The development of precipitation is promoted by the conversion of APE to vertical KE in the upper level.Latent heat released in the rainfall process in turn strengthens the APE.There is a positive feedback mechanism between APE and vertical motion in the middle and upper levels.

Diabatic processes associated with water vapor and cloud hydrometeors are important to the evolution of heavy rainfall.The mesoscale APE tendency equation is derived under adiabatic conditions.The conversion of APE to KE in the middle and upper levels is indicated by P6, while equation source terms in the middle and upper levels are not distinct.Latent heat release leads to mesoscale potential temperature perturbations strengthening APE in the middle and upper levels.Thus, methods for introducing the effects of diabatic processes to the mesoscale APE tendency equation will be the emphasis for further study.

Funding

This study was supported by the Strategic Priority Research Program of the Chinese Academy of Sciences [grant number XDA17010105 ],the National Key Research and Development Program [grant number 2018YFC1507104],the Key Scientific and Technology Research and Development Program of Jilin Province [grant number 20180201035SF ],and the National Natural Sciences Foundation of China [grant numbers 41775140,41575065, and 41790471] .

Supplementary materials

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.aosl.2021.100030 .