SIMULATION OF BOUNDARY LAYER EFFECTS ON A HEAVY RAINFALL EVENT CAUSED BY A MESOSCALE CONVECTIVE SYSTEM OVER THE YELLOW RIVER MIDSTREAM AREA

The boundary layer is the main source of the power and water vapor in mesoscale convective systems (MCSs). Zhang et al. found that during the early stages of northeast cold vortex type MCS development, the mesoscale convergence vortex in the upper boundary layer is an important transport system of both energy and water vapor, mainly formed by the convergence of various environmental fields and boundary layer friction pumping ^[1]. Romero concluded that strong mesoscale updraft is generated by the convergence of outflow from different convective systems in the process of convection propagation ^[2]. Boundary layer outflow is an important factor in the development, movement and interaction of strong convective systems (Romero ^[2]; Fiuley ^[3]; Marwitz ^[4]). In the boundary layer, there are two kinds of important lifting mechanism: Ekman suction and adjustment from Ekman non-equilibrium flow to an Ekman equilibrium one, in addition to the terrain lifting ^{[5, 6]}. Zhao et al. surmised that boundary layer processes can affect the fields of basic meteorological elements, and through them, atmospheric energy, water vapor and the dynamic structure are affected ^[5]. Consequently, heavy rainfall will also be affected. Zhao et al. pointed out that some disturbances in the boundary layer may influence the generation and development of MCSs ^[7]. Ge et al. found that potential energy at approximately 500 hPa, when converted into a standing wave, may be an important trigger for the rapid development of heavy rainfall ^[8]. Meng et al. also reported that formation of MCSs corresponds to a cyclonic disturbance in the 500-hPa flow field, and their organization and development are associated with positive feedback between a mid-level disturbance and convection ^[9]. RON McTaggart-Cowan et al. reported that a disturbed eddy current in the boundary layer can rapidly change the characteristics of ground meteorological elements through the transport of heat, momentum and water vapor ^[10]. Wu et al. studied easterly effect of the boundary layer during a night rainstorm in the Beijing area, and found that easterly activity was characterized by small scale, an obvious temperature drop, and high humidity ^[11]. Therefore, the boundary layer clearly plays an important role in the formation and development of MCSs, which can trigger heavy rainfall.

In recent years, a new understanding of the role of shear lines (Zhang et al. ^[12]), horizontal velocity (Ding et al. ^[13]), surface fluxes and condensation heating (Meng et al. ^[14]) on MCS rainstorms has been obtained. Meanwhile, others have focused on improving the parameterization scheme of the boundary layer ^[15]. There are also many studies of rainstorms over the Yellow River midstream area(Wu et al. ^[11]; Zhao et al. ^[16]; Qiu et al. ^[17]; Li et al. ^[18]; Zhao et al. ^[19]; Wang et al. ^[20]; Sheng et al. ^[21]; Wang et al. ^[22]; Zhang et al. ^[23]). However, the terrain in this area is varied and the characteristics of the boundary layer are complex, leaving the role of the boundary layer in MCS rainstorm development unclear. In this paper, using a variety of detection, NCEP / NCAR reanalysis, and numerical simulation data, we analyzed the three-dimensional airflow structure, disturbances of wind and water vapor fields, characteristics of energy conversion and the propagation within the boundary layer in a MCS rainstorm over the Yellow River midstream, which occurred during 7-9 July 2016. The adjustment of Ekman non-equilibrium flow to an equilibrium one is discussed. The role of boundary layer in the formation and development of this MCS rainstorm is described in detail, contributing to our understanding of its formation and development.

From 08:00 (UTC+8) on the 7th to 08:00 on the 8th of July (Fig. 1a), there were moderate to heavy rainfalls in Erdos city of Inner Mongolia and Yulin city of Shaanxi, related to a mesoscale convective complex (MCC). This caused local torrential rainfall in Wushen in Inner Mongolia, yielding a 24-h rainfall of 109 mm (designated as area A). Meanwhile, from 08: 00 on the 8th to 08: 00 on the 9th of July (Fig. 1b), there was a large area of heavy rainfall in Inner Mongolia, Shaanxi, and Shanxi (designated as area B), related to regenerated MCSs, once the MCC weakened. Eight counties were recorded a 24-h rainfall of more than 100 mm. The maximum amount was 179 mm in Linxian of Shanxi. A short-term heavy precipitation event occurred in a few counties and cities, with maximum rainfall intensity of 26.6 mm h^-1 and 29.6 mm h^-1 over the 2 days, respectively. The main rain belt moved from northwest to southeast. The MCC weakened as it moved southeast, generating five MCSs behind it. These MCSs also were mobile.

Figure 1.  Distribution of 24-h rainfall (unit: mm) from 08:00 on the 7th to 08:00 on the 8th (a) and from 08:00 on the 8th to 08:00 on the 9th (b) of July 2016. Hourly rainfall (unit: mm) of Wushen from 15:00 on the 7th to 08:00 on the 8th (c) and Linxian from 03: 00 on the 8th to 08:00 on the 9th of July 2016 (d).

Hourly precipitation in Wushen (Fig. 1c) formed a single peak of 26.6 mm h^-1 at 02: 00 on the 8th, while precipitation in Linxian (Fig. 1d) formed a double peak, with values of 15.4 mm h^-1 and 17.8 mm h^-1, occurring at 10: 00 on the 8th and 02: 00 on the 9th of July, respectively. From 10-min precipitation evolutions (Fig. omitted), the rainfall had obvious pulse characteristics. The precipitation in Wushen varied from large to small amounts, with a maximum of 6.5 mm in these 10-min intervals. The precipitation in Linxian increased continuously for 4-5 consecutive hours, then decreased suddenly to less than 1 mm/10-min interval. In this case, there were seven distinct peaks, with a maximum of 13.5 mm / 10-min interval. After 15: 10, precipitation rapidly decreased to less than 3.5 mm/10-min interval.

Clearly, the precipitation was short and intense on the 7th, but remained relatively weak on the 8th of July. The 10-min precipitation over both days had obvious pulse characteristics. This fluctuation in Wushen was small in amplitude but high in frequency, while in Linxian, the amplitude was relatively large but the frequency was low.

Before the heavy rainfall event, an MCS formed and developed into an MCC within the front of a 200-hPa South Asia high (Fig. 2a), near the cyclonic vortex (330 km ×470 km) at 500-hPa (Fig. 2b) over the Hetao area. Subsequently, a 200-hPa northwest jet appeared to branch in the middle of Shaanxi. The 500-hPa cyclonic vortex moved eastward, causing its wind field to strengthen and its size to increase to 850 km × 500 km. MCSs were continuously formed behind the MCC and spread southeast, resulting in rainstorms over area B.

Figure 2.  Contour lines of (a) 200-hPa height (unit: dagpm) and wind field (unit: m s^-1); (b) 500-hPa height (unit: dagpm) and wind field (unit: m s^-1) at 08:00 on the 8th of July 2016.

The southwest current at 700 hPa (Fig. omitted) developed into a jet, before the rainstorm occurred over area A. The easterly wind at 850 hPa (Fig. omitted) continued to strengthen. The MCC formed and developed in regions characterized by 700-hPa wind field convergence, 850-hPa easterly wind convergence, and the maximum potential temperature gradient. With the occurrence of heavy precipitation in area A, the convective system moved eastward, and low-level wind fields weakened, causing the operation to fail to predict rainstorms over area B.

Formation of the MCC was closely related to the 500-hPa cyclonic vortex. However, compared with most MCS rainstorms, the uplift and cold air currents were obviously weak. The unusual conditions forcing the rainstorm require further investigation. For example, we need to understand why only one county received heavy rainfall over area A during the development of the low-level jet, while a large area received heavy rainfall over area B after weakening of the low-level wind field. We also need to establish the physical mechanisms forming new MCSs, and how these developed and were maintained after the MCC weakened. Given that the easterly wind components of the lower and boundary layers (Fig. omitted) were strengthened during the heavy precipitation in area B, we also need to clarify their role in the rainstorm over area B.

An MCS is a weather system with strong convective motion over horizontal scales of 10-2000 km, defined by a black body temperature (TBB) of -32℃. An MCC is a special case of MCS ^{[24, 25]}.

To understand the development and propagation characteristics of an MCS, the hourly evolution of the TBB was analyzed. On the afternoon of the 7th of July, the MCS began to form in area A; it continued to develop and moved eastward. At 02:00 on the 8th (Fig. 3a), the MCS strengthened rapidly, while the TBB decreased and cloud structure became denser, producing heavy rainfall over Wushen. The MCS developed to be close to the MCC standard at 04:00. Around 05:00-06: 00 (Fig. 3b), the MCC matured. The area of -52℃ was 58080 km², the ratio of long axis to short was 0.83, and the lowest TBB was -61℃. Rainfall intensity was more 10 mm h^-1 during the mature period of the MCC. The structure of the MCC became less dense and the TBB increased during its southeastward propagation. After 10:00 (Fig. 3c), it weakened to become an MCS (recorded as C), which covered Erdos city in Inner Mongolia, Yulin city in Shaanxi, and central Shanxi. The precipitation in these areas continued, although rainfall intensity was low. At 14: 00 (Fig. 3d), a newly formed one - γ - scale MCS developed behind the original cloud (recorded as D) and strengthened while undergoing southeastward propagation. At 20: 00 (Fig. 3e), it strengthened to a meso - β elongated convective system (MβECS; recorded as E). At the same time, a γ - scale MCS (recorded as F) formed on the southwest side of C, and moved eastward to affect area B. After 00:00 on the 9^th (Fig. 3f), another γ - scale MCS formed at the rear of the MCS matrix, which developed rapidly and strengthened, resulting in the second rain peak in Linxian, while a β-scale MCS (recorded as G) developed during its eastward migration, producing continuous rain over area B.

Figure 3.  Evolution of black body temperature (TBB; unit: K) during 8-9 July 2016. (a) 02:00, (b) 06:00, (c) 10:00, (d) 14:00, (e) 20:00 on the 8th, and (f) 00:00 on the 9th of July 2016.

Therefore, this rainfall event was affected by one MCC and five MCSs. After the MCC weakened to become a MCS, smaller scale MCSs were continuously formed in or behind the parent cloud, propagating southeastward, and resulting in continuous precipitation. These MCSs were constantly emerging, developing and moving.

To study the boundary layer characteristics and their effects on the heavy rainfall caused by the MCSs, numerical simulation using the Weather Research and Forecasting (WRF) model was carried out. On the basis of successful simulation, a detailed analysis of these high-resolution model output data was made.

In this paper, the WRFV3.4 model with a two-level bidirectional nesting scheme was used to simulate this event. The grid intervals were 18 km and 6 km, respectively. The grid points were 152 × 170 and 253 × 259, respectively. The vertical direction of the model was divided into 33 layers. The pressure of the top layer was set to 50 hPa. The microphysical processes were based on the WRF Single Moment 5-Class (WSM5) scheme. Long-wave and short-wave radiation schemes were the Rapid Radiative Transfer Model (RRTM) and Dudhia schemes, respectively. The boundary layer scheme was that of Yonsei University (YSU), while the near-surface layer scheme was that of Monin-Obukhov. The cumulus parameterization scheme was that of Kain-Fritsch (new Eta). The land surface processes were modeled using the thermal diffusion scheme.

NCEP / NCAR FNL reanalysis data were used to define the original field and boundary conditions. Their horizontal resolution was 1° × 1°, and the time interval was 6 h. To avoid spin-up time windows, the interval start time of the simulation was selected to be 08:00 on the 7th (UTC+8). Integration time was 48 h. Integration steps were 180 s in the outer layer area and 60 s within the inner layer area, respectively. Both inner and outer layers produced output every 1 h and 3 h, respectively.

The simulated 24-h precipitation distribution on the 7th (Fig. 4a) and 8th (Fig. 4b) were compared with real data (Fig. 1a, b). Comparison shows that moderate and heavy rainfall areas are basically consistent with actual detection. The threat score (TS) of the rainstorm was 88%. Simulated precipitation in Wushen was 125 mm, which is slightly higher than the actual rainfall (109 mm). There also was a slight error in precipitation (5-15 mm) and simulation of heavy rainfall in the Jincheng area.

Figure 4.  Simulated 24-h rainfall (unit: mm) from 08:00 on the 7th to 08:00 on the 8th (a) and from 08:00 on the 8th to 08:00 on the 9th (b) of July 2016.

Simulation of the evolution of the background circulation and low-level wind fields are basically consistent with actual detection during the event.

During 7-8 July, the 200-hPa South Asian High was stable, with a maximum wind speed of the northerly jet core of 46 m s^-1. At 20: 00 on the 8th (Fig. 5a), a branch of this jet appeared in the middle of Shaanxi. At 500 hPa, a cyclonic vortex formed over the Hetao area (black circle; Fig. 5b), which increased in scale and intensity. The 700-hPa southwesterly wind continued to strengthen, but rapidly decreased once the jet developed at 08:00 on the 8th (figure omitted). The easterly wind at 850 hPa (figure omitted) increased and then decreased, while a southerly component increased gradually.

Figure 5.  Simulated 200-hPa jet at 20:00 (a), 500-hPa wind field at 08:00 (b), cloud top temperature (CTT; unit: ℃) at 02:00 (c), 20: 00 (d) on the 8th, and at 00:00 (e) on the 9th of July 2016.

Moreover, variation of the cloud top temperature (CTT) and TBB were analyzed. Simulated positions of the MCC and MCSs were slightly to the west, although their structures and dynamics were basically consistent with actual measurements, especially during the developmental stage of the MCC (Fig. 5c) and the regeneration period of the MCSs (Fig. 5d, e). Therefore, simulation of the event was successful and produced reliable results. Therefore, these high-resolution output data were subsequently used for further analysis.

Du et al. compared three methods (potential temperature, Roche's and the national standard method) of determining boundary layer height in the Xi'an area ^[26]. They established that the national standard method produced results close to Roche's method, while the potential temperature method underestimated values. Roche's method considers that the atmospheric mixing layer is the result of interaction between thermal and mechanical turbulence, and that there is a correlation and feedback between the upper atmospheric motion of the boundary layer and surface meteorological parameters. Herein, Roche's method was used, based on the formula:

where T is the ground temperature; T_d is ground dew point temperature; u_z is average wind speed at z; z₀ is ground roughness; f is the Coriolis parameter; and p is the Pasquill atmospheric stability level (divided into six levels, with values from 1 to 6).

According to (1), the average heights of the boundary layer in areas A and B are about 800 hPa and 825 hPa, respectively.

To reveal the role of the boundary layer in development and evolution of the MCS and its associated heavy rainfall, average physical quantities (listed in Fig. 1a, b; in which A is the position of the MCC when it was mature, and B is the location where MCSs were constantly emerging) were selected to characterize the MCSs.

Given there may be different mechanisms forming and developing heavy rainfall in the cases of the MCC and MCS, field variables were analyzed for each case.

Analysis of the vorticity variation (Fig. 6a) shows that before the heavy precipitation related to the MCC, there was negative vorticity over all levels. During the heavy rainfall, there was negative vorticity in the boundary layer and the lower free atmosphere, but positive vorticity occurred in the middle layer of the free atmosphere. Its height reached to the upper level, while its center was located at 500 hPa; its intensity was 6.2 10^-2 s^{- 1}. The vorticity of the upper level was close to zero. The positive vorticity was always proximal to the negative one and occurred simultaneously. In contrast, during the heavy precipitation related to the MCS, the negative vorticity center of the boundary layer decreased and its intensity increased. Its positive center was lower than that of the MCC, which was 6 h ahead. The negative center of the upper layer was located at 350 hPa and appeared at the same time as the negative center of the boundary layer.

Figure 6.  Simulated airflow structure within the boundary layer and free atmosphere. (a) vorticity (unit: 10^-5 s^-1), (b) divergence (unit: 10^-5 s^{- 1}), (c) vertical velocity (unit: 10^-2 m s ^-1) from 20:00 on the 7th to 14:00 on the 9th of July 2016 (The black line is the mean of area A, and the red line is the mean of area B).

The divergence field (Fig. 6b) shows that before formation of the MCC, atmospheric divergence was almost zero. During formation and development of the MCC, convergence occurred within the lower boundary layer. There was no divergence from the top of the boundary layer into the free atmosphere. Once the MCC matured, convergence within the boundary layer extended upwards. There was divergence from the top of the boundary layer to the lower free atmosphere. Meanwhile, the middle free atmosphere was convergent and the upper layer was divergent, forming two vertical circulation cells near the top of the boundary layer and in the middle to upper layers of the free atmosphere. During the emergence of the MCSs, the boundary layer was weakly convergent, or non-divergent and non-convergent. A convergence layer existed deep within the free atmosphere; its intensity increased with height, peaking at approximately 350 hPa.

Analysis of the vertical velocity evolution (Fig. 6c) shows that before the development of the MCC, ascending motion within the whole layer was very weak. During development and propagation of the MCC, a weak upward motion occurred in the upper boundary layer and extended into the free atmosphere. Prior to the heavy rainfall, almost the whole atmosphere was ascending, with the strongest ascent at about 250 hPa. During the subsequent development of the MCSs, the velocity profile was different. There was ascent above the boundary layer that extended upwards. During the second rain peak, the ascent was strongest, with a maximum central value of 38 10^-2 m s^-1 at 300 hPa.

Thus, convergence began within the boundary layer, extending into the upper layers in the case of the MCC. Existence of a cyclonic vortex in the free atmosphere strengthened the ascending motion and developed heavy precipitation. Precipitation caused condensation latent heat release, strengthened the cyclonic vortex and caused rapid development of the MCC. In the case of the MCSs, ascent of the free atmosphere was continuous. High-level suction caused the MCSs to regenerate and develop continuously. The anticyclone sinking in the upper levels caused an inflow of dry air in the middle levels and prolonged the rainstorm. Ascent caused by boundary layer convergence triggered these MCSs to develop and merge over area B.

To ascertain the role of the boundary layer wind field and its disturbance, the wind vector was decomposed into longitudinal and meridional (u and v) components, and its horizontal and vertical structures and evolution characteristics were analyzed.

Analysis of the evolution of u shows that there was always a northwest-southeast easterly wind belt within the boundary layer (Fig. 7a, b) during heavy rainfall periods. In fact, the strong wind speed core corresponded to the rainstorm area. The time-height variation of u (Fig. 7c) shows that the easterly wind speed in the boundary layer fluctuated during the heavy precipitation. As the wind speed increased and extended towards the free atmosphere, the MCC developed and the MCSs regenerated, forming coincident rain peaks. Thus, the high wind speed core synchronized with the rainfall peak, whenever the rain intensity exceeded 10 mm h^-1. As the MCC moved from northwest to southeast, the extension height of the easterly was mainly concentrated within the boundary layer, and wind speed was the highest. There was only one high speed core, which corresponded to the rainstorm area. The disturbance cycle was approximately 10-14 h, in which there were some 2-3 h fluctuation cycles. In contrast, MCSs continuously emerged, developed and merged at the rear of complex. The easterly height was higher than that of the MCC, reaching to the middle troposphere. Easterly speed was lower than that of the MCC, and there were many speed cores corresponding to the rainstorm areas. The perturbation cycle was shorter than that of MCC, and its fluctuations were more frequent.

Figure 7.  Simulated distribution of easterly winds (unit: m s^-1) on the boundary layer at 02:00 (a) and 12:00 (b) on the 8th, and vertical distribution of easterly component (c), and southerly component (d) from 10:00 on the 7th to 08:00 on the 9th of July 2016 (The black line shows Wushen data and the red line shows Linxian data. The respective horizontal lines define the mean boundary layer tops in areas A and B).

Analysis of the evolution of v (Fig. 7d) shows that before the heavy precipitation related to the MCC, southerly winds formed below 500 hPa and extended into the boundary layer, forming a jet during the MCC development stage. Two rain peaks occurred, corresponding to two southerly wind jumps of 18 m s^-1. During heavy precipitation related to the MCSs, southerly winds were maintained from the boundary layer to the lower free atmosphere, but their speed was lower than that during the MCC. The height of wind speed core decreased, and several speed cores of 9 m s^-1 appeared near the top of the boundary layer.

Thus, horizontal disturbance of the easterly wind within the boundary layer caused mass convergence, which strengthened vertical ascent and triggered heavy precipitation. Because vertical disturbances cause mass exchange between the boundary layer and the free atmosphere, water vapor and energy distributions were changed. The enhancement of water vapor transport began in the lower free atmosphere. Thus, the MCC formed during a period of southerly wind intensification. Extension of southerly winds into the boundary layer, created a southerly jet in the lower free atmosphere and a mature MCC. At this stage, there was no northerly wind intrusion into the upper layer, while the easterly wind in the boundary layer gradually strengthened to become a jet. During heavy rainfall related to the MCSs, the southerly wind decreased, but extended into the boundary layer, while the easterly wind in the boundary layer developed and strengthened. Heavy precipitation related to the MCC may be triggered by the large-scale convergence and ascent caused by the southerly jet and the easterly disturbance within the boundary layer. In contrast, southerly wind fluctuations and the east wind disturbances were the important factors causing the MCSs to regenerate and develop, triggering further heavy rainfall.

A change in specific humidity can be caused by phase transformations and the mass exchange between wet air and dry air outside it. To understand the characteristics of water vapor exchange between the boundary layer and free atmosphere during heavy rainfall, the average specific humidity was calculated by selecting an area defined by 105-116° E and 33-43° N, and calculating the regional disturbance of specific humidity using:

where Q is specific humidity, $\bar Q $ is the regional average specific humidity, and Q' is the regional disturbance.

Analysis of the horizontal evolution of specific humidity (Fig. 8a) shows that before the heavy precipitation, and coincident with strengthening of low-level southerly winds, specific humidity increased from south to north, with hourly increases of 1-3 g kg^-1 (Fig. 8b). During the heavy precipitation, the positive disturbance area of specific humidity was consistent with the heavy precipitation area. Corresponding vertical evolution (Fig. 8c) shows that, before MCC-related heavy precipitation, the specific humidity increased from the boundary layer to the free atmosphere. During the mature phase of the MCC, specific humidity increased twice, reaching maxima exceeding 14 g kg^-1, associated with two rainfall peaks that occurred around 2 h later. During MCS-related heavy precipitation, the specific humidity maintained values of about 12 g kg^-1 from the boundary layer to the lower free atmosphere (mainly concentrated below 800 hPa).

Figure 8.  Simulated distribution of specific humidity (unit: g kg^-1) on boundary layer of area A at 13:00 (a), specific humidity turbulence from 13:00 to 14:00 (b) on the 7th, and vertical distribution of specific humidity (c) and its turbulence (d) from 08:00 on the 7th to 08:00 on the 9th of July 2016 (The black line shows Wushen data and the red line shows Linxian data. The horizontal lines are the separate mean heights of boundary layer tops in areas A and B).

The characteristics of the specific humidity disturbance (Fig. 8d) varied during the event. Before formation of the MCC, the specific humidity disturbance in the boundary layer was negative, while it was positive below 600 hPa, with a maximum of 2 g kg^-1 near 650 hPa. During the mature phase of the MCC, this positive specific humidity disturbance rapidly extended into the boundary layer and the upper free atmosphere, causing strong water vapor exchange between the free atmosphere and the boundary layer. During the emergence of the MCSs, before heavy precipitation, the specific humidity disturbance within the whole layer was negative, with value of − 3 g kg⁻¹ near 700 hPa. During heavy precipitation, this disturbance in the boundary layer and free atmosphere remained negative, but became positive above 700 hPa.

Clearly, formation of the MCC was closely related to southerly transport and strong exchange of water vapor between the free atmosphere and the boundary layer, while continuous regeneration and development of MCSs relied more on maintenance of an upward extension of the positive water vapor disturbance.

Ekman flow adaptation is an important mechanism in the boundary layer. The Ekman equilibrium flow field is given by ^[27]:

here, $\delta=\sqrt{2 k / f} $. After calculating the Ekman equilibrium flow field, the actual flow is subtracted from the equilibrium flow to obtain the non-equilibrium flow.

The divergence of the non-equilibrium flow field and horizontal wind distribution at the top of boundary layer is shown in Fig. 9. Clearly, the non-equilibrium flow had common characteristics during the MCC and MCSs. During the development of the MCC (Fig. 9a) and regeneration period of the MCSs (Fig. 9c), there was non-equilibrium wind convergence, with wind speeds of approximately 20 m s⁻¹. During the mature phase of the MCC (Fig. 9b) and development of the MCSs (Fig. 9d), the intensity of the non-equilibrium winds rapidly increased to 40-50 m s⁻¹, strengthening their convergence. However, the intensity of the convergence center and non-equilibrium winds in area A was markedly stronger than that in area B. In addition, there was only one convergence center corresponding to the MCC center, while there were many convergence centers corresponding to the regeneration and development of MCSs in area B. These convergence centers were mobile, consistent with the propagation characteristics of MCSs. Comparison of the divergence of non-equilibrium winds and actual winds (Fig. omitted) shows that their centers basically correspond. This indicates that the ascending motion caused by Ekman non-equilibrium flow convergence within the boundary layer plays a very important role in the maintenance and development of MCSs.

Figure 9.  Simulated distribution of the unbalanced flow field divergence (unit: 10^-5 s^-1) within the boundary layer at 800 hPa (a, b) and 825 hPa (c, d) (the solid line shows divergence, and the gray tones show horizontal wind), and the height-latitude profile of the Ekman unbalanced flow field along both mesoscale convection complex (MCC) (e) and the mesoscale convection system (MCS) (f) centers on the 8th of July 2016. (a) 00:00, (b) 08:00, (c) 10:00, (d) 14:00, (e) 00:00, and (f) 10:00.

To illustrate this forcing mechanism, a heightlatitude section of the wind field disturbance within the boundary layer is shown along the centers of the MCC (Fig. 9e) and MCSs (Fig. 9f), respectively. Analysis shows that, from formation to development of the MCC, there was a southerly convergent updraft between 108°E and 109°E within the boundary layer, with a downdraft on its eastern side. Near 109°E (MCC and heavy rainfall center), a secondary circulation formed. During the generation and development period of the first MCS, a secondary circulation consisting of an easterly convergent updraft and downdraft was formed near 110° E. During regeneration of the subsequent MCSs, a secondary circulation consisting of a southerly convergent updraft and downdraft was formed between 111° E and 112° E. This confirms that the nonequilibrium flow within the boundary layer forces a vertical updraft to develop, forming a secondary circulation, which leads to the development of both the MCC and MCSs. This verifies the important role of the easterly wind within the boundary layer in maintaining and developing MCSs.

Accumulation and conversion of atmospheric energy are important factors affecting mid-latitude weather. The propagation of tropospheric wave energy can stimulate development of ground systems (Chang EK M ^[28-29]), and the disturbed energy introduced by this baroclinic wave packet can accumulate energy and contribute to the development of rainstorms(Mei et al. ^[30]).Based on the Rossby wave dispersion theory and the theory of transient wave packets(Miao et al. ^[31]), the distribution and transformation characteristics of kinetic energy and potential energy in the troposphere and boundary layer were calculated and analyzed herein. The propagation characteristics of the troposphere and boundary layer energy disturbances and their effects on the occurrence and development of heavy rainfall were also evaluated.

In a conservative mechanical system, the total energy can be expressed by:

here,

where u and v are longitudinal and meridional wind speed, respectively. In (7), A is the amplitude of each wave; that is, A_i(x, y, z, t). Because the wave energy propagates along the wave envelope, E_a can be obtained by calculating the amplitudes of each wave. This is because meteorological data can be regarded as the combination of many fluctuations under certain conditions (Miao et al. ^[31]; Song et al. ^[32]; Xiao et al. ^[33]),

P(x, y, z, t) represents the data of a meteorological element at some time. Numbers k, l, and m are wave numbers in the directions of x, y, and z, respectively; ω is angular frequency, and ϕ is the amplitude angle. We decomposed the high-pass filtered signal P(x, y, z, t) using the Hilbert transform to obtain its analytic signal $ \hat P(x, y, z, t)$. The amplitude of signal P(x, y, z, t) is given by:

The total energy, kinetic energy and wave packet potential energy can be calculated from (5) to (8), and their units are dimensionless.

Analysis of 500-hPa energy evolution within the middle troposphere (Fig. 10a, b) shows that E always changed synchronously with E_k, while E_k was positively correlated with the wind (Fig. 11). This indicates that the total energy was mainly contributed by the kinetic energy of the vortex. The energy of the MCC was larger than that of any of the MCSs, and the MCC high-energy period was shorter than those of the MCSs. Therefore, the MCC decayed rapidly, while the MCSs decayed slowly. During the formation of the MCC, energy increased slowly. During the regeneration of the MCSs, the energy fluctuated more but maintained a higher value. With the rapid increase in energy, MCC and MCSs matured and triggered heavy rainfall. Therefore, the energy peaks were synchronized with the rainfall peaks.

Figure 10.  Simulated comparison between the total energy and its components at 500-hPa (a and b) and the top of the boundary layer (c and d) during the heavy rainfall from 7 to 9 July 2016 (a and c show MCC; b and d show MCS; the black line is the total energy, the long-dashed line is the kinetic energy, and the short-dashed line is the elastic potential energy).

Figure 11.  Simulated distribution of energy and wave packet propagation at 500 hPa (a-d) and within the boundary layer (e and f are at 800 hPa; g and h are at 825 hPa): (a) Kinetic energy (Ek) at 00:00, (b) Ek at 13:00, (c) Potential energy (Ea) at 02:00, (d) Ea at 15: 00, (e) Ek at 00:00, (f) Ea at 02:00, (g) Ek at 10:00, and (h) Ea at 13:00 on the 8th of July 2016.

Analysis of the evolution of E_k and E_a shows that during formation of the MCC (Fig. 10a), both E and E_k increased slowly, while E_a was almost zero. During the early stages of MCC development and precipitation, the energy fluctuated only slightly, before E_k and E_a began to convert. During the heavy precipitation, their conversion increased. In contrast, during the extinction period, both kinds of energy were synchronized. During generation, development, and propagation of the MCSs (Fig. 10b), there were multiple conversions between E_k and E_a, maintaining a high kinetic energy. Potential energy was larger than during the MCC, and wave packet propagation of potential energy was obvious. This suggests that development of the MCC and regeneration of MCSs were related to high levels of kinetic energy, while energy conversion triggered the heavy rainfall.

The energy of the boundary layer was 0.5-4, which is much lower than that of the middle troposphere; it also had more waves, and the effect of turbulence was more obvious. During the formation period of the MCC (Fig. 10c), the energy of the boundary layer jumped, related to conversion between E_k and E_a. Generally, during development of mid-latitude systems in the middle troposphere, momentum is transmitted downward, and energy initially develops from the boundary layer and extends upwards. However, once the MCC weakened, energy was maintained at approximately 0.5-2.5, and turbulence was still obvious. It was clearly an important energy source for the MCSs, which was re-excited, after the MCC moved eastwards and weakened. Compared with the MCC, MCSs (Fig. 10d) had lower energies and more frequent fluctuations, reflecting multiple conversions between E_k and E_a. During the continuous regeneration and maintenance of the MCSs, the effect of boundary layer turbulence was marked.

Clearly, during heavy precipitation, the energy flows within MCCs and MCSs are different.

Analysis of hourly 500-hPa energy variation (Fig. 11) reveals that the distribution of the high energy zone was basically coincident with the main rain belt (Fig. 1a). The rainstorm center corresponded to the positive disturbance center of the high energy zone. An energy jump accompanied the rainfall peak (Fig. 1b), although kinetic energy jumped 12 h ahead of potential energy. This suggests that the tropospheric middle layer played a leading role in determining the precipitation distribution. Before the heavy precipitation, energy mainly originated from kinetic energy of the westerly wind field, while the occurrence of heavy precipitation was closely related to conversion between kinetic and potential energy. During the heavy precipitation (Fig. 11a-d), energy in area A was high (1-5), being eddy energy. Under vortex rotation, the high energy zone propagated to the southeast and weakened. In area B, the eddy weakened into a shear line. The shear kinetic energy was much less than the original eddy energy. Therefore, precipitation intensity in area B was also lower than that in area A. However, given the stable maintenance of the southerly and easterly winds, the shear kinetic energy was maintained at a high value (2-3) over a long period. Corresponding to both southerly and easterly wind disturbances, there were multiple conversions between kinetic and potential energy. With the propagation of energy wave packets, MCSs constantly emerged and developed, forming a heavy precipitation area that moved southeastward.

Unlike the middle troposphere, there was no obvious vortex within the boundary layer wind field, and its turbulence was obvious. Energy values decreased markedly (0.5-2), as represented by multiple small-scale wave packets. Conversion between kinetic and potential energy was consistent with pulsations in 10-min precipitation. There was also obvious wave packet propagation to the southeast. Energy variation characteristics were clearly different over the life stages of both the MCC and MCS. During the formation and development of the MCC, southerly wind inflow dominated (Fig. 11e). The easterly flow of the boundary layer was continually strengthened, and underwent convergence (southerly and easterly). The strongest energy disturbance appeared in the convergence area, reflecting the maturity of the MCC and triggering heavy precipitation. A rainfall peak in area A (Fig. 1c) appeared, along with a potential energy jump (Fig. 11f). In area B, convergence of the wind field disappeared, and an easterly pulsation occurred. With energy wave packet propagating to the southeast, MCSs emerged and developed continuously. During MCS formation, southerly and easterly inflows were strengthened, and convergence of southerly and easterly reoccurred (Fig. 11g). As energy increased (Fig. 11h), its conversion caused many rain peaks in area B (Fig. 1d). This analysis verifies the role of southerly and easterly disturbances within the boundary layer in forming rainstorms.

We conclude that the sub-synoptic scale system in the middle troposphere played a leading role in determining the distribution of precipitation. The mesoscale systems stimulated by the sub-synoptic scale system were critical to forming the subsequent heavy precipitation. Meanwhile, small-scale disturbances or fluctuations within the boundary layer are critical factors determining rainfall intensity.

The heavy rainfall event in early July over the Yellow River midstream area was caused by one MCC and five MCSs. Unlike general rainstorms, this MCC was formed under conditions of weak uplift and cold air, producing heavy precipitation over a small range and short duration. However, MCSs continued to regenerate and develop within the weakened low-level wind field, producing heavy precipitation over a larger range and longer duration. This resulted in empty (MCC) and missing (MCS) rainfall predictions in forecasting operations. This event suggests that when the easterly component of low-level and boundary layers increases, the effect of this easterly disturbance cannot be ignored on rainfall. To test this hypothesis, the boundary layer and its disturbance characteristics were analyzed using numerical simulation. Formation and development mechanisms of this rainstorm (different from general ones) were determined, providing a reference for reducing operational errors in forecasting for this region.

(1) Convergence of the MCC started within the boundary layer. Mutual feedback mechanisms between the cyclonic vortex of the middle free atmosphere and precipitation caused the MCC to develop rapidly and led to heavy precipitation. Ascent of the MCSs was deep and continuous; while high-level suction caused MCSs to continuously regenerate. Anticyclonic sinking of the high-level free atmosphere caused dry air inflow into middle levels, which prolonged propagation and maintained the convective storm.

(2) The MCC rainstorm was triggered by large-scale convergence and ascent related to a southerly jet and disturbance of easterly winds within the boundary layer. Southerly wind fluctuation and easterly wind disturbance were important factors determining the MCS rainstorm. Formation and development of the MCC were closely related to southerly transport, which promoted major water vapor exchange between the free atmosphere and the boundary layer. In contrast, regeneration and development of the MCSs depended more upon maintenance of an upward extension of a positive water vapor disturbance.

(3) The influence of different scale weather systems on this rainstorm were revealed through energy analysis. Energy within the middle troposphere was contributed by eddy kinetic energy, while turbulent kinetic energy was the main source in the boundary layer. Formation and development of the MCC or MCSs were related to high energy centers, while energy conversions triggered rainfalls. In the process of energy conversion, wave packet propagation within the boundary layer (not only in the middle troposphere) was obvious, and signified regeneration and development of MCSs.

(4) The theory of Ekman adaptation within the boundary layer was applied to analyze this rainstorm. Some notable differences were identified between MCC and MCS rainstorms, providing a reference for further theoretical applications.