Mechanism of Atmospheric Diabatic Heating Effect on the Intensity of Zonal Shear Line Over the Tibetan Plateau in Boreal Summer

The zonal shear line (ZSL) over the Tibetan Plateau (TP) is one of the most crucial synoptic systems inducing precipitation over the TP in boreal summer. However, few studies have comprehensively explored the thermal mechanism of the intensity evolution of the ZSL. In this study, the mechanism of the atmospheric diabatic heating (hereafter referred to as diabatic heating) effect on the intensity of the ZSL was explored by the methods of composite and diagnostic analysis. Based on the fifth generation European Centre for Medium‐Range Weather Forecasts atmospheric reanalysis of the global climate hourly data sets from June to August during 1980–2019, 11 cases of the ZSL were selected by using the objective identification method. Results suggest that a close relationship exists between the ZSL’s intensity and the 10‐h‐earlier vertically integrated diabatic heating , with a high correlation coefficient of 0.81. The intensity of peaks at around 13 LST (Local Solar Time) within a day. The diabatic heating rate Q reaches the maximum values at 350 hPa. The vertical transport of temperature is the main contributor to the intensity of Q during the intensity evolution of the ZSL. The vertically non‐uniform diabatic heating effect is the primary mechanism for the intensity evolution of the ZSL. When the vertically non‐uniform diabatic heating near the ZSL enhances (weakens), it will be favorable (unfavorable) to enhance the ZSL’s intensity.

in boreal summer Ye et al., 1957). The latent heating of condensation during precipitation can reach the same magnitude as sensible heating in boreal summer, which makes a remarkable enhancement of TP diabatic heating and creates a significant temperature gradient between the TP and the surrounding regions (Ding, 1992;Flohn, 1957;Ye et al., 1957). As a result, the atmospheric circulation and climate in boreal summer are significantly affected (Duan et al., 2020;Duan & Wu, 2005; Y. M. Liu et al., 2012;G. Liu et al., 2017;Nan et al., 2009;B. Wang et al., 2008;Wu & Liu, 2016;Zhao et al., 2007). Besides, the diabatic heating of the TP also plays a crucial role in the formation and development of weather systems over the TP (Chen & Li, 2014;Liu & Wu, 2000;Wu et al., 2018). Studies have shown that diabatic heating, a conducive factor to convective instability and convective activities (Guan et al., 2018;Yanai & Li, 1994), is also one primary condition for the formation of the ZSL in boreal summer . The intensity of diabatic heating also influences the intensity of the ZSL and therefore plays an essential role in the intensity evolution of the ZSL (The Tibetan Plateau Science Research Group, 1981;Yao et al., 2014).
According to previous studies, a ZSL may vary considerably in the structure during the evolution process (Luo & Li, 2018;. So, what is the relationship between the intensity of ZSL and diabatic heating? What is the mechanism of the atmospheric diabatic heating effect on the intensity evolution of the ZSL? These two questions have not been answered to date. In addition, previous studies on the structural characteristics of the ZSL were mainly based on the results of a single experiment or case. Therefore, the understanding of the ZSL is inevitably limited, and the research of the diabatic heating effect on the ZSL is not comprehensive. Based on the fifth generation European Centre for Medium-Range Weather Forecasts (ECMWF) atmospheric reanalysis of the global climate (ERA5) hourly data sets, the study explores the relationship between the ZSL's intensity and the intensity of diabatic heating, as well as the mechanism of the diabatic heating effect on the intensity of the ZSL under the background of significant warming over the TP since the 1980s (Guo & Wang, 2011;Kuang & Jiao, 2016;Pang et al., 2020;B. Wang et al., 2008). Compared with previous studies whose data sets are of coarser temporal resolution, more detailed results can be revealed using the ERA5 reanalysis data sets with a finer resolution of an hour. This study focuses on the ZSL that induces heavy precipitation and is located in the ZSL high-frequency region over the TP. Moreover, rather than a case study, the composite analysis method is employed to draw more representative conclusions. The results can improve the understanding of the diabatic heating effect during the intensity evolution of the ZSL and provide some insight into the prediction of heavy precipitation over the TP.
This study is organized as follows: the data and methods are described in Section 2. Section 3 analyzes the diabatic heating effect on the intensity of the ZSL. Section 4 explores the mechanism of the diabatic heating effect on the intensity of the ZSL. Section 5 provides conclusions and discussions.

Data and Methods
As shown in Figure 1, the study region is 84°-96°E, 32°-35°N (orange-dashed box). The reasons for selecting this region are discussed below.

Data
The fifth generation ECMWF ERA5 hourly data sets (Hersbach et al., 2018) from June to August during 1980-2019 provided by the ECMWF are adopted in this study. The data has a horizontal resolution of 1° × 1° and 37 levels in the vertical direction. The 24-h accumulated rainfall collected from national meteorological stations, that is, the daily precipitation data sets (version 3.0), whose quality control is applied by the National Meteorological Information Centre of the China Meteorological Administration, was also used.

Objective Identification and Composite Methods for the ZSL
The objective identification method for the ZSL (Guan et al., 2018;Yao, Zhang, & Bao, 2020;Yao, Zhang, & Ma, 2020;X. Zhang et al., 2016;) is adopted in this study. The ZSL is identified by a combination of three parameters: the meridional shear of zonal wind, the vertical relative vorticity (hereafter referred to as vorticity), and the zonal wind velocity. Only when all three criteria in Equation 1 are met can a shear line be identified. Furthermore, given the scale of the ZSL, the identified shear line's zonal span must be longer than 500 km (approximately longer than five degrees of longitude) to be identified as a ZSL.
where u is the zonal wind velocity, v is the meridional wind velocity. y represents the coordinate in the meridional direction, and x represents the coordinate in the zonal direction. v Using the objective identification method, 223 cases of ZSLs with life cycles of more than one day have been identified. These cases are further filtered, considering the ZSL's birthplace, precipitation intensity, and life cycles, as shown by the following three requirements.
1. According to the geographic distribution, 97 cases situated in the high-frequency region (32°-35°N) of the ZSL (X. Zhang et al., 2016) are first selected. 2. With a focus on the cases that induced heavy precipitation around the ZSL, the standard deviation method is used, that is, if the precipitation of one day in the ZSL process exceeds the daily average precipitation of all the cases by more than one standard deviation, it can be regarded as a ZSL case. As a result, 43 out of the 97 cases of ZSL that meet this condition are selected second. 3. Based on the initiation and dissipation time of the ZSL, the life cycles of ZSL can be inferred. Therefore, 11 cases with life cycles longer than 60 h are finally selected out of the 43 cases.
Therefore, the 11 cases of ZSLs that meet the above requirements from June to August during 1980-2019 are selected and shown in Table 1. The local solar time (LST) is used for the time involved below. LST equals the coordinated universal time (UTC) plus 6 h, that is, LST = UTC+6. It can be seen from Table 1 that most of the selected cases of ZSL initiated in the afternoon (14-18 LST) and dissipated during the morning hours (04-10 LST).
The value of vorticity is used to characterize the intensity of the ZSL. The arithmetic averages of the selected cases' physical quantities are adopted for the composite analysis. The life cycle of the composited ZSL is 72 h, which initiates at 13 LST on the first day and dissipates at 12 LST on the fourth day. It covers all the processes of the initiation, maturity, and dissipation of the ZSL.
Based on the high-frequency region of the ZSL (X. Zhang et al., 2016) and the distribution region of the positive vorticity near the ZSL, the study region is selected as 84°-96°E, 32°-35°N (orange-dashed box in Figures 1 and 5). Subsequent calculations on regional average are all based on the study region.

Calculation of the Diabatic Heating
The "inverse algorithm" is used to calculate the diabatic heating over the TP, which is the most widely used calculation method at present (Lai & Gong, 2017 In Equation 2, Q 1 is the diabatic heating over the TP; C p is the specific heat at constant pressure, which is 1004. 8416 J kg −1 K −1 ; T is the temperature; V is the horizontal wind vector; ω is the vertical wind velocity in the pressure coordinate; κ = 0.2875; θ is the potential temperature and p 0 = 1000 hPa. The first term on the right side of the Equation 2 is the local variation of temperature. The second one is the horizontal advection term of temperature. The third one is the vertical transport term of temperature.
The vertically integrated diabatic heating <Q 1 > can be obtained using Equation 3.
In Equation 3, p t is the pressure at the troposphere top (usually 100 hPa), and p s is the surface pressure.
The diabatic heating rate Q can be obtained using Equation 4. The unit of Q is K/s.

The Diabatic Heating Effect on the Intensity of the ZSL
The latent heating released by precipitation can enhance the diabatic heating and give positive feedback to the development of the ZSL. Therefore, it is crucial to study the diabatic heating effect on the intensity of the ZSL. In this section, the intensity evolution, the horizontal and vertical distribution, and the diabatic heating components around the ZSL during the ZSL life cycles are studied. Figure 2 shows the time series of the regionally averaged vorticity and the regionally averaged <Q 1 >. It can be seen from Figure 2 that the vorticity reaches the maximum and the minimum around 23 and 15 LST within a day, respectively, and the maximum intensity of the ZSL is 4.74 × 10 −5 s −1 . It indicates that the ZSL exhibits a significant diurnal variation. The <Q 1 > reaches the maximum value at 13 LST within a day, and the maximum value can reach above 500 Wm −2 . However, its intensity decreased rapidly at night (20-05 LST of the next day) and was maintained at about 0-100 Wm −2 . It can be seen that the <Q 1 > also exhibits a significant diurnal variation.

Intensity Evolution of the Diabatic Heating <Q 1 >
As shown in Figure 2, the intensity variations of the ZSL and <Q 1 > show similar wave patterns, but one noteworthy finding is that the wave phase variation of <Q 1 > is 10 h earlier than that of the ZSL. Therefore, is there a correlation between the intensity variations of the ZSL and <Q 1 >? Can the change of the intensity of <Q 1 > indicate the intensity evolution of the ZSL? It will be studied by the method of correlation analysis.
The correlation between the intensity of the ZSL and the intensity of the 10-h earlier <Q 1 > is shown in Figure 3. When the significance level α is set as 0.01, the correlation coefficient is as high as 0.81. Therefore, it can  at 500 hPa (black line, unit: 10 −5 s −1 ). The abscissa represents the time series, wherein solid black triangles represent the initiation and dissipation time of the zonal shear lie (the same below). The labels of 1st, 2nd, 3rd, and 4th represent the first day, the second day, the third day, and the fourth day, respectively (the same below).

Figure 3.
Correlation between the regionally averaged vorticity E  at 500 hPa and the 10-h earlier regionally averaged <Q 1 >. be concluded that the relationship between them is significantly correlated at the significance level of α = 0.01 (passing the 99% significance test). Figure 4, the main body of the TP is a positive correlation zone between the vorticity at 500 hPa and the 10-h earlier <Q 1 >. The area with high positive correlations mainly appears near the ZSL and its southern side, with a maximum correlation coefficient exceeding 0.8. The significant positive-correlated large-value area near the ZSL indicates that the intensity variation of <Q 1 > is closely related to the intensity evolution of the ZSL. The increase (decrease) of the intensity of <Q 1 > may have an impact on the enhancement (weakening) of the ZSL.

Distribution Characteristics of the Diabatic Heating
As shown in Section 3.1, the intensity evolution of the ZSL is not synchronized with the <Q 1 >. Instead, a strong linear correlation shows a close relationship between the ZSL's intensity and the 10-h-earlier <Q 1 >. According to the life cycles of the ZSL and the intensity evolution of the vorticity, the first, second, and third days of the life cycles of the ZSL are defined as its initiation, maturity, and dissipation stages, respectively (From 13 LST on one day to 12 LST on the next day, with the daily average value representing the average situation of each stage). The horizontal and vertical distribution of the diabatic heating at the time before the initiation, maturity, and dissipation stages of the ZSL are analyzed to explore the effect of diabatic heating on the intensity evolution of the ZSL.

Horizontal Distribution of the Diabatic Heating <Q 1 >
The TP is dominated by the diabatic heating effect, showing a distribution characteristic of "high in the south and low in the north." Because the study focuses on the diabatic heating effect in the intensity evolution of the ZSL, only the distribution characteristics of the <Q 1 >in the study region (84°-96°E, 32°-35°N, the orange-dashed box) are discussed. The <Q 1 > in the study region is more robust than that in other areas of the main body of the TP. The intensity of the <Q 1 > at 10 h earlier than the initiation stage ( Figure 5a) in the study region is about 300 Wm −2, and the maximum intensity of the ZSL is about 4 × 10 −5 s −1 . At 10 h earlier than the maturity stage (Figure 5b), the range of the <Q 1 > near the ZSL expands, and the maximum value exceeds 500 Wm −2 . The intensity of the ZSL also increases subsequently. The maximum intensity of the ZSL exceeds 4.5 × 10 −5 s −1 , and the range of large-value area is significantly expanded. At 10 h earlier than the dissipation stage (Figure 5c), the range of the <Q 1 > near the ZSL changes little while the intensity decreases to 400 Wm −2 . The intensity of the ZSL also weakens subsequently, and the range of large-value area is significantly reduced.
It can be seen from Figure 5 that the <Q 1 > over the TP has a close relationship with the intensity evolution of the ZSL. When the <Q 1 > over the southeastern side of the ZSL develops strongly, the ZSL subsequently strengthens. Therefore, the change in the intensity of the <Q 1 > might be a good precursor of the intensity evolution of the ZSL.

Vertical Distribution of the Diabatic Heating Rate Q
As shown in Figure 6, the diabatic heating rate Q varies by level, and the heating zone is mainly located above 500 hPa. The maximum value is at around 350 hPa, which may be related to the deep convection and latent heating released by condensation and deposition. The intensity of Q at 10 h earlier than the initiation stage ( Figure 6a) over the ZSL is the weakest among all stages, with a maximum value of only 7 K day −1 . At 10 h earlier than the maturity stage (Figure 6b), the intensity of Q near 350 hPa is rapidly enhanced to 10 K day −1 . Combined with the evolutionary characteristics of the ZSL's intensity, it is clear that the ZSL below the strong diabatic heating zone subsequently enhances. At 10 h earlier than the dissipation stage (Figure 6c), the intensity of Q gradually decreases. The distance between the ZSL and the diabatic heating center increases as the ZSL shifts northward. It results in weaker heating near the ZSL and a subsequent weakening of the intensity of the ZSL.  at 500 hPa and the 10-h earlier regionally averaged <Q 1 >. The black thick solid line is the zonal shear line (the same below). The gray line is the Tibetan Plateau with a terrain height above 3000 m (the same below). Shaded areas are statistically significant at the 99% confidence level.

Components of the Diabatic Heating Rate Q
From Equation 4, it can be seen that the Q obtained by the "inverse algorithm" is subject to the combined effect of the local variation of temperature term, the horizontal advection term of temperature, and the vertical transport term of temperature. During the intensity evolution of the ZSL, which one of the components contributes the most to the Q? What are the dynamical and thermal processes responsible for this? The corresponding conclusions will be given by exploring the contribution of each term on the right side of Equation 4.
Since the daily average value is used to represent the average situation of the stage, the local variation term of temperature in different stages is virtually unchanged. It contributes little to the Q. The Q near and above 500 hPa is positive at 10 h earlier than the initiation stage ( Figure 7a). The profile of Q is very similar to that of the vertical transport term of temperature at the 500-300 hPa. Both of them reach the maximums at 350 hPa with intensities of about 6 K day −1 and 7 K day −1 , respectively. Therefore, the vertical transport term of temperature makes a decisive positive contribution to the intensity of Q. Above 300 hPa, the positive contribution of the vertical transport term of temperature decreases, while the negative contribution of the horizontal advection term of temperature gradually increases. The combined effect of them makes the Q tend to be around 0 K day −1 . Therefore, the diabatic heating effect on the upper levels is weaker than the lower levels.
The profile patterns at 10 h earlier than the maturity stage ( Figure 7b) are similar to those of the initiation stage. The Q and the vertical transport term of temperature still reach the peak value at 350 hPa, but the intensity is enhanced to 8 K day −1 and 9 K day −1 , respectively. It indicates that the ascending motion near the ZSL is enhanced at the maturity stage. The intensity of the vertical transport term of temperature is slightly weakened at 10 h earlier than the dissipation stage (Figure 7c), and the height of the maximum value moves up to near 300 hPa. The Q still reaches a maximum value at 350 hPa with little change in intensity. The horizontal advection term of temperature turns positive at heights from 350 hPa to near ground level, making Q unchanged. However, the vertical transport term of temperature still plays a decisive role in the intensity of Q. It can also be found that the negative contribution of the horizontal advection term of temperature gradually increases from the initiation to the dissipation stage above 300 hPa, which may be related to the cooling above 300 hPa.  In summary, the profile of Q is very similar to that of the vertical transport term of temperature at 500-300 hPa. The vertical transport of temperature is the main positive contributor to the intensity of Q.

The Diabatic Heating Mechanism on the Intensity of the ZSL
From the previous analysis, it can be seen that the diabatic heating over the TP has a close relationship with the ZSL's intensity. In addition to the horizontal advection term of vorticity and E  effect, the diabatic heating effect is also taken into account in the complete-form vertical vorticity tendency equation (X. M. Wang et al., 2016;Wu & Liu, 1998, 1999. Therefore, the equation is used to explore the mechanism of the diabatic heating on the intensity evolution of the ZSL.

The Complete-Form Vertical Vorticity Tendency Equation
The complete-form vertical vorticity tendency equation (Wu & Liu, 1999) is as follows: The terms on the right side of Equation 5 represent the effect of ascending motion, heat source, the spatially non-uniform diabatic heating (non-uniform diabatic heating is referred to as non-uniform heating, the same below), and the residual error (R, which consists of the frictional dissipation, the slantwise vorticity development, and computational error.) on the local variation of vorticity. p is the pressure; θ is the potential temperature, and 0 . Q represents the diabatic heating rate in the thermodynamic equation, and Equation 4 is used to calculate it.
Equation 5 is used to explore the mechanism of the diabatic heating effect on the vorticity. Terms on the Equation 5 right side containing the effect of diabatic heating are the heat source term and the spatially non-uniform heating term. The magnitude of the heat source term is 10 −11 s −2 , which is about two orders of magnitude smaller than the spatially non-uniform heating term (10 −9 s −2 ). Therefore, this section focuses on the mechanism of the spatially non-uniform heating on the intensity evolution of the ZSL. The relationship between them is expressed as follows: the red line represents the vertical transport term of temperature The spatially non-uniform heating term consists of the vertically non-uniform heating term and the horizontally non-uniform heating term, which characterizes the non-uniform state of the diabatic heating of the vertical and horizontal directions, respectively.

Spatially Non-Uniform Heating Effect
The vorticity variation and the spatially non-uniform heating effect near the ZSL are most significant at 500 hPa. It is clear from Figure 8 that the evolution of the local variation term of vorticity is consistent with that of the spatially non-uniform heating term.
It can be seen from Figures 9a-9c that the large value of the spatially non-uniform heating term is mainly concentrated below 400 hPa, and it always shows a heating effect near the ZSL. However, there are some differences in the heating intensity at different stages. At the initiation stage (Figure 9a), the intensity of the large-value center of the spatially non-uniform heating term is 1.6 × 10 −9 s −2 . The maximum intensity of the ZSL increases to 1.9 × 10 −9 s −2 at the maturity stage (Figure 9b). At the dissipation stage (Figure 9c), the maximum intensity of the spatially non-uniform heating term decreases to 1.6 × 10 −9 s −2 , and the distance to the ZSL becomes longer. The intensity of the spatially non-uniform heating term near the ZSL weakens to about 0.6 × 10 −9 s −2 .
In order to show the intensity variation of the spatially non-uniform heating term more clearly, we have added the analysis of the deviation, which is equal to the average of each stage minus the average of the entire life cycle. Figures 9d-9f show the deviation of the spatially non-uniform heating term in different stages. At the initiation and maturity stages (Figures 9d and 9e), there are positive deviations of the spatially non-uniform heating term near the ZSL. However, at the dissipation stage (Figure 9f), the deviation of the spatially non-uniform heating term turns negative, indicating a weakening of the heating effect near ZSL. These characteristics are consistent with the local variation term of vorticity near the ZSL, so the intensity variation of the spatially non-uniform heating term can influence the ZSL's intensity evolution. Figures 9a-9c and 10a-10c show that the distribution patterns of the spatially non-uniform heating term and the vertically non-uniform heating term are highly similar. The positive zones for both of them are concentrated below 400 hPa. Moreover, there is a large-value center at 500 hPa, corresponding to the typical level of the ZSL. Therefore, the vertically non-uniform heating term plays a decisive role in the distribution and evolution characteristics of the spatially non-uniform heating term. Figures 10d-10f show the deviation of the vertically non-uniform heating term in different stages. As similar to the spatially non-uniform heating term, there are positive deviations in the vertically non-uniform heating term near the ZSL at the initiation and maturity stages (Figures 10d and 10e). Whereas at the dissipation stage (Figure 10f), the deviation of the vertically non-uniform heating term turns negative, indicating a weakening of the heating effect near the ZSL.
To sum up, the vertically non-uniform heating effect in the vicinity of the ZSL is one of the primary mechanisms for the intensity evolution of the ZSL. When the vertically non-uniform heating effect near the ZSL enhances (weakens), it will be favorable (unfavorable) to enhance the ZSL.

Horizontally Non-Uniform Heating Effect
The magnitude of the horizontally non-uniform heating term (10 −10 s −2 ) is one order of magnitude smaller than the vertically non-uniform heating term (10 −9 s −2 ). The horizontally non-uniform heating term is composed of the meridionally non-uniform heating term and zonally non-uniform heating term, which characterizes the non-uniform state of the Q in meridional and zonal directions, respectively.
The distribution and variation characteristics of the zonally non-uniform heating term (Figures 11d-11f) are consistent with those of the horizontally non-uniform heating term (Figures 11a-11c). Therefore, the horizontally non-uniform heating term is dominated by the zonally non-uniform heating term. However, its effect on the ZSL is not apparent and mainly affects the southern regions of the ZSL. A narrow zone of horizontally non-uniform heating effect exists near 32°N on the southern side of the ZSL in all three stages, and the center of the large value of heating is located near 500 hPa. It is most significant in the maturity stage (Figures 11b  and 11e), which may be related to the abundant water vapor and precipitation occurring in this stage.

Conclusions and Discussion
Based on the ERA5 hourly reanalysis data with the spatial resolution of 1° × 1° from June to August during 1980-2019, 11 cases of heavy-precipitation-inducing ZSL with life cycles more than 60 h in the high-frequency region (32°-35°N) of the ZSL are selected. The mechanism of the diabatic heating effect on the intensity of the ZSL has been revealed by the methods of composite and diagnostic analysis. The main conclusions are as follows.
The intensity of the ZSL features a significant diurnal variation, with its peak at around 23 LST and its valley at around 15 LST within a day. The intensity of the vertically integrated diabatic heating <Q 1 > peaks at 13 LST within a day. Moreover, a close relationship exists between the ZSL's intensity and the 10-h-earlier <Q 1 >. The area with high positive correlations mainly appears near the ZSL and its southern side, with a maximum correlation coefficient of 0.81.
The diabatic heating rate Q reaches its maximum value at around 350 hPa. The profile of Q is very similar to that of the vertical transport term of temperature at 500-300 hPa. The vertical transport of temperature is the main positive contributor to the intensity of Q.  The evolution of the local variation term of vorticity is consistent with that of the spatially non-uniform heating term. The spatially non-uniform heating term always shows a heating effect near the ZSL, while the heating intensity varies in different stages. The vertically non-uniform heating term plays a decisive role in the distribution and evolution characteristics of the spatially non-uniform heating term. Therefore, the vertically non-uniform heating effect in the vicinity of the ZSL is the primary mechanism for the intensity evolution of the ZSL. When the vertically non-uniform heating effect near the ZSL enhances (weakens), it will be favorable (unfavorable) to enhance the ZSL.
In this study, the relationship between the ZSL's intensity and the intensity of diabatic heating has been revealed. The mechanism of the diabatic heating effect on the intensity of the ZSL has been obtained through the methods of composite and diagnostic analysis. The results have improved the understanding of the diabatic heating effect on the intensity evolution of ZSL and have provided some insight into the prediction of heavy precipitation over the TP. However, the conclusions obtained are based on a composite analysis of 11 cases of ZSL in a specific category. Further studies on the mechanism of the diabatic heating effect on the intensity of other types of ZSLs will be needed. Moreover, the effects of sensible heating, latent heating, and solar radiation on the evolution of the ZSL, respectively, need to be considered in the subsequent study.