Atmospheric Meridional Circulation Between South Asia and Tibetan Plateau Caused by the Change of Planetary Boundary Layer Depth

Planetary boundary layer (PBL) influences the vertical exchanges of momentum, heat, water vapor, atmospheric pollutants, and the efficacy of climate forcing between land surface and atmosphere. Over the western Tibetan Plateau (TP), PBL can stretch into the middle‐upper troposphere. In this study, we investigate an effect of the PBL depth change on atmospheric circulations between South Asia and the TP through the formula derivation, the observation, and the model data set. The derivation first gives the PBL depth‐generalized pressure equation. It reveals an effect of PBL depth on the pressure change with time. The data analysis further shows that an increase of PBL depth in the western TP can cause the subsequent development of the PBL low (high) pressure anomalies in the northwestern TP (northern South Asia) and the upper‐tropospheric high (low) pressure anomalies over the TP (South Asia), with an anticlockwise meridional‐vertical circulation (MVC) anomaly from South Asia to the TP. In this process, the peak of PBL depth may be ahead of that of the low‐pressure occurrence, which may cause the MVC development to lag behind surface heating. The anticlockwise MVC anomaly strengthens the transport of water vapor from the lower troposphere over South Asia to the TP PBL, producing convective precipitation in the TP.


Introduction
The mean elevation of the Tibetan Plateau (TP) is >4,000 m above sea level.Studying its climatic links with South Asia has been a major challenge.A century ago, Blanford (1884) and Walker (1910) noted an out-of-phase relationship between the Himalayan climate and the Indian monsoon rainfall.Using more abundant observation data, on the climatological mean map, an anticlockwise meridional-vertical circulation (MVC) from South Asia to the TP during summer was revealed (Lau & Li, 1984;Ye, 1981).Associated with this circulation are a low pressure in planetary boundary layer (PBL) over the TP, called the TP vortex, and the South Asian high (SAH) in the upper troposphere over the TP and adjacent areas.The lower-tropospheric flows over South Asia climb the southern slope of the TP and transport water vapor from South Asia to the TP, which contributes to the atmospheric "water tower" in the TP (Xu et al., 2008).Meanwhile, the skill of forecasting the TP vortices affects the uncertainties in forecasting atmospheric circulations and water vapor transport to the south of the TP (Lavers et al., 2021).Therefore, it is of great significance to investigate the physical mechanisms responsible for links in atmospheric circulations between South Asia and the TP.
The atmospheric circulations over South Asia and the TP are modified by thermal contrasts between them.Early in the 1950s, Flohn (1957), Koteswaram (1958), and Murakami (1958) found that the seasonable change in the TP elevated surface heating triggers the reversal of the meridional temperature gradient between the TP and Abstract Planetary boundary layer (PBL) influences the vertical exchanges of momentum, heat, water vapor, atmospheric pollutants, and the efficacy of climate forcing between land surface and atmosphere.Over the western Tibetan Plateau (TP), PBL can stretch into the middle-upper troposphere.In this study, we investigate an effect of the PBL depth change on atmospheric circulations between South Asia and the TP through the formula derivation, the observation, and the model data set.The derivation first gives the PBL depth-generalized pressure equation.It reveals an effect of PBL depth on the pressure change with time.The data analysis further shows that an increase of PBL depth in the western TP can cause the subsequent development of the PBL low (high) pressure anomalies in the northwestern TP (northern South Asia) and the upper-tropospheric high (low) pressure anomalies over the TP (South Asia), with an anticlockwise meridional-vertical circulation (MVC) anomaly from South Asia to the TP.In this process, the peak of PBL depth may be ahead of that of the low-pressure occurrence, which may cause the MVC development to lag behind surface heating.The anticlockwise MVC anomaly strengthens the transport of water vapor from the lower troposphere over South Asia to the TP PBL, producing convective precipitation in the TP.

Plain Language Summary
In this study, we investigate an effect of the change in planetary boundary layer (PBL) depth on atmospheric circulations between South Asia and the Tibetan Plateau (TP) through the formula derivation, the observation, and the model data set.The result first shows the PBL depth-generalized pressure equation.It reveals an effect of PBL depth on the pressure change with time.The data analysis further shows that an increase of PBL depth in the western TP can cause the development of an anticlockwise meridional-vertical circulation anomaly from South Asia to the TP, which strengthens the transport of water vapor from the lower troposphere over South Asia to the TP and produces convective precipitation in the TP.

ZHAO ET AL.
ZHAO ET AL.

10.1029/2023JD039506
2 of 15 South Asia.Subsequently, C. F. Li and Yanai (1996) revealed a relationship between the reversal and the Asian summer monsoon onset.They addressed that the temperature increase centered at the TP and associated with the local sensible heat is a major factor for this reversal, while temperature varies little over the Indian Ocean.However, the thermodynamic effects in the main platform of the TP are also argued.The diabatic heating within the TP PBL is almost balanced by the cold horizonal advection (Yanai & Li, 1994).Boos and Kuang (2010) addressed that the large-scale South Asian summer monsoon circulation is otherwise unaffected by the heating in the platform of the TP, provided that the narrow orography of the Himalayas and adjacent mountain ranges is preserved.Beyond this, almost 70% of the TP vortices occur at night when the local surface heating is weak (Che & Zhao, 2021;L. Li et al., 2014).The correlation map presents that the low vortex occurrence is not significantly related to surface heating in the main platform of TP (T.Y. Zhang & Li, 2018).These results imply an uncertainty in the effects of the TP surface heating on atmospheric circulations over South Asia and the TP.
Therefore, we expect that the PBL process could facilitate the development of atmospheric circulations in a large region from South Asia to the TP.Then, how does such a high PBL in the TP affect atmospheric circulations?Since numerical models with complicated interactions between surface and atmosphere are often difficult to isolate an individual effect of PBL depth, a simply theoretical formula can perhaps explicitly manifest this causal influence.In this study, we investigate atmospheric circulations between South Asia and the TP caused by the PBL depth change through the formula derivation and the observation and model data diagnosis.This allows us to understand the responses of atmospheric circulation and climate to PBL behaviors.

Observation, Reanalysis, and Simulation Data
The routine meteorological operational sounding observations are scarce in the western TP due to the local high elevations, naturally harsh environmental conditions, and logistic challenges.The Third TP Atmospheric Scientific Experiment (TIPEX-III) carried out the routine meteorological intensive sounding observations at Shiquanhe (SQH), Gaize (GZ), and Shenzha (SZ) stations of the western TP (Figure 1a) at 00:00, 06:00, and 12:00 UTC for the 2013 summer (June, July, and August) (P.Zhao et al., 2018).Moreover, the simultaneous routine operational (00:00 and 12:00 UTC) and intensive (06:00 UTC) sounding data at 16 stations of the east-central TP from the China  Meteorological Administration (Figure 1a) are also utilized in this study.Using the routine and intensive sounding data at these 19 stations and the potential-temperature-gradient method proposed by Liu and Liang (2010), Che and Zhao (2021) identified the PBL type (the convective boundary layer, the neutral boundary layer, and the stable boundary layer) and calculated the PBL depths at the 19 stations for the 2013-2015 summers.We apply their PBL depth data set to examine the characteristics of PBL depth and its link with atmospheric circulation.
To examine the varying characteristics of atmospheric circulation, surface heating, and precipitation associated with PBL depth changes, we also used the hourly ECMWF ERA5 reanalysis data set with a horizontal resolution of 0.25° during the 2013-2015 summers (Hersbach et al., 2020).This data set includes surface pressure, geopotential height, u and v components of wind, specific humidity, p-vertical velocity, surface sensible heat flux, surface latent heat flux, surface thermal radiation, convective precipitation, and convective available potential energy (CAPE).To compare with the data at observation stations, the bilinear interpolation method is used to interpolate the ERA5 reanalysis grid data onto the 19 observation stations.
Moreover, we also use the outputs of the Weather Research and Forecasting (WRF) model from 1 June to 31 August 2015 with 30-hr integration from 12:00 UTC (Jia et al., 2023).The model data set includes the hourly PBL depth, geopotential height, surface sensible flux, surface latent heat, and surface thermal radiation.The model outputs are for two experiments.One is the WRF-CTL experiment using the original WRF model.Another is the WRF-MEP experiment.In this experiment, surface heat fluxes are calculated with the maximum entropy production (MEP) model and are remarkably improved in the TP (Jia et al., 2023).The WRF-MEP experiment is utilized to demonstrate the robustness of the observed link between PBL depth and pressure system.A comparison between these two experiments is utilized to examine the effect of surface heating.These two experiments have the simulation domain covering East Asia, with a central point at 33.472°N and 104.238°E and a horizontal resolution of 9 km (Figure 1b).The atmospheric lateral boundary conditions and initial atmospheric fields are retrieved from the 6-hourly 1° × 1° NCEP Global Final Analysis (Kalnay et al., 1996).More formation can be found in the reference of Jia et al. (2023).The latest 24-hr outputs are analyzed.

The Derivation of the PBL Depth-Generalized Pressure Equation
In a cold and dry climate system where the roles of turbulent mixing are significant, the heat capacity of the system is proportional to PBL depth (h).Thus the complexity of the turbulent mixing processes could be parameterized through h (Esau & Zilitinkevich, 2010).For one dimensional energy budget of the lower atmosphere which is a decoupling of the PBL from the rest of the atmosphere, Davy and Esau (2016) expressed the time change of PBL virtual potential temperature (θ v ) as follows.
Here Q is the heat flux (Q 1 ) divergence across a boundary layer (W m −2 ) (from the surface pressure (p s ) to the pressure at the top of PBL (p h )), and is defined as Li & Yanai, 1996); ρ is the air density; C p is the heat capacity at constant pressure.Q 1 (W kg −1 ) can be written as follows (Yanai et al., 1973).
Here T is the temperature;  ⃖⃖ ⃑  is the horizontal wind; p is the pressure; p 0 = 1,000 hPa; θ is the potential temperature; and ω is the p-coordinate vertical velocity.According to the formula of the gas law, θ v can be expressed as (Yang & Tan, 2020).
Here R d is the dry air gas constant; and κ = R d /C p ≈ 0.286.
Substituting Equation 3 into Equation 1 and neglecting the time change of air density, we can get the following equation between h and the time change of the generalized pressure (P).5, we analyze the effect of Δh on pressure systems in the following section.

Characteristics of PBL Depth in the TP
PBL depth in the TP is characterized by a remarkable diurnal variation (Che & Zhao, 2021).Because the TP spans almost 1.5 time zones from west to east, the local time (LT) is earlier in the west (where 12:00 UTC corresponds to 17:20 LT at the westernmost SQH station) compared to the east (where 12:00 UTC corresponds to 18:50 LT at the easternmost Hongyuan (HY) station) (Figure 1a).This time difference supports an earlier transition from the daytime PBL to the nighttime one in the east than in the west.Above all, it is necessary to simply review the diurnal characteristics of PBL in the TP on the basis of the result of Che and Zhao (2021).It is seen from their figure (Figure 3 of Che and Zhao ( 2021)) that at 00:00 UTC, PBL is of the night-time property, with a low depth (generally <450 m AGL).At 06:00 UTC, PBL depth remarkably increases, with an average exceeding 1,500 m AGL, and exhibits a remarkable west-east difference, with an average exceeding 2,000 m AGL in the western TP (west of 92.5°E).At 12:00 UTC, PBL depth begins to decrease in the eastern TP, with the depth near 600 m at some stations, while at the western stations (such as SQH and GZ), PBL depth continues to increase.This increase in PBL depth is highly correlated with the past 6-hr accumulated surface sensible heat flux (Che & Zhao, 2021).Moreover, the PBL depth is characterized by a remarkable western high-eastern low structure at 14:00 Beijing standard time (06:00 UTC) and 20:00 Beijing standard time (12:00 UTC), which may be associated with the differences in surface heating, cloud coverage, solar radiation, and soil moisture between the western and eastern TP (Che & Zhao, 2021).
Because the PBL depth calculated with the potential temperature gradient method and the sounding observations has a root mean square error around 200 m (Che & Zhao, 2021;Liu & Liang, 2010), the PBL depth at 00:00 UTC (with a mean value of 370.7 m) possibly has a large uncertainty which might reduce the reliability of PBL depth at this time.The similar uncertainty possibly occurs in the eastern TP at 12:00 UTC when the PBL depth is also low (shown in Figure 3 of Che and Zhao (2021)).Therefore, we analyze PBL depth in the western TP at 06:00 UTC (the local noon) and at 12:00 UTC (the local late afternoon).At these times, the PBL depth data set has a larger reliability because PBL depth is much larger relative to the root mean square error.Moreover, we also remove the diurnal variations of all variables (unless otherwise stated) by subtracting their climatological (2013-2015) mean diurnal variations so as to reduce the possible influences of the diurnal variations on results.
To measure a change of PBL depth in the western TP, the regional mean PBL depth (after removing the diurnal variation) at eight stations west of 92.5°E (shown in Figure 1a) is defined as an index (I w ).At 06:00 or 12:00 UTC, I w is calculated when there are observation values at least seven stations of the western TP.We finally get 229 samples (70 samples at 06:00 UTC and 159 samples at 12:00 UTC).Corresponding to I w at 06:00 and 12:00 UTC, the time change of the variable A (  Ȧ ) is defined as its lagged 6-hr time difference; and ∆A (06:00UTC) = [A (12:00UTC) − A (06:00UTC) ] and ∆A (12:00UTC) = [A (18:00UTC) − A (12:00UTC) ] in turn.According to Equation 5, this calculation indicates an effect of I w at the current time on the subsequent change of A.

Pressure in the TP Caused by the PBL Depth Change
Figure 2a shows the correlation coefficient between I w and the time change of geopotential height (  Ḣ ) at 500 hPa.
Significant negative correlations cover the western and northern parts of the TP (i.e., the northwestern TP on the left side of line AB in Figure 2a), with the central value of −0.4 (at the 99.9% level), while positive corre- 6 of 15 lations appear in the southeastern part.I w has a correlation coefficient of −0.34 (at the 99.9% level) with the regional mean of 500-hPa  Ḣ over 33°-36°N, 80°-85°E (Figure 2b).Using the I w and  Ḣ data sets with the diurnal variations, we repeat the above correlation analyses and obtain the similar result, that is, the significant negative correlations also appear in the northwestern TP (Figure 2c).To increase the robustness of this link, we also calculate their correlations using the WRF-MEP model PBL depth and H data at four times (00:00, 06:00, 12:00, and 18:00 UTC) each day after removing the diurnal variations.There are 368 samples from 1 June to 31 August in 2015 (4 times/day × 92 days).Figure 2d shows the correlation between the regional mean PBL depth over the western TP (above the 3,000-m topography between 80° and 92.5°E) and the 500-hPa  Ḣ .In this figure, significant negative correlations at the 95% level cover the northwestern TP, with the central value of −0.24 (at the 99.9% level), and the positive correlations appear in the southeastern TP.This negative correlation pattern is similar to the observation.The consistency between observation and model results indicates a close link between h and the lagged 6-hr time change of the low-level pressure for both the observation data at 06:00 and 12:00 UTC and the model data at 00:00, 06:00, 12:00, and 18:00 UTC.Such a high correlation implies that the PBL depth may be used as a preceding factor for the subsequent pressure change within PBL.
To perform a composite analysis of atmospheric circulation, 20 largest and smallest I w cases are chosen from the observed 229 samples, called the high and low cases, respectively.In the western TP, the PBL depth after  removing the diurnal variation is high in the high case (Figure 3a), with the regional mean value of 963.4 m over the western TP, and is low in the low case (Figure 3b), with the regional mean value of −866.9 m.The difference in PBL depth between the high and low cases is significantly positive in the western TP (Figure 3c), with the regional mean difference of 1,830.3 m.However, this difference is not significant at almost half of the eastern stations, with a small regional mean value (617.2 m) in the eastern TP, which is much smaller compared to the western one.This zonal pattern supports a general decrease in PBL depth from west to east.The above result shows that the high (low) case indeed reflects a higher (lower) PBL depth in the western TP.
Figure 4a shows the composite difference of    between the high and low cases.In this figure, significant negative anomalies (at the 95% level) cover the northwestern TP, with the central value below −1.0 hPa, indicating an out-of-phase relationship between I w and    .This relationship in the northwestern TP is consistent with the correlation result shown in Figure 2a.Meanwhile, significant positive    anomalies appear to the south of the negative anomalies, indicating an increase of    in northern South Asia.It is evident that    caused by the I w change exhibits an opposite variation between the TP and northern South Asia.

The negative correlation between h and
in the northwestern TP can be physically explained from the first term of the right side in Equation 5. Figure 5a shows the longitude-height cross section of the JJA climatological mean  1 along the latitudes 32°--36°N.Generally,  1 increases upward in the middle-low layer of the troposphere, with the maximum value near 400 hPa, and the climatological mean   is also positive in the northwestern TP on the left side of line AB (Figure 5b).In this area, according to Equation 5, the PBL depth has an inverse relationship with    .Thus significant positive Δh (Figure 3c) is generally matched with the significant negative  Δ  (Figure 4a).In the southeastern TP, both the weak positive or negative   (mixing together) and the relatively weak Δh do not favor a significant change of    .These analyses show the consistency between the observation data diagnosis result and Equation 5.Although some errors possibly occur in the observational PBL depth, the consistence between observation, model, and physical explanation supports the reliability of the link between PBL depth and geopotential height in the western TP.Therefore, an increase of PBL depth might cause the decrease of the subsequent PBL pressure, which can help the formation and development of low pressures or the weakening of high pressures within the PBL.This result also implies that the peak of PBL depth may be ahead of that of the low-pressure occurrence.Some observation studies have revealed that in the western TP, when the PBL depth peaks in the late afternoon, the occurrence of the local TP vortices peaks at night (L.Li et al., 2014).This time difference supports that the effect of the increased PBL depth may cause the PBL low-pressure development to lag behind the peak of surface heating.

Meridional-Vertical Circulation Caused by the BPL Depth Change
The atmospheric circulation changes caused by the TP PBL depth also extend into the free atmosphere above.Figure 6a shows the cross section of composite difference in geopotential height and zonal-vertical circulation between the high and low cases along 32°-36°N.It is seen that the negative anomalies of geopotential height in the western TP expand upward to 350 hPa, with the central value of −80 m 2 s −2 near the surface.The low-level low-pressure anomalies may strengthen the local lower-tropospheric convergence (Figure 4c) and the tropospheric ascent.Generally, the anomalous ascent is located to the east of the anomalous low center in the lower troposphere and expands from the PBL to 150 hPa (Figure 6a).The anomalous ascent flows eastward in the middle-upper troposphere, which may strengthen the upper-tropospheric divergence.At 100 hPa, positive convergence/divergence anomalies appear in the central TP between 85° and 95°E, with the maximum value of 1.5 × 10 −5 s −1 , while the negative convergence/divergence anomalies appear in northern South Asia (Figure 4d).This vertical structure is in favor to the descent anomalies over South Asia. Figure 6b shows the latitude-height cross section of the composite difference of MVC along 85°-90°E.The anomalous ascent in the central TP flows southward and northward in the upper troposphere, which also strengthens the upper-tropospheric divergence.The southward air descends in northern South Asia.An anticlockwise MVC anomaly therefore appears between the central TP and northern South Asia, with the circulation center appearing between 300 and 250 hPa.
The strengthened upper-tropospheric divergence in the TP can lead to a decrease in the time change of vorticity (  ζ ) according to the classical vorticity equation, in favor of the high-pressure development in the upper troposphere.Accordingly, the positive anomalies of geopotential height appear in the upper troposphere over the central TP, with the central value exceeding 50 m 2 s −2 (Figure 6b).At 100 hPa, the positive anomalies appear between 85° and 95ºE, with the central value above 80 m 2 s −2 (Figure 4b).On the summer climatological mean map, the largest standard deviation of the SAH intensity is located in the central TP (P.Zhao et al., 2009).Thus, the large upper-tropospheric positive height anomalies indicate a strengthened SAH, which implies a modification of the TP PBL depth to the SAH.Meanwhile, the negative anomalies of geopotential height appear in the upper troposphere over South Asia.This structure in pressure between the upper and lower parts of the troposphere tilts southward.
The anticlockwise MVC anomaly associated with the TP PBL depth increase can strengthen the transports of atmospheric compositions from South Asia to the TP. Figure 7a shows the cross section of compositive difference  Figure 7b shows the composite difference in 500-hPa  q between the high and low cases.It is seen that the water vapor anomalies mainly transport into the TP through the southwestern boundary to the west of 90°E and arrive northward to 35°N. Figure 7c shows the composite difference of 500-hPa ∇  ⋅ (water vapor flux divergence) between the high and low cases.In this figure, the negative anomalies appear in the southern TP between 82° and 95°E, with the central value of −3 × 10 −7  kg m −2 hPa −1 s −1 , indicating an accumulation of water vapor in this area.The water vapor transport caused by the PBL depth change in the western TP is different from that through climbing the southern slope of the TP (Xu et al., 2014), but similar to the one lifted by convective storms over South Asia and the Himalayan foothills and then crosses the TP by the mid-tropospheric circulation (Dong et al., 2016).Thus our result suggests a role of the PBL process in the up-and-over transport of water vapor from South Asia to the TP.Of course, this does not exclude the effects of other factors on the water vapor transport.
Meanwhile, corresponding to an increase of PBL depth, the atmospheric instability indicated by the CAPE also increases (Figure 7d).There are positive anomalies of CAPE in the southern TP, with the central value exceeding 300 J kg −1 near 90°E.This result implies that an air parcel would be much warmer than its surrounding environment and therefore, very buoyant, would favor the occurrences of thunderstorms and heavy rainfall.Thus the combined role of the strengthened ascent, water vapor transport, and atmospheric instability provides a favorable condition for the occurrence of convective precipitation in the TP. Figure 7e shows the composite difference of convective precipitation between the high and low cases.In this figure, the significant positive precipitation anomalies cover most of the southern TP, indicating an increase of local convective precipitation, which may contribute to the maintenance of the atmospheric "water tower" in the TP.
The foregoing analyses show that in the western TP, the increased PBL depth can cause the PBL vortices and the upper-tropospheric SAH to develop in the subsequent 6 hr, which forms an anticlockwise MVC anomaly between South Asia and the TP and then affects the transport of water vapor from the lower troposphere over South Asia to the PBL over the TP and convective precipitation in the TP.

A Comparison of PBL Depth and Diabatic Heating Effects
Figure 8a shows the composite difference in the time change of surface heating (  Ṡ ), in which the surface heating is a sum of sensible heat flux, latent heat flux, and thermal radiation according to Ye and Gao (1979).In this figure, significant negative anomalies of  Ṡ generally cover the central and eastern parts of the TP, especially in the southeast of the TP, with the central value of −90 W m −2 .In the western TP, the negative anomalies are weak.The significant positive values mainly appear to the south of the TP.The similar feature is also seen in surface sensible heat flux.The significant negative anomalies of surface sensible heat flux appear in the TP between 80°E and 105°E (Figure 8b).A comparison with Figures 4a, 6a, and 7e shows that the decreased surface pressure, the increased ascending motion, and the increased convective precipitation in the TP generally correspond to the decreased surface heating.Thus, it is unlikely that the low-pressure development associated with PBL depth is dominated by the negative surface heating anomalies.
The simulation results also support this conclusion.Figure 9 shows the summer mean surface heating in the WRF-MEP and WRF-CTL experiments and their difference.It is seen from Figure 9a that in the WRF-MEP experiment, the large surface heating appears in the western TP between 80° and 95°E, with the maximum value of 240 W m −2 and the regional mean value of 193.8 W m −2 over 80°-90°E above the topography of 3,000 m.In the WRF-CTL experiment (Figure 9b), the surface heating remarkably increases, with the maximum value of 280 W m −2 and the regional mean value of 220.1 W m −2 .There are positive differences in surface heating between the WRF-CTL and WRF-MEP experiments in the TP, with the maximum value >30 W m −2 (Figure 9c).This implies a stronger surface heating in the WRF-CTL experiment relative to the WRF-MEP experiment.However, the negative correlation coefficient between PBL depth and 500-hPa  Ḣ in the northwestern TP is ZHAO ET AL. 10.1029/2023JD039506 13 of 15 weaker in the WRF-CTL experiment (Figure 2e) than in the WRF-MEP (Figure 2d).This result shows that the stronger surface heating does not lead to a stronger negative correlation between PBL depth and 500-hPa  Ḣ in the northwestern TP.
According to the second term of the right side in Equation 5, the PBL  Ṗ may also be caused by the heat flux divergence across a boundary layer.Here we compare the relative importance of the PBL depth term (  −  ℎ 2 Δℎ ) and the diabatic heating term (  1 ℎ Δ ).The result shows that different from general significant decreases in  −  ℎ 2 Δℎ in the western TP between the high and low cases (Figure 10a),  1 ℎ Δ does not show general significant differences in this area (Figure 10b).On the average of the western TP, although

Conclusion and Discussion
Our results demonstrate through formula derivation, observation, model a mechanism responsible for the effect of the PBL depth change in the western TP on atmospheric circulation systems over South Asia and the TP.This mechanism is summarized in Figure 11.In the western TP, the increased PBL depth can cause the development of both the PBL vortices and the upper-tropospheric SAH, forming an anticlockwise MVC anomaly between South Asia and the TP.The MVC anomaly strengthens the transport of water vapor from the lower troposphere over South Asia to the PBL over the TP, producing convective precipitation in the TP.In this process, the atmospheric circulation anomalies caused by the PBL depth change are nonclassical.The peak of PBL depth may be ahead of that of the low-pressure occurrence, which may further cause the PBL low-pressure development to lag behind surface heating.The ascent branch in the MVC anomaly generally corresponds to the decreased surface heating, which suggests that the low-pressure development associated with PBL depth could not be caused by the decreased surface heating.This is distinct from the thermally induced classical sea breezes and valley winds.In the framework of the thermally induced mountain-valley wind, surface heating is stronger (weaker) in the mountain (the valley) in the daytime, with ascent (descent) in the mountain (the valley), and then wind flows from the valley to the mountain; and vice versa.ZHAO ET AL. 10.1029/2023JD039506 14 of 15 The previous study revealed a decreasing trend of summer PBL depth in the western TP during the recent decades (Slättberg et al., 2022).According to our mechanism, the decreased PBL depth can cause an increase in PBL pressure over the TP, therefore reducing the occurrence of the local low pressure.In fact, this decreasing trend in the occurrence frequency of low pressure has been found by L. Li et al. (2019).This variation in PBL depth presents exciting challenges to improved understanding of the effects of the PBL behaviors in both the present climate and the future projections on the occurrences of extreme climatic events and the representation of PBL processes in numerical models of the atmosphere.

Figure 1 .
Figure 1.(a) Meteorological station altitudes above sea level.The dashed line is along 92.5°E and (b) the Weather Research and Forecasting model domain of 900 × 592 grid cells.
1− ; and the constant   =      0  .For convenience, Equation 4 is called the PBL depth-generalized pressure equation and may further be expressed as follows. = ( (2) −  (1) )∕Δ ; Δ indicates the mathematical differential operation of one variable; time t 2 = t 1 + Δt; and   and  ℎ are defined as the climatological mean values.According to Equation 5, the changes of h and Q at time t 1 (  Δℎ (1) and  Δ (1) in turn) can cause a variation in the intensification or reduction rate of P with time (i.e.,  Δ Ṗ ).Therefore, the PBL depth-generalized pressure equation allows us to isolate the effect of Δh and to compare the contributions of Δh and ΔQ to Δ  Ṗ .Based on Equation

Figure 2 .
Figure 2. (a) The correlation between I w and ERA5 500-hPa  Ḣ (for 229 samples), in which dots are significant at the 95% level and the dashed line AB generally indicates the southeastern boundary of the Tibetan Plateau (TP) negative values; (b) the relationship between I w and ERA5 500-hPa  Ḣ averaged over 80°-85°E, 33°-36°N, in which the correlation coefficient and the sample number are given; (c) same as in (a) but for the data with diurnal variations; (d) correlation between the Planetary boundary layer depth averaging over the western TP (above the 3,000-m topography between 80° and 92.5°E) and 500-hPa  Ḣ in the Weather Research and Forecasting (WRF)-maximum entropy production experiment; and (e) same as in (d) but in the WRF-CTL experiment.

Figure 3 .
Figure 3. Composite observational Planetary boundary layer (PBL) depth (km) in the (a) high and (b) low cases.(c) Composite difference of observational PBL depth(km)  between the high and low cases, in which "+" is significant at the 95% level.

Figure 4 .
Figure 4. (a) Composite difference of ERA5   (hPa) between the high and low cases, in which dots are significant at the 95% level; (b) same as in (a) but for 100-hPa geopotential height (m 2 s −2 ); (c) same as in (a) but for 550-500 hPa convergence/divergence (×10 −5 s −1 ) of air masses; and (d) same as in (c) but at 100 hPa.

Figure 8 .
Figure 8.(a) Composite differences of ERA5  Ṡ (W m −2 ) between the high and low cases, in which dots are significant at the 95% level; and same as in (a) but for surface sensible heat flux.

Figure 9 .
Figure 9. (a) Summer mean surface heating (W m −2 ) in the Weather Research and Forecasting (WRF)-maximum entropy production experiment; (b) same as in (a) but for the WRF-CTL experiment; and (c) the difference between (b) and (a).
is −8.89 × 10 −3 W m −3 .It is evident that the latter is much larger in absolute value compared to the former.Thus,  −  ℎ 2 Δℎ may play a more important role in helping the development of PBL low pressure in the western TP compared to  1 ℎ Δ .

Figure 10 .
Figure 10.(a) Composite values of  −  ℎ 2 Δℎ (×10 −2 W m −3 ) between the high and low cases, in which "+" is significant at the 95% level.(b) Same as in (a) but for

Figure 11 .
Figure 11.Schematic diagram of nonclassical atmospheric circulations caused by the Planetary boundary layer depth change in the western Tibetan Plateau.