The Interannual Relationship between the Diabatic Heating over the South Asia and the Snow Depth over the Southern Tibetan Plateau in Late Spring to Early Summer: Roles of the Air Temperature

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Introduction
Te Tibetan Plateau (TP) snowpack is considered to be an important factor modulating a regional hydrological cycle and exerts great impacts on agriculture and industry in populous Asia [1][2][3][4][5][6][7]. From the perspective of the annual cycle, the snow depth (SD) over the TP begins to increase in autumn and gradually melts during the following spring and summer [8,9]. It is worth mentioning that some high elevation areas (e.g., the western TP) are covered with snow all year round [10]. Te annual cycle of SD is closely related to local temperature. Te out-of-phase variation of 2-m air temperature and SD over the TP was found in a station dataset [11]. Te snow albedo efect is one of the dominant causes of local temperature and SD variations [12]. Te absorbed solar radiation over the snow-covered area led to the increase of underlying surface temperature and hence snow melting [13], and the snow albedo efect gradually decreases [14]. A recent study [15] confrmed that the deposition of absorbing aerosols from Taklimakan desert to populous Ganges plain induces decrease of the snow albedo efect by causing a positive radiative efect on snow, resulting in the reduced snow cover over the northern TP slopes during premonsoon season.
Surface temperature and snowfall are the important factors that directly afect the year-to-year variability of SD [16][17][18][19][20]. Wang et al. [21] showed that in autumn, the eastern North Pacifc and western North Atlantic Sea surface temperature anomalies excited southeastward propagating wave train, which led to snow cover anomalies by causing anomalous snowfall. In winter, Indian Ocean Dipole (IOD) and El Niño-Southern Oscillation (ENSO) induced anomalous moisture transported to the TP through diferent mechanisms. Te water vapor transport directly afected snowfall and then regulated SD over the TP [11]. However, in spring and summer, some studies [17,18] proposed that snowfall contributed little to snow cover anomalies over the TP and the dominant factor is surface temperature. Te surface temperature over the TP is closely related to the onset of Indian summer monsoon [22], which is mainly infuenced by the strongest diabatic heating in May over the Bay of Bengal and Indochina Peninsula [23][24][25]. Senan et al. [22] suggested that negative (positive) SD anomalies over the TP is accompanied by the strongest (weak) diabatic heating around Indochina Peninsula which is closely related to the monsoon onset anomalies. Te condensation heating over South Asia is usually accompanied by large-scale convective precipitation, resulting in variations of the local temperature gradient around the TP [26][27][28]. In addition, Jiang et al. [29] showed that the interannual variation of latent heat release of condensation over the TP is obviously afected by tropical convection near Indochina Peninsula during boreal summer.
Te studies of temporal and spatial snow cover are constantly being refned [30][31][32][33][34]. For the eastern part of the Nyainqêntanglha Mountains, the annual cycle of snow cover is the most dominant component and explains at 76.6% of the total variability [35]. Although the southern TP (including the Nyainqêntanglha Mountains) occupies only small part of the plateau, it is a prominent area of TP heating in summer and has signifcant impacts on the surrounding weather and climate [36][37][38][39]. From the perspective of climate states from the station dataset, most snow-free stations are concentrated in the southern part of the TP in summer [18]. Compared with the central and eastern TP, this is a unique phenomenon in this region. Note that both thermal and mechanical forcing types over the southern TP play an important role in the formation and evolution of the South Asian summer monsoon [40][41][42]. However, the efect of diabatic heating over South Asia on SD over the southern TP is unclear during spring-summer transitional season. In order to further analyze the characteristics of regional SD, two scientifc questions will be addressed. (1) Te evolution characteristics of SD and air temperature over the southern TP in late spring to early summer. (2) Te interannual relationship between the diabatic heating over South Asia and SD over the southern TP during a diferent snow melting period: roles of the air temperature.
Te present paper is organized as follows: Section 2 describes the data and model. According to the evolution characteristics of climatological SD, the features of temperature related to SD in diferent snow melting periods will be analyzed in Section 3.1. In Section 3.2, we investigate the infuences of diabatic heating over South Asia on the yearto-year variability of SD over the southern TP. Te underlying mechanisms are examined. Te discussion and conclusions of the main fndings are provided in Section 4 and Section 5, respectively.  [43] are also applied, which are relatively more reliable than passive microwave sensors data in diferent satellite platforms [44]. Daily atmospheric reanalysis data (e.g., air temperature, geopotential height, winds, omega at multiple levels, and surface pressure) from National Centers for Environment Prediction/National Center for Atmospheric Research (NCEP/NCAR) during 1979-2004 are applied in this work. In order to analyze the characteristics of SD evolution in late spring to early summer, April-May-June (AMJ) is divided into 18 pentads, excluding June 30, for example, pentad-1 corresponding to April 1-5, pentad-2 corresponding to April 6-10, pentad-3 corresponding to April 11-15 -. . .. Te southern TP SD index (SSDI) is defned as the SD anomalies averaged over the areas (28°-32°N, 88°-98°E) by using satellite-derived data [43,44]. For further analyzing the contributions of physical processes to the local temperature variations, the thermodynamic equation [45] is applied as follows:

Data and Methods
In equation (1), the four terms from left-hand to righthand are local temperature variation, horizontal temperature advection, vertical temperature advection, and diabatic heating, respectively. T is the air temperature; V is the horizontal velocity; p and p0 are the pressure and surface pressure, respectively; ω is the vertical pressure velocity; R is the gas constant; C p is the specifc heat of dry air at constant pressure. θ and Q1 are the potential temperature and the apparent heat source, respectively.

Model.
A nonlinear baroclinic model is applied in this study to confrm the potential role of atmospheric temperature in relationship between the diabatic heating anomalies over South Asia and SD over the southern TP. Te model is designed as 24 sigma levels in the vertical and spectral R30 horizontal resolution. For more details about the nonlinear baroclinic model, one may refer to Ting and Yu [46]. Te solution of the model is stable after about 15 days. Terefore, the model is integrated for 60 days, and only the average of the last 20 days is analyzed in this study. Te specifc experimental design for this study will be detailed in Section 3.2.
Te nonlinear baroclinic model is widely used in the research community of atmospheric science [11,46]. Te simplifed dynamical framework facilitates interpreting the responses of perturbations in the large-scale atmospheric dynamics, compared to the complicated atmospheric general circulation models. Additionally, the model is ideal for studying the fundamental mechanisms underlying atmospheric dynamics, such as Rossby waves, atmospheric teleconnection patterns, and baroclinic instability. However, the moist processes, e.g., large-scale condensation and convection, are not included in the model, which is not sufcient to discuss interactions between dynamics and convection. Te nonlinear baroclinic model employed in this study is a time-dependent, dry, and primitive equation anomaly model.

Te Characteristics of SD and Air Temperature Evolution over the Southern TP from Late Spring to Early Summer.
Te stations above 2500 m are mainly concentrated in the eastern TP (25.5°-40°N, 85°-105°E). According to Xu et al. [18], the southern TP is outlined by the red box (28°-32°N, 88°-98°E) in Figure 1, which contains 28 in situ stations. Te quality control (the missing value should be fewer than 7 days) is carried out for station data over the southern TP. Only 14 stations are fnally picked out in this study during 1979-2004. Te station locations are marked by a blue cross in Figure 1. Table 1 shows the specifc information of the selected stations, including the name, station ID, elevation, and the surface temperature at the frst pentad (STF), respectively. In order to further investigate the features of SD in diferent stations, stations are divided into three categories (type A: STF > 5°C; type B: 0°C < STF ≤ 5°C; type C: STF ≤ 0°C). Elevations of the type A stations (TAS) and the type C stations (TCS) are generally below 3850 m and above 4400 m, respectively, while the elevation of type B stations (TBS) is between them, except for the Zuogong station (Table 1).
Figures 2(a) and 2(b) show climatological (1979-2004) pentad mean of surface temperature and SD over the southern TP for the diferent types of stations from pentad-1 to pentad-18. Te surface temperature of the three types of stations shows a linear-like increase with the coming of summer (Figure 2(a)). Te SD in TAS is the shallowest in pentad-1 and disappears after pentad-10. Te SD in TBS begins to melt gradually after pentad-3 and is less than 0.1 cm after pentad-9. Te SD in TCS exhibits the largest standard deviation and fuctuates until about pentad-10. After that, it melts rapidly and almost disappears at pentad-18 ( Figure 2(b)). Te abovementioned analysis implies that snow melting frstly occurs in the middle and low elevation areas, after about pentad-10 snow melting over the southern TP mainly appears in the higher elevation, accompanied by the accelerated melting rate. Figure 2(c) shows climatological pentad mean of SD over the southern TP from satellite-derived data with a decreasing trend from pentad-1 to pentad-18. Te snow melting speed is not uniform during the AMJ. To verify this phenomenon, we use the running t-test method to the time series of climatological pentad mean of SD to acquire its change point [47]. Tere is a transition pentad around pentad-10, which is statistically signifcant at the 99.99% confdence level (Figure 2(d)). Considering that the SD was close to zero in pentad-16, the snow melting period can be divided into two periods: pentad-4 to pentad-9 (P1: April 16th-May 15th) and pentad-10 to pentad-15 (P2: May 16th-June 14th). Te averaged pentad change of SD from pentad-4 to pentad-9 (pentad-10 to pentad-15) is −0.21(−0.24) cm/pentad. Tese results imply that both the satellite-derived and station data demonstrate that snow melting accelerated after about pentad-10.
Te snow melts gradually over the southern TP during the period of AMJ, accompanied by the atmospheric warming (Figures 3(a) and 3(b)). Compared with P1, a warming center is located over the Bay of Bengal and accompanied by strong southerlies over the southern TP during P2. At the same time, the apparent heat source is gradually enhanced over the Bay of Bengal and the Indochina Peninsula (Figures 3(c) and 3(d)). Te apparent heat source not only shifts the temperature ridgeline at upperlevel northward accompanied by the establishment of South Asian high [48] but also causes the air-sea instability that may lead to a spring predictability barrier [49,50]. In comparison, the diabatic heating is stronger during P2 than P1 over the southern slope of the TP and Indochina Peninsula. Te diferences of atmospheric temperature between P2 and P1 at diferent levels are shown in Figure 4, which exhibits a remarkable warming below 200 hPa from P1 to P2. Notably, there is a warming center over the TP at 300−400 hpa (Figures 4(e) and 4(f )). Such a warming may be attributed to the expansion of diabatic heating from the Indochina Peninsula to the Bay of Bengal, which is accompanied by an anticyclone to the south of the TP during the P2 period (Figures 3(b) and 3(d)). Te air temperature diference between P2 and P1 reveals a signifcant warming center located at middle and upper troposphere over the southern Tibetan Plateau. During period P2, the acceleration of snow melting is predominantly observed at higher elevations and can be attributed to an increase in local air temperature.
To further illustrate the diference in temperature changes between the two periods, relative contribution of multiple atmospheric processes to the local temperature change in P1 and P2 is analyzed by the thermodynamic equation ( Figure 5). It shows that the local temperature changes over the southern TP at 200-500 hPa during both two periods are slightly positive, but the relative roles of physical processes are diferent. Diabatic heating and Advances in Meteorology meridional temperature advection contribute to the positive temperature change in the two periods, with larger values in P2 than those in P1 ( Figure 5). Te warming efect is mainly compensated by the cooling efect of vertical temperature advection in P2 and both vertical temperature advection and zonal temperature advection in P1. Te cooling efect of vertical temperature advection in P2 is nearly three times as much as that in P1, while the zonal temperature advection shows a negligible efect in P2 ( Figure 5).

Te Interannual Relationship between the Diabatic Heating over South Asia and SD over the Southern TP during Diferent Snow Melting Periods: Roles of the Air Temperature.
Time series of the annual southern TP SD indices during two periods are presented in Figure 6. On the interannual time scale, the correlation of SSDI between the two periods is 0.43, which is signifcant at the 95% confdence level. Tis refects that SD anomalies have high persistence during the two periods. Previous works [17,18] found that surface temperature is the main factor afecting SD in spring and summer. Figures 7 and 8 show the correlations of large-scale circulation and air temperature with the SSDI in P1 and P2. During positive SSDI in P1, in the upper troposphere, a negative temperature center is found over the TP and extends to southern China. Correspondingly, there is anomalous cyclonic circulation over the TP, accompanied by anomalous westerly fow over the tropical Indian Ocean and which stretches from the East Africa to the western North Pacifc (Figure 7(a)). In the middle troposphere, cold temperature anomaly appears over the southern Bay of Bengal, while warm anomalies are found to the south of Philippines and east of the Iran Plateau. Te southern TP is located at the north of the cyclonic anomaly, which is dominated by the anomalous easterlies (Figure 7(c)). Te anomalous downward motion is found the southern TP, accompanied by cold air temperature from the surface to 200 hPa (Figure 8(a)). During positive SSDI in two periods, in the upper troposphere, a negative temperature anomaly and anomalous cyclonic circulation appear over the TP, with  Table 1.  b)). Compared with the positive SSDI in P1, in the middle troposphere, the cold center over the southern TP is weaker in P2 and the anomalous cyclonic circulation to the east of the TP associated with the anomalous northerlies over the TP (Figure 7(d)). Similar to the positive SSDI in P1, negative temperature centers appear over the TP at 400−200 hPa in P2 (Figure 8(b)). Tese characteristics further illustrate the close relationship between SD over the southern TP and local air temperature [17,18].  Te diabatic heating over the South Asian monsoon region is one of the important factors to modulate air temperature over the TP [51]. In order to illustrate the role of the diabatic heating anomalies over South Asia in the yearto-year variability of SD over the southern TP, Figure 9 shows the correlations of Q1 with the SSDI in P1 and P2. During P1, the signifcant negative correlations are located from the Bay of Bengal eastward to the western South China Sea (Figure 9(a)). In comparison, the signifcant negative (positive) correlation is located over the northern Indochina Peninsula (southern China) during P2 (Figure 9(b)). Here, we propose three indices: one is defned as Q1 anomalies averaged over the region (8°-13°N, 90°-110°E) in P1 (Q1P1), the second is defned as Q1 anomalies averaged over the northern Indochina Peninsula (15°-20°N, 100°-108°E) in P2 (Q1IPP2), and the last one is defned as Q1 anomalies averaged over southern China (23°-27°N, 108°-115°E) in P2 (Q1SCP2). Te time series of the abovementioned Q1 indices in two periods is shown in Figure 6. In P1, the correlation coefcient between SSDI and Q1P1 is −0.74. In P2, the correlation coefcient between SSDI and Q1IPP2 (Q1SCP2) is −0.49 (0.49). All the correlation coefcients are signifcant at the 99% confdence level.
To further investigate how diabatic heating over diferent areas leads to anomalous SD over the southern TP in the two periods by afecting local air temperature, the large-scale circulation and air temperature related to the three Q1 indices are calculated (Figures 10 and 11). During the negative years of Q1P1 in P1, there is a cyclone anomaly and anomalous cold air temperature center at 200 hPa over the TP, accompanied by a weakened jet stream over the Indian Ocean (Figure 10(a)). In the middle troposphere, cold temperature anomaly is centered to the south of the TP (Figure 10(b)). Tis pattern bears a large resemblance to the  spatial structure of positive SSDI in P1 (Figures 7(a) and 7(c)). In addition, the linear correlation coefcient between the Q1P1 and SSDI is −0.74, signifcantly exceeding the 99.9% confdence level. Te abovementioned results indicate that Q1P1 may be one of the key factors afecting SSDI in P1. It seems that the suppressed diabatic heating from the Bay of Bengal eastward to the western South China Sea could induce an anomalous cyclone at the upper-level and downward motions over the TP through the Gill model response, leading to cold air temperature from the surface to 200 hPa (Figures 10(a), 10(b) and 11(a)) and hence above-normal SD over the southern TP. In P2, during the negative years of Q1IPP2, the cold air temperature center and cyclone anomalies appear over the western TP at 200 hPa ( Figure 10(c)). From the pressure-latitude cross-section of the air temperature and circulation averaged over (85°N-100°N), the anomalous downward motion and cold air temperature center at about 300 hPa are observed on the southern TP slope related to diabatic cooling over the northern Indochina Peninsula (Figure 11(b)). During positive years of Q1SCP2, there are two cold centers located on the TP and the Korean Peninsula at 200 hPa ( Figure 10(e)). Te pressure-latitude cross-section of air temperature associated with the positive Q1SCP2 years is similar to those       Advances in Meteorology associated with the negative Q1IPP2 years (Figures 11(b) and 11(c)). However, the anomalous cold air temperature associated with diabatic cooling over the northern Indochina Peninsula and diabatic heating over the southern China could not extend from the upper level to the land surface over the southern TP (Figures 10(d), 10(f ), and 11(b) and 11(c)). It is difcult for observational data-based statistical methods to distinguish the individual impact of Q1 over the three regions on the southern TP air temperature in diferent periods. Tus, a nonlinear baroclinic model is conducted to simulate the atmospheric circulation and temperature anomalies in response to the individual Q1 anomalies over the three regions during their corresponding period. Following previous works [11], a heating profle was utilized in the vertical direction to simulate the heating anomalies, with the maximum located at sigma 0.37 (Figure 12(a)). Te horizontal structure and magnitude of heating depend on the regressions of Q1 against SSDI during two periods. Tis involves conducting separate regressions for each period. Te idealized heating is presented as Q = V (σ) A (λ, ϕ). Te vertical structure of heating is showed V (σ). Te function A (λ, ϕ) represents the horizontal structure and magnitude of heating [11]. Te maximum value of the heating rate equals the fve times value of the regression coefcient of Q1 which is signifcant exceeding the 80% confdence level. Four experiments are conducted as     Figure 12: (a) Te vertical profle of the specifc heat source (K/day). Te x-axis and y-axis in (a) denote the magnitude of the heating process and height represented by sigma, respectively. Te spatial pattern of specifc heat sources (shading; K/day) at the level of sigma that equals 0.37 during P1 (b) and P2 (c). and positive SSDI, but it exhibits a more southward center (Figures 7(a), 10(a), and 13(a)). Te warm and cold air temperature anomalies appear over the southeastern and northwestern portion of the cyclone (Figure 13(a)). Similarly, their downward motions and cold air temperature over the southern TP are consistent with the observational results (Figures 11(a) and 15(a)). Indeed, the cold atmospheric temperature at the lower or surface layer (Figures 14(a) and 15(a)) on the southern TP slope is conducive to deepening of SD over the southern TP.

Advances in Meteorology
In P2, the cooling forcing over the northern Indochina Peninsula excites a pair of cyclonic circulation over its northeastern and southern fanks (Figure 13(c)). Te cyclonic circulation anomaly over western TP in response to the diabatic cooling over IP in the experiment is much weaker and located southeastward compared to that in observation (Figures 10(c) and 13(c)). Tere is anomalous anticyclonic circulation and warm temperature anomaly over the Indochina Peninsula at 500 hPa (Figure 14(c)). Correspondingly, the cold air temperature center appears to the south of TP at the tropopause (250−400 hPa) and did not extend to the land surface over the southern TP (Figure 15(c)). Nevertheless, the anomalous upper-level cooling and downward motions around the TP are similar to those in the observation (Figures 11(b) and 15(c)). In contrast, heating over the southern China could increase air temperature in most areas of the TP, implying that the results in the model experiment are not consistent with the statistical analysis in observation (Figures 10(e), 10(f ), 11(c), 13(d), 14(d), and 15(d)). Combined forcing types over the two regions induce patterns similar to that over the northern Indochina Peninsula (Figures 13(b), 13(c), 14(b), 14(c), 15(b), and 15(c)), implying that cooling over the northern Indochina Peninsula contributed largely to temperature and circulation changes induced by the combined forcing types.
In conclusion, the abovementioned results suggest that anomalous diabatic heating from the Bay of Bengal eastward to the western South China Sea could signifcantly afect the SD variation over southern TP by modulating local surface air temperature during P1. On the other hand, both Q1P2IP and Q1P2SC have a signifcant relationship with the SD over the southern TP during P2 in observation. But neither cooling over the Indochina Peninsula nor heating over southern China can directly afect surface temperature over the southern TP.

Discussion
In P2, the diabatic cooling over the northern Indochina Peninsula leads to an anomalous cyclone at 200 hPa over the western TP and downward motions over the southern TP slope, accompanied by negative temperature anomalies at the midhigh levels. Tis midhigh level anomalous cold temperature may be conducive to deepening of SD over the southern TP, providing that snow melting is mostly observed at high elevations during P2. However, more reliable and high resolution data are needed to further identify the results. Te current study could not provide convincing evidence that diabatic cooling over the northern Indochina Peninsula has a signifcant impact on the southern TP SD by modulating the surface temperature in P2. Te diabatic heating over southern China is associated with the cold-than-normal air temperature at the upper level over the TP during P2 in observation, but the experiments with a nonlinear baroclinic model did not demonstrate the decrease of air temperature over the TP in response to the diabatic heating over southern China. In terms of climate states, diabatic heating over the southern TP contributes larger to the local positive temperature change in P2 than that in P1 ( Figure 5(a)). However, the simple model ignores feedback of convection [37]. Given that the baroclinic model is a dry mode, an anomalous vertical motion during the P2 period may induce a local temperature change without corresponding abnormal latent heating. Such errors have the potential to magnify during the P2 period and ultimately infuence the model results. Terefore, it should pay attention to the applicability of the simple model in diferent periods when simulating the changes in air temperature over the southern TP. As global warming stoppage around 2000 and the limited number of quality control stations over southern TP, to avoid contamination of the results by these, the time period 1979-2004 is used. Nevertheless, to use the satellite-derived data during 1979-2020, climatological pentad mean of southern TP SD (fgure not shown) was the same as in Figures 2(c) and 2(d). Tese also imply that southern TP SD can be divided into two periods. Recently, ice losses at high elevations have also received increased attention in the context of global warming [52]. More high quality monitoring of SD and snow cover data over the TP need to be carried out, especially at high elevations. In addition, the efect of human action cannot be ignored, for example, the role of absorbent aerosols over TP in diferent snowmelt stages. Whether there is interdecadal variation in the southern TP SD during the two periods in recent years deserves further study. Figure 14: As in Figure 13, but at 500 hPa.

Conclusions
During the spring-summer transitional season, the concentrated area of snow cover is located over southern TP slope, which is closely related to the weather and climate in Asia.
Understanding the characteristics of snowmelt and its associated mechanisms over the TP during the transition season is critical for the regional water cycle research. From the in situ observational results, the previous work [18] found that unlike in other areas of central and eastern TP, snow over the southern TP slope could have almost completely melted in summer. Compared to snowfall, surface temperature changes are the main factors afecting SD variations during spring and summer. Tis study investigates the climatic characteristics and interannual variation of snow depth over the southern Tibetan Plateau during late spring to early summer, with a focus on local air temperature. Our analysis is based on various observational data sources for snow depth over TP, NCEP/NCAR reanalysis data, as well as experiments conducted using a nonlinear baroclinic model. Te main results are summarized as follows: (1) From the perspective of climate states, according to the characteristics of SD evolution from station data and improved satellite-derived data, the transition period of spring-summer is further divided into two periods (P1: April 16th-May 15th and P2: May 16th-June 14th). Te snow melting rate in P2 is faster than that in P1. Tis melting acceleration mainly comes from high elevations.
(2) Diference of air temperature between P2 and P1 shows a remarkable warming center at about 300 hPa  Figure 15: Te responses of pressure-latitude cross-section of circulation s (meridional vector, m/s; vertical velocity, 5 × 10 −6 Pascal/s) and air temperature (K) anomalies averaged over (85°E-100°E) to heating over BOB-IP-SCS in P1 (a) Same as in (a) but for responses to heating over northern IP and SC (b), northern IP (c), and SC (d) in P2. over the southern TP. Diagnoses of the thermodynamic equation further demonstrate that the local temperature changes over the southern TP at 200-500 hPa during both the periods are slightly positive and the warming over southern TP during the two periods is mainly attributed to the meridional temperature advection and diabatic heating in situ.
(3) On the interannual time scale, from the surface to 200 hPa, corresponding to deepening of SD over the southern TP, cold air temperature is observed over the TP in the two periods. (4) In P1, the diabatic cooling from the southern Bay of Bengal eastward to the western South China Sea induces an anomalous cyclone at 200 hPa over the TP and downward motions over the southern TP and Bay of Bengal, leading to cold air temperature anomalies from surface to 200 hPa over the southern TP. Te lower-than-normal temperature provided favorable conditions for the above-normal SD. (5) In P2, the variation of SD over the southern TP is strongly linked to diabatic cooling over the northern Indochina Peninsula and diabatic heating over southern China.
An earlier version of the manuscript Zhang et al. [53] has been published as a "Preprint" in research square.

Conflicts of Interest
Te authors declare that they have no conficts of interest.