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The AHS is the sum of surface sensible heating, condensation heating, and radiative heating based on direct method (formula (1)), and <Q1> is the vertically integrated AHS. Similarly, the AMS is defined by formula (5) and <Q2> is the vertically integrated AMS. The components of <Q1> are obtained from formulas (2)-(4), respectively. QL, QSH, and <QR> are condensation heating, surface sensible heating, and vertically integrated radiative heating, respectively.
$$ <Q_{1}>=<Q_{R}>+Q_{\mathrm{SH}}+Q_{L} $$ (1) $$ <Q_{R}>=\left(S_{\infty}^{\downarrow}-S_{\infty}^{\uparrow}\right)-\left(S_{0}^{\downarrow}-S_{0}^{\uparrow}\right)-\left(F_{0}^{\downarrow}-F_{0}^{\uparrow}\right)-F_{\infty} $$ (2) $$ Q_{\mathrm{SH}}=c_{p} \rho_{\mathrm{air}} C_{\mathrm{D}} V_{10}\left(T_{\mathrm{s}}-T_{\mathrm{a}}\right) $$ (3) $$ Q_{L}=P_{r} \times L \times \rho_{w} $$ (4) $$ <Q_{2}>=L\left(P_{r}-E\right) $$ (5) In the above formula, angle brackets represent the integration of the whole atmosphere. S and F are the shortwave and longwave radiative fluxes. The subscripts "∞" and "0" represent the fluxes at the top of the atmosphere and at the surface of the Earth. Upward arrows denote upward radiative fluxes, and vice versa. cp =1004J kg−1 K−1 and it is the drag coefficient for heat, and CD=0.004 and it is the specific heat of dry air at constant pressure. ρair and ρw are air density and water density, respectively. Ts, Ta, V10, Pr and E represent the surface temperature, 2-m air temperature, 10-m wind speed, precipitation, and evaporation, respectively. L= 2.5 × 106J kg−1 and it is the condensation heating coefficient.
The indirect method is also called the"residual diagnosis method". <Q1> and <Q2> are defined by formulas (6) and (7), which are the sum of the local variation term, the advection variation term, and the vertical variation term. According to formulas (6) and (7), we can obtain the AHS and AMS at each layer, also known as the heating rate (K d−1). The overbar in the formulae represents the regional average value. θ and q are potential temperature (K) and specific humidity (g kg−1), respectively. $\vec{V}$ and ω are horizontal wind speed (m·s−1) and vertical velocity (Pa s−1).
$$ <Q_{1}>=\frac{c_{\mathrm{p}}}{g} \int_{p_{T}}^{p_{s}}\left[\left(\frac{p}{p_{0}}\right)^{k}\left(\frac{\partial \bar{\theta}}{\partial t}+\vec{V} \cdot \nabla \bar{\theta}+\bar{\omega} \frac{\partial \bar{\theta}}{\partial p}\right)\right] \mathrm{d} p $$ (6) $$ <Q_{2}>=-L \frac{c_{\mathrm{p}}}{g} \int_{p_{T}}^{p_{s}}\left[\left(\frac{\partial \bar{q}}{\partial t}+\vec{V} \cdot \nabla \bar{q}+\bar{\omega} \frac{\partial \bar{q}}{\partial p}\right)\right] \mathrm{d} p $$ (7) For simplicity, we used Q1 to represent <Q1> and Q2 to represent <Q2> hereafter. A value of Q1 greater (less) than zero indicates that the atmosphere has a net heat gain (loss). In general, a positive value of Q1 is called a heat source and a negative value is called a heat sink. A value of Q2 greater (less) than zero means that there is a net moisture loss (gain). If the spatial distributions of Q1 and Q2 are consistent and both are positive, this indicates that the AHS is mainly dominated by precipitation latent heating. Section 4 shows the AHS as Q1 and the AMS as Q2 for simplicity. According to formula (1), the present study used station data, radiation data and four reanalysis data to calculate the AHS of the TP in the 75°E-103°E, 28°N-38°N area. Meanwhile, reanalysis data based on formula (6) and formula (7) were used to calculate the AHS and AMS in the 20°S-45°N, 30°E-120°E area. The TIO is defined in the 15°S-5°N, 60°E-100°E area.
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The Pearson correlation coefficient (rkl) defined by formula (8) is used to measure the correlation between the observed AHS values and those from the four reanalysis data. In formula (8), x is the AHS, and rkl is the correlation coefficient calculated from observational data (k) and reanalysis data (l), respectively. Temporal correlation coefficients in Fig. 2 and Table 1 were calculated after averaging the AHS over the TP (75°E-103°E, 28°N-38°N) which maskouts the altitude ≥2500m for observational and reanalysis data from 1984-2008.
$$ r_{\mathrm{kl}}=\frac{\sum_{i=1}^{n}\left(x_{\mathrm{ki}}-\bar{x}_{k}\right)\left(x_{\mathrm{li}}-\bar{x}_{l}\right)}{\sqrt{\sum_{i=1}^{n}\left(x_{\mathrm{ki}}-\bar{x}_{k}\right)^{2}} \sqrt{\sum_{i=1}^{n}\left(x_{\mathrm{li}}-\bar{x}_{l}\right)^{2}}} $$ (8) Figure 2. The monthly variations of correlation coefficients for Q1 between the observational data and those from four reanalysis datasets from 1984 to 2008 on the TP (The average area is in the 75°E-103°E, 28°N-38°N which maskouts the altitude ≥2500m; I and D represent the indirect method and the direct method, respectively).
JRA-55 NCEP/DOE ERA-I MERRA2 Observed data Direct method 0.611 0.546 0.483 0.490 Indirect method 0.634 0.585 0.492 0.312 Table 1. The correlation coefficients for the summer Q1 on the TP (The average area is in the 75° E-103° E, 28° N-38° N which maskouts the altitude ≥2500m) between the observations and the four reanalysis datasets based on two methods (Italics indicate a correlation coefficient does not pass the 95% significance test).
Figure 2 shows that the correlation coefficient is greater in July-September while the JRA-55 dataset is the greatest among the four reanalysis datasets. In summer, the correlation coefficients all have passed the 95% significance test except for the MERRA2 with indirect method (Table 1). The JRA-55 dataset not only assimilates the upper tropospheric atmospheric observations but also uses a 4D assimilation technique for the upper tropospheric observations since 1958 (Fujiwara et al. [26]). Hence, we can see that no matter which method is used, the JRA-55 data shows the best correlation with the observational data (Table 1). Hu and Duanalso concluded that the JRA-55 data can best describe the TP thermal heating [14].
On the basis of the above analysis, and in view of the scarcity of observational data in the TP, we used the JRA-55 data to further study the temporal and spatial characteristics of the AHS in the TP-TIO region, and theirs link to the SASM.
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The TP (75°E-103°E, 28°N-38°N) and TIO (15°S-5°N, 60°E-100°E) regions are located to the south and the north of the SASM respectively. The Asian monsoon regions are heat sources in summer, while the TP and TIO are strong heat source centers along their latitudes (Fig. 3). The TP has a strong heat source center, with the maximum heating (Q1≥300 W m−2) located on the southern slope of the TP, and the TIO maximum also reaches 300 W m−2 in the south of the equator. The AHS in the TP is accompanied by lower wind convergence, while the AHS in the TIO is located in the area of southeast trade winds and equatorial westerly winds (Fig. 3(a) and (b)). Studies have shown that the TP thermal forcing and the zonal land-sea thermal contrast between East Asia and the Pacific region have a profound influence on the East Asian monsoon system (He et al. [27]; Zhang et al. [28]); therefore, it is necessary to study the meridional thermal contrast between the TP and the TIO.
3.1. Method to determine the AHS and AMS (Luo and Xu [8])
3.2. Screening data
3.3. Selecting the study area
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The seasonal variations of AHS in the TP and the TIO are almost reversed (Fig. 4). The TP is a heat source from April to September and that the strongest intensity is in July (Q1 = 113 W m-2), while the TIO AHS gets the minimum in June (Q1=46W m-2) and the maximum in January (Q1 = 163 W m-2). In summer, the TP AHS is mainly dominated by precipitation latent heat, which coincides with the strongest precipitation in July (Feng and Zhou [29]). Therefore, the TP AHS reaches the maximum in July. The TP is a cold source in winter and the strongest intensity is in January (Q1 = -113 W m-2), which is consistent with the monthly AHS variation in Duan et al. [30]. However, quantitative estimations of the monthly AHS in previous studies (Yanai et al. [1]; Zhao and Chen [13]; Ji et al. [16]) are considerably different, which may be due to differences in regions, calculation methods, data, study periods, and so on (Liu and Li [31]). For the TIO, it's a heat source all year round due to the convection precipitation latent heat. The standard errors of AHS in the TP and TIO are 78.97 and 38.56 respectively, which indicate that the seasonal variability in the TP is more obvious.
Figure 4. The monthly variations of Q1 from 1980 to 2016 in the TP (The area is in the 75°E-103°E, 28°N-38°N which maskouts the altitude ≥2500m) and the TIO (60°E-100°E, 15°S-5°N) (Black bars indicate the standard error; units: W m-2).
In Fig. 5(a1), the heat sources center in the east and west of the TP from March to September and are strongest in summer. The intensity is stronger, and the extent is wider for the eastern heat sources center than those for the western heat source center, and Q1 ≥ 100 W m-2 occurs in the east from May to July but only occurs in July in the west. The AMS intensity in the western part of the TP is about twice as strong as that in the eastern TP (Fig. 5(a2)). The AMS is the bias of precipitation and evaporation which represents the precipitation latent heat (formula (5)). By comparing the Fig. 5(a1) and (a2), we can infer that although the AHS is dominated by the precipitation latent heat in the TP, the contribution of AMS to AHS shows large zonal inhomogeneity. The AHS is stronger in the east than in the west, and vice versa for the AMS. This is probably because the surface evapotranspiration is much weaker in the west than in the east (Su [32]), which results in the AMS being smaller in the east than that in the west over the TP. The seasonal variations of the AHS and AMS at high altitude (Fig. 5(b1) and (b2)) are the same as the mean distribution and the value of the AMS and AHS at high altitude are similar because the less is affected by the underlying surface.
Figure 5. The temporal-zonal distributions of Q1 (1) and Q2 (2) from 1980 to 2016 over (a) the TP, (b) the TP altitude ≥2500 m, and (c) the TIO. The black dash lines represent the TP (75°E-103°E) in a1, a2, b1 and b2, and represent the TIO (60°E-100°E) in c1 and c2 (W m-2). The averaged latitudes are 28°N-38°N for the TP and 15°S-5°N for the TIO.
The temporal-zonal distribution of the AHS and the AMS in the TIO are basically the same (Fig. 5(c1) and (c2)), which indicates that the AHS is mainly dominated by the precipitation latent heat in this region. In summer, the intensity of the heat sources and moisture sinks are weaker than that in the TP. In addition, the summer atmospheric thermodynamic properties on both sides of 100° E are very different, and the gradient of latitudinal variation is also large. The region of 100° E-120° E, corresponding to Indonesia, is a cold source and moisture source, and the area between 60° E and 100° E is a heat source and moisture sink. The reason for this phenomenon may be related to the distribution of land and sea, and ocean currents.
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The BOB, the southern slope of the TP, and the west of the India Peninsula are the strongest heat sources in summer (Fig. 6(a1)). The strong heat sources in the central and eastern TP in summer is due to latent heating (Fig. 6(a2)). Jiang et al. divided the TP into western, central and eastern domains and reached similar conclusions [12]. For the TIO, there is a strong AHS and AMS in the northwest-southeast direction, which indicates that the AHS is dominated by the precipitation latent heat, and the heat sources and moisture sink centers are located at 10° S near 90° E (Fig. 6(a2)). The heat sources in the TIO, BOB and the TP constitute the meridional distribution, while the AHS in the Arabian Sea, Indian Peninsula, BOB, and Indochina Peninsula constitute the zonal distribution. There are cold source centers located to the southeast of the TIO in summer. Zhang et al. also found that there is an obvious cold source in summer in the southeast of the TIO [20].
Figure 6. The zonal anomalies of Q1 (a1) and Q2 (a2) and their linear trends (b1 and b2, W m-2 yr-1) in summer from 1980 to 2016. The TIO is indicated by a green box and the green curve indicates the TP altitude ≥2500 m. The dotted areas passed the 95% significance test.
In general, the land is a strong AHS in summer, such as the"elevated heat source"of the TP, and the ocean is relatively a weak heat source or a strong heat sink. The intensity of Q1 in the TP and TIO in July can reach 113 W m-2 and 58.4 W m-2, respectively. The thermal contrast between the sea and land in summer can be measured by the difference in Q1 between the TP and the TIO. The larger the difference in Q1, the stronger the meridional thermal contrast.
According to Fig. 6(b1), the TIO Q1 shows a significant increasing trend (the maximum is about 40 W m-210yr-1), which indicates that the atmospheric heating is significantly enhanced in the area. In the TP, the Q1 increased on hinterland with the trend about 10 W m-210yr-1, while the southeast of the TP shows a significant decreasing trend (the maximum is about -40 W m-210yr-1). The increasing trend of Q1 in the TIO is greater than that in the TP, which indicates that the thermal contrast between the TP and the TIO in summer is decreasing. The linear trend distribution of Q1 has an obvious meridional feature, in that Q1 at 30°N, 10°-20° N, and 10° S-0° along 90° E has an increasing trend, while Q2 does not (Fig. 6(b1) and (b2)). The spatial distributions of the linear trends for Q1 and Q2 in the TP are different. In addition, both Q1 and Q2 are increasing significantly in the BOB.
The Hadley circulation is a fundamental regulator of the earth's energy budget due to the redistribution of energy from tropics to higher latitudes (Liu et al. [33]), and its location and intensity are closely related to the AHS. The TIO Hadley circulation in the southern hemisphere extends across the equator to around 30° N, and the northward mass transport center lies between 0° and 15°S at 600-400 hPa, with an intensity of about -3.5 × 109 kg s-1 (Fig. 7(a)). The strong ascending branch of the Hadley circulation is located at the south of the TP, while the descend branch lies in 30° S-15° S. The southern hemisphere Hadley circulation shows a weakening trend driven by the strengthened AHS in the TIO (Fig. 6(b1), Fig. 7(b)), while the northern hemisphere Hadley circulation has an increasing trend due to the enhancement of the vertical wind near 15° N (Fig. 7(b)). The decreased winter northern Hadley circulation in the TIO indicates that the meridional energy transported from the tropics in southern hemisphere to the northern hemisphere is reduced.
Figure 7. (a) The mass stream function (shaded, units: 1010 kg s-1) and vertical velocity (black curve, units: Pa s-1) of zonal averaged along 30°E-100°E in summer from 1980 to 2016. (b) The linear trends (Shaded is mass stream function trend (1010 kg s-1 yr-1), and black curve is vertical velocity trend (0.01 Pa s-1 yr-1).
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Due to the decrease of AHS in the southeast and the surrounding of the TP (Fig. 8, Fig. 6 (b1)), the AHS has a weakening trend (Fig. 8). It implies that the ability of the TP heating environment decreases; at the same time, the ascending motion, the lower layer convergence and the upper divergence, and the suction effect of the TP are all weakened (Liu et al. [34]). The southwesterlies over the northern Indian ocean also weakened when the TP heating decreased (Wang et al. [18]).
Figure 8. The interannual variations of Q1 in the TP (The area is in the 75° E-103° E, 28° N-38° N which maskouts the altitude ≥2500m) and the TIO, the IQ, and the SASM-v in summer from 1980 to 2016. The IQ linear trend is shown with a black dotted line and the linear regression coefficient is -0.075. All data are standardized.
The TIO AHS shows a significant increasing trend before 1998, and then a weaker decreasing trend (Fig. 8). The IQ (formula (9), where the overbar indicates the regional average) is used to measure the thermal contrast between the TP and the TIO. It shows a significant weakening trend, which indicates that the thermal difference between land and sea decreased quickly. The summer heat source on the TP plays an important role in the formation and evolution of the SASM (Wu et al. [35]). We defined an SASM index (SASM-v) by meridional wind shear between 850Pa and 200hPa (formula (10)). Fig. 8 shows that the SASM-v and the QI are similar in interannual variation. The SASM-v also shows a weakening trend during 1980-2016 and the correlation coefficient between the IQ and SASM-v is 0.801, passing the 95% significance test.
$$ \mathrm{IQ}=\overline{Q 1}_{\mathrm{TP}}\left(75^{\circ} \mathrm{E}-103^{\circ} \mathrm{E}, 28^{\circ} \mathrm{N}-38^{\circ} \mathrm{N}\right)-\overline{Q 1}_{\mathrm{TIO}}\left(60^{\circ} \mathrm{E}-100^{\circ} \mathrm{E}, 15^{\circ} \mathrm{S}-5^{\circ} \mathrm{N}\right) $$ (9) $$ \mathrm{SASM}_{-v}=V 8_{50 \mathrm{hPa}}-\mathrm{V}_{200 \mathrm{hPa}}\left(0^{\circ} \mathrm{E}-20^{\circ} \mathrm{N}, 40^{\circ}-100^{\circ} \mathrm{E}\right) $$ (10) -
The TP heating and the Hadley circulation decreased, while the TIO heating increased during 1980-2016, especially during 1980-1998. The IQ shows a significant weakening trend during the period of 1980-1998, whereas during 1999-2016 it maintains a stable low level with no obvious trend (Fig. 8). It indicated that the thermal contrast between the TP and the TIO has changed in the two periods, and during 1999-2016, the thermal contrasts is weaker. In Fig. 9, the southwest airflow at the lower troposphere and the easterly airflow at the upper troposphere are both weak, which implies that the SASM circulation has weakened during 2007-2016 compared with that during 1980-1989. Hence, as the meridional thermal contrast in the TP-TIO region weakens, the SASM circulation also has weakened.
Comparing the period of 2007-2016 with 1980-1989, we find that there is much more precipitation in the Arabian Sea, the BOB, eastern China and the northwest Indian ocean (Fig. 10(a)). The anomaly precipitation with strong convection is in the Arabian Sea and eastern China where an anticyclone and a cyclone appear, respectively (Fig. 10). The two places are the strong water vapor convergence regions (figure omitted). The AHS is an important factor in determining the South Asian High. The position of South Asia High moves westward because the TP AHS decreased and the AHS in the Iran Plateau and the northwest of the Indian Peninsula increased (Fig. 6(b1), Fig. 9(b), Fig. 10(b)). The south slope of the TP, the Indian Peninsula, the central and southern Indochina Peninsula and southeast Indian Ocean have less precipitation associated with anomalous anticyclones.
Figure 10. (a) The bias of summer precipitation (shaded, mm d-1) and 850 hPa horizontal wind (vector, m s-1) between 2007-2016 and 1980-1989 in the TP-TIO region. (b) The bias of summer outgoing longwave radiation (shaded, W m-2), and 12560gpm geopotential height (black curve represents 1980-1989, and red curve represents 2007-2016, gpm).
The equatorial Indian Ocean is controlled by abnormal west wind (Fig. 10(a)), and then the sea temperature rises (figure omitted) though the wind-evaporation-SST feedback (Wang et al. [18]). The increased SST further increases the TIO AHS, resulting in the abnormal ascent flow near 5° S (Fig. 11(a)). Therefore, the TIO southern hemisphere Hadley circulation weakened.
Figure 11. (a) The profile of v-w wind bias between 2007-2016 and 1980-1989 (along 90°E; units: m s-1). (b) The same as (a), but for u-w wind (along 15°N; units: m s-1).
The meridional section of 90° E and the zonal section of 15° N were used to analyze the vertical circulation in the TIO and the BOB (Fig. 11). It can be seen that there is obvious ascending motion in the whole atmosphere in these two places because the AHS increased (Fig. 6(b1)). The enhanced heat sources can trigger two abnormal meridional circulations in the northern 15°S (Fig. 11(a)). The decreased heat source in the south slope of the TP (Fig. 6(b1)) triggers abnormal downdraft (Fig. 11(a)), resulting in less precipitation. The abnormal zonal circulations appear in the SASM region, with an abnormal descending branch located to the Indian Peninsula and the Indochina Peninsula, and a strong ascending in the BOB (Fig. 11(b)).