Corresponding author: B. Rajagopalan, Department of Civil Environmental and Architectural Engineering, University of Colorado, Boulder, CO 80309 USA. (firstname.lastname@example.org)
 Despite recent challenges, conventional wisdom has held that heating over the Tibetan Plateau leads to increased Indian summer monsoon rainfall via enhancement of cross-equatorial circulation aloft, and a concurrent strengthening of both the Somali Jet and westerly winds that bring moisture to southern India. We show that such heating, quantified by monthly estimates of moist static energy in the atmosphere just above the surface, correlates with summer monsoon rainfall, but only in the early (20 May to 15 June) and late (September 1 to 15 October) monsoon season. Correlations during the main monsoon season (15 June to 31 August) are small and insignificant. The positive correlations with early and late monsoon season, however, allow for heating over Tibet to modulate as much as ~30% of the total rainfall. Furthermore, we demonstrate that heating over Tibet is independent of the El Niño Southern Oscillation, so that together they explain a substantial portion of variability in the early and late season rainfall, providing potential predictability. These links may also explain the wet conditions over India during early Holocene time and provide a quantitative link between a rise of Tibet and stronger Somali Jet.
 A long tradition has associated the South Asian monsoon with heating of the atmosphere directly over the Tibetan Plateau [e.g., Flohn, 1968; Yanai and Wu, 2006], but recent theoretical [e.g., Emanuel, 1995, 2007; Lindzen and Hou, 1988; Neelin, 2007; Plumb and Hou, 1992; Privé and Plumb, 2007a] and numerical calculations [e.g., Boos and Kuang, 2010; Bordoni and Schneider, 2008; Privé and Plumb, 2007a, 2007b] have challenged this view. Both views, however, rest on strong theoretical foundations, and the question posed by these differing views may not be, which view is correct?, but rather, how does heating of the atmosphere over Tibet affect the strength of the South Asian monsoon?
 Although the monsoon is clearly tied to the seasonal cycle, measures of its strength do not smoothly follow the gradual annual march of seasons. Rather the monsoon begins abruptly in a period as short as two weeks, as measured not only by precipitation [e.g., Ananthakrishnan and Soman, 1988, 1989; Joseph et al., 2006; Pai and Nair, 2009; Soman and Krishna Kumar, 1993], but also by reversals in both low-level winds [e.g., Boos and Emanuel, 2009; Fieux and Stommel, 1977; Halpern and Woiceshyn, 1999; Krishnamurti et al., 1981] and upper troposphere circulation [e.g., He et al., 1987, 2003; Li and Yanai, 1996; Wu and Zhang, 1998; Yanai and Wu, 2006; Yanai et al., 1992]. Moreover, Goswami et al.  showed that the reversal in winds aloft correlates with onsets of monsoons defined by various rainfall indices. Thus, insofar as heating over the Tibetan Plateau affects the temperature structure above it, surface conditions over Tibet would seem to be important for the South Asian monsoon.
 Several arguments do support an association of a warm upper troposphere with a high plateau. The General Circulation Model (GCM) runs consistently show a stronger monsoon for a higher Tibetan Plateau than for lower elevations in that region [e.g., Hahn and Manabe, 1975; Kutzbach et al., 1989, 1993, 1997; Prell and Kutzbach, 1992; Yasunari et al., 2006], and analyses of recent GCM runs show that heating is an essential element to these calculated circulations [Chakraborty et al., 2002; Wu et al., 2012a]. More simply, calculations for radiative-convective equilibrium over surfaces of different elevations call for a warmer upper troposphere over higher surfaces, warmer by ~6°C per kilometer of surface elevation [Molnar and Emanuel, 1999]. Thus, it is difficult to deny that the heating of the atmosphere over Tibet has a role in the South Asian monsoon.
 Arguments that contradict that view include the observation that the warmest area in the upper troposphere is not centered over Tibet, but overlies northern India and the southern slope of the Himalayas [e.g., Boos and Kuang, 2010]. This contradictory view also accords with two theoretical arguments. First, Lindzen and Hou  inferred that the maximum temperature in the upper troposphere should overlie the poleward edge of the cross-equatorial circulation, which commonly develops in a monsoon. Second, the maximum temperature aloft should overlie the region of maximum subcloud moist entropy or, virtually equivalently, the maximum subcloud moist static energy [e.g., Clift and Plumb, 2008, Chapter 1; Emanuel, 1991; Emanuel et al., 1994; Neelin, 2007; Plumb, 2007]. Both modern data [Bordoni and Schneider, 2008; Hurley and Boos, 2013; Nie et al., 2010] and numerical calculations [Bordoni and Schneider, 2008; Privé and Plumb, 2007a, 2007b] corroborate these relationships among subcloud moist entropy or moist static energy, maximum temperature aloft, and the poleward edge of the cross-equatorial circulation. Thus, the observed maximum in moist static energy over northern India at the monsoon onset [Bordoni and Schneider, 2008] and its relation to the large-scale circulation would seem to make the heating over Tibet unimportant, and perhaps not necessary. In fact, Boos and Kuang  showed that a key role of Tibet is to block cool dry air, with low moist entropy and low moist static energy, from mixing with hot, moist air from the Indian Ocean. Such blockage, however, does not require a vast high plateau; rather, the Himalayas, the southern edge of Tibet, suffices. Finally, GCM runs with an idealized plateau suggest that such topography can enhance precipitation east and southeast of it, but not over terrain analogous to where India lies [e.g., Liu et al., 2012; Wu et al., 2012b].
 Given the two different views, we ask the question: Does heating over the Tibetan Plateau correlate with the strength of the monsoon as measured in different ways? Toward that end we sought correlations of moist static energy (MSE) in the atmosphere just above the surface over Tibet with different measures of monsoon strength. Moist static energy is given by
where Cp is the heat capacity at constant pressure, T is temperature in Kelvin, Lv is latent heat of vaporization, q is specific humidity, g is gravity, and Z is height. Because Z does not change with time, we ignored it in calculations of time variations in MSE.
 We briefly describe the data used in the analysis, followed by results and conclusions.
 We estimated annual variations in moist static energy for different seasons or portions of the annual cycle using values of monthly and daily temperature and specific humidity in the atmosphere just above the surface given by National Centers for Environmental Prediction (NCEP) Reanalysis [Kalnay et al., 1996] averaged over the region 30°N–36°N; 75°E–90°E, which comprises the high central portion of the Tibetan Plateau (Figure 1a). We performed principal component analysis [Wilks, 1995] of MSE over this region during May, June through August, and September, the early, middle, and late monsoon seasons, respectively. For the early and late seasons, we found the leading mode of variability not only to capture 50–60% of the variance, but also to be highly correlated (ρ > 0.9) with the regional average MSE (Figures 1b and 1c). (Because of the poor correlation with monsoon rainfall, we omit presentation of such plots for the middle, or main, monsoon season.) This suggests that the box average captures the dominant variability. We carried out similar analyses for other portions of Tibet, including extending the region northward to 38°N, northwestward as far as 75°E, and eastward to 100°E, and all shared large variance with that shown in Figure 1a. We selected the region shown in Figure 1a because it correlated slightly better than the others with rainfall over India and winds over the Arabian Sea.
 We used NCEP Reanalysis [Kalnay et al., 1996] to obtain large-scale atmospheric variables such as 850 mb wind velocities and upper troposphere (200–400 mb average) temperatures. We used monsoon onset and withdrawal dates based on tropospheric temperatures by Goswami and Xavier  and Xavier et al. . For rainfall we used the gridded (1° × 1°) daily rainfall data over India developed by Rajeevan et al. . Monthly sea surface temperatures (SSTs) and El Niño Southern Oscillation (ENSO) indices were from Kaplan et al. . A common period of all the data sets, 1951–2009, was used in the analysis.
 As discussed below, we sought correlations with monsoon rainfall and ocean and atmospheric variables to understand the role of Tibetan Plateau heating in modulating the Indian monsoon.
 We correlated average MSE of surface air in the region 30°N–36°N; 75°E–90°E, hereafter “Tibet MSE” with gridded daily rainfall of [Rajeevan et al., 2006] over India during early, middle, and late periods of the monsoon season (Figure 2). Correlations between rainfall and MSE were made for the same period. Rainfall in the early period (20 May to 15 Jun), exhibits significant positive correlations exceeding 0.4 over central India and its west coast (Figure 2a). The correlation weakens markedly to become insignificant during the peak monsoon season (15 June to 31 August, Figure 2b) before reappearing quite strongly during the late monsoon period (1 September to 15 October, Figure 2c). This raises the interesting suggestion that the heating over the Tibetan Plateau correlates with the Indian monsoon only during the early and late periods of the monsoon season.
 Consistent with this suggestion, the Tibet MSE in the early season is negatively correlated (ρ = –0.47) with monsoon onset, and that in the late season is positively correlated (ρ = 0.62) with withdrawal dates given by Goswami and Xavier  and Xavier et al. , which suggests that Tibet heating facilitates a lengthening of the monsoon season and thus the rainfall amount (Figure 3). Following others, Goswami and Xavier  and Xavier et al.  suggested that the monsoon season should be defined by a north-south gradient in temperature aloft. Specifically, they compared temperatures in the longitude band between 50°E and 90°E in two latitude bands, 15°S–10°N and 10°N–35°N. They defined the monsoon onset as when the average temperature between 700 and 200 mb in the northern region exceeded that in the southern region and withdrawal when that temperature difference reversed. Because the northern region overlies part of Tibet, we might expect heating over Tibet to affect temperature aloft in that region.
 To understand the mechanism responsible for the correlations in Figures 2 and 3, we first correlated Tibet MSE with upper tropospheric temperature, in the pressure range of 200–400 mb (Figure 4). For the early season, correlation coefficients exceed 0.6 for the upper troposphere directly over Tibet. For the late season, correlation coefficients are yet higher, and the band of high correlation extends southwest from Tibet. These correlations suggest a direct relationship between heating of the atmosphere directly above Tibet's surface, and the temperature in the upper troposphere, which many link both to the strength of the monsoon [e.g., Goswami et al., 1999; He et al., 1987, 2003; Li and Yanai, 1996; Wu and Zhang, 1998; Yanai and Wu, 2006; Yanai et al., 1992] and, as Chakraborty et al.  suggested, to its onset [e.g., Goswami and Xavier, 2005; Xavier et al., 2007; Webster and Yang, 1992].
 Among distinctive features of monsoon circulation are the band of easterly winds just south of the equator, the cross-equatorial Somali Jet, and the strong westerlies across the Arabian Sea and southern India [e.g., Hoskins and Rodwell, 1995; Rodwell and Hoskins, 1995]. Accordingly, we correlated Tibet MSE with 850 mb wind speed for early and late periods of the monsoon season (Figure 5). For both periods, significant correlations that exceed 0.3 for the early season and 0.5 for the late season are seen in the canonical wind pattern. The combination of these winds and temperatures aloft are consistent with heating over Tibet that results in ascent and a corresponding descent over Indian Ocean to produce a strong monsoon jet.
 Given the link between early and late monsoon rainfall with ENSO [e.g., Rajagopalan and Molnar, 2012], we ask the question—could the links between Tibet heating and monsoon identified above be manifestations of ENSO's influence on both? To answer this, we correlated Tibet MSE with global SST (Figure 6). In the early season there is no coherent correlation pattern (Figure 6a), but a weak ENSO-like pattern emerges during the peak monsoon season (Figure 6b), and becomes more distinct and significant during late monsoon period (Figure 6c). These differing correlations suggest that during the early monsoon period, heating over Tibet exerts an influence on the monsoon rainfall independent of that associated with ENSO, but in the late period, heating over Tibet and ENSO somehow reinforce one another. To assess the importance of heating over Tibet, we regressed early and late monsoon rainfall at each grid point of Rajeevan et al.  with the NINO4 index for May and for September, respectively. We do not have daily SST data for the period of 1951–2009 to compute the ENSO indices. Hence, this part of the analysis was performed using monthly index, but given the persistence in the SSTs we expect the results to be similar for the early and late seasons. Rajagopalan and Molnar  found early and late monsoon rainfall to correlate better with the NINO4 index than either the NINO3 or NINO3.4 indices. We then removed the variability associated with those regressions and correlated the residuals with Tibet MSE (Figure 7). The correlation patterns in the early (Figure 7a) and late monsoon (Figure 7b) periods are similar to correlation patterns in Figures 2a and 2c, respectively, but slightly weaker. Those for the early season remain as high as 0.4, and for the late season, they reach 0.5, but not 0.6 as in Figure 2c.
 A multiple linear regression of early season all-India monsoon rainfall (computed as the average of all of the grid-point daily rainfall amounts) with May NINO4 and May Tibet MSE yields R2 = 0.23, but the same regression with just NINO4 gives R2 = 0.08. For the late season rainfall, the R2 values are 0.48 and 0.17, respectively (Figure 8). Clearly, Tibet MSE correlates with, and therefore might explain, a substantial fraction of early and late season rainfall independently of ENSO in the early season and in conjunction with it at the end.
 To the best of our knowledge, this analysis indicates a hitherto unknown finding, that heating over Tibet could modulate Indian summer monsoon rainfall, but only in specific windows, the early and the late monsoon season, not the main monsoon season. We found this connection to be insensitive to rainfall data sets used; the Aphrodite gridded (0.5°) daily precipitation data set over Asia [Xie et al., 2007] and Climate Research Unit precipitation data [Mitchell and Jones, 2005] yield similar results.
 At present, all-India mean daily rainfall over the 26 days in the early period from 20 May to 15 June is 3.8 ± 1.2 mm/d and that over the 45 days from September 1 to October 15 in the late period is 5.3 ± 1.2 mm/d. The total for early and late seasons averages to be 337 mm/yr, comprising of about 33% of the total monsoon season rainfall. The multiple regressions yield the following relationships between perturbations to mean daily all-India rainfall ΔAIR in the early (20 May to 15 June) and late (1 September to 15 October) periods to the NINO4 index and to Tibet MSE in May and in September, respectively:
 Therefore, ignoring ENSO, if MSE were greater by 1 kJ/kg, we would expect 10 mm more precipitation in the early period, and 26 mm more in the late, or 36 mm more annual precipitation.
4 Discussion: Possible Relevance to Paleoclimate
 The correlations and regressions above do not, by themselves, assign cause and effect. In fact, if the atmosphere is in a quasi-equilibrium state, as many assume for large-scale monsoon circulation [e.g., Bordoni and Schneider, 2008; Emanuel, 2007; Emanuel et al., 1994; Neelin, 2007; Plumb, 2007; Privé and Plumb, 2007a, 2007b], cause and effect have no meaning. Nevertheless, changes in Tibet's surface elevation and surface properties have occurred in geologic time, and it seems possible that such changes have altered atmospheric circulation over South Asia. With these considerations in mind and using the regressions and correlations presented above, we address possible impacts of changes in surface conditions over Tibet on the South Asian monsoon.
 Let us consider two time periods in the geologic past for which these regressions might be relevant. In early Holocene time, not only were lakes widespread in northern India where desert conditions now prevail [e.g., Bryson and Swain, 1981; Enzel et al., 1999; Prasad and Enzel, 2006; Prasad et al., 1997; Singh et al., 1972, 1990; Sinha et al., 2004], but winds associated with the Somali Jet seem to have been stronger [e.g., Gupta et al., 2003]. By contrast, before ~10 Ma, winds associated with the Somali Jet seem to have been weaker than today, and some have inferred that the monsoon strengthened since that time [e.g., Harrison et al., 1992; Kroon et al., 1991; Molnar et al., 1993; Prell and Kutzbach, 1992].
 In early Holocene time at ~6 ka, summer radiation on Tibet during the monsoon season, from early May to the end of September, was higher than present by a maximum of ~24 W/m2 [e.g., Braconnot et al., 2000]. Huybers  showed that for latitudes of 35° or higher, summer surface air temperatures vary linearly with insolation, at ~ 1 °C per W/m2, with temperature lagging insolation by 30 days. Because of Kepler's second law, the duration of summer, and therefore the monsoon season, should have been shorter in the period of enhanced insolation due to precession [Huybers, 2006]. Consequently, determining the early and late monsoon periods that correspond to those today requires somewhat aribitrary decisions, but as an example let us assume that average summer radiation was 5 W/m2 greater than it is today. Following Huybers’s  correlation, the surface of Tibet would have been warmer by ~5 °C than today. Also, specific humidity at saturation increases with temperature by ~7%/°C [e.g., Held and Soden, 2006]. If we assume that relative humidity changed little from today's average, then if early and late monsoon season temperatures in Tibet were warmer than today by 5°C, q at saturation should have been greater by 1.4 times than today's values of 0.51 g/kg and 0.67 g/kg in May and September, respectively. Thus, q would have been greater by 0.7 g/kg and 0.9 g/kg in those seasons, and from (1), with surface air warmer by 5 °C and enhanced moisture, Tibetan MSE would have been greater by 5.7–5.9 kJ/kg. The regressions in (2) and (3) would then call for 212 mm/yr more rainfall than today. Moreover, at ~6 ka, the eastern tropical Pacific Ocean was cooler than today by ~1 °C [e.g., Kienast et al., 2006; Koutavas et al., 2002, 2006; Leduc et al., 2007, 2010; Pahnke et al., 2007]. If we assume a NINO4 index of –1°C, this could correspond to 17 mm/yr more rainfall early and late monsoon seasons than today, and the combination of a warmer Tibet by 5 °C and a cooler NINO4 region by 1 °C would lead to ~230 mm, or ~23%, more annual rainfall than today. Thus, perhaps insolation over Tibet at ~6 ka, plus the more La Niña like conditions in the eastern Pacific, account for the wetter northern India then than now.
 Much evidence suggests that the tectonic evolution of Tibet underwent some kind of change near 10–15 Ma. One explanation for these changes is that at that time the surface of the plateau rose abruptly 1000 m or more [e.g., Harrison et al., 1992; Molnar et al., 1993], but much less than the full 5000 m present-day elevation of the plateau. Estimates of paleo-elevations of southern Tibet do not support, but rather contradict, this idea; essentially all such estimates show little change since 10 Ma to perhaps 25–35 Ma [Currie et al., 2005; DeCelles et al., 2007; Garzione et al., 2000a, 2000b; Rowley and Currie, 2006; Rowley et al., 2001; Saylor et al., 2009; Spicer et al., 2003]. Because uncertainties in all are ~1000 m, however, let us consider the possibility that the average elevation of Tibet was 1000 m lower at 10–15 Ma than today.
 If Tibet had risen by 1000 m, MSE of the air directly over it would have increased by 9.8 kJ/kg, ignoring any change in surface temperature or specific humidity. The regressions, ignoring ENSO, would suggest an increase in annual rainfall of nearly 350 mm, or from ~35% less than today's average to present-day amounts. More importantly, the correlation of winds over the Arabian Sea with early and late monsoon season Tibet MSE (Figure 5) are consistent with the geologic inference of stronger winds today than earlier when Tibet might have been 1000 m lower. Because we lack a quantitative estimate of the change in wind strength, however, we cannot perform a more quantitative analysis of such a relationship, but the present-day correlations do concur with the inference that a modest rise of Tibet led to a strengthening of monsoon winds [e.g., Harrison et al., 1992; Kroon et al., 1991; Molnar et al., 1993; Prell and Kutzbach, 1992].
 Recently, Boos and Kuang  argued that the principal role that Tibet plays in affecting the Indian monsoon is to block cool dry air from northwest of Tibet. Although they did not deny a warming over Tibet a role in the monsoon, their work implies that such warming has a modest influence. We found an insignificant correlation between Tibetan heating, as quantified by moist static energy of surface air, and rainfall in the main monsoon period (15 June to 31 August) (Figure 2b). We show, however, that heating over the Tibetan plateau does correlate with, and therefore may modulate Indian monsoon rainfall in the early (20 May to 15 June) and late (1 September to October 15) monsoon seasons, which together contribute about a third of the seasonal rainfall. Simple regressions suggest that variations in heating over Tibet might account for as much as 20% of seasonal total rainfall. Furthermore, we demonstrate that heating over Tibet is largely independent of ENSO, so that together they can explain a substantial portion of variability in the early and late season rainfall, and therefore provide potential predictability at crucial times of crop management—sowing and harvesting, respectively. These links between heating over Tibet and ENSO with rainfall over India may explain the wet conditions over India during early Holocene time and provide a quantitative link between a rise of Tibet and a stronger Somali Jet. They might also provide some insights into mechanisms that could play a role in the monsoon variability under a warmer climate that the current crop of dynamical models need to capture better.
 This research was supported in part by the National Science Foundation under grants EAR-0507730, EAR-0909199, and EAR-1211378. Thanks are also due to Chinese colleagues with whom one of us, PM, collaborates on the National Science Foundation of China grant 40921120406. We thank two anonymous reviewers for constructive comments.