Relationship between the tropical tropopause and tropical easterly jet streams over Indian monsoon region

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• Cold point tropopause altitude and temperature are driven by adiabatic processes when TEJ core lies in the vicinity of tropical tropopause.
• It indicates that the TEJ plays an important role in the tropical tropopause variability which needs to be taken into account.

Introduction
Indian summer monsoon (ISM) is one of the dominant climatological features of the global circulation and it originates from the differential heating of the land and sea during summer season (Koteswaram, 1960).ISM brings several changes in the meteorological and dynamical features from the surface to the upper troposphere (UT).A noticeable feature in the UT is the development of the tropical easterly jet (TEJ) streams with speeds often exceeding 30 m/s.TEJ spans around the equator to 20 o N latitude and 50-90 o E latitude (Krishnamurti & Bhalme, 1976;Roja Raman et al., 2009).TEJ is a thermal wind maintained by the meridional temperature gradient between land and ocean (Hastenrath, 1995;Koteswaram, 1958).Other dominant features of the ISM are the shift of the intertropical convergence zone poleward, development of the low-level jet streams (Joseph & Sijikumar, 2004), increase in cloudiness and rainfall (Sikka & Gadgil, 1980) which leads to the enhancement in tropospheric humidity (Fasullo & Webster, 2003), and the increase in the frequency of deep convection which generally couples with the transport of the pollutants from the surface to the UT and lower stratosphere (LS; UTLS) (Garny & Randel, 2016).ISM can affect the UTLS thermal structure either directly due to diabatic heating associated with the convection or indirectly due to convectively generated phenomena such as propagation of atmospheric waves (Krishna Murthy et al., 2002;Tsuda et al., 1994), the occurrence of the cirrus clouds (Tseng & Fu, 2017) and transport of surface pollutants (Pan et al., 2016).
The tropical tropopause here is defined as the level of the coldest point in the UTLS called the cold point tropopause (CPT).CPT plays an important role in entry of the water vapor into the LS and hence regulates the climate variability (Gettelman et al., 2009;Holton et al., 1995).CPT shows connections with various tropospheric and stratospheric phenomena on different time scales.It has been linked with Madden Julian Oscillation (Zeng et al., 2012) and Brewer-Dobson circulations (Birner, 2010) on a seasonal and annual scale, respectively.On the interannual scale, CPT shows connections with El Nino Southern Oscillation (Zhou et al., 2001) and quasi-biennial oscillations (Baldwin et al., 2001;Reid & Gage, 1985).On longer-term scale, an increase in the tropopause height was associated predominantly due to the increase in the well-mixed greenhouse gases (Santer et al., 2003).
Over the Indian monsoon region, 60% of the day to day variability of CPT (i.e.out of phase variation of the CPT height ( ) and temperature ( )) is driven by adiabatic process (Mehta et al., 2010;Jain et al., 2011;Mehta et al., 2011) indicating a strong connection with ISM.The adiabatic process is due to hydrostatic adjustment to convective heating or cooling (Holloway & Neelin, 2007;Kim et al., 2018).While the in-phase variation of and is governed by the diabatic processes such as radiative heating/cooling from cirrus clouds (Hartmann et al., 2001;Boehm & Verlinde, 2000), turbulent mixing of the overshooting air with the environment (Sherwood et al., 2003, a large-scale westward propagating Rossby wave and eastward propagating Kelvin wave response (Highwood and Hoskins, 1998;Randel et al., 2003) or a combination of these.Recently, a link between the onset of ISM and tropical tropopause are observed (RavindraBabu et al., 2019).Kulkarni and Verma (1993) observed that the tropopause is at a higher altitude during active monsoon when compared to weak monsoon years (Varikoden & Preethi, 2013).TEJ core has been found in between the peaks of the frequency distribution of the tropopause altitudes obtained over a few stations in the ISM region (Ramanadham et al., 1969).Jain et al. (2011) observed that the occurrence of the extreme CPT was due to the westward propagating wave associated with TEJ.Fujiwara et al. (2003) observed a persistent temperature inversion layer in the UT which they attributed to TEJ.Ratnam et al. (2011) noticed that sometimes TEJ penetrates to the LS which may lead to the transport of ozone into the UT.
Thus, TEJ has been associated with various studies such as occurrence of cirrus clouds (Das et al., 2011), gravity wave generation (Ramkumar et al., 2010;Sasi et al., 2000) and horizontal transport of the constituents (Orbe et al., 2015;Ploeger et al., 2017) which in turn may modify the CPT.However, to the best of our knowledge, no systematic study has been reported on the relationship between TEJ and CPT.Hence, here we make an attempt to understand the relationship between the day to day variability of the CPT and TEJ.The main objectives of the present study are to (i) investigate the plausible connection between and , and, (ii) delineate the effect of the TEJ on the relationship between and .

Database
High-resolution radiosonde (Väisälä RS- shows that the broader tropopause is colder (by ~ 5 K) when compared to the sharp tropopause in contrast to the generally known fact that the tropopause is warmer and lower when compared to the sharper tropopause (Seidel et al. 2001;Schmidt et al. 2004;Kim and Son, 2012) which needs a detailed investigation; however, it is out of the scope of the present study.(Supplementary Fig. S1) .
Observed similar structures in the temperature and zonal wind around the tropopause region (Figure 1) are expected due to thermal wind balance.The thermal wind equation, which describes the relationship between the vertical gradient of zonal wind speed and the meridional gradient of temperature under hydrostatic equilibrium, is Where * is the zonal wind, + is the acceleration due to gravity, , is Coriolis parameter andis the northward distance (Andrews, 2010).It is observed that tropopause temperature gradient is greater (i.e.sharp tropopause) in the presence of relatively stronger zonal wind shear (Figures 1ab) when compared to the cases when broad and multiple tropopauses are observed (Figures 1c-f).
Also, the tropopause with broad and multiple structures are colder than the sharp tropopause.It is important to mention here that the warm (cold) air advection is associated with the wind which turns clockwise (counterclockwise) with height (Holton, 2004).The relatively warmer (colder) tropopause in the case of the sharper (broader and multiple) tropopause could be related to warm (cold) air advection due to the TEJ streams.The thermal wind balance due to TEJ streams is described in Supplementary Figure S2.

Temporal variation of ./0 and an approach to quantify its relationship
The temporal variability of and on day to day scale during JJA 2006 is shown in Fig. 2a and for JJA 2007-2014 in the Supplementary Figures S3a-S10a, respectively.In general, ( ) has a large day to day variability (Mehta et al., 2010;Ratnam et al., 2011) and varies in the range of 15.2-19 km (13-19 km) within the monsoon season itself.Though CPT is generally lower during JJA , it can occur as high as 19 km on a few occasions (Mehta et al., 2011).We have calculated tendency (day-to-day difference) as shown in Supplementary Fig. S11a b).
However, as we know that tropopause structure can be significantly modified due to convection (Sherwood et al., 2003;Muhsin et al., 2018) and associated planetary wave propagation

Statistical analysis of the relationship between TEJ and CPT: Plausible link with adiabatic and diabetic processes
In total 707 days observations of and are available out of 828 days during JJA 2006-2014.After filling one day data gap, in total 731 days data are available for the analysis.
Out of which 471 (65%) days and 260 (35%) days are observed for the cases when and are "close to each other" and "far apart" respectively.Among these "close to each other" cases, 352 (76%) are found under category1 and the remaining 115 (24%) cases are found to be isolated.
Figures 3d-f show the scatter plots of and indicating the random relationship in the overall data while they are strongly correlated (r = 0.70) significant at 95% confidence level under the category1 and no correlation under the category2.Note that when considering all the and "close to each other" and "far apart" cases, results remain the same (Figs 3e-f).A good correlation between and under the category1 indicates TEJ is linked to the variation of the CPT.That is if TEJ lies in the tropopause vicinity influences the HCPT variabilities.
In category2, TEJ does not affect the CPT variability.
Figures 3g-i show the scatter plots of and for overall monsoon data, category1 and category2, respectively.In the overall monsoon data, and are moderately anticorrelated (r = -0.32)significant at 95% confidence level (Figure 3g) unlike the correlation between and .It indicates that is more sensitive to tropospheric processes especially infrared warming and therefore tropospheric temperature profile (Thuburn & Craig, 2000).Whereas the weak correlation observed between and in overall monsoon data (Figure 3d) indicates that is more sensitive to the ozone heating and dynamical warming (Thuburn & Craig, 2000) associated with stratospheric meridional circulation (Yulaeva et al., 1994).and are moderately anticorrelated (r = -0.55)significant at 95% confidence level and weakly anticorrelated (r = -0.16)but not significant under the category1 and category2, respectively (Figures 3h-i).Thus, day to day variability of , and are linked under the category1.
It is interesting to observe that and are moderately anticorrelated in the overall monsoon season (r = -0.36)as well as under the category1 (r = -0.55)significant at 95% confidence level while weakly anticorrelated (r = -0.20)but not significant under the category2 as shown in Figures 3j-l.Thus, it appears that the adiabatic process is prominent when TEJ is nearby the CPT.However, and may not always be driven by adiabatic processes alone and can be affected by diabatic processes such as dynamical heating, ozone heating and occurrence of cirrus clouds (Mehta et al., 2010;Reid & Gage, 1996;Thuburn & Craig, 2000) which may be TEJ peak speed and obtained from averaging daily data are found to be 40.7±6.9m/s and 16.3±0.9km for overall data, -42.1±6.7 m/s and 16.5±0.6km for category1 and -40.0±6.7 m/s and 15.5±1.3km for category2 which are also relatively faster by ~ 3 -5 m/s and higher by ~ 0.1 -0.2 km respectively when compared to those obtained from the mean profile.It indicates that results for overall, category1 and category2 obtained from the mean profiles and individual profiles remain consistent.On average TEJ occurs 0.2 km (1.3 km) below the CPT under the category1 (category2).Both temperature and zonal wind profiles have sharper peaks under the category1 whereas under the category2 they are relatively broader.Also, TEJ becomes relatively stronger when it is closer to the CPT which can enhance the troposphere-stratosphere exchange processes due to horizontal advection (Holton et al., 1995;Park et al., 2007;Das et al., 2011).The probability distribution of indicates that < 191K occurs more frequently under the category1 when compared to category2 (Figure not shown).Therefore, entry of water vapor from the troposphere to the stratosphere with the mixing ratio less than 3 ppmv is likely to occur more frequently in category1.

Summary and Conclusions
TEJ shows a large day to day variability which is expected because of variation in the meridional temperature gradient due to ISM variability.About 65% times of the total observations and occurs "close to each other" and 35% times occur "far apart".Out of these "close to each other" cases, 76% times they occur continuously for three days or more (category1) during which adiabatic processes dominate.Finding from this study has far-reaching implications in understanding the variability and trend of surface energy balance and stratospheric chemistry due to enhanced cross-tropopause transport of the surface pollutants via Asian summer monsoon anticyclone (Pan et al., 2016;Mehta et al., 2020).The plausible relationship between and investigated over a tropical station Gadanki using high-resolution daily radiosonde observations (JJA 2006(JJA -2014) ) are summarized below: 1.The effect of the TEJ is observed in the CPT when they occur close to each other.and show in phase variation and are significantly correlated under this category.Whereas TEJ does not affect CPT when they are far apart.
2. When CPT and TEJ are close to each other, and are significantly anticorrelated indicating the prevalence of the adiabatic processes, whereas when they are far apart, no relationship found between them indicating the dominance of the diabatic processes.
3. Thus, when TEJ and CPT are close to each other it can serve as an indicator for the dominance of adiabatic processes.

Introduction
This supporting information provides the additional figures and tables and their description to support the main article.

Thermal wind balance
To illustrate the thermal wind balance due to TEJ streams we have obtained the temperature profiles from the India Meteorological Department (IMD) station, Chennai (13.0 o N, 80.04 o E) which is meridionally separated by about half a degree from Gadanki.The IMD radiosonde data for Chennai (Madras) station code (43279 or VOMM) is available from the link http://weather.uwyo.edu/upperair/sounding.html.However, as the radiosonde observations over Chennai simultaneous to Gadanki observations on the typical dates mentioned in Figure 1 (main article) were not available.Thus, we have taken another set of similar typical examples as shown in Figure S2.For the sharp case, and occur at the same altitude ~ 16.6 km as observed on 10 July 2013.A strong TEJ stream with peak speed ~53 m/s located exactly in the vicinity of the tropopause ( ~190 K) is observed.We have calculated the meridional temperature gradient between Chennai (13.0 N) and Gadanki (13.48 N) and then obtained the right-hand side term of equation 1 (hereafter referred as meridional temperature gradient ( ) term).It is observed that the zonal wind shear ( ) and term between the altitudes 15.1 -17.7 km are roughly the same indicating that the TEJ is in the thermal wind balance in the above-mentioned layer.Similarly, the case observed on 18 August 2010 when TEJ has broad (15.9-16.9km) peak, the tropopause is also observed to be relatively broader.The presence of the temperature inversions at 15.9 km and 16.9 km on the lower and upper edges of the TEJ broad peak can also be noticed.In this case, and term show a good similarity between 14.4 -17.4 km indicating that TEJ is in thermal wind balance.In the case of the multiple TEJ peaks observed at 16 km (speed ~39.4 m/s) and 18 km (speed ~ 34 m/s) are associated with multiple tropopauses occurring at the same altitudes 16 km (temperature ~193.2K) and 18 km ( ~191 K) respectively.In this case peak of the TEJ ( ) lies ~ 2 km below the coinciding with temperature inversion present in the UT (Fujiwara et al. 2003) which is in thermal wind balance.

Relationship between CPT, LRT and TEJ
During ISM season deep convections occur frequently and it is known that and altitude of the lapse rate tropopause (LRT) ( ) may coincide at the same altitude (Seidel et al., 2001).Note that LRT is defined based on the lapse rate criteria (Highwood & Hoskins, 1998).To understand the relationship between , and , their day to day variations are shown in Supplementary Figure S11.We found that LRT coincides to the CPT ~26% times under category1 while 15% times under category2.Out of these coincident cases, the majority (89% under category1 and 85% under category2) occurs during convection however not necessarily with deep convection always.TEJ lies in between CPT and LRT ~24% and 7% times under category 1 and category 2, respectively.Note that TEJ frequently (77% times) occur above the LRT under category1 while it frequently (74% times) occur below the LRT under category2.However, as LRT has limited physical relevance, we have focused on the relationship between CPT and TEJ only.

Correlation analysis
Table ST1 lists the correlation coefficients between and , and , and estimated for overall data, and category1 for each monsoon season during the period 2006 -2014.For category 2, only number of the days observed are listed in the Table ST1.As adequate data was not available under category 2 for the correlation analysis, we have obtained the correlation coefficients tropopause and TEJ parameters for all the cases belonging to "far apart" cases as well as "close to each other" cases as listed in the Supplementary Figure ST2.From Tables ST1 and ST2, we observed that our findings for category 1 and category 2 do not change even when all the cases belonging to "close to each other" and "far apart" respectively are taken into consideration.Similar to overall data, no correlation is observed between and for each monsoon season.As the total data in a monsoon season is an amalgam of partly in phase and partly out of phase variations that results in no correlation between and .However, it is interesting to note that and show moderate to strong correlation ( = 0.43 − 0.78) significant at 95% confidence level under the category1 during each monsoon season ( 2006 between them for all the monsoon seasons except the monsoon season 2011 suggesting a lack of adiabatic influence in this year.It is to be noted that and may not always be driven by adiabatic processes alone and can be affected by other processes such as dynamical heating, ozone heating and occurrence of cirrus clouds (Mehta et al., 2010;Reid & Gage, 1996;Thuburn & Craig, 2000).Thus, when TEJ occurs very close to the CPT and they are strongly correlated it can be considered as an indicator of the prevalence of adiabatic processes.On the other hand, in category2 both and and and are poorly correlated which indicates the dominance of the diabatic processes.
An example of the double tropopauses and double peaks in the zonal wind is observed on 09 July 2010 as shown in Figures1e -1f.The temperature profile shows at ~ 17.9 km and the Lower Tropopause (Mehta et al., 2011) at ~ 16.5 km.The zonal wind profile shows at ~ 17.6 km with a lower peak at altitude ~16.4 km similar to the temperature profile.These typical examples indicate that the zonal wind and temperature profiles around the tropopause behaves in a similar fashion which further indicates the possibility of a direct relationship between and

(
Boehm and Verlinde, 2000;Munchak and Pan, 2014), their possible roles in association with relationship between CPT and TEJ are also analyzed.The presence of the convective activities is investigated using IRBT data as shown in Fig 2c and Figs.S3c-S10c.From Fig 2, it is observed that are affected due to deep convection activities.However, both category1 and category2 occur during the clear sky days as well as convective days indicating that the relationship between and is not always linked to local convection and appears to be a response of large-scale synoptic condition (Supplementary Fig. S12).To examine the role of planetary wave, the continuous timeseries of the temperature anomalies averaged over 16-17 km observed from 26 June -22 August 2006 is subjected to Morlet wavelet analysis (Figure 2d).It is seen that the waves with periods 8-12 days are significant (above the cone of influence) during 20 July to 09 August 2006 during which coincides with .However, they also coincide other timings irrespective of the wave occurrence.The wavelet analysis for JJA 2008-2014 is shown in Supplementary Figs S4d-S10d except JJA 2007 which has a large data gap.The one-day data gaps are filled by linear interpolation to have continuous times for the wavelet analysis.

Figure 4
Figure4presents the mean and standard deviation of the temperature and zonal wind

Figure 1 .
Figure 1.Typical temperature and zonal wind profiles showing (a-b) sharp tropopause and TEJ observed on 02 July 2006.(c -f) and (e -f) are the same (a-b) but observed on 12 June 2010 and 09 July 2010 showing broad and multiple tropopauses and TEJ cases, respectively.Solid dots and open circles denote the and ,respectively.

Figure 2 .
Figure 2. Time series of (a) and , (b) ∆ 2222 3 (c) IRBT and (d) wavelet spectrum of temperature (in terms of power) at 16-17 km during JJA 2006.The up (green) and down(magenta) hatches indicate the catogory1 (category2) case.Horizontal dashed line in (b) represents ∆ 2222 456 over the period 2006-2014 and white curve in (d) represents the cone of influence.

Figure 3 .
Figure 3. Probability distribution of

Figure 4 .
Figure 4. Average profiles of temperature (T; black line) and zonal wind (U; red line) along with their one standard deviation during (a) overall monsoon, (b) category1 and (c) category2.CPT altitude and temperature and TEJ altitude and TEJ peak value are also shown.

Figure S2 .
Figure S2.Typical profiles of (a) temperature, (b) zonal wind and (c) zonal wind shear (left-hand side of equation 1) and the term involving meridional temperature gradient (right-hand side of equation 1) for sharp tropopause and TEJ observed on 10 July 2013.(d -f) and (g-i) are the same as Figures 1a-c but for broad tropopause and TEJ and multiple tropopauses and TEJ observed on 23 July 2013, respectively.Dashed and dash-dotted lines represent the altitudes between which TEJ is in the thermal wind balance.

Figure
Figure S4 (a) Day to day variability of and during the Indian summer monsoon seasons 2006.(b) Time series of ∆H (the difference between and ) along with mean ∆H over the period.(c) day to day variation of the Infrared brightness temperature (IRBT) and (d) Wavelet spectrum of temperature (in terms of power) at 16 km altitude.White curve represents cone of influence.

Figure S13 .
Figure S13.Day to day variability of , and during the Indian summer monsoon seasons (2006-2014).
−2014) except 2014.For the year 2014, we have observed four episodes on 23 July -02 August, 7-12 August, 16-19 August and 25-27 August under the category1, in which the first episode shows that and are not in phase as an exceptional case of category1 resulting in an insignificant correlation.and are significantly anti-correlated ( = (−0.32)− (−0.40)) during different monsoon season except 2011 and 2014.and are also significantly anti-correlated ( = (−0.48)− (−0.79)) under category1 for each monsoon year except 2011.For each monsoon season, out of phase variation of and are more dominant when compared to their inphase variation resulting in significant correlation except during the monsoons of 2011 and 2014.Similar to overall data, and show weak to moderate ( = (−0.23)− (−0.63)) correlation significant at 95% confidence level during different monsoon years.The correlation between and under category1 shows moderate to strong anticorrelation ( = (−0.47)− (−0.83))