On the cross-tropopause transport of water by tropical convective overshoots: a mesoscale modelling study constrained by in situ observations during TRO-Pico ﬁeld campaign in Brazil

. Deep convection overshooting the lowermost stratosphere is well known for its role in the local stratospheric water vapour (WV) budget. While it is seldom the case, local enhancement of WV associated with stratospheric overshoots are often published. Nevertheless, one debatable topic persists regarding the global impact of this event with respect to the temperature-driven dehydration of air parcels entering the stratosphere. As a ﬁrst step, it is critical to quantify their role at a cloud-resolving scale before assessing their impact on a large-scale in a climate model. It would lead to a nudging scheme for large-scale 5 simulation of overshoots. This paper reports on the local enhancements of WV linked to stratospheric overshoots, observed during the TRO-Pico campaign conducted in March 2012 in Bauru, Brazil, using the BRAMS (Brazilian version of RAMS) mesoscale

(e.g., Schoeberl and Dessler, 2011;Wright et al., 2011;Ueyama et al., 2015). Schoeberl et al. (2012) cannot rigorously conclude on the quantitative characterisation of convective moistening of the stratosphere because of its small contribution. Furthermore, 55 it is below the precision level of satellite H 2 O measurements. Nonetheless, Schoeberl et al. (2012) parameterise the impact of deep convection producing gravity waves to mitigate the TTL hydration. Ueyama et al. (2015) estimate an enhancement of ∼0.3 ppmv of H 2 O across 100 hPa at a large-scale in the southern hemisphere during the Austral summer of 2006-07 from a trajectory-based study; the trajectories are initialised from the satellite observed convective cloud tops. Advancing further, Ueyama et al. (2018) report an enhancement of about 0.6 ppmv WV at this level between 10°S-50°N during the 2007 Boreal 60 summer. Carminati et al. (2014) obtain an indirect signature of the stratospheric overshoots at a global scale by studying the diurnal cycle of the EOS Aura MLS (Microwave Limb Sounder) H 2 O mixing ratio due to deep convection overshooting the 100 hPa layer, highlighting the most active convective regions. However, the critical impact of stratospheric overshoots on the global distribution of WV has so far proven difficult to estimate.
Another potential strategy is to upscale stratospheric overshooting effects by forcing them into a large-scale simulation, where the overshoots are explicitly resolved in cloud-resolving numerical simulations. However, cloud-resolving simulation studies of several cases must be conducted before proceeding with this phase. The combined study of results corroborated by observations would encourage a stratospheric overshoot nudging strategy in a larger-scale or Brazilian size simulation.
Furthermore, utilising the superparameterization method (Grabowski, 2001;Khairoutdinov and Randall, 2001;Khairoutdinov et al., 2005), explicitly adding cloud-resolving simulation in each grid or sub-grid point of a general circulation model (GCM) 70 simulation or sub-GCM simulation to consolidate the local-scale aspects such as the diurnal cycle and convection strength (e.g., Khairoutdinov and Randall, 2006;Randall et al., 2016) would provide information on the influence of overshoots at a large scale. The goal of this research is to learn more about cloud-resolving simulations.
Here, we perform three simulations of an observed case of stratospheric overshoots using the BRAMS (Brazilian version of RAMS) mesoscale model. They are different from each other over the microphysical setup or the vertical grid structure. 75 It produces a range of estimates on the ice injection into the stratosphere and the remaining water after the sublimation. We use the data from a well-documented case on 13 March 2012 in Bauru, São Paulo State, Brazil, during the TRO-Pico, a small balloon campaign Ghysels et al., 2016). On that particular day, two lightweight balloon-borne hygrometers intercepted a hydrated stratospheric air parcel emanating from two distinct overshooting plumes. However, no ice particles were detected by the particle counter/backscatter sondes. It is also worth noting that at these altitudes, the relative 80 humidity with respect to ice was reported to be about 40-50%.
The paper is organised as follows: sect. 2 gives a concise description of the observed case, as well as the TRO-Pico campaign and the balloon-borne devices utilised for WV measurements. The BRAMS model and the setup of the three simulations are described in sect. 3. The TRO-Pico observed dataset is used to validate the simulations in sect. 4. The key findings are discussed in sect. 5, which depicts the structure and composition of overshooting plumes. The stratospheric WV mass budget is studied 85 quantitatively in sect. 6. Finally, sect. 7 summarises the work's primary findings as well as upscaling strategies.

Overview of TRO-Pico campaign
TRO-Pico is a French initiative based on a small balloon campaign in Bauru (22.36°S,49.03°W), State of São Paulo, Brazil, and funded by the Agence Nationale de la Recherche (ANR). Its purpose is to study the stratospheric water vapour entry in the 90 tropics at different spatial and time scales. In particular, TRO-Pico main's goal is to better quantify the role of overshooting convection at a local scale in order to better quantify its role at a larger scale with respect to other processes. It took place in March 2012 for the first intensive observation period (IOP) and from November 2012 to March 2013, with regular soundings including a second IOP in January and February 2013. The case under investigation in this paper is part of the first IOP while Behera et al. (2018) investigated the November 2012 to March 2013 TRO-Pico period. Several light-weight devices were 95 used in this campaign, including the Pico-SDLA, which weighs 8 kg, the FLASH-B, which weighs 1 kg, and the COBALD, which weighs 1.3 kg. Hydrogen/helium-inflated Raven Aerostar zero-pressure plastic (open) balloons with volumes of 500 m 3 and 1500 m 3 , as well as 1.2 kg Totex rubber balloons that were somewhat larger than conventional radiosonde balloons, were used. The TRO-Pico campaign provided measurements of CO 2 , CH 4 , O 3 , and NO 2 using a large set of equipment. On the other hand, WV and particle measurements were the campaign's main sampling. Only the Pico-SDLA and FLASH-B WV measuring 100 devices, along with the LOAC and COBALD particle measurement equipment, were flown on March 13, 2012. The balloons collected data with a vertical resolution of approximately 20 m. Readers interested in balloon-borne measurement technology may read Vernier et al. (2018) and Pommereau et al. (2011), as well as the references in those papers, which are based on large balloon campaigns, BATAL and HIBISCUS, respectively.
Pico-SDLA is an infrared laser hygrometer emitting at 2.61 µm in a 1 m long open optical cell . Its 105 uncertainty is about 4% in the TTL conditions. FLASH-B is a Lyman-alpha hygrometer measuring WV at night-time only with an uncertainty of 5% in the UTLS (Khaykin et al., 2009). LOAC is an optical particle counter based on the scattered light at 60°b y ambient aerosol or particles for different wavelength channels (Renard et al., 2016). COBALD, developed at ETH-Zürich, is a backscatter sonde that applies several wavelengths (Brabec et al., 2012). Here, we use both the particles/aerosol instruments for the ice particle detection above the tropopause level.
convective activity in the area of interest for the TRO-Pico campaign was about 100 km east of Bauru near Botucatu, and later between Botucatu and Bauru with a series of short-lived and almost stationary convective cells. The reader is referred to sect. 4 and the animation on cloud tops in the supplementary material for the time evolution of the convective cells at these locations. where both the hygrometers recorded two particular local enhancements of the WV mixing ratio at 18.5 km and 17.8 km 130 altitude, respectively. Besides, they registered a third local enhancement at 17.2 km altitude, albeit of smaller magnitude in comparison to the earlier two. One remarkable point is that the LOAC particle counter detected no ice particles within these altitudes during the flight train. Moreover, the COBALD backscatter sonde flown under the same balloon as FLASH ruled out the presence of ice particles.
The trajectory study of Khaykin et al. (2016) establishes a well-documented link between the local enhancement of WV in 135 the stratospheric part of the TTL, seen by Pico-SDLA and FLASH-B, and the air mass advected from stratospheric overshooting plumes. However, based on a more extensive investigation of a deep convective system that developed during the local afternoon of March 13, 2012, in the southeast of Bauru, and decayed in the evening, the current work provides additional insights into the time evolution of this meteorological state. A comparison between Bauru S-Band radar images with model outputs is made in sect. 4 to monitor the detected convective activity and development of specific plumes.

S-Band radar
This modelling study benefits from the echo tops product of convective systems observed by the Doppler S-Band radar, located at IPMet/UNESP in Bauru. It facilitates the validation of our simulations. The echo top measurements depend highly on the technical specifications of the radar, such as wavelength, beam width, pulse width (PW), pulse repetition frequency (PRF), and radial and azimuth resolution. In the case of Bauru S-band radar, the beam width is 2°; the PW is 0.8 µs at PRF 620/465 145 pulses per second, limiting the range to 240 km with a radial resolution of 250 m and 1°in azimuth. Thus, the Bauru radar can only identify raindrops, liquid, or frozen particles, with a general threshold of 10 dBZ, corresponding to a rainfall rate of 0.15 mm h −1 to 0.3 mm h −1 when the beam cross-section is filled. The radar records reflectivity, spectral width, and radial velocities at 16 different elevations between 0.3°to 45°. Due to the 2°beam width, it may underestimate the altitude and size of the overshooting plumes containing small cloud droplets and mostly ice particles when they are at a relatively long distance 150 from the station.

Brazilian developments on the Regional Atmospheric Modeling System (BRAMS)
BRAMS, version -4.2, maintained at Centro de Previsão de Tempo e Estudos Climáticos (CPTEC) (Freitas et al., 2009), is a 3D regional and cloud-resolving model based on the RAMS model, version -5.04, developed at Colorado State University 155 (CSU)/ATMET (Cotton et al., 2003). The Brazilian developments, tuned for the tropics, are essentially on the cumulus convection, surface scheme, and surface moisture initialisation. It simulates the turbulence, sub-grid scale convection, radiation, surface-air exchanges, and cloud microphysics with the 2-moment configuration at different scales ranging from large continental to large-eddy scale simulations. Additionally, it can simulate seven types of hydrometeors, viz., cloud, and rain as liquid particles and pristine ice, snow, aggregate, hail, and graupel as ice particles (Walko et al., 1995). Here, the mixing ratios of hy-160 drometeors and concentration are prognostic variables (Meyers et al., 1997). A gamma distribution represents all hydrometeors, where ν, the shape parameter, determines both the modal diameter and the maximum concentration at that diameter.
In Eq. 1, f gam denotes the probability density function for the modified gamma distribution of hydrometeors with a diameter of D, as obtained from (Walko et al., 1995). Γ(ν) is the normalisation constant, and D n is the characteristic diameter of the 165 modified gamma distribution. A bigger ν indicates a narrower distribution width and a larger modal diameter. As a result, the proportion of smaller and bigger hydrometeors in the distribution is modulated. The size distribution of hydrometers would be more peaked as the modal diameter increased.
Furthermore, using a smart grid-nesting system that solves equations simultaneously between computational meshes while applying any number of two-way interactions, the BRAMS/RAMS can solve the fully compressible non-hydrostatic equations 170 (Tripoli and Cotton, 1982). It also includes a deep and shallow cumulus system based on the Grell and Dévényi (2002) mass flow approach, which can be used to simulate tracer convection. Marécal et al. (2007)  in limited quantitative data on overshoots. However, S-band radars are used in the current investigation to better constrain deep convective cells both spatially and temporally.

Simulation setups
We use the BRAMS model to run three cloud-resolving simulations, including multiple grid-nesting to explicitly address the stratospheric overshoots associated with the case study in sect. 2. In these simulations, the modelling strategy is to assess 180 the sensitivity of the stratospheric water budget linked to overshoots to the model setup, such as microphysical parameters or vertical resolution, resulting in various hydration or ice injection amounts. It is likely to have an impact on our conclusions about the underlying physical characteristics related with overshoots, as well as the mechanism for setting them up in largescale H 2 O nudging scheme simulations (or Brazilian size). We employ the same domain (mother-grid) as a step forward from Behera et al. (2018) seasonal scale study, where the model cannot explicitly resolve the overshoots. Then we raise the spatial 185 resolution until we reach the third grid, ensuring that the overshoots are explicitly resolved. We start the simulation several hours before the onset of deep convection activity in the radar data, because we will use Bauru radar observation to evaluate the development of convective cells, as mentioned in sect. 2.3, and to give the model enough time to spin up.
Following that, we run three simulations with a spatial resolution of 800 m × 800 m.  Each simulation begins at 12:00 UT on March 12, 2012, and ends 48 h later. To reduce computing costs, we activated the third grid only at 10:00 UT on March 13 and recorded model outputs every 7.5 min after that. This data record frequency 205 corresponds to the volume scans produced by the IPMet S-band radar. These are used to validate the cloud top models. To ensure numerical stability, the simulation integration time step varies between 2 s to 10 s for the coarsest grid. It is five times smaller for the second grid and twenty-five times lower for the third grid. Invoking the radiation module has a time resolution of 300 s to 500 s. The ECMWF operational analyses with 1.0°spatial resolution initialise all simulations and force the first grid's boundary conditions every 6 h. Following the work of Liu et al. (2010), there is no nudging of ECMWF data at the domain's 210 centre.

REF, NU21
, and HVR simulations deviate from each other over the following points.

Validation of the simulations
We validate the three BRAMS simulations using observations from the S-Band radar of IPMet, located in Bauru, and the balloon-borne measurements of the TRO-Pico campaign, respectively. Note that the balloon-borne measurements are part of the first IOP phase of the two-year field campaign.

Validation of modelled cloud tops against radar echo top observations 230
We examine the BRAMS model's capacity to initiate and describe deep convection activity at an accurate time and location by comparing simulated outputs to S-Band radar data. To do so, we estimate the modelled cloud top layers every 1 km at altitudes ranging from 9 km to 20 km, much like the echo top products. We determine the modelled cloud top height for this altitude range if the concentration of condensed water, i.e., ice plus liquid, exceeds a specified mixing ratio threshold within a specific layer. The cloud top altitude assignment for a given (x, y) grid mesh is conclusive once all the vertical levels are read because 235 this criterion is implemented in a bottom-top loop. We use a threshold of condensed water concentration to a cloud top based on its range of altitudes to account for the drop in hydrometeor concentration with altitude inside the TTL linked to a deep convective cell. It is 1 g kg −1 for the layers ranging from 9 km to 10 km to 15 km to 16 km. It is 0.45 g kg −1 for 16 km to 17 km, 0.2 g kg −1 for 17 km to 18 km, and 0.008 g kg −1 for layers above 18 km. These thresholds are chosen as a function of typical hydrometeor concentrations within overshooting plumes (see Liu et al., 2010). grid, not near or at the edges of this grid. We observe that the model can reproduce relatively well these highly unpredictable convective systems. There exist similar deep convective clusters around Bauru in the radar images and the simulations, although at slightly different times. The radar image at 16:46 UT (13:46 Local Time; Fig. 1a) shows a storm cluster comprising three cells near Botucatu, southeast of Bauru with the echo top of the furthest west one reaching higher than 18 km level. We should emphasise that small cloud droplets and ice particles, which are the principal components of overshooting plumes, are 250 considerably less sensitive to the S-band radar because they do not sufficiently fill the beam cross-section. In REF (Fig. 1b), we notice a comparable convective storm complex to have developed at 16:15 UT west of Bauru, depicting two cloud tops of height greater than 17 km and 18 km, respectively. At 15:45 UT, NU21 (Fig. 1c) indicates a similar convective system in the west of Bauru, as seen on the radar image ( Fig. 1a) one hour later in the southeast of Bauru, but with only one cloud top greater than 18 km level. HVR (Fig. 1d) also produces a convective cluster at 15:45 UT in the west of Bauru, but comprising three 255 cells in the proximity of Bauru, 100 km, with two cloud tops of height greater than 17 km and one greater than 18 km.

265
The convective cells are overgrown in the area than in NU21 at 14:15 UT, though in a similar position. By 15:00 UT, the deep convection altitude in HVR is also higher than in REF and the radar echo tops. It is also located much more west than the radar observations. However, stratospheric overshoots are present in the simulations as well as in the radar observations with the echo top above 17 km at the peak of the convective activity, i.e., during 16:00 -17:00 UT. In the three simulations, convective activity increases in height and spreads over larger areas in the TTL as time passes. In HVR, it is further west-southwest of 270 Bauru. Thus, all simulations predict the onset of convective activity to be slightly earlier than observed. Given the uncertainties in modelling and S-band radar perceptions of deep convective activity, associating one-by-one simulations with radar convective cells in spatial and temporal terms is a difficult task (e.g., Li et al., 2008;Rowe and Houze, 2014;Weisman et al., 1997).
As a result, it may not be the most appropriate criterion for evaluating these disorganised deep convective cloud simulations. To further understand the situation, one can expect HVR to determine more reliable dynamics across the tropical tropopause than REF and NU21, respectively. Contrary to expectations, it tends to intensify massive deep convection activity. A plausible fact to explain such behaviour in HVR is the ratio between vertical and horizontal grid points, which overestimates vertical motions due to grid cell saturation (Homeyer et al., 2014;Homeyer, 2015). It might be the model's Courant-Friedrichs-Levy 290 (CFL) limit, which in finite-difference simulation techniques constrains the relationship between infinitesimal increases in space grid points and infinitesimal time step increments. In the BRAMS model, the von Neumann stability assessment (Deriaz and Haldenwang, 2020) is necessary for the transport equations related to convection. Aside from that, Eulerian model simulations of high vertical resolution, high-frequency wave motions, such as inertial-gravity waves (e.g., Staquet, 2004;Young, 2021), can be overdetermined. As a result, they can exaggerate cloud microphysics (Aligo et al., 2009) and cause erroneous 295 cloud conditions near the TTL (Jensen and Pfister, 2004). Therefore, we leave HVR out of the next sections to describe the details, and we do not look at this simulation's water budget in the lower stratosphere.
In sect. 4.1, we essentially outline several principal aspects by closely studying the simulated convective plumes. First, we locate the position of deep convective activity further west-northwest in the model, typically 50 km to 60 km west-northwest.
Second, the time evolution of the convective clusters reveals that they are moving north-northwest while most of the convective 300 activity remains in the west of the Tietê river in both cases. Overall, we cannot expect the model to predict precisely the position and time of convective activity development. REF and, to a certain extent, NU21 provide reasonable predictions in space and time. They generate good estimates of convective cloud tops but initiates the plumes generally earlier to the radar observation.
In contrast, HVR yields unfavourable conditions and exaggerates its size.

305
The WV and particle measurements performed in the proximity of overshoots in the frame of the TRO-Pico campaign establish a well-documented database to validate model simulations. For our study, as the balloon-borne measurements belong to a moment several hours after the overshooting event -this time interval between the overshooting event and the balloon-borne measurements is indicated as δt om hereafter, the simulation validation strategy is as follows. We observe the modelled overshooting plume at 17.2 km and 17.8 km altitudes, respectively, where FLASH-B and Pico-SDLA hygrometers captured the 310 WV local enhancements (see Khaykin et al., 2016). Then, after the same δt om , we investigate the WV enhancement at these levels in the model. streamline to follow the direction of the moving plume at this height. We prepare this kind of plot every 7.5 min to follow the evolution of the overshooting cell at that height. For simplicity and space limitations, we show only these three plots in the 320 paper.  Then, we implement the same strategy to validate the hydration due to overshoot at 17.8 km altitude, see Fig. 3b is 7 h from the overshooting event till the FLASH-B measurement. It is similar as in Fig. 2 and is provided in the supplementary material (Fig. S1). The plume spreads horizontally, slightly southeastward, and finally northward, where most of the original plume is north to 22.4°S and east to 48.8°W at 23:15 UT.
In ing at this level, and the total H 2 O is only in the vapour phase as observed by the LOAC particle counter and the COBALD backscatter sonde. Then, we analyse the WV enhancement in NU21 at 17.8 km altitude at 20:52 UT, that is δt om = 4 h40 min after the 16:15 UT overshooting event (see Fig. 4b). This δt om is the same as the time interval between the Pico-SDLA mea-365 surement and the overshooting event. In Fig. 4b, we obtain many pixels, located at the border of the overshooting plume, with a ∼0.7 ppmv H 2 O enhancement without any ice remaining -a very similar way of observation by Pico-SDLA and LOAC.
Furthermore, there are many pixels near the Tietê River giving very high WV enhancement, up to 6 ppmv. This sort of large water enhancement from overshoots has already been identified by the FISH hygrometer onboard the Russian M55 Geophysica high-altitude aircraft in the SCOUT-AMMA field campaign in West Africa (see Schiller et al., 2009 we give a quantitative interpretation of the overshooting plumes from REF and NU21. Unfortunately, HVR appears to produce excessively severe convective activity, making it unsuitable for further analysis.

Analyses of overshooting turret
We provide the five conceivable combinations of hydrometeors inside an overshooting plume to document the quantitative information collected from the simulations on the structural characteristics of a typical overshooting plume. Its base is at the 395 380 K isentropic level, which is the stratosphere's lowest layer. At the 380 K isentropic level, the instantaneous mass flux of individual hydrometeors is also estimated. Between 380 K to 430 K isentropic levels, it comprises the estimation of total ice mass and the five types of ice particles. Finally, a table provides the quantities that could lead to a road map of a nudging scheme of the water vapour enhancement in the lower stratosphere due to overshoots in large-scale simulations, which could lead to the quantification of the influence of overshoots on a large scale.

Structure and composition of overshoots
We assess all the five types of ice hydrometeors during an overshooting event. The series of plots in Fig Table 1). We present this calculation from 15:00 -18:52 UT for REF and NU21, which can be found in the animation of horizontal cross-sections in the supplementary materials.

405
Above the tropopause, we find pristine ice and snow to be the primary ice hydrometeors (∼16.6 km altitude). However, aggregates and a trace amount of graupel are present. It is only true for REF. The full-time evolution of the horizontal cross-section can be found in the Supplementary material. The lack of this in NU21 could be attributed to its microphysical configuration, which allows larger hydrometers to be placed deeper within the convective plumes, resulting in a lower convective updraft and inability to reach the tropopause layer. This is evident in Table 2 and sect. 6.1, where REF is shown to release approximately ence of hail particles is negligible, as shown in Fig. 5, which confirms the results of Homeyer and Kumjian (2015), obtained using S-band radar measurements of deep convective activity over the extratropics. It is consistent with the results reported in Chemel et al. (2009). Using the WRF model, they investigate the Hector thunderstorm and find (pristine) ice and snow as the primary components. However, the current study makes use of the BRAMS model, which combines five types of ice 415 hydrometeors rather than three in the WRF version used by Chemel et al. (2009) thermodynamic structure, which is controlled by particle size distribution and affects the convective updraft.
The contact area or spreading (km 2 ) of the overshooting plume at the lowest layer of the stratosphere, i.e., the 380 K isentropic level, is then determined. Fig. 6  respectively. The latter one with the large surface area indicates that changes in the particle size distribution, the shape parameter ν, may modulate the spreading of overshooting convection while penetrating the stratosphere. In the following sections, we estimate the mass budget corresponding to UTLS, set as a preferred range of isentropic levels.

6 Stratospheric Water mass budget
We estimate each hydrometeor's instantaneous mass-flux rate across the 380 K isentropic level. The rates are the average over the domain that comprises only the third grid of simulation. Please note that it is not representative of a property of any particular overshooting plume but preferably addresses a realistic estimation on the flux rates of ice particles entering the 380 K isentropic layer. Besides, we evaluate the net H 2 O mass budget prevailing within the slice of 380 K to 430 K isentropic levels. it is regularly higher than NU21. It is already explicit that the number of overshooting events is different in REF and NU21 (please refer to Table 1). Eventually, the differences in the mass-flux rate between REF and NU21 would be critical to explain as their values are also proportional to the vertical wind velocity (see Sang et al., 2018). graupel, and hail, as well as water vapour. It is worth mentioning that the amount of liquid in this calculation has no bearing.

Mass budget above 380 K isentropic level
The simulations' third grid, which has a domain size of 201 km × 165 km and isentropic values ranging from 380 K to 430 K, is used for time-integrated estimation. Because none of the convective plumes in the simulations exceed this isentropic level, the maximum level is 430 K. Our mass budget estimation begins with an unperturbed state (zero total mass), i.e., the time before deep convection begins in each simulation, which is 15:00 UT for REF and 14.00 UT for NU21, respectively, and ends at 17:30 465 UT for both. This is because the WV time evolution reaches a near plateau profile without including any further overshoots, which would otherwise make the study more difficult. Furthermore, the ice profile (dotted red) is descending, indicating that deep convection activity in the model has ended. Simultaneously, the WV profile (dotted blue) rises and settles around 17:30 UT.
In both simulations, the total H 2 O (ice+vapour) mass budget estimations with respect to the unperturbed state show a net 470 increment of 8 kt accumulated over 17:30 UT. In contrast, the vapour increment due to overshoots is only 2 kt in REF and 3 kt in NU21. The difference in vapour enhancement is attributed to the simulations' different particle size distribution, implying a variation in the sedimentation process. Another interesting fact is that NU21 has a longer lifetime than REF since the last overshoot above 17 km. As a result, ice particles injected into the stratosphere in NU21 should have a longer time to sublimate than ice particles injected into the stratosphere in REF.

475
In REF, we explain the peak of total water content at 16:22 UT with the last two overshooting events that occurred at 16:15 UT, refer to Fig. 8a and Moreover, we determine the standard amount of hydration for each overshoot, providing both the upper and lower limit by 485 reflecting the two extreme cases on the fate of ice. Such as (1) the upper limit would assume all the remaining ice sublimates in the stratosphere, and (2) the lower limit would indicate all the remaining ice is falling back to the troposphere without sublimating at all. The upper limit is about 8 kt 6 ≈ 1.34 kt in REF, whereas it is 8 kt 4 = 2 kt in NU21. The lower limit of hydration for REF is 2 kt 6 ≈ 0.34 kt, whereas for NU21, it is 3 kt 4 ≈ 0.75 kt. In both the cases during 15:00-17:30 UT, the denominator denotes the total number of overshooting turrets, denoted by arrows in Fig. 8, and the numerator gives the net amount of WV 490 enhancement. The lower limit is an important point, which is unlikely to be reached because of the very weak fall speed of the small size pristine ice and snow particles. strategy for NU21 at 15:07 UT, the ice enhancement due to single overshooting event is 8 kt 2 = 4 kt. Several mesoscale modeling studies (e.g., Liu et al., 2010;Lee et al., 2019) and satellite observations (e.g., Iwasaki et al., 2010;Lelieveld et al., 2007) have already reported regarding this type of total water enhancement due to overshoots in the tropical lower stratosphere. On the other hand, Dauhut et al. (2018) provides the estimation of the individual contributions of each overshooting plume hydrating the stratosphere, leading to a lower estimate. However, the method applied to get this estimation is absent. Overall our estimations on the total H 2 O enhancement are compatible with most of these studies. They could pave the way for forcing 505 the impact of overshoots in a large-scale computing cost-effective simulation, which cannot resolve overshoots due to coarser horizontal representation.
To get quantitative information on the mass distribution of five different types of ice hydrometeors within the overshooting plumes constrained within the thin layer of 380 K to 430 K isentropes (see Fig.5), we estimate the percentage of each type of ice particles. It follows in two ways: (1) ρ 1 = mi Mi × 100, where m i corresponds to the mass of a particular type of ice particles 510 i within a layer of 380 K to 385 K, and M i corresponds to the mass of the same type of ice particles i within a layer of 380 K to 430 K; (2) we express them as a percentage of the mass of a given kind of ice particle to the total mass M of ice particles, M = 5 i=1 M i , within a layer of 380 K to 430 K, namely, ρ 2 = Mi M × 100. We tabulate the results in Table 2. One of the major inferences drawn from Table 2 is the amount of ice injected by various overshooting plume remaining within a layer of 380 K to 385 K, ρ 1 : ∼ 72% in REF and ∼ 65% in NU21. The ρ 1 and ρ 2 highlight the conclusions of sect. 515 5.1, i.e., the overshooting plume is essentially comprised of pristine ice, snow, and aggregates, though it can contain a small amount of graupel, present mostly at 380 K to 385 K, the base of the plume. Furthermore, within 380 K to 430 K, hail is negligible in the overshooting plume for both the simulations but is always the dominant hydrometeor in the base of the plume, featuring the results of radar observations in Homeyer and Kumjian (2015). We also recognise competition in the growth of pristine ice over aggregates and graupel concurrently within the plume. Whenever aggregates and graupel are relatively large 520 in mass inside the plume, e.g., 15:37 UT in REF and 15:30 UT in NU21,pristine ice prevails relatively low,e.g.,16:37 UT in REF and 15:52 UT in NU21. It signifies the existence of the weak vertical velocity, which results in settling back of larger particles. Thus, hail and graupel fall back to the troposphere, allowing further growth of smaller ice particles (see Homeyer and Kumjian, 2015;Qu et al., 2020) in the lower stratosphere within an environment comprising a significant quantity of supercooled liquid water content. In Table.2, the variations in the quantities of individual ice particles above 380 K 525 layer between the two simulations are possibly due to the small change in the microphysics adopted to investigate the impact of shape parameter (ν) on producing overshoots. Since the ν value is higher in NU21, the particle size distribution is more limited than in REF. The particle size distribution resulted from a gamma function becomes narrower as the ν value increases (see Eq. 1). Consequently, the lesser variability present in the particle size distribution of NU21 could lead to a more efficient falling back process of larger ice particles to the troposphere in comparison to REF. Besides, recalling the results from Fig. 8,   530 the longer prevalent behaviour of overshoots above 17 km in NU21 than REF could lead to higher sublimation of ice in NU21, confirms our observation of the less injection of ice in NU21 to the lower stratosphere but results in more hydration.

Conclusions
This paper describes several cloud-resolving simulations of convective overshoots penetrating the lower stratosphere using the BRAMS mesoscale model, corresponding to an observed case on March 13, 2012, during the TRO-Pico field campaign 535 in Bauru, Brazil. During this series of overshooting convection events, several plumes reached the stratosphere. As a result, it accounts for the hydration heterogeneity produced by overshoots of variable intensity, even when they occur under similar circumstances (e.g., stratospheric humidity). The S-Band radar stationed at Bauru, as well as the balloon-borne measurements from this campaign, allow the simulation results to be validated. These simulations, which have been validated as realistic when compared to TRO-Pico measurements, are then used to obtain the main physical characteristics of overshooting plumes.

540
The main results are as follows.
1. Primarily, the simulated overshooting plume reaching the lower stratosphere comprises pristine ice and snow, and to some degree aggregates but only at the base, the 380 K isentropic level. 2. The cross-section of the overshoots at the 380 K isentropic level is about 450 km 2 and interestingly, it is close to the mother grid resolution, 20 km × 20 km, at which BRAMS cannot determine explicitly the overshooting convection (see 545 Behera et al., 2018).
3. Within the limited layer of 380 K to 385 K, 68% of the overall ice mass exists. It also suggests that the remaining 32% of ice (mostly pristine ice and snow) moves higher in the stratosphere. Because of the very slow fall speed at altitudes above 385 K and the subsaturated conditions with respect to ice, that 32%, which is pristine ice and snow, is anticipated to stay in the stratosphere and sublimate. 5. The stratospheric WV enhancement due to one overshooting event is estimated to range between 1.34 kt to 2 kt as the upper limit and 0.34 kt to 0.75 kt as the lower limit after sublimation and (or) sedimentation of the stratospheric ice. If we consider complete sublimation of ice, as in REF, it confirms our estimate that the 32% of 4.3 kt of ice irreversibly 555 traveling further up to the stratosphere results in the stratosphere having the lowest hydration in the upper limit range.
These data can be utilised to develop a nudging method that quantifies the influence of overshooting convection on the stratospheric water vapour using a low-cost, large-scale simulation. Though the findings are limited to a case study in Brazil and may not be generalisable, more of similar case studies should be conducted in order to gain a better knowledge of the events, and this work is in keeping with that goal. This instance would be the next stage in the current research, offering a road 560 map for extending the impact of overshooting convection on stratospheric water vapour on a continental (Brazilian) scale.
Video supplement. Two videos are provided for the time series analysis made every 7.5 min in the supplementary material: one for the modelled cloud tops and corresponding S-band radar echo tops; the second one for the vertical distribution of horizontal cross-section of different hydrometeors within the overshooting plume.
Author contributions. EDR and AKB conceptualised the study design, methodology, validation, and analysis. JB provided the support to run BRAMS in different HPC machines, and EDR provided the resources to achieve the simulations. AKB  overshoots are calculated by taking into account the height of each plume in the 7.5-minute time-lapse imagery, which must be greater than or equal to 17 km, as well as the spatial spread of each plume. Fig. 6 depicts a scenario in which the spatial extent of the overshoot is also taken into account.       Table 1. The colour contours show certain levels from 0.04 g kg −1 to 0.14 g kg −1 of total H 2 O content to highlight the outer part of the overshooting plumes. The solid black lines give the approximate range of each figure in km.

Cases
Pristine Snow Aggregates Graupel Hail      Figure 8. Water mass budget (ice and water vapour) for (a) REF and for (b) NU21 in the third grid between the 380 K to 430 K isentropic levels. The ice budget contribution includes the five ice hydrometeors (pristine ice + snow + aggregates + graupel + hail). The colour and length of the arrows indicate the cloud top altitude of each occurrence, with the smallest arrows (brown) referring to cloud top heights of