Damien Héron
email: damien.heron@univ-reunion.fr

Stéphanie Evan

Joris Pianezze

Thibaut Dauhut

Jerome Brioude

Karen Rosenlof

Vincent Noël

Soline Bielli

Christelle Barthe

Jean-Pierre Cammas

Stephanie Evan
email: stephanie.evan@univ-reunion.fr

Vincent Noel

Stephanie Evan

Mesoscale simulations of tropical cyclone Enawo (March 2017) and its impact on TTL water vapor

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

35

Water vapor in the low stratosphere regulates up to 10% of the greenhouse effect at the earth's surface [START_REF] Solomon | 795 Contributions of Stratospheric Water Vapor to Decadal Changes in the Rate of Global Warming[END_REF]. The stratospheric water vapor concentration is primarily affected by the freeze-drying at the tropical tropopause [START_REF] Brewer | Evidence for a world circulation provided by the measurements of helium and water vapour distribution in the stratosphere[END_REF] and the production of water vapor by methane oxidation [START_REF] Le Texier | The role of molecular hydrogen and methane oxidation in the water 800 vapour budget of the stratosphere[END_REF]. It has https://doi.org/10.5194/acp-2020-870 Preprint. Discussion started: 21 October 2020 c Author(s) 2020. CC BY 4.0 License.

been established that freeze-drying process at the cold point temperature of the tropical tropopause is the main driver of the annual and interannual variability in the entry value of stratospheric water vapor [START_REF] Mote | An atmospheric tape recorder: The imprint of tropical tropopause 745 temperatures on stratospheric water vapor[END_REF]40 Randel et al., 2004). On a long-term and global scale, air enters the stratosphere through the tropical tropopause [START_REF] Brewer | Evidence for a world circulation provided by the measurements of helium and water vapour distribution in the stratosphere[END_REF]. This air regulates the radiative and chemical balance of the global Upper Troposphere Lower Stratosphere by carrying trace species with it. In the tropics, between 14 km and 19 km in altitude, the tropical tropopause layer (TTL), is a transition layer between two different dynamical regimes from rapid vertical transport in the troposphere associated with moist tropical convection to slow ascent in the stratosphere due to the Brewer 45 Dobson circulation. The TTL is often referred to as the "gateway to the stratosphere" for water vapor and other chemical constituents (Fueglistaler et al., 2009). Processes occurring in the TTL control the hydration of the stratosphere [START_REF] Jensen | Ice nucleation and dehydration in the Tropical Tropopause Layer[END_REF]. The overall contribution due to transport of air by passing the cold trap is not well quantified, but it may contribute during extreme events (e.g. the strong 2016 El Niño; Avery et al., 2017).

Very deep convection may overshoot the tropical tropopause (~17km), injecting water vapor and ice crystals 50 directly into the stratosphere (Avery et al., 2017;[START_REF] Corti | 650 Unprecedented evidence for deep convection hydrating the tropical stratosphere: CONVECTIVE HYDRATION[END_REF]. In addition, overshooting convection plays a critical role in transporting short-lived chemical compounds from near the surface to the lower stratosphere, which is hard to achieve via a large-scale slow ascent [START_REF] Bergman | Seasonal differences of vertical-transport efficiency in the tropical tropopause layer: On the interplay between tropical deep convection, large-scale vertical ascent, and horizontal circulations: VERTICAL-TRANSPORT EFFICIENCY IN THE TTL[END_REF][START_REF] Shepherd | Dynamics, stratospheric ozone, and climate change[END_REF]. [START_REF] Dessler | Transport of ice into the stratosphere and the humidification of the stratosphere over the 21st century: TWENTY-FIRST CENTURY STRATOSPHERIC WATER TREND[END_REF] hypothesize that injection of ice into the lower stratosphere could account for 20 to 50% of the 1 ppmv increase in lower stratospheric water vapor expected in a warming climate. As the role of tropical 55 convection on the Upper Troposphere/Lower Stratosphere (UTLS) composition is still under discussion, observational and modeling studies are needed to further assess the net effect of convection on UTLS water vapor and other short-lived chemical compounds.

Deep convection and in particular overshooting convection have a direct impact on lower stratospheric water vapor. The net effect (hydration or dehydration) will depend on the depth of the injection, the size of the injected 60 ice particles, and the conditions (i.e. relative humidity with respect to ice RHi) of the environment into which the overshoots inject ice [START_REF] Dauhut | The Mechanisms Leading to a Stratospheric Hydration by Overshooting Convection[END_REF][START_REF] Jensen | Can overshooting convection dehydrate the tropical tropopause layer?[END_REF][START_REF] Schoeberl | Convective Hydration of the Upper Troposphere and Lower Stratosphere[END_REF][START_REF] Ueyama | Convective Influence on the Humidity and Clouds in the Tropical 805 Tropopause Layer During Boreal Summer[END_REF] In subsaturated TTL air, condensed ice is not removed quickly enough to produce net dehydration [START_REF] Jensen | Can overshooting convection dehydrate the tropical tropopause layer?[END_REF].

Deep convection associated with tropical cyclones can play an important role in the transport of chemical constituents from the troposphere to lower stratosphere [START_REF] Ray | Hydration of the upper troposphere by tropical cyclones[END_REF][START_REF] Zhan | Contribution of tropical cyclones to stratosphere-troposphere exchange over the northwest Pacific: Estimation based on AIRS satellite retrievals and ERA-Interim data: CONTRIBUTION BY TCS TO STE OVER WNP[END_REF].

65

From 23 years of infrared brightness temperature (IR-BT) measurement, [START_REF] Romps | Overshooting convection in tropical cyclones[END_REF] showed that a large fraction of overshooting tropical convection occurs within tropical cyclones (15% of all the convection that overshoot the tropopause). Using Lagrangian trajectories and airborne measurements, [START_REF] Vogel | Fast 810 transport from Southeast Asia boundary layer sources to northern Europe: rapid uplift in typhoons and eastward eddy shedding of the Asian monsoon anticyclone[END_REF] showed that the combination of rapid uplift by a typhoon and eastward eddy shedding from the Asian monsoon anticyclone is a fast transport pathway that carries boundary pollutants from Southeast Asia/West Pacific within 70 approximately 5 weeks to the lowermost stratosphere in northern Europe. Analyses of balloon-borne sensors launched from Lhasa, China, in August 2013 show that nearly half of the measured ozone profiles in the upper troposphere were influenced by tropical cyclones occurring over the western Pacific (Li et al., 2017).

Several studies based on model results have also demonstrated that deep convection can efficiently transport water vapor and pollutants to the UTLS [START_REF] Hassim | A model study on the influence of overshooting convection on TTL water vapour[END_REF][START_REF] Jensen | Can overshooting convection dehydrate the tropical tropopause layer?[END_REF][START_REF] Marécal | Modelling study of the impact of deep convection on the utls air composition -Part I: Analysis of ozone precursors[END_REF]. Recently, 75 [START_REF] Allison | Simulations of Vertical Water Vapor Transport for TC Ingrid[END_REF] used high-resolution (1.33km) simulations with the Weather Research and Forecasting (WRF) model to investigate the water vapor transport to the UTLS within TC Ingrid (a category 1 storm on the https://doi.org/10.5194/acp-2020-870 Preprint. Discussion started: 21 October 2020 c Author(s) 2020. CC BY 4.0 License.

Saffir Simpson Scale) in the Gulf of Mexico. They identified dehydration between 14.5 and 17.5 km due to ice sedimentation and hydration between ~17.5 and 21 km due to the sublimation of ice crystals.

In addition, [START_REF] Preston | Simulation of Chemical Transport by Typhoon Mireille[END_REF] investigated transport of O3/CO/water vapor by typhoon Mireille (a category 3 80 storm) over the Western North Pacific using the WRF model with chemistry (WRF-Chem). Their high-resolution (3km) simulations showed positive vertical fluxes throughout the troposphere and the tropopause, which increased the CO/water vapor concentration in the UTLS region. Despite having different intensities (category 1 versus category 3 storm), overshooting tops were identified for both systems that transported large quantities of water vapor to the UTLS. Both studies also agree in terms of estimation of net water vapor flux within 50%.

85

The current study focuses on an intense TC that occurred over the SWIO in March 2017. [START_REF] Tao | Global Distribution of Hot Towers in Tropical Cyclones Based on 11-Yr TRMM Data[END_REF] For the period 1979-2008, an average of ~90 TCs having maximum sustained winds ≥ 63 km/h occurred each year globally (cf. Table 2.5 WMO 2017). The most active TC basin is the Western North Pacific (WNP, ~30% of the global total), followed by the Eastern North Pacific (ENP, ~19% of the global total), the Southwest Indian Ocean (SWIO, ~15% of the global total) and the North Atlantic (NA, ~13% of the global total). The SWIO has 90 been poorly studied so far despite having tropical-cyclone activity that is comparable to that of the NA. Using 11year Tropical Rainfall Measuring Mission (TRMM) precipitating hydrometeor satellite observations, [START_REF] Tao | Global Distribution of Hot Towers in Tropical Cyclones Based on 11-Yr TRMM Data[END_REF] identified overshooting tops in tropical cyclones (above 14 km) and showed that the South Indian Ocean is the second basin after the Northwest Pacific in terms of total number of overshooting tops (cf. Table 2 of [START_REF] Tao | Global Distribution of Hot Towers in Tropical Cyclones Based on 11-Yr TRMM Data[END_REF].

95

The event analyzed is the intense TC Enawo (category 3 on the US Saffir Simpson Scale), that made landfall in northeastern Madagascar on 7 March 2017, killing more than 80 people and causing extensive damage. In a previous study, Evan et al. (2020) investigated the effect of deep convection on the TTL composition over the SWIO during austral summer (December-March). They focused on the origin of convective signatures in two balloon-borne water vapor profiles observed in the vicinity of tropical storms in January 2016 (Tropical Storm 100 Corentin) and March 2017 (TC Enawo). The balloon-borne measurements were made in coordination with lidar observation at the Maïdo Observatory on Réunion Island (21°S, 55°). Using lagrangian backtrajectories, convective activity in both tropical storms was shown to produce significant hydration in the upper tropos phere (UT). In contrast, no water vapor anomaly was found near or above the tropopause region on 3 March 2017 over Réunion Island as the tropopause region was not downwind of TC Enawo. In addition, the balloon was launched 105 at a distance of ~1000 km from Enawo when the storm was still intensifying. Results from [START_REF] Allison | Simulations of Vertical Water Vapor Transport for TC Ingrid[END_REF] and [START_REF] Preston | Simulation of Chemical Transport by Typhoon Mireille[END_REF] suggest that overshooting convection and subsequent water vapor transport to the lower stratosphere (LS) mostly occurs in the eyewall region of TCs. Here, we extend the Evan et al. (2020) analysis of TC Enawo using a mesoscale model to quantify the impact of TC Enawo on UTLS water vapor.

With a background ranging from 2 ppmv to 6 ppmv (Fueglistaler et al., 2009;[START_REF] Rosenlof | Stratospheric water vapor increases over the past half-century[END_REF], the water 110 vapor content in the TTL is very sensitive to small variations. Most GCMs with coarse horizontal and vertical grid spacings underestimate convective transport and its effect on UTLS water vapor. High-resolution modeling allows a better representation of deep convection within TCs and is therefore useful to understand t he relative roles of vertical transport of and ice microphysics on UTLS water vapor [START_REF] Allison | Simulations of Vertical Water Vapor Transport for TC Ingrid[END_REF]Chaboureau et al., 2007;[START_REF] Dauhut | Large-eddy simulations of Hector the convector 655 making the stratosphere wetter[END_REF]Frey et al., 2015;Mrowiec et al., 2012;Ravindra Babu et al., 2015). The main goal of 115 this study is to further our understanding of the impact of TC on the TTL by simulating the TC Enawo over the SWIO basin, for the period 2-7 March 2017 when the storm was intensifying from tropical storm to intense tropical https://doi.org/10.5194/acp-2020-870 Preprint. Discussion started: 21 October 2020 c Author(s) 2020. CC BY 4.0 License. cyclone. over the SWIO. We take advantage of the Meso-NH model that has been previously developed for the simulations of TCs in the SWIO [START_REF] Hoarau | Impact of the Generation and Activation of Sea Salt Aerosols on the Evolution of Tropical Cyclone Dumile[END_REF][START_REF] Pianezze | A New Coupled Ocean-Waves-Atmosphere Model Designed for Tropical Storm Studies: Example of Tropical 760 Cyclone Bejisa (2013-2014) in the South-West Indian Ocean[END_REF]. This study is also part of the CONCIRTO (CONvection CIRrus over the Tropical indian Ocean) project that aims to further our knowledge on 120 how deep convection and cirrus clouds affect the TTL over the SWIO.

The present paper is organized as follows. Section 2 describes the Meso-NH model setup as well as balloon-borne in situ measurement and satellite observations used to evaluate the model representation of TC Enawo. Section 3 presents an overview of the evolution of TC Enawo in both observations and simulations. Section 4 investigates simulated water and ice transport to the low stratosphere. The global impact of TCs to the tropical lower 125 stratospheric water vapor is assessed in Section 5. The model results are discussed in Section 6. Finally, Section 7 contains the conclusions and a summary of our study.

Observations and Mesoscale model

Satellite observations

METEOSAT 8 is a geostationary satellite located at 41.1°E that monitors for the Indian Ocean since March 2017. [START_REF] Avery | Cloud ice water content 630 retrieved from the CALIOP space-based lidar: CALIOP ICE WATER CONTENT[END_REF]. Between March 2 and 7, there were 9 CALIPSO overpasses over TC Enawo. However, only the overpass on 5 March at 21:30 UTC was over TC Enawo's eye region (cf. Figure 7).

Balloon-borne observations.

150

A balloon launch was specifically planned using a Lagrangian model and geostationary infrared images to sample the convective outflow from TC Enawo on 3 March 2017 at 18 UTC. The balloon sonde payload consisted of the Cryogenic Frostpoint Hygrometer (CFH) as well as the Intermet iMet-1-RSB and Meteomodem M10 meteorological radiosondes. A detailed description of the balloon measurements is provided in Evan et al. (2020). The Cryogenic Frost Point Hygrometer (CFH) is an in-situ instrument that measures the water vapor mixing ratio 155 profile from the surface to the stratosphere (~28km).

The CFH was developed to provide highly accurate water vapor measurements in the TTL and stratosphere where the water vapor mixing ratios are extremely low (~2 ppmv). CFH mixing ratio measurement uncertainty ranges from 5% in the tropical lower troposphere to less than 10% in the stratosphere [START_REF] Vömel | Validation of Aura Microwave Limb Sounder water vapor by balloon-borne Cryogenic Frost point Hygrometer measurements[END_REF] ; a recent study shows that the uncertainty in the stratosphere can be as low as 2-3% (Vömel et al., 2016). The M10 radiosonde 160 provides measurements of Relative Humidity (RH), temperature, pressure, vertical velocity, wind speed and direction from which zonal/meridional winds are derived.

Meso-NH model

Simulations of TC Enawo were performed with the Mesoscale, anelastic, and nonhydrostatic model Meso-NH version 5.3 [START_REF] Lac | Overview 720 of the Meso-NH model version 5.4 and its applications[END_REF]. Recent Meso-NH simulations have been used successfully to study tropical 165 storms/cyclones over the SWIO [START_REF] Barbary | The orographic effect of Reunion Island on tropical cyclone track and intensity[END_REF][START_REF] Hoarau | Impact of the Generation and Activation of Sea Salt Aerosols on the Evolution of Tropical Cyclone Dumile[END_REF][START_REF] Lac | Overview 720 of the Meso-NH model version 5.4 and its applications[END_REF][START_REF] Pianezze | A New Coupled Ocean-Waves-Atmosphere Model Designed for Tropical Storm Studies: Example of Tropical 760 Cyclone Bejisa (2013-2014) in the South-West Indian Ocean[END_REF].

Meso-NH has also been used to study overshooting convection and stratospheric hydration (Chaboureau et al., 2007;[START_REF] Dauhut | Large-eddy simulations of Hector the convector 655 making the stratosphere wetter[END_REF].

Different simulations (Table 1), were performed with the Meso-NH model. The simulations have vertical grid spacings less than 100 m in the boundary layer and 300m up to 30km (140 verticals levels), with a damping layer 170 in the uppermost 25 km and a model top at 1hPa. All simulations are initialized and forced at the boundaries with 6-hourly analyses from the operational European Centre for Medium Range Weather Forecasts -Integrated Forecast System (ECMWF-IFS) with a grid spacing of ~9km and 137 vertical levels. Simulations were run from 2 March 2017, 00UTC to 7 March, 00UTC to encompass Enawo's evolution from tropical depression to very intense TC just before landfall over Madagascar. The turbulent scheme is based on [START_REF] Cuxart | A turbulence scheme allowing for mesoscale and large-eddy simulations[END_REF]. We use 175 a single-moment bulk mixed-phase cloud parameterization ICE3 [START_REF] Lac | Overview 720 of the Meso-NH model version 5.4 and its applications[END_REF]Pinty and Jabouille 1998). It solves the microphysics of five hydrometeors which are three precipitable species (snow, rain, and graupel) and two non-precipitating hydrometeors (cloud water, and cloud ice). The longwave radiative scheme used in Meso-NH is the rapid radiation transfer model (RRTM; [START_REF] Mlawer | Radiative transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the longwave[END_REF]. The shortwave radiative scheme is based on [START_REF] Foucart | COMPUTATIONS OF SOLAR HEATING OF THE EARTH'S ATMOSPHERE: A NEW PARAMETERIZATION[END_REF]. The subgrid shallow convection is based on the eddy-diffusivity mass flux and 180 Kain-Fritsch approach of entrainment and detrainment in cumulus clouds [START_REF] Pergaud | A Parameterization of Dry Thermals and Shallow Cumuli for Mesoscale Numerical Weather Prediction[END_REF]. Meso-NH is coupled with the surface model SURFEX (Surface Externalisée, Masson et al., 2013) and uses COARE-3 parameterisation for ocean-atmosphere fluxes [START_REF] Fairall | Bulk Parameterization of Air-Sea 675 Fluxes: Updates and Verification for the COARE Algorithm[END_REF]. The first model level is at 10m. Initial simulations were run to test the model's sensitivity to different parameterizations on a domain A covering 46°E-69°E in longitude, 32°S-8°S in latitude at a horizontal grid-spacing of 10 km (Simulation S1). Tests on 185 domain limits have been performed to identify the sensitivity to the eastern boundary. Then, five simulations were performed (Table 1) to test the horizontal resolution, nested domains and sensitivity to SST. Simulations were run in domain A with a horizontal grid-spacing of 10km and 5km (Simulations S1 and S2). The Kain Fritsch cumulus parameterization was used to simulate deep convection in S1 and S2. A second domain, called domain B, centered over a region that encompasses Enawo's life cycle was designed (Figure 1) for simulations with a horizontal grid-190 spacing of 2km (Simulations S3, S4 and S5). Deep convection was explicitly resolved at that resolution. Simulation S3 had nested domains having grid spacings of 10 (domain A) and 2km (domain B). It was found that using one-way grid-nesting did not improve the model's representation of Enawo, so higher resolution simulations https://doi.org/10.5194/acp-2020-870 Preprint. Discussion started: 21 October 2020 c Author(s) 2020. CC BY 4.0 License. at 2km were run without nesting (Simulations S4, S5). The sensitivity to the Sea-Surface-Temperature (SST) was also tested. In simulations S1 to S4, the Sea-Surface-Temperature (SST) data from ECMWF were used and 195 updated every 6 hours. Simulation S5 is coupled with the oceanic model CROCO (Coastal and Regional Ocean COmmunity model, http://www.croco-ocean.org, [START_REF] Debreu | Two-way nesting in split-explicit ocean models: Algorithms, implementation and validation[END_REF]Penven et al., 2006). Further details on the coupling are provided in [START_REF] Voldoire | SURFEX v8.0 interface with OASIS3-MCT to couple atmosphere with hydrology, ocean, waves and sea-ice models, from coastal to global scales[END_REF] and [START_REF] Pianezze | A New Coupled Ocean-Waves-Atmosphere Model Designed for Tropical Storm Studies: Example of Tropical 760 Cyclone Bejisa (2013-2014) in the South-West Indian Ocean[END_REF]. The oceanic model has a horizontal resolution of 2km and 32 vertical levels from the surface to the ocean bottom (about a depth of 5km below Enawo) and shares the same domain of simulation as the Meso-NH model. Between 2 and 4 March, Enawo intensified slowly from TD to TS because of a strong east-southeast vertical wind shear. On 4 March, Enawo stalled over the ocean while intensifying. Very cold cloud tops (<-90°C) were observed 215 at that time. Enawo evolved from TS to TC on 5 March at 06UTC with an eyewall with a poorly defined structure.

Later, the intensification speed was slowed by an Eyewall Replacement Cycle (ERC), observed on satellite microwave images. An ERC occurs when the pressure forces at the center of the TC push inward the eyewall. At some point, the eyewall collapses and a new eyewall forms afterward. Because of a decrease in vertical wind shear, Enawo further intensified to reach the ITC stage on 6 March at 12UTC (Category 2-3 on the Saffir-Simpson 220 scale), with 10-minute maximum sustained winds of 46.3 m s-1 (90kts). The 10-minute maximum sustained winds (VMAX) increased by 23 m.s -1 (45 kts) in 24 hours, larger than the top 5% percentile of rapid intensification over the SWIO basin (Leroux et al., 2018). Enawo reached peak intensity on 7 March at 06 UTC, with ten-minute maximum sustained winds at 56.5 m.s -1 (110 kts) and the central pressure at 932 hPa. TC Enawo reached Madagascar's northeastern coast on March 7 at around 09:30 UTC and was the third strongest tropical cyclone on 225 record to strike the island. It was also the strongest TC of the Southern Hemisphere for the 2016/2017 TC season.

The RSMC La Réunion provides 6-hourly best-track data that include the location of the storm center, minima of mean sea level pressure (MSLP) and 10-min maxima sustained wind. Root mean square errors (RMSE) between the Best Track and the simulations were calculated for track (in km) and MSLP (in hPa) following the approach of [START_REF] Chandrasekar | Sensitivity of tropical cyclone Jal simulations to physics parameterizations[END_REF] and [START_REF] Allison | Simulations of Vertical Water Vapor Transport for TC Ingrid[END_REF]. The RMSE for the track and MSLP for each simulation 230 are presented in Table 1. Based on the results of MSLP and RMSE, simulation S4 does a better job in representing https://doi.org/10.5194/acp-2020-870 Preprint. Discussion started: 21 October 2020 c Author(s) 2020. CC BY 4.0 License.

the intensification phase and the trajectory of Enawo. The comparison of S4 to Enawo's best track, precipitation and balloon-borne measurements are presented in the subsequent sections. Simulation S4 will be used in section 4 to investigate the vertical structure of the TTL and water vapor/ice transport to the lower stratosphere.

Trajectory/intensification

235 Figure 1 compares the simulated trajectory of simulation S4 to the best-track data from March 2 at 06UTC (top right) and March 7 at 00 UTC (bottom left). The trajectory in the simulations is defined using a minimum of Mean Sea Level Pressure (MSPP). The simulated trajectory is to the south of the one provided in the best-track data but with a RMSE of 97±54km. After March 4, the simulated trajectory is even more to the south when compared to the best track. However, the westward propagation of the tropical cyclone is relatively well represented with 240 comparable propagation speed. On March 4, the simulation was able to show that Enawo stalled over the ocean near 13.6°S/56.5°E. In the rest of the study, we use the minimum MSLP to define the storm center. (2,3 and4 March). The simulation has a RMSE for MSLP less than 6hPa. Since no nudging was applied, it is remarkable 245 that the Meso-NH simulations can represent Enawo's initial development from tropical depression on 2 March, 00UTC to moderate tropical storm on 3 March, 18UTC. This is most likely due to the high-resolution operational ECMWF analyses used for initialization and the fact that the initial storm structure was present in the ECMWF analysis on 2 March 00UTC. When initialized a few days before, the Meso-NH did not generate the initial tropical depression that would become TC Enawo.

250

On 5 March 00UTC, Enawo stalled over the ocean after the ERC. The ERC was not reproduced by the simulation and the simulation started to diverge compared to Enawo's MSLP. An ERC is particularly difficult to simulate and a resolution less than 500 m is necessary to resolve this process (S. Bielli, personal communication). Between 60h and 96h, the intensification is slower in the simulation as indicated by the slower decrease in the simulated MSLP. After 96h (6 March, 00 UTC), the rapid intensification when Enawo evolves from TC to intense TC is 255 shown in the best-track data with a drop of 30 hPa in the MSLP over 12 h. The model is not able to capture this rapid intensification but instead simulates a steady intensification phase. As a consequence, the error in the MSLP increases to 20 hPa at the end of the simulation.

Precipitation

260

For this comparison, simulated precipitation was interpolated to the GPM grid (0.1°x0.1°) and integrated over the period 2 March, 06 UTC to 7 March, 00 UTC. Overall, the simulated total rainfall agrees with observations and Meso-NH captures the north-south asymmetry.

Between March 4 and March 5, heavy rain (in red on Figure 5) is observed in the eyewall. Precipitation for this period tends to be overestimated in the S4 simulation. Precipitation within the secondary rainbands are consistent 265 with those observed, especially south of Enawo's trajectory. The model tends to produce lighter precipitation over a larger region. In addition, simulated precipitation over the eastern coast of Madagascar is not observed in the GPM data. The detrainment of water vapor at ~13 km is resolved in the simulation but remains lower than the observed one.

In the troposphere between 2 and 14 km in altitude, the simulation has a wet bias of +450 ppmv, resulting from a higher moisture transport with an explicit representation of convection at a 2 km grid-spacing. In the TTL (14-18km in altitude), the mean water vapor difference at the location of the Maïdo Observatory is about -1ppmv in 280 S4.

The simulated temperature profile is colder than the M10 temperature profile in the troposphere between 2 and 14 km with a mean bias of -1 K. A cold bias of -2 K is also observed in TTL (14-18 km). However, both the model and the observation indicate a CPT at ~16 km.

On Figure 4, the simulated and observed profiles of zonal and meridional wind speed are in good agreement. The 285 peak in meridional wind at 13km associated with Enawo's convective outflow in the UT is captured by the model.

Infrared brightness temperature

315

The CALIOP lidar cannot penetrate deep convective clouds, therefore observed IWC is not shown below ~10 km.

From the distribution of IWC on Figure 8, we can see that the model tends to produce less ice in the convective core below ~15km in altitude, and more ice above. On the contrary, less ice is produced in the upper troposphere in Enawo's outer regions (south of 18.5°S and north of 11°S). In the upper troposphere, IWC values range from 10 -4 to 10 -2 g.m -3 in both the observation and the simulation. Maximum values of IWC are observed in the eyewall: 320 ~0.01 to 0.05 g.m -3 in the observation versus ~0.05 to 0.1 g m -3 in the simulation. Simulated IWC is a factor 10 larger than CALIPSO IWC above the CPT. The location of the convective center is fairly well reproduced by the simulation (13°S,55°E in S4 versus 14°S,54.7°E in the CALIPSO observation). The simulation does show ice above the CPT between 11 and 15°S (IWC ranging from 10 -5 to 10 -4 g.m -3 ). However, CALIOP only shows ice above the CPT in the eye region (according to the best-track data the storm center was located at 13.96°S, 55.02°E 325 on 5 March, 18 UTC).

Average mass (φmass), ice (φice) and water vapor (φvapor) flux density (kg.m -2 .s -1 ) to the low stratosphere (~18 km) can be computed as a function of time and distance from the TC center using the equations:

330 𝜑 𝑚𝑎𝑠𝑠 = ( ∑ 𝜌(𝑟 𝑖 )𝑤(𝑟 𝑖 ) 𝑟≤𝑟 𝑘+1 𝑟 𝑖 <𝑟 𝑘 ) 𝑁 𝑘 (1a) 𝜑 𝑖𝑐𝑒 = ( ∑ 𝜌(𝑟 𝑖 )𝑤(𝑟 𝑖 )𝑞 𝑖𝑐𝑒 (𝑟 𝑖 ) 𝑟≤𝑟 𝑘+1 𝑟 𝑖 <𝑟 𝑘 ) 𝑁 𝑘 (1b) 𝜑 𝑣𝑎𝑝𝑜𝑟 = ( ∑ 𝜌(𝑟 𝑖 )𝑤(𝑟 𝑖 )𝑞 𝑣𝑎𝑝𝑜𝑟 (𝑟 𝑖 ) 𝑟≤𝑟 𝑘+1 𝑟 𝑖 <𝑟 𝑘 ) 𝑁 𝑘 (1c)
ri corresponds to a model grid point, ρ is the air density (kg.m -3 ), qice is the ice mixing ratio (kg.kg -1 ), qvapor is the 335 water vapor mixing ratio (kg.kg -1 ) and w is the vertical velocity (m.s -1 ). Figure 7 illustrates the calculation of φmass and can be applied to φice and φvapor by adding the qice/ qvapor term. We sum the ρ×w term at individual grid point over ring circle regions around the TC center (red symbol on Figure 7) defined by radiuses (rk) varying from 20 to 700 km by 20 km increment (ie., rk+1-rk = 20 km) and divide by the number Nk of grid points in the ring circle region to define average φmass, φice, φvapor (kg.m -2 .s -1 ). Some studies have proposed to calculate upward flux using 340 only grid points containing upward vertical motion (Chaboureau et al., 2007;[START_REF] Dauhut | Giga-LES of Hector the Convector and Its Two Tallest Updrafts up to the Stratosphere[END_REF]Mrowiec et al., 2012). [START_REF] Wei | A New Formulation of the Exchange of Mass and Trace Constituents between the Stratosphere and Troposphere[END_REF] has estimated mass transport across the tropopause by looking at the contribution from diabatic processes, the temporal change of the tropopause potential temperature and mass exchange due to the potential temperature gradient along the tropopause (Ravindra Babu et al., 2015;[START_REF] Wei | A New Formulation of the Exchange of Mass and Trace Constituents between the Stratosphere and Troposphere[END_REF].

Overshooting convection on 4 March.

As indicated on Figure 8, positive ice flux to the LS was observed on 4 March, when the storm was intensifying over the ocean. In this section, we show an example of an overshooting convective event that occurred on 4 March between 11:55 UTC and 12:45 UTC (Figure 9). At 11:55 UTC, vertical winds in the lower TTL troposphere (14-16.5 km) are relatively weak. The 380 K isentropic surface (black lines on Figure 9) is deformed, possibly due to eddies or convectively generated gravity waves. A dry layer can be observed below 380 K, which is linked with the cold point tropopause. Higher values 365 of water vapor mixing ratio ~20 ppmv above the tropopause could be due to a precedent overshooting event within Enawo.

At 12:05 UTC, a stronger updraft develops near 13.5°S which further deforms the 380 K isentropic surface. Direct ice injection can be seen between 17 km and 19 km (ice mixing ratio of 10 ppmv to 1000 ppmv at 18 km) and dehydration below the tropopause between 13.4°S to 13.6°S becomes more important.

370

At 12:15 UTC, stronger upward motion and tropopause's deformation are still observed. The water vapor mixing ratio above 380K increases from 15 ppmv to more than 45 ppmv.

10 minutes later, at 1225 UTC ice mixing ratio values decrease by a factor of 100 in the l ower stratosphere (17-19km, 13.4°S-13.6°S) while water vapor mixing ratios increase by a factor 4 compared to the initial condition (40 versus 10 ppmv initially). This suggests that ice was transported in the lower stratosphere and sublimated in a 375 subsaturated environment thereby hydrating the LS (the full processes are described at high temporal resolution in [START_REF] Dauhut | The Mechanisms Leading to a Stratospheric Hydration by Overshooting Convection[END_REF]. The 380 K potential temperature surface between 13.4°S and 13.6°S is smoother and returns to its initial altitude (17km). The deformation of the 380 K surface between 12:05 UTC to 12:45 UTC A second hydration event near Enawo's center can be observed after 4 March 12 UTC. It is related to injection of ice in the TTL discussed in section 4.1 and 4.2 and depicted on Figure 8. The water vapor mixing ratio increased up to 7 ppmv in a 100 km radius around Enawo's center. Then, as observed for the injection on 3 March, the water 410 vapor positive anomaly propagates outward Enawo's center, with water vapor mixing ratio of 5 ppmv transported 500 km away from Enawo's storm after 1.5 day of transport. At the end of the simulation, the water vapor mixing ratio background rose from 3.3 ppmv to 4.8 ppmv, an increase of 45%, 500 km away from Enawo's center.

Global impact of TCs to the tropical lower stratospheric water vapor

We compute a net vertical water vapor flux Fmean (t.hr -1 , where t corresponds to the metric ton) at 18 km which 415 corresponds to the lower-stratosphere using:

𝐹 𝑚𝑒𝑎𝑛 = ∑ 𝜌 𝑖 𝑞 𝑣𝑖 𝑤 𝑖 × 𝐴 × 3.6 𝑖 ( 2
)
Where ρ is the density (kg.m -3 ), w the vertical velocity (m.s -1 ) at a grid point, qv the water vapor mixing ratio (2018). TC Mireille and TC Enawo have a comparable intensity (maximum sustained winds of 51.4 m s-1 and a central pressure of 925 hPa.) as category 3 TC, but Mireille was a larger system with a 900 km radius.

We can use our estimate of average net water vapor flux to the low stratosphere associated with Enawo to estimate 440 the contribution to stratospheric water vapor from SWIO storms. Using the Best-Track data produced by RSMC La Réunion and focused on the most reliable 18-year period of the geostationary satellite era encompassing the 1999/2000-2016/17 cyclone seasons, we found an average of 4.8 TCs per year formed over the SWIO, in agreement with Leroux et al. (2018). We also estimated an average duration of 74±49 hours (± refers to the standard deviation) per cyclone. Using an average net water vapor flux of 2.7x103 t.hr -1 from Enawo's high-

445

resolution simulation, we estimate that TCs over the SWIO could transport 9.6x105 t of water vapor into the lower stratosphere. Figure 10 shows that Enawo moistened the region between ~18 and 20 km. [START_REF] Dauhut | Large-eddy simulations of Hector the convector 655 making the stratosphere wetter[END_REF] found moistening associated with a Hector thunderstorm between potential temperature levels 380-420 K (∼17-18.5 km). Using CALIOP data, Avery et al. (2017) reported that convective ice could be observed up to up to 2 km above the tropopause over the Central Eastern Pacific (Figure 2a 3 can be compared to Table 2.5 of WMO ( 2017) and Table 3 of [START_REF] Schreck | The Impact of Best Track Discrepancies on Global Tropical 785 Cyclone Climatologies using IBTrACS[END_REF].

Discussion

The global TC induced LS water vapor anomalies can be compared to previous studies that have quantified the impact of convection on tropical lower stratospheric water vapor.

Using Lagrangian trajectories driven by 6-hourly interim reanalysis of the ECMWF Forecast (ERA-Interim), Therefore, our estimate of global TC tropical lower stratospheric moistening of 0.3 to 0.5 ppmv agrees with previous studies that have considered deep convection on a regional scale.

The Asian Monsoon in the Northern Hemisphere is clearly the most important source region but our analysis suggests that the most intense TCs may contribute to the tropical lower stratospheric water vapor budget, 510 especially in the Southern Hemisphere where there is no similar monsoon circulation. Because climate models and observations predict more intense TC with warming sea surface temperatures (Elsner et al., 2008;[START_REF] Kossin | Global increase in major tropical cyclone exceedance probability over the past four decades[END_REF][START_REF] Sobel | Human influence on tropical cyclone intensity[END_REF], accurate understanding of the stratospheric impact of TC convection is critical in the context of global warming. This is important not only for the lower stratospheric water vapor budget but also for the transport of other chemical species (e.g. ozone, CO, ozone depleting substances) to the UTLS.

515

There are several limitations to the present study. First, we consider a single TC in the SWIO to assess the net TC water vapor transport to the stratosphere in the SWIO basin. TC Enawo may not be representative of other TCs in other basins as it was an intense TC (the strongest TC of the Southern Hemisphere for the 2016/2017 TC season). Then, large-eddy simulations may be needed to better resolve deep convection and associated convective updrafts, especially in the eyewall region. Heath et al. (2017) used 450 m WRF large-eddy simulations to study 520 deep convection during a real-world case (a case of continental convection over Northern America on 2 September 2013) and concluded that moving from grid-spacing of 1.35 km to 450 m yielded results that better compared with ground-based radar and aircraft observations. [START_REF] Dauhut | Large-eddy simulations of Hector the convector 655 making the stratosphere wetter[END_REF] found that a grid spacing on the order of 100 m may be necessary for a reliable estimate of hydration in a Meso-NH simulation of a Hector thunderstorm observed on 30 November 2005 over the Tiwi Islands. Large-eddy simulations of TC Enawo would be valuable,

525

especially for convective updrafts in the eyewall region, but would require more computer power.

Finally, we use a single-moment microphysics scheme in our 2-km simulation of TC Enawo. One conclusion from [START_REF] Allison | WRF simulations of water vapor content for TC Ingrid[END_REF] for TC Ingrid is that double-moment microphysics schemes produce more realistic tropical clouds and precipitation, which are important for the representations of updrafts and transport of ice to the TTL.

While our comparison to the GPM satellite observations suggests that the simulation seems to reproduce well both Indian Ocean) show that these storms moisten the lower stratosphere (83 hPa/~18 km) from 0.3 to 0.5 ppmv in a ~5 to 10° region around the eye.

Summary and Conclusions

We extended the analysis of Evan et al. (2020) Our simulation of TC Enawo suggests that TCs over the SWIO (0-30°S, 30-90°E) could produce a moistening of 600 0.4 ppmv over a region which represents ~8% of the global tropics (30°S-30°N). We extended our results to estimate the global impact of TCs to the tropical lower stratospheric water vapor using the estimates from published work [START_REF] Allison | Simulations of Vertical Water Vapor Transport for TC Ingrid[END_REF][START_REF] Preston | Simulation of Chemical Transport by Typhoon Mireille[END_REF] and by calculating statistics on TC numbers and durations using the IBTrACS dataset. We estimated a global impact of TC induced tropical lower stratospheric moistening of 0.3 to 0.5 ppmv.

130

  The Brightness Temperatures (BT) of the infrared channel at 10.8 µm are used to identify deep convective clouds within TC Enawo and validate their representation in the Mesoscale simulations. METEOSAT 8 data used in this study are provided by National Oceanic and Atmospheric Administration National Centers for Environmental Prediction (NCEP) and correspond to globally merged (60°S-60°N) infrared BT from various geostationary satellites (John Janowiak, 2017). They have a temporal resolution of 30 minutes and a horizontal resolution of 4 135 km. The Global Precipitation Measurement Integrated Multi-satellitE Retrievals (GPM-IMERG) product from the National Aeronautics and Space Administration (NASA) is used to evaluate simulated rainfall. It uses an algorithm that merges precipitation radar, microwave precipitation estimates, microwave-calibrated infrared, and rain gauge analyses at a spatial resolution of 0.1• over the latitudinal belt 60°N-60°S (Huffman et al., 2018). The 140 GPM-IMERG product has a temporal resolution of 30 minutes. Measurements from the Cloud and Aerosol Lidar with Orthogonal Polarization (CALIOP) lidar onboard the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellite are used to validate the distribution of simulated ice clouds in the UTLS. Original CALIOP observations correspond to backscatter measurements at 532 nm and 1064 nm since June 2006 (Level 1 data). CALIOP Level 2 data (version V4.10) 145 contain extinction and Ice Water Content (IWC) profiles at 60-m vertical and 5-km horizontal resolutions, which are retrieved from the 532-nm extinction coefficient

  https://doi.org/10.5194/acp-2020-870 Preprint. Discussion started: 21 October 2020 c Author(s) 2020. CC BY 4.0 License.

  Oscillation (MJO) was active at the end of February and during the first week of March 2017 with a signal centered over Africa and the Indian Ocean. Favored by the MJO active phase and the arrival of an equatorial Rossby wave, Enawo initially formed as a tropical disturbance on March 2 with 10-minute maximum 205 sustained wind speeds ~ 40 km.h -1 . The Regional Specialized Meteorological Center (RSMC) La Réunion, in charge of TC's forecasts for the SWIO, named the storm Enawo on 2 March 2017 at 00 UTC. The best track data used in this study are provided by RSMC La Réunion. In the SWIO, different stages of TCs are defined using a 10-min maximum sustained as follows: Tropical Depression (TD, < 17.4m s-1), Moderate Tropical Storm (MTS, ≥ 17.4 m.s -1 ), Severe Tropical Storm (STS, ≥ 210 24.6 m.s -1 ), Tropical Cyclone (TC, ≥ 32.9 m.s -1 = Category 1 on the US Saffir-Simpson Scale), Intense TC (ITC, ≥ 43.6 m.s -1 , Categories 2-3 on the US Saffir-Simpson Scale) and Very Intense TC (VITC, ≥ 59.6 m.s -1 , Categories 4-5 on the US Saffir-Simpson Scale).

Figure 2 compares

 2 Figure 2 compares Enawo's simulated intensity (MSLP) with the corresponding RSMC La Réunion best-track data. Enawo's intensity is relatively well represented in the simulation in the first 60 hours of the run (2,3 and 4

Figure 3

 3 Figure 3 displays a comparison of GPM observed rainfall (left) to the one simulated in the S4 simulation (right).

  https://doi.org/10.5194/acp-2020-870 Preprint. Discussion started: 21 October 2020 c Author(s) 2020. CC BY 4.0 License.

3. 4

 4 Comparison to balloon-borne measurements. We further compare the Meso-NH model results to balloon-borne measurements at the Maïdo Observatory on 3 270 March 2017 at 18 UTC. At the time of the balloon launch at the Observatory, Enawo was a tropical storm located near 13° south latitude and 56.42° east longitude, about 900 km northwest of Réunion Island. For this comparison, the model fields of water vapor mixing ratio, temperature, zonal and meridional winds are interpolated onto the balloon's location and put on a regular 200-m vertical grid. Comparisons between the simulated profiles and CFH/M10 radiosondes are shown on Figure 4. The CFH water vapor profile has fine-scale structures at 6 and 275 10km which are not reproduced in the simulation (Figure 4, right).

Figure 5

 5 Figure 5 compares simulated (top panel) and observed (bottom panel) infrared Brightness Temperatures (BT) at different stages of Enawo's lifecycle. The simulated infrared BT is estimated using the RTTOV-v11 radiative model RTTOV-v11[START_REF] Saunders | An update on the RTTOV fast radiative transfer model (currently at version 780 12)[END_REF] Senf and Deneke, 2017). Infrared BTs are shown on 3 March, 18 UTC 290

Figure 6

 6 Figure 6 represents an along-track cross-section (latitude versus altitude) comparing IWC profiles from the CALIOP observations to the Meso-NH simulation. The simulated IWC variable includes both cloud ice and 310

  https://doi.org/10.5194/acp-2020-870 Preprint. Discussion started: 21 October 2020 c Author(s) 2020. CC BY 4.0 License. The maximum mass flux density is simulated on 4 and 6 March around 00 UTC within ~100km of the TC center 345 (eye and eyewall regions) with values ranging from 0.5 to 1x10 -3 kg.m -2 .s -1 . Similarly, the maximum water vapor flux density is observed on 4 and 6 March, with values ranging from 1.5 to 2.5 x10 -8 kg.m -2 .s -1 . Large negative values are simulated on 4 March at 12UTC for both mass and water vapor fluxes density. During the same time period, sporadic transport of ice across 18km is simulated within a 300 km region around Enawo's center. At that time, Enawo was still forming and thus updraft regions were more scattered within the storm. TC Enawo stalled 350 over the ocean on March 4&5 and intensified (Figures 1&2). An enhancement of ice flux in the eye/eyewall regions (150 km around the TC center) can be observed on those days which is consistent with high (cold) convective clouds observed on Figure 5. After March 5, the ice flux at 18 km decreased although the observed storm reached peak intensity on 7 March. Comparison of the ice and water vapor fluxes on Figure 8, clearly indicates that positive water vapor flux density into the stratosphere doesn't necessary mean direct injection of 355 ice, and vice versa.

  Figure 9 depicts north to south cross sections (at longitude 360 56.09°E) through the simulated overshooting cloud on 4 March. Simulated higher vertical velocity near 13.4°S is coherent with the location of the storm center in the best-track data (13.65°S, 56.85°E on 4 March, 12UTC).

  suggests first strong deformation by the overshoot and then horizontal vertical propagation of high-frequency gravity waves triggered by deep convection. At 12:35 UTC, ice mixing ratio contours become more similar to 380 their initial values in the LS. Ice, which previously sublimated, is diluted in the LS. At 12:45 UTC, vertical motion is very weak in the lower TTL and the 380 K isentropic surface has returned to its initial 11:55 UTC altitude. https://doi.org/10.5194/acp-2020-870 Preprint. Discussion started: 21 October 2020 c Author(s) 2020. CC BY 4.0 License. During the overshooting event on 4 March, the average LS water vapor mixing ratio increased from 6.1 to 7.4 ppmv around the TC center. It suggests transport of ice/water vapor from the troposphere. Ice sublimation in a sub-saturated LS leads to moistening. These results are further discussed in the discussion section.

3854. 2

 2 Water vapor in TTLWe estimated the temporal change in TTL water vapor mixing ratio between the beginning and end of the Meso-NH simulations. Water vapor profiles were averaged over a 500 km region surrounding Enawo on 2 March 06 UTC (6 hours after the start of the simulation) and 7 March 00 UTC (end of the simulation). The average water vapor mixing ratio difference between these two dates is shown on Figure10for the Meso-NH simulation. A 390 minimum of water vapor hydration can be seen at 16.5 km, near the tropical tropopause. A weak dehydration of -0.1 ppmv can be seen near the tropopause at 16.5 km. Using CFH and MLS water vapor profiles, Evan et al.(2020) estimated dehydration ranging from -0.4 to -0.1 ppmv at 100 hPa from a monthly mean MLS climatology (Figure9ofEvan et al., 2020). Between 17 to 19km an increase in water vapor mixing ratio up to 2 ppmv can be seen.[START_REF] Allison | Simulations of Vertical Water Vapor Transport for TC Ingrid[END_REF] reported hydration between 17.5 and 21 km associated with Hurricane Ingrid (Category 395 1) over the North Atlantic, with a maximum of 2.6 ppmv. Ice crystals were transported to the LS by deep convection, sublimated and produced hydration.

Figure 11

 11 Figure 11 shows time versus distance from Enawo's center simulated lower stratospheric water vapor mixing ratio, averaged over the 17-19 km altitude range, from 2 March, 06 UTC to 6 March, 18 UTC. Enhanced mixing 400

(

  Figure 12 displays the evolution of net water vapor flux Fmean at 18 km for 4-5 March 2017. The average net water vapor flux of 2.7x10 3 t.hr -1 is positive, indicating that Enawo is a source of vapor for the lower stratosphere. The net water vapor flux varies from -1.3 to 1.7x10 4 t.hr -1 with local peak values on 4 March 06 UTC, 5 March 06 UTC and 20 UTC (Enawo first achieved TC status on 5 March 12 UTC). Chaboureau et al. (2007) found observed peak water vapor flux of 2.8x10 4 t.hr -1 across the tropical 380 K level (~ 100 hPa) for a case of land-convection 430

  , 2b ofAvery et al., 2017) due to the strong 450 2015-2016 El Niño. With a mean air density taken to be 0.1 kg.m -3 between 18 and 20 km, TCs over the SWIO (0-30°S, 30-90°E) could produce a moistening of 0.4 ppmv, over a region which represents ~8% of the global tropics (30°S-30°N).While an individual TC may not contribute much to stratospheric water vapor, collectively all TCs on the globe may have a larger impact. The global TC transport of water vapor to the stratosphere can be computed as:455 𝐺𝑙𝑜𝑏𝑎𝑙 𝑇𝐶 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 𝑣𝑎𝑝𝑜𝑟(𝑡) = 𝐹 𝑚𝑒𝑎𝑛 × NTC × 𝐷𝑇𝐶 (3)Fmean is the mean estimate of net water vapor flux at the tropopause (t.hr -1 ) for an individual TC, NTC is the average global number of TCs and DTC is the mean duration of a TC (in hours). We can estimate that Fmean https://doi.org/10.5194/acp-2020-870 Preprint. Discussion started: 21 October 2020 c Author(s) 2020. CC BY 4.0 License. ranges from 2.7 to 4.6x10 3 t.hr -1 using the net water vapor flux estimates from Allison et al. (2018), Preston et al. 460 (2019) and our simulation. We derive NTC and DTC of tropical cyclones from the International Best Track Archive for Climate Stewardship (IBTrACS) (Knapp et al., 2010). IBTrACS is a composite dataset of track estimates for TCs, which combines data from multiple agencies to facilitate analysis. We specifically use data from version 4 for the period of global satellite coverage 1981-2017. The IBTrACS dataset defines 6 TC basins which are the North Atlantic, the West 465 Pacific, the East Pacific, the South Pacific, the North Indian and the South Indian (Souwestern + Southeastern Indian Ocean). Agencies differ in their definition of maximum winds. Agencies in the United States use a 1-min wind, RSMC New Delhi reports a 3-min wind but most RSMCs use a 10-min wind. To compare our results to previous estimates (WMO 2017 and Schreck et al., 2014), the IBTrACS 10-min maximum sustained winds from RSMCs Tokyo, Fiji, Wellington, La Réunion, and the Australian Bureau of Meteorology are divided by 0.88 to 470 approximate a 1-min wind (hereafter VMAX). The data from RSMCs Miami and New Delhi are used in their original form. For each of TC basin, we consider only systems that reach the TC stage (ie. VMAX ≥ 64 kt) and compute their mean duration as the period during which VMAX ≥ 64 kt. We also consider VMAX at peak intensity. The results for individual basins and the global tropics are summarized in Table 3. Number of TCs shown in Table

  The mean 475 global NTC is 45±9 for the period 1981-2010. On average, these systems have a DTC of 78±19 hours. Using equation (3), we can estimate that TCs could contribute annually from 0.3 to 0.5 ppmv to the tropical lower stratospheric water vapor. Several uncertainties arise for the estimate of global TC transport of water vapor from equation (3). The annual estimate of global TC water vapor transport has a combined uncertainty of 27% due to the NTCxDTC term in 480 equation (3). But the largest uncertainty in equation (3) arises from the estimate of Fmean which in turn depends on TC structure/intensity and representation of microphysical as well as dynamical processes. It is difficult to assess the uncertainty due to the microphysical processes in the models (thus the uncertainty on water vapor mass mixing ratio and vertical velocity change due to latent heat release). In addition, Dauhut et al. (2017) discuss uncertainty in Fmean estimate due to an Eulerian versus Lagrangian approach. The Eulerian approach leads to 485 larger estimates that can be attributed to reversible motions like gravity waves, which actually do not transport mass. Mrowiec et al. (2015) compare the Eulerian and isentropic computations of the vertical mass flux for a deep convective event around Darwin. The Eulerian computation based on a positive velocity threshold gives a 50% larger estimate than the isentropic computation. Thus, the Eulerian approach used in Allison et al. (2018), Preston et al. (2019) and the present study could bias the Fmean flux estimate by up to 50%.490

  [START_REF] Ueyama | Convective Influence on the Humidity and Clouds in the Tropical 805 Tropopause Layer During Boreal Summer[END_REF] assess the impact of convection on the humidity and clouds in the TTL during boreal summer 495 2007. They estimated that convection moistens the 100-hPa level by 0.6 ppmv averaged over the 10°S-50°N domain. ~50% of this increase (~0.3 ppmv) is due to the effect of the Asian monsoon (0-40°N, 40-140°E) convection. Nützel et al. (2019) performed a 4-year simulation with the chemistry-transport model Chemical https://doi.org/10.5194/acp-2020-870 Preprint. Discussion started: 21 October 2020 c Author(s) 2020. CC BY 4.0 License. Lagrangian Model of the Stratosphere (CLaMS) driven by the ERA-Interim data and established that water vapor from the Asian Monsoon region contributes on average at most 0.65 ppmv to the water vapor in the tropical 500 stratosphere at 450 K (~19 km). The Asian monsoon region corresponds to an area roughly 13% of the tropics and is mainly active in July-August. Avery et al. (2017) used CALIOP observations of ice, MLS observations of water vapor and lagrangian trajectories to estimate large anomalies in lower stratospheric water vapor and ice during the 2015-2016 strong El Niño. A 0.9 ppmv tropical lower stratospheric moistening was observed during this event, with 0.5-0.6 ppmv due to anomalously warm Tropical Warm Pool tropopause temperatures during 505 December 2015 and 0.3-0.4 ppmv due to deep convection over the Central Pacific (~11% of the tropics).

530

  location and amplitude of the observed precipitation, our comparison to CALIOP IWC indicates that ice above the tropopause is most likely overestimated in the simulation.[START_REF] Hoarau | Impact of the Generation and Activation of Sea Salt Aerosols on the Evolution of Tropical Cyclone Dumile[END_REF] performed a 2-km cloud resolving Meso-NH simulation of TC Dumile (10-min maximum sustained wind of 36 m.s -1 or 70 kts at peak intensity) using the ORILAM (Organic Inorganic Log-normal Aerosol Model;[START_REF] Tulet | ORILAM, a three-moment lognormal aerosol scheme for mesoscale atmospheric model: Online coupling into the Meso-NH-C model and validation on the Escompte campaign[END_REF] aerosol scheme and the LIMA (LIMA, Liquid Ice Multiple Aerosols;[START_REF] Vié | LIMA (v1.0): A quasi two-moment microphysical scheme driven by a multimodal population of cloud condensation and ice freezing nuclei[END_REF] two-moment microphysics scheme. Using a 535 one-moment microphysics scheme (ICE3, the scheme used in the present study) for the simulation of TC Dumile led to a larger, more symmetric and more intense system than using a two-moment microphysics scheme coupled with an aerosol scheme. It would be interesting to use the same aerosol-microphysics coupling for TC Enawo and https://doi.org/10.5194/acp-2020-870 Preprint. Discussion started: 21 October 2020 c Author(s) 2020. CC BY 4.0 License. assess the impact on the model's representation of TTL ice and water vapor transport to the UTLS, however the computation time is expected to increase by a factor 3. In addition, Jiang et al. (2019) investigated the effects of 540 sea salt aerosols on precipitation and UTLS water vapor in TCs with the WRF model. They simulated typhoonHato in the Northwestern Pacific using two nested domains with horizontal resolutions of 9 km and 3 km. They performed two numerical experiments with the same two-moment microphysics scheme but different sea salt emission intensity. The experiment with increased sea salt emission intensity indicated an increase in precipitation as well as more intense vertical movement in the eyewall and thus more water vapor transport to the upper 545 troposphere, which promoted cloud ice deposition. This experiment was drier in the UTLS (above 17 km) and had a 18-20 km domain-averaged water vapor mixing ratio ~0.02 lower than the experiment with reduced sea salt emission. The enhanced air drying was explained by the enhancement of cloud ice deposition growth, which consumes more water vapor in the upper troposphere. The aerosol-microphysics schemes presented in[START_REF] Hoarau | Impact of the Generation and Activation of Sea Salt Aerosols on the Evolution of Tropical Cyclone Dumile[END_REF] can be used in an ocean-waves-atmosphere coupled system[START_REF] Pianezze | A New Coupled Ocean-Waves-Atmosphere Model Designed for Tropical Storm Studies: Example of Tropical 760 Cyclone Bejisa (2013-2014) in the South-West Indian Ocean[END_REF] to include the effects 550 of sea-salt aerosols on the microphysical structure of tropical cyclone. It could also be interesting to use this version of Meso-NH to further investigate water vapor transport to the UTLS in TCs. The large uncertainty in our estimate of net flux of water vapor requires additional modeling (convectionpermitting) and analysis of TTL in-situ/satellite observations of TCs in various basins but this is left to further study. A preliminary analysis of 17-years MLS observations of water vapor for the most intense TCs (categories 555 4&5 on the Saffir-Simpson Scale) over 3 TC basins (Western North Pacific, North Atlantic and Soutwestern

  on the impact of TC Enawo on the TTL water vapor using the 560 Meso-NH cloud resolving Mesoscale model. Between 2 and 4 March, Enawo intensified from TD to TS. On 4 March, Enawo stalled over the ocean while intensifying. Enawo evolved from TS to TC on 5 March, and reached peak intensity on 7 March. The Meso-NH high-resolution (2 km) simulation used in this study covers Enawo's lifecycle from 2 to 7 March for a model domain covering the SWIO. Five configurations were used to test the sensitivity of the model to 565 domain extent, horizontal resolution, and SST boundary conditions. The westward propagation of Enawo was relatively well represented by the model simulations with comparable propagation speed to the best track, and a maximum deviation between the simulated and observed tracks of ~100km. All the simulations were able to show that Enawo stalled over the ocean while intensifying on 4 March. Overall, simulation S4 achieved the most realistic representation of Enawo's intensity and propagation. 570 Precipitations in simulation S4 were compared to GPM satellite observed rainfall. Precipitation in the eyewall tends to be overestimated in simulation S4, while precipitation within the secondary rainbands were consistent with those observed by GPM. Infrared brightness temperatures in simulation S4 were compared to the METEOSAT 8 satellite images. The horizontal structure of the cloud tops within Enawo is relatively well represented. Simulation S4 had slightly higher convective clouds, as simulated convective clouds were 2°C colder 575 than the observed ones.https://doi.org/10.5194/acp-2020-870 Preprint. Discussion started: 21 October 2020 c Author(s) 2020. CC BY 4.0 License. Profiles of IWC in simulation S4 were compared through a vertical cross section of a CALIPSO overpass over the eyewall on 5 March 21:30 UTC. Observed and simulated IWC have similar ranges in the upper troposphere but simulated ice above the tropopause is overestimated by a factor 10. The location of the convective center was fairly well reproduced by the simulation, but the distribution ice above the CPT in simulation S4 covers a larger 580 region than in CALIPSO. Net mass fluxes of water vapor and ice into the stratosphere were estimated within a 700 km region around Enawo's center. Injection of water vapor and ice was maximum during the intensification phase of Enawo, when it stalled over the ocean on 4 March. Injection of ice decreased after March 5, although Enawo reached its peak intensity on 7 March. 585 An overshooting convection event on 4 March was analysed in detail. Direct injection of ice was simulated between 17 and 19 km altitude, associated with dehydration below the tropopause. Ice between 17 and 19 km altitude sublimated in a subsaturated environment and thereby hydrated the lower stratosphere. On average, the overshooting event simulated on 4 March 12UTC increased the lower stratospheric water vapor mixing ratio by 1.3 ppmv in a 50 km region around the TC center. 590 Water vapor profiles simulated by the 2 km Meso-NH simulations were averaged over a 500 km region surrounding Enawo's center. A negative water vapor change of -0.1 ppmv was found at 16.5 km altitude near the tropical tropopause. Between 17 and 19 km in altitude, an increase of ~2 ppmv in water vapor mixing ratio was simulated. Comparison of net mass flux of water vapor and ice indicated that positive net mass fluxes of water vapor into the 595 stratosphere are not necessarily associated with direct injection of ice by overshooting convection. The positive anomaly in the lower stratosphere started from the eye region of the storm and propagated outward Enawo's center. At the end of the simulation, the water vapor mixing ratio background rose by 1.5ppmv, an increase of 45%, 500 km away from Enawo's center.

  https://doi.org/10.5194/acp-2020-870 Preprint. Discussion started: 21 October 2020 c Author(s) 2020. CC BY 4.0 License.

  Cat 1 TC Ingrid in the NA 1.33 km grid-spacing, net flux estimated over 43 doi.org/10.5194/acp-2020-870 Preprint. Discussion started: 21 October 2020 c Author(s) 2020. CC BY 4.0 License.

Figure 2 :Figure 3 :

 23 Figure 2: Time series of MSLP in the Meso-NH 2km simulation (red line) and in the RSMC La Réunion best-track 865

Figure 4 :

 4 Figure 4: Simulated (red) versus observed (black) profiles at the location of the Maïdo Observatory on 3 March 18 UTC: a) temperature, b) water vapor mixing ratio, c) meridional wind and d) zonal wind. CFH and M10 sonde observations are shown in black while simulated fields are shown in red. On the temperature profiles the location of the observed/simulated Cold Point Tropopause is indicated by black and red stars respectively.

  880

Figure 5 :

 5 Figure 5: Observed (bottom panels) versus simulated (upper panels) infrared brightness temperature on 3 March, 18 UTC (left), 4 March, 12 UTC (middle) and on 5 May, 21:30 UTC. The orange lines correspond to CALIPSO orbit tracks on 5 March at 21:30 UTC. On 4 March, 12 UTC the small vertical black line on the simulated infrared brightness temperature indicates the south-north cross section shown on Figure 8.885

Figure 6 :

 6 Figure 6: Cross-section (Latitude versus altitude) of CALIOP Ice Water Content (IWC in g m-3, bottom) along CALIOP track over TC Enawo on 5 March, 2130UTC. The corresponding simulated IWC for S4 is shown on the top panel. The black curves on both panels correspond to the simulated CPT which has a mean height of 16.5km. The numbers on the top left corner of each plot indicate the mean IWC above the CPT.895

Figure 7 :

 7 Figure 7: Diagram illustrating the computation of average net mass flux density (kg.m -2 .s -1 ) in the simulation. Average net mass fluxes density is computed for ring regions around the TC center (red star) for 20 km radius increment.

Figure 9 :

 9 Figure 9: North to south cross sections through the simulated overshooting cloud on 4 March. Plots are every 10 minutes on 4 March from 11:55 UTC to 12:45 UTC. Color contours correspond to the water vapor

Figure 10 :

 10 Figure 10: Left, simulated average water vapor mixing ratio profiles on 2 March 06 UTC (blue line) and 7 March 00 UTC (red line). The profiles were averaged over a 500 km region surrounding Enawo's center

Figure 11 :Figure 12 :

 1112 Figure 11: Time versus distance from the TC center of simulated water vapor mixing ratio averaged over the 17-19 km altitude range. Values correspond to bins of 20 km for a radius of 0 to 700 km around the TC center and are shown every 3 hours from 2 March 06 UTC to 7 March 00 UTC.

Table 1 : Definitions of Meso-NH simulations used in the study. All simulations are from 2 March 00UTC to 7 March 00 UTC just before Enawo's landfall over Madagascar. Root Mean Square Error (RMSE) between the Best Track and simulated values of track (in km) and MSLP (in hPa) are calculated for each simulation. The values in brackets represent the standard deviation.

 1

	840
	Simulatio n name	Horizontal grid-spacing (km)	Model domain	Interactive SST	Initial and boundary conditions	Track RMSE (km)	MSLP RMSE (hPa)
	S1	10	A	Forced (IFS)	ECMWF IFS	167±68	7.4±5.8
	S2	5	A	Forced (IFS)	ECMWF IFS	141±67	8.0±7.1
	S3	2	A&B	Forced (IFS)	ECMWF IFS	105±50	6.2±5.5
	S4	2	B	Forced (IFS)	ECMWF IFS	97±54	5.7±5.1
	S5	2	B	Coupled (CROCO)	ECMWF IFS	87±48	8.9±8.7
	845

Table 2 : TC total net flux of water vapor (x 10 3 t.hr -1 ) to the lower stratosphere from Allison et al. (2018) and from the present study.

 2

Acknowledgments

This work was partly funded by the French LEFE CNRS-INSU Program (VAPEURDO) and by the French 620 Agence Nationale de la Recherche CONCIRTO project (ANR375 17-CE01-0005-01). Computer resources were allocated by GENCI (project 1100297). The Meso-NH code is publicly available at http://www.mesonh.aero.obsmip.fr/. The simulations were performed with version 5-3. This work was done during the PhD of D. Héron who was financially supported by a MENRT fellowship from the University of Réunion Island.


Shiyun Xiong

Haoxue Han

Sebastian Volz
email: volz@iis.u-tokyo.ac.jp

Heat transport through nanoscale gaps -A perspective

This perspective describes the key physical concepts at play capturing transport regimes in gaps with sizes ranging from the micron down to the Ångström. The roles of photons, phonons and electrons are highlighted and illustrated across several examples from the literature. Particularly, two situations for which atomistic calculations provide insights in the microscopic mechanisms at play in thermal transport across nanoscale gaps will be expounded, namely thermal transport across silica clusters and in 2D materials. While experimental investigations are highly challenging and a vast field of opportunities still remains open in this matter, several related domains of application such as Thermophotovoltaics, Thermoionics, Thermal management, Imaging and 2D materials are involved.

INTRODUCTION 1.1 Nanogap Energy conversion and management

A nanogap might seem a bit of an odd object and the question of energy transfer across it is a rather fundamental issue. Indeed, this question clearly raises exciting perspectives on how physics may capture those apertures where the "particle" picture fails and electrostatic forces as well as tunneling of photons and electrons are at play. However, a set of rather concrete situations can be considered as in connection with this heterodox heat transfer. The first one is certainly Thermophotovoltaics [1,2] where the frequency of the slit radiation can be controlled to fit the electron gap and consequently lead to an optimal conversion. The second one might be Thermoionics [3,4] where the emission of hot electrons through a slit leads to the cooling of the emitting plate. A more expected field would be the one of nanoporous materials where radiation can finally predominate over solid and air conduction [5]. The last and very active area to be cited here is the one of the Van der Waals materials where atomically thin layers introduce sub-nanometer gaps inside bulk matter, as is the case in graphite or bismuth telluride for instance. A broad range of thermoelectric materials does display this type of lattice cells yielding a reduced phonon transport [6].

Beyond far-field radiation

Radiative heat transfer between two parallel surfaces set at two different temperatures is a matter of bach-elor textbooks when it comes to describe photon emission, propagation and absorption between non-ideal surfaces, usually characterized by spectral or grey emissivities. When the distance between the two surfaces is larger than Wien's wavelength divided by 2π, photons wavepackets can be defined and their emission, reflection, absorption and eventually transmission are well captured by the Radiative Transfer Equation or ray tracing techniques. A simple analytical formula that includes the effect of multireflections, for instance, provides the heat flux between two surfaces as a function of their emissivities.

However, when the distance between the surfaces reduces below Wien's wavelength divided by 2π, typically below one micron in the vicinity of room temperature, electrostatic direct exchange between the two surfaces -which can also be seen as the overlap of the evanescent tails of the field above the surfaces-rapidly predominates as the gap shrinks down to a few Ångströms [7]. This near-field heat transfer has been the subject of rising interests since twenty years [8,9], and has more recently yielded new experimental confirmations accessible to micron-scale cleanroom technologies [10][11][12][13]. Nearfield radiation is still described by classical electromagnetics and either analytical -in elementary geometries-or numerical solutions are available.

In this perspective, we will also reach the point where surface atomic displacements, or phonons, will directly transmit energy by exciting the phonon modes of the opposite side. This phonon tunneling is expected in a very specific range where the gap remains small enough for the dipole-dipole approximation to be dismissed but large enough to preserve the relevance of Maxwell's pre-1 This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0021205 dictions.

Electrons

When reaching aperture widths of a few Ångströms, wave functions of electrons of opposite surfaces may merge and a quantum description of the interaction is required. This interaction is typically of the scope of Van der Waals forces. This regime can also be described as the transition from radiation to conduction or as 'pseudo-conduction'. The electric field in this picture is replaced by the electron density which constitutes the source of direct interatomic forces.

In the following, the approach will remain mostly fundamental with a constant care of revealing the physical mechanisms at play. In a first section, we will start by describing energy transfer in large gaps -a few microns at most-down to a few Angstroems where radiation and finally 'pseudo-conduction' occur. In the second term, Van der Waals materials will be tackled where nanogaps between atomically thin sheets can be chemically controlled to manipulate phonon scattering.

NEAR-FIELD RADIATION IN NANOGAPS

The energy exchange in nanoscale gaps plays important roles in modern electronic devices, where the dimensions have been scaled down to a few nanometers. In nanoscale gaps, the evanescent electromagnetic wave emited by one body can reach the other one and excite atomic vibrations, i.e., phonons, which makes the heat transfer orders of magnitude larger than the one of black-body limit [14,15]. The mechanism of heat transfer across gaps of a few nanometers is still an open question and sometimes conflicting results have been obtained in the literature [10,16,17]. In the mean time, this field is of great importance for new technologies such as heat management in computers, energy harvesting, heat dissipation and so on.

Theoretically, the prediction of near-field radiation has been mostly formulated by the Maxwell equations [START_REF] Rytov | Principles of statistical radiophysics. 4. Wave propagation through random media[END_REF], which characterize all contributions by electromagnetic waves. When the separation between two bodies is comparable to interatomic distances, heat conduction by phonons should take place. So an open question is how the heat transfer regime transits from near-field radiation to conduction in gaps with only a few nanometers, i.e., from evanescent waves to phonons? The conventional theory of fluctuational electrodynamics has proven to be valid down to hundreds of nanometers while it is still questionable for its application in ultra short gaps as it does not capture the phonon contributions, typically from a few nanometers to even Ångströms. However, other theoretical works indeed demonstrate that phonons can be tunnelled from one body to another in nanoscale gaps [START_REF] Pendry | [END_REF][20][21]. The heat transfer due to the phonon tunnelling can be much larger than the value predicted by the Rytov's theory of macroscopic fluctuational electrodynamics [START_REF] Rytov | Principles of statistical radiophysics. 4. Wave propagation through random media[END_REF]. The previous models on phonon assisted heat transfer through nanoscale gaps has been done for acoustic modes, which illustrates the mechanical coupling between the entire bodies through piezoelectric forces [20,21]. However, for polar materials, the interactions between ionic charges can also promote the tunnelling of optical phonon modes. The optical phonon modes in dielectrical materials correspond to dipole and multipole oscillations, which can emit electromagnetic waves and thus excite the optical phonon modes in the other objects at the corresponding resonant frequency, i.e., coupling through electric field [22,23]. In such a picture, the coupling of optical phonons between two dielectrical materials is similar to the mechanism of heat transfer by evanescent modes. As a result, there are typically two types of coupling forces for phonon tunneling in the classical limit, i.e., the piezoelectric coupling [21] and the electric field coupling [22,23]. The piezoelectric coupling originates from the polarization of the entire body due to structure deformation. It treats the objects as a whole and could play an important role in non-ionic materials. While the electric field coupling comes from the oscillations of charged ions, thus allowing for the direct coupling between each atom pairs, which is especially important in ionic and polar materials. To quantify the heat tranfer mediated by the ionic charges in dielectric materials, the atomistic Green's function method has been adopted in literatures. The Green's function technique has the advantages of taking into account the interactions between each atom specifically, thus solves the heat transfer problem from the microscopic point of view. Note that compared to the elastic wave model, the phonon Green's function model explicitly considers the heat carried by each mode, including both acoustic and optical ones.

The first work to study heat transfer in nanoscale gaps by implementing phonon Green's function was achieved between Silica clusters (figure 1 top) [22]. In such a cluster system, three different heat transfer behaviors were found with a particle distance below 20 nm. The first regime starts from contact to a particle size independent gap distance of 4 Å, where the conductance decays rapidly with distance through a d -12 dependence. Below 4 Å, the electron clouds of the neighboring clusters starts to merge together, forming chemical bonds between the atoms of neighboring clusters. With the increase of gap distance beyond 4 Å, the conductance decays with the power law of d -3 until the particle distance reaches 3-5 times the cluster size, which corresponds to the surface charge-charge interactions. In this distance range, the interaction between the ions of two adjacent surfaces is larger than that between other atoms, hence the heat transfer is predominated by the interactions of surface ions. This mechanism is different from the acoustic tunnelling mechansim considered by other researchers [20,21] , where the couplings take place through the entire particles. Beyond a gap distance 5 times of the cluster size, the conductance follows the trend of d -6 . In this range, each cluster can be treated as a dipole formed by ions with positive and negative charges, which eventually promote the heat transfer with the decay law of d -6 . The transition from electron overlap to electrostatic interactions in the gap distance of 4 Å thus correponds to a quantum to classical transition of heat transfer. It is worth to note that the heat transfer behavior observed in Ref [22] is shape dependent. If the geometry of the system changes to nanorods or planes, the conductance power laws, especially at the distances beyond chemical bond formation, will be changed as observed by Chiloyan et al [23], where phonon Green's function was also applied to study the heat transfer between two semi-infinite NaCl structures. It is worth to note that electron tunneling might happen beyond 4 Å if there are free electrons as shown recently by Alkurdi et al [24], such as in metal systems. However, the heat transfer contribution due to electron tunneling decreases much faster with gap distance compared to phonon contribution and starts to be less important beyond 4 Å.

Experimentally, previous studies of near-field radiation has been focused on gap distances larger than hundreds of nanometers due to the technology challenges. With the recent improvement on device fabrications and temperature control, the measurement of heat transport across gaps of a few Ångströms to several nanometers has been realized recently in groups led by Reddy and Meyhofer [10,16] and Kittel [17]. The measurements were done in customized SThM under high vacuum conditions based on a commercial scanning tunnelling microscope (STM) (figure 2). To hold a stable gap distance of a few nanometers or even Ångströms, the probe tip should possess large stiffness. In Reddy and Meyhofer group's set up, the temperature of the probe tip was measured by the embedded Au-Cr nanoscale thermocouples.

The incident laser was applied to measured the deflection of the cantilever, which approaches to the substrate with a constant rate (typically 0.1-0.5 ns/s). The first heat transfer quantification by them [10] was achieved in down to 2-3 nm gaps and extremely large enhancement of radiative heat transfer in such small gaps between both dielectric and metal surfaces was found. Moreover, based on the fluctuational electrodynamics theory, they modelled the heat transfer in such extreme gaps and found good agreement with experimental values, indicating the validity of the traditional fluctuational electrodynamics in predicting the near-field radiation through gaps of a few nanometers. Latter measurements in their group as well as Kittel group pushed the gaps down to 0.2 nm in the Au-Au system with the improvement of tip stiffness up to 10 4 N/m [16]. In the work by Kittel et al [17], where the probe temperature was measured by a thermoelectric couple, giant heat transfer was observed when the gaps are smaller than 6 nm. The measured heat flux is more than five orders of magnitude larger than the black body limit and four orders of magnitude larger than the values predicted by conventional fluctuational electrodynamics theory. They ascribed the origin of such large heat flux to phonon tunnelling in those ultra small gaps. However, such a large heat flux might caused by the 3 This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0021205 contamination of the tip and the substrate [16]. After the cleaning of both probes and substrates by both plasma-cleaning and controlled crashing procedures, Cui et al [16] found that the thermal conductance between gaps was largely reduced. However, due to the large noise in their measurement, it is still unclear to which gap sizes the conventional fluctuational electrodynamics fails to describe the radiative heat transfer.

NANOGAP CONTROLLED HEAT CONDUC-TION IN 2D MATERIALS

When the gap distance between two objects is in the range of the nanometer, the heat transfer between them can also be tuned greatly by bridging them with small molecules, which brings important applications in thermal switches and molecular thermoelelctrics. Here we demonstrate that the nanogap between graphene sheets and functionalized graphene oxide (FGO), formed due to the functional intercalated molecules, allows for engineering the inter-layer thermal coupling and the intra-layer heat transfer in a graphene system [25,26]. Phonon transport on the nanoscale is investigated comprehensively by means of molecular dynamics simulations and atomistic Green's function, considering both the respective contribution of phonons and electrons. These theoretical predictions are corroborated by a set of experimental works including the chemical synthesis of freestanding graphene and graphene oxide with and without functionalization, their composition characterization with Raman spectroscopy and thermal characterization with Fourier transform infrared spectroscopy. Different molecules including 3-Aminopropyltriethoxysilane (APTES) have been tested both in calculations and experiments. This work provides not only insights into the fundamental understanding of heat transport in graphene, but also tackles the key technological challenge of efficient thermal management in the industry of the next-generation integrated circuit.

To explore the effect of functional molecules on the in-plane thermal conductance of the graphene sheets, molecular dynamics simulations are firstly perform to study a nanoscale molecular junction between two stacks of multilayer graphene nanoflakes. The in-plane thermal conductivity κ of the graphene sheet and its interfacial thermal resistance R with the FGO substrate is plotted as a function of the graphene layer number in the film in Fig. 3a andb, respectively. The molecule density is ρ = 0.081nm -2 . It is firstly shown that the presence of the functional molecule (APTES) results in an unexpected increase both in the graphene film thermal conductivity κ and in R for multilayer graphene. An overall decaying trend of the in-plane thermal conductivity of the graphene film and its resistance R with the substrate versus the layer number is observed until approaching the value of bulk graphite. For a single layer of graphene, κ is reduced by the molecules, which is on the contrary to the case where no molecule links the graphene film and the substrate. This breakdown of the thermal conductivity enhancement is due to a saddle-like surface generated around the molecule's chemical bonds of amino and silano groups connecting the graphene, with the bond center as the saddle point, as shown in the inset A of Fig. 3a. The saddle-like surface strongly scatters all phonon modes, thus decreasing κ of the graphene film. We further study the microscopic origin of the thermal conductivity κ enhancement in the graphene sheets by calculating the m phonon relaxation time. The phonon relaxation time τ indicates the time needed by a phonon mode to relax back to equilibrium due to phonon-scattering mechanisms. The phonon dispersion of the supported graphene film for ρ = 0.081nm -2 and supported graphene layer number l G = 2, and the calculated relaxation time for all the phonon modes are shown in Fig. 4. By inserting the APTES molecule, the relaxation time of the acoustic flexural modes largely increase at low frequencies, whereas the longitudinal and transverse modes undergo a slight decrease in their relaxation times. The notable increase in accounts for 4 This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. the enhancement τ of the flexural modes of the graphene sheet bonded to the substrate. The detailed phononic and electronic transport properties of the APTES molecule to disclose its role in the cross-layer heat conduction have also been investigated. It has been found out that low-energy phonons are mainly responsible for heat conduction due to van der Waals (vdW) interlayer force, whereas high-frequency phonons propagates along the covalent bonds in the molecules.

PLEASE CITE THIS ARTICLE AS

Finally, the supported graphene is integrated in a micro heater to demonstrate its capacity of improving thermal management. The functionalized graphene oxide introduces alternative heat-escaping channels into a graphene-based sheets bonded to functionalized graphene oxide through amino-silane molecules. Using a resistance temperature probe for in situ monitoring we manage to evidence that the micro heater surface temperature was lowered by ∼ 28 • C for a chip operating at 1,300 W cm -2 . Thermal resistance probed by pulsed photothermal reflectance measurements demonstrated an improved thermal coupling due to functionalization on the graphenegraphene oxide interface.

CHALLENGES AND PERSPECTIVES

Perspectives on Radiation

Understanding the mechanisms of near-field radiation at the nanoscale is beneficial for improving a variety of technologies ranging from thermal informatics, radiative cooling, energy conversion and non-invasive imaging. Current theoretical and experimental investigations are still behind the enssence of extreme near-field heat transfer (gaps below a few nanometer). Theoretically, the validity of the widely used theory based on fluctuational electrodynamics is still questionable to describe the heat transfer behaviors at such small gaps, at which non-locality of the electromagnetic field becomes nonlocal. The atomistic Green's function method can be helpful to describe the phonon tunnelling phenomenon under nanoscale gaps. It is an ideal method to study the crossover between radiation and heat conduction. However, the atomistic Green's function method relies on the accurate description of interatomic force constants across the gap. The full description of interatomic interactions under different distances is still unclear. Typically, chemical bond interactions is considered for distances comparable to interatomic spacing in crystals [27] while van der Waals forces and/or Coulomb forces are considered for distances from a few nanometers to dozens of nanometers [START_REF] Pendry | [END_REF]22]. The interatomic forces decrease rapidly with distances and the relative numerical errors could be large for force constant matrices at large distances, which can bring numerical instabilities in Green's function calculations. Another possible way to study the heat transfer in nanoscale gaps is the atomic molecular dynamics (MD) simulations [28]. Similar to the atomistic Green's function method, the value predicted by MD also relies on the accuracy of interatomic forces. As a result, it is enssential to develop unified interatomic forces models at different distance ranges. It is worth to note that the near-field radiation is a classical description of heat transfer. Recently, it was also demonstrated that the Casimir force, which is originated from the vacuum fluctuations and thus is a quantum effect, can also assist phonon tunneling in moderate distances [29,30]. The quantum effect assisted heat transfer in ultra-short gaps is a new mechansim and is also a new direction. Although the experimental measurements of near-field radiation at nanoscales has been pushed to the gaps of sub-nanometers with the recent development of fabrication technology, the challenges still remain for accurate measurements with gaps from ∼100 nm to a few Ångströms. First, the large attraction forces between objects seperated by subnanometers gaps subject to the residual electrostatic charges makes it difficult to create and robustly maintain such gaps.

Second, the near-field flux is usually in the orders of the pico Watt, which makes it difficult to be detected with high accuracy. Third, both the substrate and probe tip could be easily contaminated by adsorbing unwanted particles, which will largely affect the heat flux and restrict the smallest achievable gap size. The contamination of unwanted particles could also lead to misleading results. Fourth, to fully characterize the heat transfer from near-field radiation to conduction, it is required to measure heat transfer with gaps sizes from hundreds of nanometers to a few Ångströms. For small distances, sharp tips are required to perform well defined measurements. However, it is hard to realize high sensitivity required in measuring the small heat flux at large distances with sharp tips. Consequently, the future experiments on near-field radiation in nanoscale gaps might focus on the solutions of the above challenges, especially the sensitivity and tip shape issues.

Perspective on Heat Conduction

In so far as heat conduction in nanogaps is in relation with the developments of the several decades old field of energy transfer in molecular systems -which is an above highlighted topic-, the perspectives of expansion are multiple when crossing purposes such as heat exchange, management and conversion with the immense toolbox of available chemical compounds. The second more recent and active field involved is the one of 2D-Materials, which are by a predominant part, constituted of Van der Waals systems. Combining the family of 2Dmaterial polymorphs with the one of existing intercalates is a promising strategy to multiply the range of systems and uncover unexpected thermophysical properties.

CONCLUSIONS

This perspective had the ambition to highlight the considerable range of domains from physics involved in the description of energy transfer in a simple gap. At slit sizes larger than a micron, radiative transfer equation is well-known from engineers, but Maxwell equations have to be solved below the micron. At one or two nanometers, Maxwell equations start to become irrelevant due the non-locality of the field -the local dielectric constant is not defined anymore-, and below, the scale of the electron cloud is reached, the classical charge description has to be replaced by the quantum one. At this point, a gap appears as a defect in a quasi-continuous crystal as for instance in 2D-materials or layered bulk materialsamong which a large set of thermoelectric materials can be found-. While the fundamental conceptual frames are available, several experimental proofs have still to be im-plemented, which will certainly be the focus of coming and exciting scientific investigations.

FIG. 1 .

 1 FIG. 1. Schematic illustration of the Green's function calculation set up (up) and the thermal conductance between Silica clusters with different sizes at 300 K as a function of the separation distance d. Reproduced with permission from Phys. Rev. Lett. 112, 114301 (2014). Copyright 2014 American Physical Society.

FIG. 2 .

 2 FIG. 2. Schematic of the experimental set-up, in which an SThM probe is in close proximity to a heated substrate. Reproduced with permission from Nature 528, 387 (2015). Copyright 2015 Springer Nature.

FIG. 3 .

 3 FIG. 3. Thermal resistance and in-plane thermal conductivity of the GBF versus the graphene layer number. (a) Molecular dynamics simulation results of in-plane thermal conductivity of the graphene film and (b) interfacial thermal resistance R between the FGO substrate and the graphene film versus the graphene layer number lG in the film. Reproduced with permission from Nat. commun. 7, 11281 (2016). Copyright 2016 Springer Nature.

FIG. 4 .

 4 FIG. 4. Phonon dispersion and lifetimes of the graphene film. (a) Phonon dispersion of the graphene film bonded to the APTES-FGO substrate from molecular dynamics simulations, for ρ = 0.081nm 2 and lG = 2. (b-d) Mode-wise phonon relaxation time for longitudinal modes including longitudinal acoustic (LA) and optical (LO) branches, for transverse modes including transverse acoustic (TA) and optical (TO) branches, and for flexural modes including flexural acoustic (ZA) and optical (ZO) branches, respectively. Reproduced with permission from Nat. Commun. 7, 11281 (2016). Copyright 2016 Springer Nature.

This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0021205

ACKNOWLEDGEMENT

This work was supported by the National Natural Science Foundation of China (No. 11804242) and the CREST Japan Science and Technology Agency (JP-MJCR19I1).

Data sharing is not applicable to this article as no new data were created or analyzed in this study.