Sub-cloud rain evaporation in the North Atlantic winter trade winds derived by pairing isotopic data with a bin-resolved microphysical model

. Sub-cloud rain evaporation in the trade wind region signiﬁcantly inﬂuences the boundary layer mass and energy budgets. Parameterizing it is, however, difﬁcult due to the sparsity of well-resolved rain observations and the challenges of sampling short-lived marine cumulus clouds. In this study, sub-cloud rain evaporation is analyzed using a steady-state, one-dimensional model that simulates changes in drop sizes, relative humidity, and rain isotopic composition. The model is initialized with relative humidity, raindrop size distributions


Introduction
Shallow precipitation is a sporadic but energetically significant feature of marine cumulus clouds in the trade wind tropical ocean basins (Byers and Hall, 1955;Nicholls and Leighton, 1986;Paluch and Lenschow, 1991;Short and Nakamura, 2000;Jensen et al., 2000;Stevens, 2005).Rain rates on the scale of 1 mm d −1 , commonly associated with shallow cumulus precipitation, are capable of producing roughly 28 Wm −2 of latent heat flux through rain evaporation in the sub-cloud layer (Fig. 1), which is comparable to the radiative and surface fluxes computed using mixed-layer models (e.g., Caldwell et al., 2005) and within stratocumulus-tocumulus transition regions (e.g., Kalmus et al., 2014).
Such large fluxes, even if localized, may influence the vertical moisture and energy distribution and affect the boundary layer stability (e.g., Srivastava, 1985;Paluch and Lenschow, 1991).The evaporatively cooled air mass also facilitates downdrafts below the cloud base, which initiate or strengthen cold pool formations (Srivastava, 1985;Jensen et al., 2000;Seifert, 2008;Zuidema et al., 2012;de Szoeke et al., 2017).The downdraft can further feed its cool and moist air into large-scale circulations, leading to moisture recycling (Stevens, 2005;Worden et al., 2007).A schematic of these processes is shown in Fig. 1.
The rain evaporation efficiency, or the fraction of rain evaporated in the sub-cloud layer, impacts the amount of rain that reaches the surface.Depending on the fraction of rain reaching the surface and the sub-cloud moisture circulation, clouds could either remain intact or break up, thus affecting the local albedo (Paluch and Lenschow, 1991;Sandu and Stevens, 2011;Yamaguchi et al., 2017;O et al., 2018;Sarkar et al., 2020).Overall, accurate rain evaporation estimates in shallow cumulus regions are needed to better predict surface rain estimates in weather and climate models and understand the shallow rain life cycle.
Past field campaigns have sampled precipitation from shallow cloud systems.For example, the Atlantic Stratocumulus Transition Experiment (ASTEX; Bretherton and Pincus, 1995) conducted over the east-central Atlantic Ocean in June 1992 sampled the cloud systems, with drizzle evaporating into the sub-cloud layer beneath overlying stratocumulus clouds.Similarly, the Rain in Cumulus over the Ocean (RICO; Geoffroy et al., 2014;Snodgrass et al., 2009) campaign was conducted off the Caribbean islands of Antigua and Barbuda over the Atlantic Ocean in 2012-2013, where cumulus rain was sampled.Furthermore, the Cloud System Evolution in the Trades (CSET; Albrecht et al., 2019;Mohrmann et al., 2019;Sarkar et al., 2020) was conducted over the Pacific Ocean between California and Hawaii in July-August 2015 to sample stratocumulus and cumulus rain events.These campaigns support the idea that shallow precipitation and sub-cloud evaporation is important for the local energy budget.However, a more dedicated study is needed to characterize the shallow cloud rain evaporation as a function of the local thermodynamic and microphysical conditions.
Questions also remain about the rain evaporation flux (F e ) variability in different cloud conditions and its sensitivity to boundary layer microphysical and thermodynamic characteristics.How is the vertical structure of F e linked to microphysical and thermodynamic processes?Could F e reinforce or weaken sub-cloud stability at local scales?These questions are inherent to our understanding of shallow rain processes and constraining F e accurately.
A major challenge when observationally constraining rain evaporation is sampling rain in and below cumulus clouds, due mainly to their temporal and spatial variability and the limitations in the existing rain retrieval methods.The airborne millimeter wavelength radar used during field campaigns provides a wide and homogeneous array of cloud and precipitation samples in terms of radar moments.However, accurate microphysical retrievals from the radar moments are difficult due to Mie scattering and atmospheric and liquid attenuations (Fairall et al., 2018;Schwartz et al., 2019;Sarkar et al., 2021).Rain observations from satellites, although they provide a large array of datasets, are often limited in their sensing accuracy of shallow rain.This is due to factors like high atmospheric attenuation and surface radar reflections (e.g., Kalmus et al., 2014).
In comparison, in situ cloud and rain probes, although limited in their sampling volume when compared to radar, provide well-resolved, direct, and accurate microphysical raindrop size distributions (RSDs).In situ measurements also provide stable isotope ratios of hydrogen and oxygen in water vapor, which can be used to independently assess rain evaporation.This is because as rain evaporates into the unsaturated sub-cloud layer, the isotopically light water transitions to the vapor phase more efficiently, causing the drops to become increasingly heavy (Salamalikis et al., 2016;Graf et al., 2019).
This study makes a novel attempt to characterize rain evaporation, its vertical structure, and its dependence on microphysical (i.e., raindrop concentration, size, and distribution width) and thermodynamic (i.e., surface relative humidity) features using a one-dimensional, steady-state evaporation model initialized by in situ field observations of both RSD and water vapor isotope ratios.The in situ samples were measured by the NOAA WP-3D Orion (P3) aircraft during the Atlantic Tradewind Ocean-Atmosphere Mesoscale Interaction Campaign (ATOMIC), which was a component of the international field campaign known as EUREC 4 A (ElUcidating the RolE of Clouds-Circulation Coupling in ClimAte).For the first time, the isotopic enrichment of rain is modeled using RSDs measured in the field and evaluated using surface-based isotopic rain observations.First, the rain observations are characterized at the cloud base in terms of microphysical and thermodynamic conditions.Second, the vertical distribution of the sub-cloudmodeled rainwater content (RWC) and rain evaporation fluxes (F e ) are discussed in terms of their microphysical and thermodynamic sensitivities.Last, the modeled isotope ratios at the surface are also compared with the surface isotope ratio observations in the P3 vicinity to validate the accuracy of the model.We expect results from this work to pave the way toward a better representation of shallow rain evaporation in climate models and to serve as a model for comparing rain evaporation processes in a wide range of convection.

ATOMIC and EUREC 4 A campaign and datasets
The ATOMIC field campaign was conducted in the North Atlantic trade wind region, roughly between 10-15 • N and 51-60 • W, to study mesoscale circulations in the atmosphere and ocean (Pincus et al., 2021).ATOMIC was the NOAAsponsored component of the larger, international EUREC 4 A field campaign, which took place in January-February 2020 near Barbados (Stevens et al., 2021).Both the NOAA P3 aircraft and the NOAA R/V Ronald H. Brown (hereafter Ron Brown) were deployed as part of ATOMIC.Other platforms, such as the R/V Meteor and Barbados Cloud Obser-vatory (BCO), discussed in this paper were part of the larger EUREC 4 A effort.
The P3, integrated with radar, in situ instruments, and dropsondes, was flown through cloud and rain transects to collect thermodynamic and microphysical boundary layer observations and facilitate investigations of aerosol-cloudprecipitation interactions.An example of the trajectory of the P3 is shown in Fig. 2 for 9 February, where a series of stacked 10 min horizontal legs were flown to sample the boundary layer extensively.The horizontal legs were flown at 150, 500, and 700 m and 2, and 3 km between 54 and 56 • W.During most flights, a level circle was also conducted at 7.5 km altitude, and seven to eight dropsondes were released to obtain high-resolution thermodynamic observations reaching the surface.The surface relative humidity, which is integral to the rain evaporation model used in this paper, is obtained at ≈ 10 m altitude.Its values for 9 February are noted at the dropsonde locations in Fig. 2b.
This paper characterizes the rain structure during ATOMIC using the Cloud Imaging Probe (CIP) and Precipitation Imaging Probe (PIP) instruments on board the P3, which sampled the raindrop size distributions in situ.  of 25 µm-1.6 mm, while the PIP samples across 100 µm-6.2 mm (Pincus et al., 2021;Leandro and Chuang, 2021).
The CIP and PIP observations are stitched together to obtain 1 Hz raindrop size distributions for diameters spanning 100 µm-6 mm (total 23 bins).Bin sizes smaller than 100 µm and bigger than 6 mm are not reliable and are not used in the current analysis.Drops across 400-1800 µm, 1.8-5 mm, and 5-6 mm drop sizes are binned at 200 µm, 400 µm, and 1 mm resolutions, respectively.This paper is based on the latter part of the ATOMIC campaign, when the CIP and PIP instruments were properly functioning and mean rain rates greater than 0.01 mm d −1 were observed during 22 10 min in-cloud horizontal legs on 4, 5, 9, and 10 February.The in-cloud RSD is assumed to accurately represent cloud base RSD.The rain rates (in mm d −1 ) are calculated from the observed RSD, using R = 6π × 10 −7 23 i=1 N(D i )v i D 3 i , where N (m −3 ) is the raindrop concentration for the drop diameter D i (mm), v i (m s −1 ) is the terminal velocity associated with D i , and i is the index of the RSD bin.The rain rates for each 10 min leg are averaged and noted in the legend of Fig. 3.Even though the probe instruments were working on 31 January and 11 February, the mean rain rates from those days were below 0.01 mm d −1 during all of the 10 min in-cloud horizontal legs and are therefore not included in this study.
To model the isotopic evolution of the RSDs, 1 Hz water vapor mixing ratio and water vapor isotope ratios for hydrogen and oxygen (δD v and δ 18 O v , respectively) were obtained from the Picarro L2130-i water vapor isotope analyzer flown during ATOMIC (Bailey et al., 2023).When airborne, the analyzer drew in ambient air through a 0.25 in.(6.35 mm) backward-facing tube, which ensured the selective sampling of water vapor as opposed to liquid water (Pincus et al., 2021).δD v and δ 18 O v represent the ratios D/H and 18 O/ 16 O, respectively, normalized to VSMOW (Vienna Standard Mean Ocean Water) and reported in units of per mille (‰).The standard deviations associated with the 1 Hz P3 δD v and δ 18 O v for a specific humidity of 1-18 g kg −1 are 2 ‰ and 0.8 ‰, respectively (Fig. 8; Bailey et al., 2023).
The accuracy of the sub-cloud rain evaporation model used in this study is evaluated using the rain isotope ratios and rain rate measurements from the NOAA research vessel Ronald H. Brown.During ATOMIC, Ron Brown sailed in the trade wind region between Barbados and the Northwest Tropical Atlantic Station (NTAS), a buoy station (near 15 • N, 51 • W), to provide a ground-based perspective for the P3 flying overhead.The isotopic composition of 12 precipitation samples collected aboard Ron Brown has been characterized with 0.2 ‰ and 0.8 ‰ of uncertainty in δD v and δ 18 O v , respectively (Bailey et al., 2023).While the Ron Brown measurements (collected across a wide geographic area between 5 January and 11 February) are not exactly co-located in space or time with the P3, they still provide a useful assessment of the trade cumulus environment in which the P3 flew.
Isotope ratios were also sampled in surface precipitation at two other stations, viz. the Barbados Cloud Observatory (BCO) and the German R/V Meteor that were part of the EUREC 4 A campaign.These provide further observational constraints for the rain evaporation model used in this study.The BCO is a land-based observatory on the eastern shores of Barbados, where 42 precipitation samples were collected from 16 January and 18 February (Villiger et al., 2021).The Meteor sailed along a north-south transect defined by the 57.24 • W meridian and sampled 15 rain events between 20 January and 19 February.Uncertainties associated with the Meteor samples are 0.2 ‰ and 0.5 ‰ for δ 18 O p and δD p , respectively (Galewsky and Los, 2020).More details regarding isotopic observations, stations, and measurement techniques during EUREC4A are described in Bailey et al. (2023).

Sub-cloud rain evaporation model
Observed raindrop size distributions are used to initialize the sub-cloud rain evaporation model using aircraft data from flights on 4, 5, 9, and 10 February.This one-dimensional, The cloud base in the model is deduced from ceilometer observations aboard Ron Brown.The 10 min resolved ceilometer observations (Quinn et al., 2021) show that the median cloud bases on 4, 9, and 10 February are between 700 and 800 m.Consequently, the raindrops are initiated from a 700 m cloud base and modeled to fall through a sub-saturated sub-cloud layer.The relative humidity at the cloud base is assumed to be 100 %, decreasing linearly towards the surface (verified from the dropsonde observations; Fig. S2) and with surface relative humidity varying from 65 % to 80 %, as determined from nearby dropsonde observations.The subcloud layer is well mixed, with an average specific humidity from dropsondes varying within 13-15 g kg −1 across the sub-cloud layer (Fig. S2).The rainwater content (RWC) is computed at cloud base, using the stitched CIP-and PIPbased raindrop size distribution.
The model is integrated downward from the initial condition at the cloud base.A nominal step size ( z) of 1 m is used, but an adaptive step size is employed to ensure the stability of the explicit time integration method.The adaptive time stepping is active for droplets smaller than about 1 mm.Following Graf et al. (2019), the raindrop diameter evolves according to where F v (unitless) is the mass ventilation coefficient, D va (m 2 s −1 ) is the diffusivity of water vapor in air, R v (461.5 J kg −1 K −1 ) is the gas constant for water vapor, RH (%) is the relative humidity, e v,sat and e r,sat (Pa) are the saturation vapor pressure at ambient temperature and drop surface, T a (K) is the ambient temperature, T r (K) is the raindrop surface temperature, D (m) is the raindrop bin diameter, v (m s −1 ) is the raindrop terminal velocity, ρ w (10 3 kg m −3 ) is the density of water, and z (m) is the altitude.The vertical variation in the T r is given by (Graf et al., 2019) dT r dz =  where F h (unitless) is the heat ventilation coefficient, k a (J m −1 s −1 K −1 ) is the thermal conductivity of air, c w (4187 J g −1 K −1 ) is the specific heat of water, and L (2.25 × 10 3 J g −1 ) is the latent heat of vaporization.
While each raindrop size bin (indexed by i) has its own diameter (D i ), temperature (T r,i ), fall speed (v i ), and vapor pressure (e r,sat,i ), the subscripts showing the bin index (i) have been omitted in the equations above for clarity.Note also that size of the raindrops in each bin D i (z) varies with height, and the number of droplets in that bin N(D i ) remains fixed for all heights until the droplets evaporate, which is assumed to occur when D i (z) < 1 µm.
The calculated D at vertical level z is then used to model the steady-state RWC (g m −3 ) at z, using the following: The precipitation flux F p (z) (Wm −2 ) at each level z for the bin index i is modeled using The rain evaporation flux produced as the z m 3 box falls through z depth is given by F e (z) (Wm −2 m −1 ) at level z, using the following: The total rain evaporation flux produced over the entire subcloud layer F eT (Wm −2 ) is obtained from The rain-evaporated fraction (REF) is the fraction of rain evaporated in the sub-cloud layer and is computed based on To model the isotopic composition of the precipitation, the vertical change in δ p (‰) of raindrops as they evaporate is given by (Graf, 2017) where δ p applies to both δD p and δ 18 O p , n is equal to 0.58, and D va is the diffusivity of HDO or H 18 2 O in air.Equation ( 8) includes the influences of the both evaporation of raindrops and the exchange of isotopes between raindrops and ambient vapor during equilibration.δ va is the mean ambient water vapor isotope ratio expressed in per mille (‰), obtained from isotope ratio observations at 150 m altitude.All the parameters discussed in the model are derived from Pruppacher et al. (2010), Graf (2017), andSalamalikis et al. (2016) and are described in the MATLAB code attached.
The rain isotope ratios used to initialize δ p are determined using in situ water vapor isotope ratios and the measured temperature at cloud base by assuming that the raindrops are in equilibrium with the water vapor (Risi et al., 2020) and scaling by a temperature-dependent equilibrium fractionation factor (α p−>v =(δ p /1000 + 1)/(δ v /1000 + 1)), as defined in Majoube (1971).The modeled δ p at the surface is later compared with the surface rain isotope ratio observations from the BCO, Ron Brown, and Meteor to validate the accuracy of the model.
Because isotope ratios are typically measured in bulk precipitation, we evaluate the mass-weighted isotopic composition of the integrated raindrop size distribution in the simulations.This is done by integrating δD p and δ 18 O p over the observed RSD to estimate the mean (mass-weighted) δD p and δ 18 O p at each vertical level z, as follows: The deuterium excess, or d p , a quantity useful in sub-cloud rain evaporation analysis, is defined as d p = δD p − δ 18 O p .δD p and δ 18 O p are affected by both equilibrium and nonequilibrium processes in the sub-cloud layer.However, d p cancels out the equilibrium effects in δD p and δ 18 O p and thereby only represents the non-equilibrium effects that take place due to rain evaporation in the unsaturated sub-cloud layer.

Moisture concentration after rain evaporation
Finally, the bulk change in sub-cloud layer absolute humidity resulting from rain evaporation q v (g m −3 ) can be es-timated by assuming an appropriate integration time t (s) as follows: When the rain-evaporated water vapor mixes with the ambient water vapor, then the net isotope ratio at a vertical level z is a combination of the background vapor isotope ratio and the isotope ratio evaporated from the drop, as given by Noone (2012), as follows: where δ e , δ va and δ v are the isotope ratios (‰) of the evaporated rainwater, the ambient water vapor prior to rain evaporation, and the total water vapor after rain evaporation at level z, respectively.q v is the result from Eq. ( 10) and depends on both the length of time over which rain evaporation is presumed to occur and on the assumption that the fluxes derived from the steady-state rain evaporation model are constant over the integration interval.δ e (z) is computed from the difference between the product of δ p and RWC at every z depth using

Microphysical parameters using lognormal fitting
The role of microphysical processes in influencing modeled rain evaporation and rain isotopic composition is investigated in terms of the total raindrop concentration (N 0 ), geometrical mean diameter (D g ), and the lognormal distribution width (σ ) at the sampling level.These parameters (N 0 , D g , and σ ) provide physically meaningful quantities to interpret the microphysical conditions of rain and are helpful in evaluating the sensitivity of rain evaporation to microphysical changes.These are derived by fitting the observed RSDs to a lognormal distribution (Feingold and Levin, 1986), as follows: where µ is the log of D g (i.e., D g = e µ ).N(D) substituted into Eq.(4) gives Notice that when N(D) is substituted into Eq.( 9) for δ p , then N 0 is canceled out in the numerator and denominator, making δ p (δD p and δ 18 O p ) independent of raindrop concentration and only dependent on D g and σ .Similarly, REF is also almost independent of N 0 .
https://doi.org/10.5194/acp-23-12671-2023Atmos.Chem.Phys., 23, 12671-12690, 2023 For simplicity, collision-coalescence (i.e., raindrop selfcollection) and breakup processes are ignored, as is the impact of turbulence and mesoscale variability.We have assumed that the N 0 , D g , and σ sampled at the in-cloud legs represent the cloud base precipitation well.This assumption is backed by the small difference between the observed N 0 , D g , and σ for a given rain rate, whether it is sampled at cloud base or higher (Fig. 5).This result is similar to Wood (2005), whose result suggests that the rain rate is near constant in the lower 60 % of stratocumulus clouds.

Observed rain characteristics
The 10 min (1 Hz) horizontal leg mean rain rates sampled for 20 out of 22 cases on 4, 5, 9, and 10 February (Fig. 3) vary between 0.01 and 3 mm d −1 , with a rain frequency between 1 % and 10 %.The other two cases have more intense rain rates of 22 and 31 mm d −1 and rain frequencies of 10 % and 50 %, respectively, as sampled on 9 February at altitudes of 1630 and 2112 m.The leg mean rain rates are calculated using the 1 Hz samples, with rain rates higher than 0.01 mm d −1 .The rain frequency is defined as the ratio of the number of raining samples to the total number of raining and non-raining samples within a 10 min horizontal leg.Overall, barring two cases, the rain rates sampled over 20 horizontal legs by the P3 are weak and comparable with rain usually witnessed in stratocumulus clouds.
The highest and lowest rain rates were observed on 9 February (31 mm d −1 ) and 4 February (0.01 mm d −1 ), respectively.The low rain rates on 4 February are due to the higher concentration of small raindrop diameters (< 200 µm) and almost no raindrops larger than 500 µm when compared to the other days.Similarly, the higher rain rates for the two cases on 9 February are due to the high concentrations of larger drops compared to other cases.In total, 7 out of 22 cases were sampled within ±100 m of cloud base (700 m) while the other cases had sampling altitudes higher than 1.3 km.No rain was detected at any of the 150 m altitude legs (except in one case on 9 February), suggesting that rain either evaporated completely before reaching the surface or was not sampled when it reached the surface.
Vertical and horizontal variability in rain structure is evident in the radar images (Fig. 4), which reveal heterogeneous cloud bases and some heavy precipitation pockets with radar reflectivity higher than +10 dBZ.These heavier precipitating samples partially evaporate before reaching the surface.The more weakly precipitating segments, with smaller radar reflectivities, evaporate completely within the sub-cloud layer.Vertical changes in the rain structure are also evident from in situ observed RSDs measured at different altitudes within the same cloud system.For example, on 9 February, the RSDs shift towards smaller drop sizes as sampling altitudes decrease from 2112 and 1630 to 1500 and 1053 m (Fig. 3c), which could be due to both microphysical and thermodynamic processes in the cloud layer.

Observed microphysical and thermodynamic variability compared with CSET and RICO
A strong positive correlation is observed between the rain rates and microphysical parameters N 0 , D g , and σ at cloud base (Fig. 5a-c).The higher D g and σ indicate a higher concentration of larger drops, which account for more liquid water and higher rain rates.While D g and σ vary modestly (σ by approximately a factor of 2), N 0 varies by several orders of magnitude over 22 P3 cases, with rain rates between 0.01 and 35 mm d −1 .The 1 Hz distributions of N 0 , D g , σ , and rain rates are plotted in Fig. 6 to give an overall microphysical statistical characterization for all the P3 cases.The variability in the rain parameters is the lowest on 4 February and highest on 9 February.The P3 cases also show a weak negative correlation between the surface relative humidity (RH sf ) and rain rate (Fig. 5d).This may be due to the downdrafts drying the surface layer and lowering RH sf .Note that the correlation of RH sf and the rain rate compared to the microphysical variables is weaker, as indicated by the r values.

CSET comparison
Compared to the average P3 cases, the cumulus rain events sampled over five cases during the CSET campaign in the northeastern Pacific Ocean have higher rain rates (1-100 mm d −1 ), along with higher N 0 (10 3 -2 ×10 4 m −3 ) and σ (2.3; Fig. 5a).However, the average D g for the CSET cases lies within the P3 ranges (Fig. 5b, c).Since D g and σ did not vary significantly across the five CSET cases, the higher rain rates during CSET could be due mainly to their larger N 0 .A total of four out of five cases during CSET have RH sf of 84 %, which is higher than for most of the P3 cases.The correlation between the RH sf and rain rate during CSET is much weaker compared to the P3 cases (Fig. 5d).RH sf for CSET remains constant at 84 % for rain rates from 1 to 100 mm d −1 .That said, it is worth noting that RH sf measurements during CSET were collected using aircraft observations at 150 m altitude and therefore might differ slightly from the actual surface relative humidity.
The F eT values during CSET within some heavily precipitating cumulus transects are between 10 and 200 Wm −2 , which is comparable to the P3 F eT range of 1-350 Wm −2 .The high variability in F eT for both the P3 and CSET events suggests that the heterogeneity of the cumulus rain processes is a common feature across different ocean basins.

RICO comparison
During the RICO campaign, which was based in the Caribbean like the ATOMIC and EUREC4A field campaigns, the rain rates sampled were stronger than the P3 cases, as in CSET.The cloud base rain rate is 5 mm h −1 during RICO (Fig. 2; Geoffroy et al., 2014).Comparing Fig. 6 with Fig. 2 in Geoffroy et al. (2014), the median rain rates, N 0 , and raindrop diameters during RICO at cloud base were much higher than the P3 cases sampled during ATOMIC.Geoffroy et al. ( 2014) have used a mean volume diameter D v to describe the variability in their raindrop sizes, which is mathematically different but still comparable to the D g values that we have used in this study.D v at 500 m during RICO is 750 µm, which is much higher than D g values of 200 µm during the P3 cases.Similarly, the median N 0 and rain rates during RICO are 6 × 10 4 m −3 and 12 mm h −1 at 500 m altitude, compared to the 2 × 10 3 m −3 and 3 mm d −1 , respectively, averages over all 22 P3 cases.This suggests that the higher rain rates sampled by RICO could have been due to the high N 0 and D v values when compared to that sampled by the P3.
All flights during RICO were designed to randomly sample clouds above the cloud base (except one on 19 January), and as a result, most flights did not sample any precipitation.But the precipitation samples on 19 January suggest a 6 % reduction in the cloud base rain rate (3 mm h −1 ) due to rain evaporation (Snodgrass et al., 2009).This roughly translates to 130 Wm −2 of rain evaporation flux (based on Fig. 10 in Snodgrass et al., 2009) and is comparable to the CSET and the P3 values.

Vertical distributions of RWC and F e
The sub-cloud variability in the rain evaporation over 22 cases from ATOMIC and EUREC 4 A is reflected in the vertical profiles of the modeled RWC, rain rate, and F e in Fig. 7df.Cases on 9 February, with their highest rain rates and RWC at the cloud base also have the highest RWC reaching the surface (> 0.02 g m −3 ; see Fig. 7d and e).In all, 10 out of 22 cases have RWC higher than 10 −3 g m −3 at the surface, 4 of which are on 9 February.
In contrast, one case on 4 February evaporates completely within 400 m from the cloud base, with no rain reaching the surface.This is because all drops in the RSD for this case are smaller than 300 µm (Fig. 3a  susceptible to evaporation.The cases on 5 and 10 February have RWCs ranging between those on 4 and 9 February, with rain intense enough to reach the surface after partial evaporation. RWC decreases at a faster rate for cases with smaller RWC at the cloud base, like on 4 February.This leads to an increase in F e near the cloud base compared to near the surface (Fig. 7f).Conversely, cases with higher RWC at the cloud base, like on 9 February, have a slower rate of decrease in RWC near the cloud base.This is primarily due to the higher concentration of larger drops in these cases that evaporate the most as they reach closer to the surface.

Vertical distributions of N 0 , D g , and σ
The modeled microphysical parameters N 0 , D g , and σ are shown in Fig. 7a-c, where 9 February cases have the highest cloud base N 0 (> 1000 m −3 ).The decrease in N 0 with decreasing altitude corresponds well with that in the RWC, as seen earlier.The net modeled D g increases and σ decreases from the cloud base to the surface across all 22 P3 cases.Changes in D g and σ are much smaller than in N 0 .In general, D g increases and σ decreases whenever smaller drops in the RSD evaporate completely.In this way, the complete evaporation of smaller drops makes the RSD narrower and centered over larger D g .In contrast, if the RSD only has larger drops that only partially evaporate, then the D g decreases and σ increases, making the RSD wider and centered over smaller D g .
The higher terminal velocity for bigger drops helps them reach the surface faster, while the longer residence time of slower-falling smaller drops in the sub-cloud layer leads to more complete evaporation of those drops.Thus the lower terminal velocity aids in the overall shift in the RSD towards larger D g , narrower σ , and lower N 0 from the cloud base to the surface.

Sub-cloud stability due to the vertical distribution of F e
How bottom heavy or top heavy a profile of F e is may have an effect on the boundary layer stability.For example, if most moisture from rain evaporation is closer to the cloud base than to the surface (top-heavy profile), then the evaporationcooled air near the cloud base could mix with the surfacebased relatively warmer air more readily.This could potentially help with circulating the surface moisture to the cloud base and help the cloud stay intact.
In contrast, a bottom-heavy rain evaporation profile, where the maximum evaporation-produced moisture is concentrated close to the surface, could lead to a stable configuration.This is because the cooler air close to the surface is not invigorated to mix with the relatively warmer air close to the cloud base.This could inhibit any mixing or vertical https://doi.org/10.5194/acp-23-12671-2023Atmos.Chem.Phys., 23, 12671-12690, 2023 transport of moisture from the surface to the cloud base.Such profiles should be more susceptible to cloud dissipation and boundary layer decoupling and may promote the formation of cold pools.Examples of such top-and bottom-heavy profiles, with their relation to boundary layer stability are discussed in Paluch and Lenschow (1991).In this study, we have used the modeled F e profiles to differentiate between top-and bottom-heavy profiles.
To assess which of the 22 P3 cases is top heavy or bottom heavy, we have summed up F e values over the bottom 350 m (surface to 350 m altitude) and the top 350 m (350-700 m altitude) to obtain F top and F bottom , respectively.The ratio of F bottom /F top for all the cases is calculated (Fig. 9).F bottom /F top > 1 denotes bottom-heavy profiles and F bottom /F top < 1 top-heavy profiles.All of the cases on 4 February and one on 5 February, where most of the rain evaporated within 100 m from the cloud base, have F bottom /F top of 0-0.2 and are therefore top heavy.In total, 11 out of 22 cases have a top-heavy profile, making it more likely for these cloud layers to remain connected with the surface layer.
Next, we evaluate which microphysical conditions are more likely to generate a top-or bottom-heavy F e profile.Since the F e structure is dependent on the microphysical state at the cloud base, F bottom /F top should also be dependent on the microphysical parameters N 0 , D g , and σ .To demonstrate this here, we have determined the correlation of N 0 , D g , and σ at cloud base with F bottom /F top for each case (Fig. 9).A strong correlation is found between F bottom /F top and D g and σ .Comparatively, F bottom /F top and N 0 correlate weakly.This might be because the net effect of N 0 is canceled in the numerator and denominator of F bottom /F top .In all, over the 22 cases, the bottom-heavy sub-cloud profiles, which could be prone to cloud breakup and boundary layer decoupling, have higher values of D g and σ at the cloud base.Conversely, the top-heavy profiles that could facilitate more intact clouds and higher mixing with the surface layer have smaller D g and σ values at the cloud base.
A lower RH sf is also modeled to produce more top-heavy profiles (smaller F bottom /F top ), and vice versa (Fig. 9).This is because the lower the RH sf , the faster the evaporation rate of drops, leading to the accumulation of moisture and latent flux closer to the cloud base and thus a top-heavy profile.
In summary, high D g , σ , and RH sf are all linked to a bottom-heavy energy profile, and vice versa.This shows how the microphysical and thermodynamic parameters of the subcloud layer are associated with changing the vertical energy structure and potentially, therefore, affecting the sub-cloud stability.S1f, h).This is because a higher D g and σ value at the cloud base signifies an RSD with a high proportion of bigger raindrops that are more likely to reach the surface without completely evaporating.Conversely, smaller D g and σ at the cloud base have higher modeled REF, since smaller drops evaporate more efficiently, thus reducing the overall mass of the rain more.The influence of N 0 on REF is smaller compared to D g and σ (Fig. S1d).This is because when REF is expanded in terms of N 0 , D g , and σ values, the N 0 appears in the numerator and denominator and almost cancels out.

Microphysical and thermodynamic influence on
F eT , on the other hand, is strongly impacted by N 0 (and D g and σ ).This is because F eT is proportional to N 0 .
In short, while the influence of N 0 is not prominent in REF, its influence dominates F eT .Most of the P3 cases with higher D g and σ also have higher N 0 .Due to this, lower REF cases are mostly correlated with higher F eT .But in some cases, like on 9 February, D g and σ are small but N 0 is large, leading to large REF and large F eT .Similarly, two cases on 10 February have large D g and σ values but small N 0 , leading to small REF and small F eT .Overall, the link between REF and F eT may not be linear due to the underlying microphysical processes.More microphysical observations over shallow rain datasets are required to affirm this connection in a robust way.
b. Thermodynamic influence.The correlation of REF with RH sf is not as strong as with the microphysical parameters (Fig. S1a, b).But in a sensitivity study, where the microphysical parameters are fixed and RH sf is varied in 10 % interval jumps, a lower RH sf is correlated with higher REF (Fig. 10), and vice versa.Accordingly, change in RH sf is a contributing factor for the changing REF.
F eT also increases as RH sf decreases.As RH sf decreases and the sub-cloud layer becomes drier, the rate of change in drop size increases ( dD dz in Eq. 1).The sensitivity test suggests that for every 10 % increase in RH sf , F eT decreases by ≈ 2-6 Wm −2 .For 17 out of 22 cases, RH sf is between 67 % and 74 %.The remaining five cases are on 5 February and have higher RH sf values of 76 %-87 %.Holding the microphysical parameters constant, an increase in RH sf from 67 % to 87 % would decrease the REF and F eT by 60 % and 53 %, respectively.

F eT vs. F p,cb
A scatterplot between F p,cb and F eT is shown for 20 of 22 cases (Fig. 9a).The other two cases are from 9 February, where F p,cb values are higher than 500 Wm  The slope of F p,cb versus F eT shown in Fig. 9a is 0.63, indicating that on average 63 % of the rain mass sampled by the P3 has evaporated in the sub-cloud layer.The magnitude of F eT is between 15 and 352 Wm −2 for 9 out of 22 cases.This is analogous to 2-50 K d −1 of net evaporative cooling rate for the sub-cloud layer, which is estimated using δT δt = 1 H , with ρ a ,c p and H as the density of air, the heat capacity of dry air, and the cloud base height.This is comparable to a typical longwave radiative cooling rate over the marine boundary layer depth of 4-10 K d −1 and should therefore contribute significantly to the boundary layer energy budget in shallow convective environments where rain is present.The surface-based observations of δD p , δ 18 O p (Fig. S3), and d p (Fig. 11a) from Ron Brown, the BCO, and Meteor range between 0 ‰-20 ‰, − 2.5 ‰-1.2 ‰, and 4 ‰-18 ‰, respectively.δD p for the BCO is slightly smaller than for Ron Brown and Meteor, and the Meteor d value is slightly smaller compared to the BCO and Ron Brown.Overall, these values correspond well to those across other platforms during the EUREC 4 A and ATOMIC campaign (refer to Bailey et al., 2023).In particular, the rain sampled by Ron Brown shows surface rain rates of 1-5 mm h −1 at an average RH sf of 85 %.These values are higher compared to the average P3 rain rate and RH sf .The modeled d p values at the surface for the P3 cases are between −2 ‰ and 9 ‰ (Fig. 11b; blue line).Of these, the cases with RH sf values higher than 73 % have the higher d p between 3 ‰ and 9 ‰.These higher modeled d p cases overlap with some of the Ron Brown observations of 8 ‰-18 ‰.Moreover, when all P3 cases are run at an increased RH sf level of 85 % to replicate the Ron Brown thermodynamic conditions, the modeled surface d p value increases to 6 ‰-10 ‰ (Fig. 11b; red line).This finding is consistent with the idea that we would expect measurable rain with higher d p to reach the surface when RH sf is higher.

Rain evaporation analysis using rain isotope ratios
Similarly, the modeled d p also shifts closer to the Ron Brown values when the model is run at larger D g and σ values compared to the P3 ranges.Running the model at D g to 0.5 mm and RH sf of 85 %, and keeping σ within the P3 range (1-2.5), the modeled surface d p increases to 8 ‰-13 ‰ (Fig. 11b; yellow line).Furthermore, increasing σ to 3, along with D g and RH sf , also further increases the modeled d p to 14 ‰ (Fig. 11b; purple line).The choice of increasing σ to 3 is consistent with the upper range of σ during RICO (Fig. 4 in Geoffroy et al., 2014).
A higher D g and σ at the cloud base lead to a lower fraction of rain mass evaporation or lower REF.A lower REF then leads to less change in d p between the cloud base and surface and hence larger surface d p .The evaluation of the model outputs against the station observations also lends credibility to our model.These experiments demonstrate the strong thermodynamic and microphysical influence of the sub-cloud layer on the surface d p .Equivalently, the reliability of using d p as a metric for sub-cloud rain evaporation studies is also demonstrated.
Note that both δ p and d p values are independent of N 0 and only depend on D g and σ .This can explain why an "amount effect" (Dansgaard, 1964) is not always present in low-latitude isotopic datasets.The amount effect suggests that for a given rain sample, if the rain rate is high, then δ p should be low, and vice versa.However, this may not always hold true for all microphysical conditions.If N 0 is large and D g and σ values are small, then the rain rate could still be high due to its strong sensitivity to N 0 .But, due to the small D g and σ , the δ p will also be high.Similarly, if N 0 is small and D g and σ are large, then both the rain rate and δ p will be low.Consequently, the amount effect may not be appropriate for explaining all rain events, especially when the microphysical variability is pronounced.

Water vapor isotope ratio variations
Next, we assess whether raindrop evaporation during the P3 cases could cause a detectable isotopic change in the subcloud layer water vapor.The maximum simulated F e , associated with 9 February, was 0.7 Wm −2 m −1 , corresponds to a moisture flux of 3.1 × 10 −4 g m −3 s −1 ( F e L ).Over the course of a 15 min rain shower, and neglecting dilution or advection, this flux would cause a change in absolute humidity of about 0.3 g m −3 ( F e ×900 s L ).Since the measured absolute humidity on this day was 15 g m −3 , these results indicate that rain evaporation may have contributed 2 % to the moisture content of the sub-cloud layer.Given the observed δD v of −71 ‰ and the simulated δD e of 5 ‰, we can estimate the isotopic change in the sub-cloud layer water vapor due to raindrop evaporation from Eq. ( 11), which yields an isotopic change of 1 ‰.Since variations of 1 ‰ δD v are readily detectable with today's airborne water vapor isotopic analyzers, we surmise that the rain on 9 February should have caused a measurable shift in the water vapor isotope ratios of the subcloud layer.

Conclusions and discussion
This study evaluates shallow rain evaporation characteristics in the North Atlantic Ocean near Barbados using a onedimensional sub-cloud rain evaporation model initialized by observations from the EUREC 4 A and ATOMIC campaign.The focus is on 22 raining cases sampled by the P3, where the cloud base leg mean rain rates and RWC are between 0.01-31 mm d −1 and 0.0001-0.1 g m −3 , respectively.These cases show interesting variability in their sub-cloud rain evaporation characteristics and their dependence on the microphysical and thermodynamic state of the boundary layer.
The total rain evaporation flux (F eT ) over 22 P3 cases is modeled to be 15-352 Wm −2 , which is close to the 3 d mean 100 Wm −2 latent heat flux at 200 m altitude that was measured remotely from aboard R/V Maria S. Merian, another EUREC 4 A research vessel that sampled to the south of the P3 study region (Stevens et al., 2021).The F eT for the P3 cases are also comparable with estimates from ASTEX (42 Wm −2 ), RICO (130 Wm −2 ), and CSET (10-200 Wm −2 ).These differences and the variability, especially between the P3 cases and during RICO and CSET, are a result of differences in their RH sf , D g , σ , and N 0 values in the sub-cloud layer.
F eT of 15-352 Wm −2 over a 700 m deep sub-cloud layer is equivalent to 2-50 K d −1 of evaporative cooling.This is comparable to the typical stratocumulus cloud-top radiative longwave cooling (4-10 K d −1 ) and with the rain evaporation cooling rate at cloud base in the marine sub-cloud stratocumulus deck of 2-20 K d −1 (shown in Wood, 2005).This shows that shallow rain evaporation can contribute significantly to the local energy budget and sub-cloud cooling rates.
Depending on the vertical distribution and magnitudes of F e , the sub-cloud layer could be energetically top or bottom https://doi.org/10.In contrast, the other 11 cases that are top heavy accumulate moisture near the cloud base and are more prone to mixing with warmer air below.This could lead to a mixed boundary layer in which clouds could remain intact for longer.A follow-up modeling study is needed to confirm these processes and to see the degree to which the boundary layer stability depends on the representation of rain evaporation within the model.
A top-heavy F e profile is linked with lower D g and σ at the cloud base.This makes physical sense, since a lower D g and σ at the cloud base would mean that the raindrops are small and the RSD is narrow enough for the drops to evaporate closer to the cloud base.Conversely, a bottom-heavy F e profile is linked with higher D g and σ values due to the higher concentration of larger drops that reach the surface without evaporating completely.This emphasizes the influence of microphysical characteristics of rain at cloud base on the sub-cloud vertical F e profile.
Additionally, given the constant microphysical parameters at the cloud base, a top-heavy F e profile is also linked with lower RH sf values.This is because lower RH sf increases the rate of rain evaporation, especially for smaller drops, facilitating more accumulation of moisture close to the cloud base.In contrast, higher RH sf favors bottom-heavy F e profiles.This depicts the influence of thermodynamic conditions, in addition to microphysical conditions, in modulating the vertical rain evaporation flux distribution.
The model also shows that, on average, 63 % of the rain mass evaporated in the sub-cloud layer for 22 P3 cases.Most of these cases with higher REF are associated with smaller D g , σ , and RH sf values, and vice versa.However, the effect of RH sf on REF is lower compared to D g and σ .
Moreover, if N 0 , D g , and σ values are all large, then F eT tends to be large and REF small, as seen for most of the 22 P3 cases.However, there are cases when D g and σ are large but N 0 is small.This leads to small F eT and small REF.A few cases also have small D g and σ but large N 0 values, resulting in fairly large F eT and large REF.Effectively, therefore, the fraction of rain evaporated (or REF) and the amount of rain evaporated (or F eT ), are more intrinsically dependent on the RSD microphysical parameters rather than on the bulk RWC itself.
In terms of the rain isotopic composition, our results show that sub-cloud conditions with higher RH sf , higher D g , and σ values are prone to higher surface d p .This is because a higher RH sf and higher cloud base D g and σ lead to less evaporation of raindrops and low REF and, thereby, smaller changes in d p between the cloud base and the surface.In general, the REF varies linearly with the fractional change in d p between the cloud base and the surface (or 1 − d p,sf /d p,cb ).Isotope differences in the rain between the cloud base and the surface thus provide an independent measure of REF.
The model results also suggest why the amount effect or a negative correlation between rain rate and δ p is not always found in low latitudes.It is a result of the underlying microphysics of the RSD.If the high rain rate is due to large D g and σ values, then the δ p should be low due to the small REF.In contrast, if the rain rate is high because of high N 0 and small D g and σ values, then δ p should be high due to high REF.This is especially relevant for shallow rain regimes where microphysics play a significant role in determining rain characteristics.
In general, our isotope-initialized microphysics-resolved model performs reliably well in characterizing the sub-cloud rain evaporation in the shallow rain regime sampled during the ATOMIC and EUREC 4 A campaign.This model also only requires in situ microphysical and rain isotope observations and is independent of any remotely sensed rain observations.However, a comparison between rain evaporation evaluated from remote-sensing platforms (e.g., millimeter wavelength radars) and our in-situ-based model could be useful for suitable error analysis.
The results from the model emphasize the role of microphysical and thermodynamic processes in accurately simulating sub-cloud rain evaporation.The variability in the modeled rain evaporation fluxes across 22 P3 cases also highlights the need for more samples in similar shallow cloud regimes for a more robust statistical interpretation that could be used to evaluate general circulation model (GCM) parameterizations.The model also provides an opportunity to extend the rain evaporation study from other field campaigns conducted over different ocean basins and different seasons, which is crucial for a wider understanding of sub-cloud rain processes.
Author contributions.MS and AB designed the study.MS performed the analysis and wrote the paper.AB, PB, SPdS, DN, and EQM revised the paper and provided useful feedback on the figures and text.EQM processed the Ron Brown isotope datasets.MDL and PYC collected all of the P3 microphysical datasets.MDL stitched the CIP and PIP microphysical datasets for all of the flights.
Competing interests.The contact author has declared that none of the authors has any competing interests.
Disclaimer.Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements.This material is based upon work supported by the National Center for Atmospheric Research (NCAR), which is a major facility sponsored by the National Science Foundation (NSF).The research conducted by MS was sponsored by the Advanced Study Program (ASP) at NCAR.We acknowledge the entire team of ATOMIC and EUREC4A for collecting and processing the data from all the platforms used in this study.We thank the two internal reviewers at NCAR, Lisa Welp, and three anonymous referees for their thoughtful comments.
Financial support.This research has been supported by the NSF (grant no.1852977).The support for the EUREC4A isotopic campaign has been provided by the NSF (grant no.1937780).Peter Blossey's contribution to this work has been supported by the NSF (grant no.AGS-1938108).
Review statement.This paper was edited by Yuan Wang and reviewed by Lisa Welp and three anonymous referees.

Figure 1 .
Figure 1.Schematic showing rain from a cumulus-topped boundary layer, with the latent and sensible heat fluxes near the surface.The longwave and shortwave fluxes and free-tropospheric entrainment mixing are shown at the cloud top.Rain can evaporate completely or partially as it falls toward the surface.This could lead to differences in the vertical profiles of the rain evaporation fluxes depicted by the solid vertical curves.Complete evaporation of rain could cause the maximum rain evaporation flux close to the cloud base (top heavy) compared to partial evaporation, which could bring the maxima closer to the surface (bottom heavy).A 1 mm d −1 rain rate can potentially produce 28 Wm −2 of a rain evaporation flux.The aircraft measurements are made at horizontal above-cloud, in-cloud, cloud base, and near-surface legs, as shown by airplane cartoon and the dashed red line trajectories.

Figure 2 .
Figure 2. P3 trajectory on 9 February (a) in time-altitude axes and (b) in longitude-latitude axes, with contour colors showing the altitude (in meters) of the P3.The red lines in panel (a) denote the legs with mean rain rates greater than 0.01 mm d −1 that are selected for this study.Numbers in panel (b) denote the surface relative humidity in a fraction of 1 over the dropsonde locations.

Figure 3 .
Figure 3. Raindrop size distribution is shown for 10 min horizontal legs on (a) 4, (b) 5, (c) 9, and (d) 10 February.The legend shows the altitude of the horizontal legs, dropsonde-derived surface relative humidity, and leg mean rain rates.

Figure 4 .
Figure 4.The 94 GHz radar reflectivity (in dBZ) on board the P3 on 9 February pointing downwards for all the six horizontal level legs shown in Fig. 2. The red line is the flight trajectory, and the contour shade represents the radar reflectivity.

Figure 5 .
Figure 5. (a) N 0 , (b) D g , (c) σ , and (d) RH sf are scattered against 10 min leg mean rain rates for 22 cases observed by the P3.Red circles show the cases sampled at 700 ± 100 m altitude, and black circles are cases sampled at altitudes higher than 800 m.Blue circles are for the CSET campaign obtained from Sarkar et al. (2020).Only the average D g and σ over five CSET cases were available and are shown by single dots in panels (b) and (c).N 0 and RH sf were available for five cases during CSET and are shown in panels (a) and (d).The correlation coefficients (r) and p value are mentioned in all figures.

Figure 6 .
Figure 6.Lognormally fitted 1 Hz rain parameters (a, e, i, m) N 0 , (b, f, j, n) D g , and (c, g, k, o) σ and (d, h, l, p) rain rates are depicted as box plots for all 22 cases on (a-d) 4 February, (e-h) 5 February, (i-l) 9 February, and (m-p) 10 February.The box plots denote the 25th, 50th, and 75th percentiles.The minimum and maximum extents of the whiskers denote the minimum and maximum data points that are not outliers.Outliers are shown with red plus signs (+).Outliers are considered data points outside the ±2.7× standard deviation and 99.3 % coverage.

Figure 7 .
Figure 7. Modeled (a) N 0 , (b) D g , (c) σ , (d) RWC, (e) rain rate, (f) F e , (g) δ 18 O p , (h) δD p , and (i) d p vs. height for all 22 P3 cases.The cases on 4, 5, 9, and 10 February are shown with red, blue, green, and black lines, respectively.The modeled RSD is averaged over every 50 m vertical length and then fitted using a lognormal distribution to obtain smooth N 0 , D g , and σ vertical profiles.

Figure 8 .
Figure 8. Modeled REF (= F eT /F p,cb ) scattered along the fraction of change in d p between the cloud base and surface (1−d sf /d cb ) for 21 out of 22 P3 cases, where the rain reaches the surface after partial evaporation.Circle color codes are red, blue, green, and black for 4, 5, 9, and 10 February, respectively.The black line represents a linear fit of y = 0.59x +0.18, with a correlation coefficient (r) of 0.62 and p value of 0.07.Note that the 4 February cases (red circles) have REF smaller than 1.The x-axis values higher than 1 are for cases where d cb is positive but d sf is negative, causing 1 − d sf /d cb to be higher than 1.

F
eT and REF REF in the sub-cloud layer is useful for determining the amount of rain reaching the surface and for formulating the amount of F eT .F eT , on the other hand, is an estimate of the column total rain evaporation flux generated in the sub-cloud layer that could indicate the average evaporative cooling rate of the sub-cloud layer.Both REF and F eT depend on the microphysical and thermodynamic processes in the cloud and sub-cloud layer, as shown by the following model results.a. Microphysical influence.REF is a strong function of D g and σ (correlation coefficient = −0.7 and −0.8, respectively).The higher the D g and σ value at the cloud base, the smaller the REF (Fig.

Figure 9 .
Figure 9. (a) Rain flux at cloud base (F p,cb ) is scattered against the column total sub-cloud rain evaporation flux (F eT ).Only 20 out of 22 cases are shown, excluding the highest two cases on 9 February, with F eT above 300 Wm −2 .The 4, 5, 9, and 10 February cases are shown in filled red, blue, green, and black circles, respectively.The blue line is the slope through all 22 cases and is 0.63.The dashed black line is the one-to-one ratio line for reference.The F bottom /F top ratio is plotted with (b) N 0,cb , (c) D g,cb , and (d) σ cb .F top and F bottom are the summation of F e over 350-700 and 0-350 m, respectively.F bottom /F top higher than 1 denotes bottom-heavy cases, and F bottom /F top less than 1 denotes top-heavy cases, as shown with the gold font.
δD p and δ 18 O p 3.4.1 Modeled δD p , δ 18 O p and d p for the P3 cases Changes in δD p , δ 18 O p , and d p are modeled for all 22 P3 cases (Fig.7g-i).As rain evaporates in the sub-cloud layer, the modeled δD p and δ 18 O p increase, and d p decreases towards the surface.The decrease in d p is caused by the preferential evaporation of D in the water molecule, owing to their lower mass, higher vapor pressure, and larger diffusivity compared to 18 O, leaving the rain less enriched in δD p compared to δ 18 O p .The P3 cases with the higher modeled surface d p have either high RH sf (> 75 %), large D g and σ (compared to average P3 values), or both.The model also shows a positive correlation between the fractional change in d p from cloud base to the surface (1 − d p,sf /d p,cb ) and REF for 22 P3 cases (Fig.8).This is logical, since a small REF suggests a smaller fraction of rain mass evaporation, which would correspond to a smaller change in d p from the cloud base to the surface.3.4.2Comparison of model results with surface δD p , δ 18 O p , and d p observations

Figure 11 .
Figure 11.(a) Histograms of surface d p (d sf ) observed by Ron Brown (red), Meteor (yellow), and BCO (blue).(b) Histograms of modeled surface d p for all the P3 cases run at observed cloud base D g (0.16-0.26 mm), σ (1.2-2.4),d p (7 ‰-15‰), and RH sf (66 %-87 %; where blue is the default condition).Histograms of the P3 cases run at default D g , σ , and d p levels but at RH sf of 85 % (red).Histograms of the P3 cases run at default σ and d p levels but at RH sf and D g of 85 % and 0.5 mm, respectively (yellow).Histogram of modeled d sf at cloud base D g , σ , d p , and RH sf of 0.3 mm, 3 ‰, 14 ‰, and 85 %, respectively (purple).
5194/acp-23-12671-2023 Atmos.Chem.Phys., 23, 12671-12690, 2023heavy and potentially influence the boundary layer stability through downdrafts or decoupling.In total, 11 out of 22 cases have most of their rain evaporated closer to the surface.This bottom-heavy configuration should inhibit mixing with the warmer air near the cloud base and therefore should aid the boundary layer in decoupling faster.This could also facilitate cold-pool formation.