Better understanding how convective processes impact the isotopic composition of atmospheric water has implications for understanding phenomena such as squall lines or tropical cyclones, and for reconstructions of past rainfall extreme events. With this motivation, we implemented water stable isotopologues (HD16O and H218O) in the non-hydrostatic mesoscale atmospheric model Meso-NH and its one-moment bulk mixed-phase microphysics scheme. The water stable isotopologues are subject to the same dynamical and physical processes as the light water, but undergo isotopic fractionation during water phase changes. Both equilibrium and kinetic fractionation processes that occur during water phase changes involving water vapor are taken into account. The implementation is validated on a test case of a 2D simulation of a tropical squall line observed in June 1981 during the COPT 81 field campaign in the Sahel region. The isotopic version of Meso-NH (Meso-NH-ISO) captures the expected evolution of the isotopic composition of both precipitation and water vapor along the squall line. This work opens the door to future isotopic studies using realistic cases of mesoscale convective systems (squall lines, tropical cyclones).
Agence Nationale de la Recherche24-CE01-6978Introduction
The isotopic composition of water vapor and precipitation (deuterium and oxygen-18) is a useful tool to better understand convective processes in the present-day water cycle, such as the contribution of rainfall evaporation to the moistening of the lower troposphere or the contribution of convective detrainment and sublimation of ice crystals to the moistening of the upper troposphere and lower stratosphere .
The isotopic composition of precipitation recorded in climate archives has also significantly contributed to the reconstruction of past changes in precipitation in tropical regions . This is based on the observation that precipitation is more depleted when precipitation rate is larger, called the amount effect . Convective processes, such as convective downdraft, mesoscale descent, rain evaporation below cloud, and rain melt under stratiform clouds, contribute to the amount effect . Since these processes are expected to vary with the organization and characteristics of tropical convection, the water isotopic composition also depends on the proportion of stratiform versus convective rain , on the mesoscale organization of convection or on the convective depth .
All these applications of water stable isotopologues observations require a better understanding of how convective processes impact the isotopic composition of water vapor and precipitation. A large number of modeling studies have relied on models with parameterized convection e.g., but these models are limited by the shortcomings and uncertainties associated with the parameterization of convection . To explicitly resolve convective motions, we need models that resolve the non-hydrostatic equations of motion at a resolution of the order of the kilometer or finer, such as cloud-resolving models or large-eddy simulation models. Several such models have been implemented with water stable isotopes in the past few years. The DHARMA cloud model integrates the evolution of HD16O within a bin microphysics scheme explicitly representing cloud condensation nuclei, water droplets, and ice crystals using 16 mass bins, as described by . The 2-moment bin mixed-phase microphysics scheme DESCAM has recently been extended to simulate the evolution of oxygen-18 within a 1.5D dynamical framework . Such bin microphysics schemes are undoubtedly an advantage for accounting for different isotopic compositions depending on particle size, but it comes at a very high computational cost. Thus, DHARMA and DESCAM typically track only one water stable isotopologue in addition to light water species. On the other hand, numerical models employing bulk microphysics schemes usually simulate the evolution of both HD16O and H218O. This includes models such as SAM-ISO , COSMO-ISO , WRF-ISO , and, more recently, NICAM-WISO . All these models incorporate the evolution of the two isotopologues into a bulk microphysics scheme. The microphysics schemes in SAM-ISO, WRF-ISO, and NICAM-WISO typically describe the evolution of water vapor, cloud water, rain, cloud ice, snow, and graupel mass. However, graupel is not considered in COSMO-ISO.
Here, we implemented water stable isotopologues in the non-hydrostatic atmospheric model Meso-NH . This model is flexible enough to be used for idealized simulations, realistic case studies or global simulations, and can deal with scales ranging from synoptic to large eddy scales. In the past few years, it has taken part in various model intercomparison projects, such as RCEMIP or DYAMOND . Its physical package can also be shared with the LMDZ general circulation model and can be used in the non-hydrostatic version of the icosahedral DYNAMICO model . Our ultimate goal is to simulate realistic case studies with various mesoscale convective systems, including tropical cyclones and squall lines. In the meanwhile, a first step is to implement water stable isotopologues in Meso-NH. The goal of this article is to describe this implementation, and to validate it on a simple case. The Meso-NH model and its one-moment microphysical scheme are shortly described in the first section. The second section is dedicated to the description of the newly implemented water isotope scheme in Meso-NH. In a third section, first results from a 2D simulation of a Sahelian squall line observed during the COPT 81 field campaign are presented.
The Meso-NH model
The water stable isotopologues scheme described in Sect. is implemented in version 5-5-0 of the Meso-NH model, and is coupled to the one-moment bulk microphysics scheme ICE3,.
Short overview of Meso-NH
Meso-NH is a non-hydrostatic mesoscale atmospheric model . It enables simulating atmospheric phenomena from the small-scale (down to a few meters) to the synoptic-scale (up to several tens of kilometers). A large set of physical parameterizations are available for convection , cloud microphysics , turbulence , aerosols , and radiation . Meso-NH can be coupled with the surface modeling platform SurfEx that accounts for natural land surface, urbanized areas, lakes, and oceans. Thus, Meso-NH offers a perfect setting for any simulation of physico-chemical processes in the atmosphere. The reader is referred to for a more complete description of Meso-NH capabilities for a range of Earth system prediction applications.
The ICE3 microphysics scheme
ICE3 is a bulk mixed-phase one-moment microphysics scheme that predicts the mass mixing ratio r of six water species (water vapor, cloud water, raindrops, primary ice crystals, snow aggregates, and graupel). For any species, the mixing ratio is the mass of the species divided by the reference mass of dry air ρa.
For cloud droplets, the total number concentrations (Nc) is fixed at 300×106m−3 over land and 100×106m−3 over oceans. For pristine ice, the total number concentration Ni is diagnosed based on the parameterization of heterogeneous nucleation. The concentration of the precipitating particles (raindrops, snow/aggregates and graupel) is parameterized according to , with the total number concentration given by N=Cλx. C and x are empirical constants deduced from observations (see Table ). λ is the slope parameter of the particle size distribution. In ICE3, the particle size distribution is assumed to follow a generalized Gamma distribution:
n(D)=Ng(D)=NαΓ(ν)(λD)ανD-1e-(λD)α
where D is the diameter of the particle, g(D) the normalized generalized Gamma distribution and Γ() the Gamma function. α and ν are free shape parameters; their values are given in Table . The pth moment of the law writes:
M(p)=∫0∞Dpg(D)dD=1λpΓ(ν+p/α)Γ(ν).
Set of parameters used to characterize each hydrometeor category in the ICE3 microphysics scheme
ParametersCloud dropletsRaindropsPristine iceSnow/aggregatesGraupelα3 on sea; 1 on land1311ν1 on sea; 3 on land1311a5245240.820.0219.6b332.51.92.8c3.2×1078428005.1124d20.810.270.66C–8×106–55×105x–-1–1-0.5f0–110.860.86f1–0.26–0.280.28f2––0.14––C1–0.51/π1/π0.5
It is also assumed that the mass (m) and terminal fall speed (v) of hydrometeors are related to the particle diameter D following power laws:
m(D)=aDb
and
v(D)=cDdρ0ρa0.4
where a, b, c and d are constants given in Table . ρ0 is the reference air density at the surface. Then the mixing ratio is defined by:
r=∫0+∞m(D)n(D)dD=aNM(b)
while the slope parameter of the particle size distribution writes:
λ=ρarΓ(ν)aNΓ(ν+b/α)-1/b.
Each type of hydrometeor has one or more initiation and growth processes as shown in Fig. . Warm-phase processes are based on the scheme. Raindrops are formed by autoconversion of cloud droplets (AUT), grow through accretion of cloud droplets (ACC), and can evaporate (EVA). Pristine ice crystals are initiated through heterogeneous nucleation (HEN) or by homogeneous nucleation (HON) when the temperature is below -35 °C. These ice crystals grow by deposition (DEP) and through the Bergeron-Findeisen process (BER). Snow/aggregates are formed by autoconversion of pristine ice crystals (AUT), then grow by aggregation of ice crystals (AGG) and by light riming due to collection of cloud droplets (RIM) or to accretion of raindrops (ACC). Then graupel are formed by heavy riming of snow (RIM and ACC) or by contact freezing of ice crystals on raindrops (CFR). They further grow by dry and wet growth mode (DRY, WET). Snow/aggregates and graupel can grow or ablate by water vapor deposition (DEP) or sublimation (SUB). When the temperature drops below 0 °C, ice crystals are immediately transformed into cloud droplets (MLT). Snow/aggregates are converted progressively into graupel particles that melt while falling. The fast vapor exchanges with cloud droplets (CND/EVA) and pristine ice crystals (DEP/SUB) are treated using an implicit adjustment scheme.
Diagram of the microphysical processes of ICE3. Red arrows show processes involving isotopic fractionation.
The time-step dependency in the original ICE3 scheme is suppressed according to . To eliminate time-step dependency, key modifications include integration of heat budgets to constrain physical processes (e.g., melting) and to fix flawed calculations (e.g., snow-to-graupel conversion). Other adjustments include graupel growth modes (dry/wet), continuous cloud droplet shedding, and symmetric hail/graupel processes, reducing time-step biases. For large time steps (>10s), time-splitting enables more frequent process interactions. These changes significantly reduce time-step dependency with a modest computational overhead see Appendix B in.
Formulation of water stable isotopologues in Meso-NH-ISOWater stable isotopologues variables
The introduction of water isotopologues into Meso-NH was achieved using a similar approach to previous studies in the development of isotopic models e.g.. Analogously, the original water prognostic variables in the model are taken to represent the most common standard light water, H216O. To integrate heavy isotopes in Meso-NH, prognostic variables and equations describing the water cycle of each isotopologue are introduced into the model. As for light water, the mass mixing ratio of each heavy water isotopologue (riso) for each water species is a prognostic variable of the model. In practice, each water variable for light molecule H216O is duplicated for heavy molecules HD16O and H218O. Therefore 12 additional variables are tracked in the model. These additional variables are subject to the same physical processes as the light water variables, and evolve according to:
∂∂t(ρariso)+∇⋅(ρarisoU)=ρaSiso
where U is the 3D air velocity. The source term Siso includes the turbulent diffusion, the sedimentation by gravity, the microphysical evolution of the particles, and their isotopic fractionation if any. The equations for the source term are given in Sect. for non-fractionating processes, and in Sect. for fractionating processes. The introduction of water isotopologues in Meso-NH does not interfere with any of the model physics or dynamics. We checked that the model results before and after the introduction of isotopologues are exactly the same.
During the post-processing of model outputs, several diagnostics are computed. The water content in heavy isotopes (HD16O or H218O) is expressed as:
δ=RRVSMOW-1
where R stands for either RD or R18O, and VSMOW is the Vienna Standard Mean Ocean Water. RD and R18O are defined as the ratio of deuterium over hydrogen atoms and of 18O over 16O atoms in the water, respectively. The isotope ratio R is thus defined for each water species as riso/r. Although δ is dimensionless, in what follows, δ from Eq. () is multiplied by 1000 to express it in ‰, the common unit.
To first order, δD variations in water phases are 8 times those in δ18O. However, slight deviations in δD-δ18O slopes occur and are mainly due to kinetic effects such as evaporative effects. The later can be quantified by deuterium excess (d-excess) defined as follows :
d-excess=δD-8×δ18O.
It is computed for each hydrometeor, and reflects the diffusivity differences between H218O and HD16O. As a result, when rain evaporation takes place deuterium excess in precipitation decreases.
Non-fractionating processes
The mass exchange of heavy isotopes during microphysical processes not involving isotopic fractionation is proportional to their relative mass mixing ratio in the reservoir from which the flux comes from. Thus, for each microphysical process without isotopic fractionation, the mass transfer rate for heavy water (Δriso) is proportional to the mass transfer rate calculated for standard water provided by the microphysics scheme (Δr). For example, during the accretion of cloud droplets by snow (ACC), the mass mixing ratio transfer rate for HD16O and H218O writes:
ΔrisoACC=ΔrACC×risor.
Microphysical processes that do not involve any phase changes do not fractionate, such as processes converting cloud droplets to rain (autoconversion of cloud droplets AUT, growth of raindrops by accretion of cloud droplets ACC) or ice crystals to snow (autoconversion of ice crystals to snow AUT, growth of snow by aggregation of ice crystals AGG). Some microphysical processes involving phase changes are also assumed not to fractionate. For example, when cloud ice melts into cloud droplets (MLT), we assume total melt of each ice crystal, so that there is no fractionation. The same rationale applies for all processes between snow, rain and graupel (MLT, RIM, HON).
Concerning the Bergeron process (BER), we assume it does not fractionate. The Bergeron process is the evaporation of cloud droplets followed by the ice deposition in mixed-phase clouds, when the air is subsaturated with respect to liquid and supersaturated with respect to ice. Since ice deposition in supersaturated conditions is associated with kinetic fractionation, the Bergeron process is often assumed to fractionate . When the Bergeron process is at play in convective updrafts, it acts to enrich the vapor and decrease its d-excess at altitudes above the 0 °C isotherm . In ICE3, the mass transfer rate from cloud droplets to ice crystals is assumed to equal the water vapor deposition rate onto pristine ice crystals, which in turn equals the cloud droplets' evaporation rate. This keeps the water vapor reservoir neutral. Therefore, we ignore fractionation during the Bergeron process, as in . Due to this assumption, we may slightly overestimate the isotopic depletion and the d-excess in the upper troposphere. This is not an issue for science applications focusing on surface precipitation or low-level water vapor, but future refinements might be required for applications in the upper-troposphere.
Fractionating processes
Isotopic fractionation occurs due to differences in mass and symmetry between the different water molecules. Molecular mass differences induce equilibrium fractionation. Due to a lower saturation vapor pressure for heavy isotopes, the heavier molecules concentrate in the condensed phase. Additionally, kinetic fractionation is induced by diffusivity differences, with a lower diffusivity of heavy isotopes. Then, in order to provide a comprehensive understanding of the distribution of isotopes in water and of the related physical processes, it is necessary to take into account both equilibrium and kinetic fractionation processes that occur during water phase changes.
The following sections explain how isotope fractionation processes are incorporated into Meso-NH. Logic variables controlling the code segments of the model that account for isotopic fractionation can be enabled or disabled to simplify sensitivity analysis, as used by .
Condensation and evaporation of cloud water
In the ICE3 microphysics scheme, as in most one-moment bulk microphysics scheme, the parameterization of the condensation/evaporation processes consists of a saturation adjustment aimed at restoring the thermodynamic equilibrium between water vapor and cloud droplets. Since the equilibration time for small droplets is normally of the order of seconds, an equilibrium approach may also be used for heavy isotopes . Thus, the isotopic fractionation that occurs during droplet condensation within the cloud is considered to be at equilibrium , and the differences in molecular diffusivity between the molecules are not taken into account.
At equilibrium:
Rc=αl/v×Rw
where Rc and Rw are the isotopic composition of cloud droplets and water vapor, respectively, and αl/v is the isotopic equilibrium fractionation factor over liquid. Then if the water variables are advanced by one model time step:
rciso+ΔrisoCND/EVArc+ΔrCND/EVA=αl/v×rviso-ΔrisoCND/EVArv-ΔrCND/EVA.
Given B=rc+ΔrCND/EVArv-ΔrCND/EVA, Eq. () leads to:
ΔrisoCND/EVA=αl/vrvisoB-rciso1+αl/vB.
Cloud droplets evaporation is also treated in Eq. () when ΔrCND/EVA is negative; it is also assumed to be at equilibrium.
Rain evaporation
For raindrops, due to their larger size, the isotopic equilibrium assumption is not valid, and the mass transfer between the drop and the surrounding vapor must be modeled explicitly. In Meso-NH, the evaporation rate of a raindrop is derived following and , and the rate of change of a raindrop mass (mr) finally writes
dmrdtEVA=4πC1DfSlAw-1
where D is the raindrop diameter, f the mean ventilation coefficient, C1 the parameter of the capacitance-diameter relationship (see values in Table ), and Sl the supersaturation over liquid water. Aw is a thermodynamic function that writes
Aw=RvTesw(T)Dv+Lv2kaRvT2
with Rv the specific gas constant for water vapor, esw(T) the saturation vapor pressure at the ambient temperature T, Lv the latent heat of vaporization, and ka the heat conductivity of air. Dv is the molecular diffusivity of light water vapor in air. As established by for temperatures between -80 and 40 °C, it follows:
Dv=0.211×10-4TT01.94p0p
with p the pressure, T0=273.15K and p0=1013.25Pa.
The mean ventilation coefficient f is parameterized following :
f=f0+f1χ+f2χ2
where χ=NSc,v1/3NRe1/2, and f0, f1 and f2 are ventilation coefficients whose values follow and are given in Table . NSc,v is the Schmidt number for water vapor; it is set to 0.63. NRe is the Reynolds number of the flow around a particle of diameter D:
NRe=v(D)Dν(T)=v(D)Dρaη(T)
with ν(T) the kinematic viscosity of air, and η(T) (Pas) the dynamic viscosity of air which can be approximated by η(T)=1.718×10-5+0.0049×10-5(T-T0).
To get the mass mixing ratio rate of change for raindrops, Eq. () is integrated over the whole size distribution
ΔrrEVA=1ρa4πC1SlAw-1∫0∞D(f0+f1χ+f2χ2)⋅n(D)dD.
By replacing the Reynolds number with its expression in χ and substituting the expression for v(D) from Eq. ()
χ=NSc,v1/3×ρ0ρa0.2ρacDd+1η(T)1/2.
If c′=NSc,v1/3×ρ0ρa0.2ρacη(T)1/2, the expression of χ=c′Dd+12 is introduced in Eq. (). Using the definition of the pth moment of the size distribution law (Eq. ), the variation in raindrop mixing ratio during evaporation is
ΔrrEVA=1ρa4πC1SlAw-1N[f0M(1)+f1c′Md+32+f2c′M(d+2)].
Assuming f2=0 for raindrops (Table ) in Eq. , the mixing ratio transfer rate for evaporating raindrops is
ΔrrEVA=1ρa4πC1SlAw-1N[f0M(1)+f1c′Md+32].
For H218O and HD16O isotopologues, Eq. (14) writes:
dmrisodtEVA=4πC1DDvisofisoρwiso-ρw,Diso
with miso the mass of a raindrop of diameter D containing heavy isotopes, and ρwiso and ρw,Diso eq the density of heavy water vapor for the environment and on the surface of the raindrop, respectively. The molecular diffusivity of the heavy molecules Dviso is deduced from the molecular diffusivity of standard water, H216O, with the ratio of the diffusivity coefficients Dviso/Dv obtained from the experiments of for H218O and HD16O. fiso is the mean ventilation factor for heavy water: fiso=f0+f1χiso+f2χiso2 with χiso=(NSc,viso)1/3NRe1/2. The same f0, f1 and f2 parameters as for light water are used (Table ). However, the Schmidt number is scaled with the specific molecular diffusivity of the heavy molecules: NSc,viso=NSc,v×Dv/Dviso. Using the same reasoning as for light water to derive the variation in mass of an evaporating raindrop of heavy isotope water, the rate of change of a raindrop containing heavy isotopes is
dmrisodtEVA=4πC1DDvisofisoesw(T)RvT⋅[Rw(Sl+1)-Rlαl/v⋅1+Lv2RvkafisoDT2dmrdtEVA]
with Rw and Rl the isotope ratio in water vapor and liquid condensate, respectively, and αl/v=Rl/Rw the isotopic equilibrium fractionation factor between liquid and vapor. This equation can thus be integrated over the raindrop size distribution to get the evolution of the raindrop mixing ratio for heavy isotope water
ΔrrisoEVA=1ρa4πC1Dvisoesw(T)RvTN⋅[Rw(Sl+1)-Rlαl/v⋅f0M(1)+f1c′isoMd+32+Rlαl/vLv2RvkaT2ρaΔrrEVA]
with
c′iso=(NSc,viso)1/3×ρ0ρa0.2ρacη(T)1/2=c′DvDviso1/3.
Since ICE3 is a bulk microphysics scheme, diffusion and kinetic effects are not explicitly treated for each particle size. In Eq. (), the bulk effect of particle size is expressed in M(1) and M((d+3)/2) (see Eq. ). A high slope parameter of the size distribution λ means a narrow particle size distribution and numerous small particles. On the contrary, a low λ means a large size distribution and presence of large particles. For large raindrops, the ventilation effect increases e.g., and it is expected to be further amplified for a raindrop containing heavy isotope water (Eqs. and ).
Diffusional growth of ice hydrometeors
For ice particles, an equation similar to the one for liquid particles (Eq. ) is derived in the ICE3 scheme:
dmdtDEP=4πC1DSiAi-1f
where Si the supersaturation over ice, which is explicitly calculated by the microphysical scheme as Si=rv/rsi-1. rsi is the saturation vapor mixing ratio over ice: rsi(T)=Mvesi(T)/[Md(p-esi(T))], with p the pressure (Pa), esi(T) the saturation vapor pressure over ice (Pa) at ambient temperature T, and Mv and Md the molar mass of water vapor and dry air (kgmol-1), respectively. Ai is a thermodynamic function that writes
Ai=RvTesi(T)Dv+Ls2kaRvT2
with Ls the latent heat of sublimation (Jkg-1).
In the case of heavy isotopes, the same approach as in SAM-iso is followed. By analogy with the evaporation of rain, the rate of change of the mass of a precipitating ice particle can write:
dmisodtDEP=4πC1DDvisofisoesi(T)RvT⋅[Rw(Si+1)-Riαi/v⋅1+SiAi-1Ls2RvkaT2]
with Ri the isotope ratio in ice, and αi/v the equilibrium fractionation factor between ice and water vapor. Due to the low diffusivity of heavy isotopes, it is assumed that water vapor interacts with a thin layer at the surface of ice particle during deposition. Then the ratio riso/r in the outer layer can be approximated by the ratio (ΔrisoDEP/ΔrDEP) at the surface of ice particle. Therefore, the isotope ratio in ice also writes
Ri=ΔrisoDEPΔrDEP.
Using Eq. () in Eq. () to eliminate C1, one finally get
ΔrDEP=αi/vαKRwΔrDEP
where αK is the kinetic fractionation coefficient defined by :
αK=(1+F)(Si+1)αi/vfDvfisoDvisoSi+1+F(Si+1)
with F=DvLs2esi(T)kaRv2T3. neglected the influence of ventilation for water vapor deposition on ice crystals. In their appendix, they computed the f/fiso ratio for columnar ice crystals: it is a decreasing function of the length of the column, but with values very near to 1. Here, for small ice crystals, the f/fiso ratio is 1, while for larger particles, this ratio decreases, leading to a slight enhancement of αK.
Sublimation of ice, snow and graupel particles is assumed to occur without isotopic fractionation. As in previous studies , it is assumed that the mass transfer rate for heavy water (Δriso) associated with sublimation is proportional to the mass transfer rate calculated for standard water and provided by the microphysics scheme (ΔrSUB) ratio equal to its mean ratio
ΔrisoSUB=risor×ΔrSUB
where r and riso are the mixing ratio of ice, snow or graupel for H216O, and H218O or HD16O, respectively.
Simulation of a 2D Sahelian squall lineThe West African squall line on 23–24 June 1981 during COPT 81
We tested Meso-NH-ISO with a 2D simulation of a West African squall line that occurred during the night of 23 to 24 June 1981 in the northern Ivory Coast (5°37′ W, 9°25′ N). This tropical squall line was extensively observed by several radars, soundings and a network of surface observations as part of the COPT 81 field campaign and simulated in different 2D and 3D numerical experiments . This case was chosen because a previous simulation was done with a 2D version of Meso-NH and successfully reproduced the major observed features. In short, the radar observations clearly identified an intense convective region, a well-developed stratiform part with a forward anvil cloud, and the transition zone in between . Specifically, the squall line exhibited in its convective part a line of short-lived convective cells that fastly propagated (around 50 kmh-1) toward the south-east. In the stratiform region, a trailing anvil cloud developed above 6 km. estimated that 80 % of precipitation occurred in the convective region, whereas the rest occurred in the stratiform region. They also roughly estimated substantial evaporation of rain in the stratiform region below the anvil cloud (around 40 % in mass). A density current of cold air in the stratiform region induced a low-level frontward flow that initiated and maintained updrafts in convective region. We also chose to test Meso-NH-ISO with a squall line simulation due to the isotopic observations available in both water vapor and precipitation in the West African region during such events, and idealized simulations of such events in previous studies .
Simulation set-up
The horizontal axis is composed of 320 grid-points with a horizontal grid spacing of 1.25 km. The vertical grid contains 46 levels up to an altitude of 22 km, with a grid spacing varying from 70 m on the ground to 700 m at the top of the domain.
The simulation is initialized following . The atmosphere is initially homogeneous and the initial sounding for temperature and humidity comes from . The isotopic composition of water vapor is initialized following a Rayleigh distillation, assuming initial conditions at the surface of δDv=-110 ‰ and δ18Ov=-15 ‰, leading to d-excessv=10 ‰, consistent with initial conditions in .
A cold pool is used to initiate convection: a 0.01 K cooling rate is applied for 10 min in a region 12 km long and 4 km height. A Galilean transformation of 13 ms-1 is applied all along the simulation to keep the convective system in the simulation domain. The simulation lasts 8 h which corresponds to the time needed by the squall line to reach and stay in a mature stage according to . Open boundary conditions are used in the x-direction. It means that where inflow occurs at the domain boundary, the prognostic variables, including the isotopic composition, are imposed by the values in the initial soundings at that height .
The one-moment ICE3 microphysics scheme presented in Sect. was used, along with the water stable isotopologues scheme. Vertical and horizontal turbulent fluxes are computed with the turbulent mixing length equal to the squared root of the grid mesh .
For the sake of simplicity, surface fluxes are deactivated. This is justified by the fact that over the 8 h of simulation, the influence of surface fluxes is small, and there is no time to reach an equilibrium between surface fluxes and precipitation.
Evolution of rain and water vapor isotopic composition during the 8 h simulation
Figure shows the evolution of precipitation rate and the isotopic composition of precipitation at the surface along the course of the simulation. The squall line builds and precipitation rate grows during the first 5 h of the simulation. Then, precipitation rate reaches a plateau between 5 and 6 h before declining. During the last 3 h of the simulation, the isotopic composition of precipitation (δ18Op, δDp and d-excessp) settles into a quasi-steady state. Figure shows the same for the near-surface water vapor. Although water vapor mixing ratio reaches a steady state after 5 h, the isotopic composition of water vapor (δ18Ov, δDv) keeps depleting, suggesting that the simulation is not into steady-state for this phase.
Temporal evolution of (a) the instantaneous surface rain rate (mmh-1), and the isotopic composition of the rain (‰): (b)δ18Op, (c)δDp and (d)d-excessp. Variables are averaged over the whole domain every 10 min.
Temporal evolution of (a) the near-surface water vapor mixing ratio (gkg-1), and the isotopic composition of water vapor (‰): (b)δ18Ov, (c)δDv and (d)d-excessv. Variables are averaged over the whole domain every 10 min.
We investigated to understand why the isotopic composition of rain reaches a quasi-steady state in contrast to the isotopic composition of water vapor. During the simulation, convective mixing dries out and depletes the boundary layer (below 1.5 km), and moistens and enriches the free troposphere (Fig. a–b). These trends persist throughout the simulation, fading at the end of the simulation as convection weakens significantly after 6–7 h. Water vapor mixing ratio reaches a quasi-steady state at the end of the simulation because the drying effect of convective mixing is offset by the moistening effect of droplet evaporation (Fig. c). The isotopic composition of water vapor does not reach equilibrium at the end of the simulation because the depleted effect of convective mixing is reinforced by the depleted effect of droplet evaporation. The isotopic composition of the precipitation appears to reach equilibrium, but this is because two effects compensate each other: (1) the water vapor in the boundary layer, with which the rain equilibrates, is increasingly depleted, so it tends to deplete the rain; (2) the water vapor in the free troposphere, where the droplets form, is more enriched, so it tends to enrich the rain (Fig. d).
Evolution of some vertical profiles along the course of the simulation: (a) water vapor mixing ratio (rv, gkg-1) anomaly with respect to the initial vertical profile, (b) isotopic composition of water vapor (δ18Ov, ‰) anomaly with respect to the initial vertical profile, (c) rain evaporation rate (gkg-1d-1), (d) difference between the isotopic composition of rain and that of the water vapor (δ18Op-δ18Ov).
Structure and dynamics of the squall line
We describe here the structure and the dynamic of the squall line after 6 h of simulation when rain rate is at its highest level and the squall line has reached a mature stage as already observed in the simulation done by. Figure shows the cross section of several parameters sensitive to squall line's structure and dynamic that are shown schematically on Fig. for a better understanding of the description of Fig. .
Vertical cross section of the (a) total condensed water mixing ratio (gkg-1), (b) rain mixing ratio (gkg-1), (c) relative humidity (%) and (d) moist static energy (kJkg-1) after 6 h. The total water condensed mixing ratio is the sum of the mixing ratio of all hydrometeors (cloud droplets, rain, cloud ice, snow/aggregates and graupel). The relative humidity is calculated for saturation over water for temperatures over 0 °C, and for saturation over ice for temperatures below 0 °C. The black line corresponds to the 0 °C isotherm.
Schematic of the main structural components of a squall line moving from right to left with the three convective, transition and stratiform zones along with horizontal and vertical dynamic.
To visualize the cloud shape, Fig. a shows the cross section of the total condensed water (the sum of the mixing ratio of all hydrometeors) along the x-direction. Strong values of condensed water content correspond to strong updrafts. We can see that there is a series of several updrafts from about 135 to 165 km, about 10 km apart from each other, corresponding to various convective cells at different stages, from the shallowest near the front of the squall line (at around 135 km) to the deepest at the rear (at around 165 km). From about 165 to 230 km, most of the condensed water is confined above the melting level, corresponding to the stratiform region, or anvil, of the squall line. This structure is consistent with previous studies .
Figure b shows the cross section of rain water content. The rain mixing ratio is the strongest below each convective updraft where most of it reaches the ground, whereas below the anvil, most of the rain evaporates before reaching the ground.
Figure c and d show the cross section of the relative humidity and the moist static energy, respectively. The high values of relative humidity near or at saturation correspond to the cloud, while lower values correspond to the environment or to subsiding air. The high values of moist static energy correspond to ascending air from the boundary layer to higher altitude, whereas lower values correspond to mid-tropospheric environment or subsiding air. The two snapshots exhibit expected features for well-developed squall lines. We can clearly see the convective region composed of several convective updrafts transporting air from the boundary layer to higher levels from about 135 to 165 km as mentioned above (high relative humidity and moist static energy). We also clearly detect lower relative humidity and moist static energy within downdrafts. The stratiform region is clearly developed. It corresponds to the cloudy area that extends behind the convective zone above around 4 km height from about 195 to 260 km. Below the stratiform region, the cold pool is identified by the dry air with low moist static energy (Fig. c and d). It extends frontwards towards the front of the line, around 130 km. Between convective and stratiform zones, the transition region is identified in the simulation by patches of dry subsiding air between around 165 an 195 km and below 4 km height (Fig. c).
Simulated isotopic composition of rain and water vapor after 6 h of simulation
Updrafts in the convective zone are transient, i.e. their exact location varies with time (not shown). Thus, rather than calculating temporal averages when the squall line is most intense, we analyze snapshots at a given time step. In the following, we chose to show results after 6 h of simulation as we can clearly distinguish between the convective and stratiform zones as described in the previous section. We checked that results are qualitatively similar whatever the snapshot we chose during the time interval of 5 to 6 h. Although the stratiform zone is in development earlier in the simulation, we also show isotopic results after 4 h of simulation in the supplementary material to show that (1) the non isotopic steady state has no impact on results and (2) the expected isotopic characteristics are well reproduced elsewhere in the simulation with a squall line at a different stage of development.
To document the isotopic results, we plot two figures. Figure a–d shows the cross section of anomalies of the isotopic composition (δ18O and d-excess) of both water phases. The isotopic anomalies are relative to the domain-mean at each level. In addition, the cross section of the isotopic composition of water vapor and rain are shown in Fig. S1 in the Supplement. We also show on Fig. e the difference between the isotopic composition of rain (δ18Op) and the isotopic composition of rain in equilibrium with water vapor ((δ18Op)eq deduced from αl,v=(δ18Ov+1)/((δ18Op)eq+1)), hereafter named the isotopic disequilibrium for δ18O (δ18Op-(δ18Op)eq). A similar disequilibrium is calculated for d-excess (d-excessp- (d-excessp)eq) and shown on Fig. f. The absolute isotopic values are shown on Fig. S1a–d. Figure shows the isotopic composition of both water phases at the surface along the x-direction.
Vertical cross section after 6 h of (a)δ18Ov, (b)δ18Op, (c)d-excessv, (d)d-excessp, (e)δ18Op- (δ18Op)eq and (f)d-excessp- (d-excessp)eq. Panels (a) to (d) are anomalies calculated by subtracting the average value of the variable at a given altitude from the local value of the variable. The black line corresponds to the 0 °C isotherm. Similar panels with absolute values can be seen on Fig. S1.
Evolution of the surface rain rate (a), δ18O (b), and and d-excess (c) along the x-direction after 6 h of simulation. In (b) and (c), the blue, black and green lines correspond to the isotopic composition of rain, rain in isotopic equilibrium with water vapor, and water vapor, respectively. In (b) and (c), the isotopic composition of rain (water vapor) is on the left-y (right-y) axis.
Description of the isotopic variations in the 2D domain
In the convective zone, we clearly distinguish on Fig. a the previously identified updrafts with enriched water vapor exported from the surface layer and, in between, downdrafts with lower δ18Ov reflecting export of depleted water vapor from higher altitude. The narrow vertical plumes of higher δ18Op (see Fig. b from 1 to 3.5 km) and lower d-excessp (see Fig. d from 1 to 3.5 km) reflect the rain evaporation which preferentially occurs within downdrafts consistent with previous studies . The lower d-excessp when evaporation processes are at play is interpreted as the kinetic effects during rain evaporation. The rain evaporation in narrow downdrafts is also suggested by positive (negative) isotopic disequilibrium for δ18Op (d-excessp) (Fig. e–f) rain evaporation leads rain to be more enriched than expected at isotopic equilibrium and d-excessp to be lower than expected at isotopic equilibrium, see for example. Both vertical motions and rain evaporation in the convective zone can be seen also in d-excessv (Fig. c). The lower d-excessv in updrafts suggests the export of low d-excessv from the surface layer toward higher altitude. The higher d-excessv in downdrafts is related to rain evaporation (under strong rain, a low fraction of rain evaporation tends to increase d-excessv) and to air subsidence exporting higher d-excessv from higher altitude.
In the stratiform zone, under the anvil cloud, the water vapor is more depleted in average than in the convective zone (Fig. a) as expected from the progressive depletion of water vapor by rain evaporation, meso-scale downdrafts and higher condensation altitude . We can see lower values of δ18Op at around 210 km and above 3 km (Fig. b). This could reflect that rain originates from snow melt, which is more depleted than the rain that would has formed locally because the snow has formed at higher altitude as already suggested by (see also Fig. S2). This is in agreement with the negative disequilibrium for δ18Op in this area (Fig. e). In contrast, between 200 and 215 km and below 3 km, δ18Op is higher and d-excessp is lower down to the surface (Fig. b–d) reflecting the enriched effect of rain evaporation on δ18Op and the lowering effect on d-excessp, consistently with the positive (negative) disequilibrium for δ18Op (d-excessp) in this area (Fig. e–f). The impact of rain evaporation is also seen on δ18Ov in this part of the domain (Fig. a) with the expected depleted effect on δ18Ov. The expected higher d-excessv is also seen between 200 and 215 km but in a restricted region between 0.5 to 2.5 km height (Fig. c).
In the transition zone, the expected isotopic characteristics are more visible on the precipitation phase. We identify in the three dry air patches shown on Fig. c (roughly located at 165, 175 and 190 km) both higher values of δ18Op and lower values of d-excessp suggesting that evaporation processes are at play, consistently with strong positive (negative) disequilibrium for δ18Op (d-excessp) (Fig. e–f).
Given the major role of evaporation processes in controlling the isotopic composition of both rain and water vapor, we further analyzed theses processes in Sect. .
Description of temporal evolution of the surface isotopic composition
Our simulation exhibits four precipitation maxima in the convective zone corresponding to the aforementioned convective updrafts, followed by lower precipitation in the transition region with two peaks (Fig. a). Two precipitation peaks are also seen in the stratiform region: the first one located at 195 km is attributed to stratiform rain as the later falls diagonally toward the front of the system as shown on Fig. b. This is consistent with surface observations although usually only one convective precipitation maximum is found .
Our simulation shows a W-shaped δ18Op (Fig. b, blue lines). Two local isotopic minima are observed in the convective zone and at the onset of stratiform region at about 160 and 195 km respectively. In the transition region, the peak in the middle of the W is actually formed in our simulation by a double-isotopic peaks (at around 175 and 190 km). This W-shape has often been observed in the isotopic composition of precipitation of squall lines . Typically, δ18Op in our simulation can be compared to the isotopic variations observed in precipitation collected along the squall line that occurred on 18 August 2006 in Niamey see Fig. 2 in.
Regarding the simulated δ18Ov, there is a sharp decrease right after 130 km corresponding to the cold pool front which is observed for more than 85 % of squall lines in Niamey from 2010 to 2012 . Then, δ18Ov decreases along the convective zone before slightly increasing (about 1 ‰) in the transition and stratiform zones as observed in about 30 % of squall lines in .
According to previous studies dealing with conceptual and cloud resolving models , the main processes depleting near-surface water vapor in convective and stratiform zones are mesoscale descents, rain evaporation in a moist environment, and enhanced rain-water vapor diffusive exchanges (as rain falls into layers that are more and more enriched, diffusive exchanges tend to enrich the precipitation and deplete water vapor around it). The isotopic decrease in precipitation along the convective zone follows to first order that in the water vapor, both phases being in close equilibrium at the surface (Fig. b, black lines).
The decreasing trend in δ18Op is however interrupted from the transition zone. Superimposed on the increasing δ18Op trend, the two peaks that form the middle of the W reflect the enrichment of rain by evaporation during its fall in dry air (Fig. c) as suggested by . Rain is always enriched by evaporation processes but the drier the air, the more enriching evaporation is for a constant fraction of evaporated rain.
The δ18Op recovery after 195 km, corresponding to the right limb of the W-shaped pattern, is attributed to increasing evaporative enrichment in the stratiform zone in a drier environment (see also next section).
Deuterium excess in precipitation continuously falls along the simulated squall line and attains strong negative values (-10 ‰) after 210 km during the second precipitation peak in the stratiform zone (Fig. c, blue lines) as observed for some squall lines in . This is consistent with rain evaporation aforementioned increasing from the transition zone. We also observe two decreases in d-excessp in the transition region in phase with the δ18Op double peaks consistently with rain evaporation. Deuterium excess in water vapor also decreases along the squall line as observed by for more than 85 % of observed squall lines.
Analysis of the rain evaporation processes
Figure a shows the disequilibrium for δ18Op at different altitudes (surface, 1 and 4 km). Positive values mean that the rain is more enriched than if it was at equilibrium with water vapor, reflecting evaporative processes. Negative values mean that the rain is more depleted than if it was at equilibrium with water vapor, reflecting rain falling from higher altitude and further depleted.
Difference between the isotopic composition of the rain and of the rain at isotopic equilibrium with the vapor at different altitudes for δ18O(a) and d-excess (b) along the x-direction after 6 h of simulation. (c) Scatter plot of the difference between the δ18O in the evaporation flux and in the rain (δ18Oe-δ18Op), as a function of the δ18O in the rain and in the vapor at isotopic equilibrium (δ18Op-(δ18Op)eq), for all x-values and altitudes where rain occurs. Markers are colored by relative humidity. (d) Fraction of rain that evaporates along the x-direction after 6 h of simulation at different altitudes. The blue, golden and red lines correspond to the isotopic composition at the surface, 1 km altitude and 4 km altitude, respectively.
At 4 km altitude, rain is more depleted than expected from isotopic equilibrium with water vapor, meaning that it falls from higher altitude (Fig. a). This phenomenon increases with the x-direction, reflecting the transition from the convective to the stratiform region, where condensation occurs higher (Fig. a). At 1 km, rain is more enriched than expected from equilibrium with water vapor, reflecting evaporative enrichment. This phenomenon increases with x-direction, reflecting the drier and drier air in the mesoscale descent under the anvil. At the surface, the disequilibrium for δ18Op is still positive but weaker than at 1 km. The rain is closer to the isotopic equilibrium with the vapor as described in . The effect of rain evaporation on isotopic results at the surface is also likely reduced because of the presence of a humid surface layer (Fig. c). Diffusive exchanges are thus favored instead of rain evaporation leading to first order to isotopic equilibrium between rain and water vapor (Fig. , black lines).
The same phenomenon is at play for deuterium excess (Fig. b). At 4 km altitude, the rain has a higher d-excessp than if at equilibrium with water vapor, because the rain falls from higher altitude and d-excessv typically increases with altitude. At 1 km height, the rain has a smaller d-excessp due to the impact of rain evaporation that enhances with x-direction. At surface, the disequilibrium for d-excessp is slightly negative but we can not exclude that the humid surface layer reduces this disequilibrium through diffusive exchanges between both water phases.
The processes controlling the disequilibrium between rain and water vapor are illustrated in Fig. c, showing the difference between the δ18O in the evaporation flux and in the rain (δ18Oe-δ18Op), as a function of the disequilibrium for δ18Op for all x-values and altitudes where rain occurs. Where relative humidity is high (dark blue shades), any small disequilibrium between rain and water vapor implies diffusive exchanges between both phases to bring them in equilibrium. For example, if rain is more depleted than expected (negative δ18Op-(δ18Op)eq), then δ18Oe is much more depleted than δ18Op to bring rain and water vapor to equilibrium. As a result, rain and water vapor are close to equilibrium (near-zero δ18Op-(δ18Op)eq). In contrast, where relative humidity is small (beige shades), the fraction of rain that evaporates is large, and thus the evaporation flux has almost the same δ18O as rain (near-zero values of δ18Oe-δ18Op). The strong evaporation leads to evaporative enrichment of rain (high values of δ18Op-(δ18Op)eq). This behavior is expected, giving us confidence in our implementation of isotopic processes associated with rain evaporation.
(a) Vertical cross section of the fraction of rain that evaporates (colors; %) after 6 h of simulation. The dotted, dashed and solid lines show respectively the 30 %, 60 % and 90 % isolines of vertically integrated evaporated fraction (fEVA). The estimate of the vertically integrated evaporated fraction assumes a drop fall velocity of 5.6 ms-1. Similar results are obtained for a lower (2.8 ms-1) and a higher (11.2 ms-1) drop fall velocity. (b) Scatter plot of the isotopic disequilibrium (δ18Op-(δ18Op)eq) as a function of the vertically integrated evaporated fraction (fEVA), for all x-values and altitudes where rain occurs. Markers are colored by relative humidity (%).
As a first exploration, we defined an estimate of the evaporated fraction of rain in the model. We show on Figs. d and a the ratio between the tendency of rain evaporation (evaporation flux derivative as a function of time) and the mixing ratio of rain. This ratio is the rain-normalized evaporated fraction of rain in each grid (0 % means that no evaporation occurred, 100 % means that all rain evaporated):
REVA=Δr|EVA×Δtrr×100
with Δt the model time step.
We also calculated at each level z the fraction of the rain that has evaporated during its fall since it was produced, fEVA, as the ratio between the rain evaporation flux to the rain flux if the evaporation was absent (Fig. ):
fEVA(z)=E(z)P(z)+E(z)
where P(z) is the rain flux at level z and E(z) is the rain evaporation flux between level z and the top of the domain. P(z) is calculated as P(z)=rr×ρa(z)×Vt where rr is the rain mixing ratio and Vt is a terminal velocity taken as 5.6 ms-1. E(z) is calculated as:
E(z)=∫z′=zztopΔr|EVA(z′)×ρa(z′)×dz′
In the convective zone, evaporation occurs in the narrow dry downdrafts between 2 and 4.5 km height and evaporation rate can attain up to around 25 % in a few grids (Figs. d and a). In the transition zone, rain evaporation is present within the dry patches of subsiding air from about 0.5 to 3.5 km with an evaporation rate varying between 0 % and 10 % at a given level. At last, Figs. d and a clearly show that rain evaporation is present almost all over the domain under the anvil cloud and reaches a maximum at the edge of the stratiform zone (at about 215 km) where evaporation rate attains close to 25 % all along the vertical dimension from the near-surface to 3.5 km height. The vertically integrated evaporated fraction of rain reaches a maximum (higher than 60 %) in the convective zone in downdrafts where relative humidity is lower and below the stratiform zone with values higher than 90 % (Fig. a). The expected influence of evaporative effects on the isotopic composition of precipitation is clearly captured by our simulation as shown on Fig. b. The isotopic disequilibrium (δ18Op-(δ18Op)eq) increases with positive values as the vertically integrated evaporated fraction increases and the relative humidity decreases.
This 2D spatial pattern of the rain evaporation is consistent with the spatial isotopic variations of water vapor and precipitation, giving us confidence again in our implementation of isotopic processes associated with rain evaporation. Our estimate for the vertically integrated evaporated fraction of rain can be compared to previously published values. Based on a box model aiming at reproducing the near-surface observations, concluded that for a majority of squall lines, the rain evaporation rate varies between 10 % and 35 % with a maximum at the rear of the stratiform zone that can attain almost 60 % in a few cases. Using cloud resolving model in radiative-convective equilibrium to simulate an idealized squall line, simulated a similar range for the rain evaporation rate in the convective and stratiform zones, increasing up to 90 % in the trailing environment as also obtained in our simulation below the stratiform cloud.
Conclusions
This paper presents the implementation of water stable isotopologues in the non-hydrostatic mesoscale model Meso-NH. This development is tested with the simulation of a squall line that occurred at night on 23–24 June 1981 during the COPT 81 intensive field campaign. We chose this squall line as it was subject to comprehensive observations on the field and as a 2D simulation was done by with Meso-NH. Our simulation successfully reproduces the main expected spatial structure of a mature and intense squall line after 6 h of simulation: a convective zone, a transition zone and a stratiform zone where different processes are expected to produce different isotopic fractionation on water vapor and precipitation.
It is worth noting that even though the isotopic composition of near-surface vapor isotopes continues to evolve late in the simulation, while water vapor amounts and isotopic composition of precipitation isotopes settle into a quasi-steady-state, the results are actually consistent with observations after 6 h. This is also true earlier in the simulation as shown for example after 4 h of simulation when the convective zone is formed and the stratiform region is developing (Figs. S3 to S7). This result suggests that the non-isotopic steady state in near-surface water vapor at the end of the simulation does not prevent us from exploring the isotopic variations of water in our simulation.
The Meso-NH-ISO model captures well the main isotopic features expected as seen in many observations:
Regarding the spatial pattern of the isotopic composition of water in the 2D domain: (i) In the convective zone, our simulation well reproduces the enriched and depleted water vapor in updrafts and downdrafts respectively reflecting both vertical motions of water and rain evaporation processes. (ii) In the transition zone, the impact of rain evaporation processes on the isotopic composition of precipitation is also well reproduced in the dry plumes of subsiding air with an enrichment of δ18Op, low – even negative – values of d-excessp and a positive disequilibrium for δ18Op. (iii) In the stratiform zone, our simulation captures the expected processes. The low δ18Op in altitude reflects the higher altitude of condensation in this zone. The negative values of d-excessp and the highest values of δ18Op below the anvil cloud reflect rain evaporation processes, specifically at the rear of the stratiform zone where our estimate of the fraction of rain that evaporates is the stronger. Indeed, the fraction of the rain that has evaporated during its fall can be higher than 90 %. The analysis of evaporation processes in our simulation shows that these processes act as expected in modulating the isotopic composition of water in the 2D domain.
Regarding the comparison with the observations of the isotopic composition of water at the surface: (i) Along the squall line, δ18Op evolves along a W-shaped pattern as observed for numerous squall lines by , , and . The increasing δ18Op in the middle of the W and at the end of the W, attributed in previous studies to rain evaporation in a drier environment in the transition zone and at the rear of the stratiform zone, are well reproduced in our simulation. (ii) δ18Ov decreases along the convective zone before slightly increasing in the transition and stratiform zones as observed in about 30 % of squall lines in . The lowering of δ18Ov has been explained in previous studies as reflecting mesoscale descents, rain evaporation and favored diffusive exchange between rain and water vapor in moist environment. (iii) Deuterium excess in precipitation and water vapor decreases along the squall line as already observed in and respectively that is consistent with rain evaporation, mesoscale descents and presence of a enhanced diffusive exchanges at surface.
The plans for this implementation is to use Meso-NH-ISO for realistic cases of squall lines and cyclones in order to better understand what are the controls on the isotopic composition of water in convective systems. For example, recently showed the presence of a very organized signal in the isotopic composition of water vapor within cyclones on an hourly scale, empirically linked to the spatial structure of cyclones. Observations alone and general atmospheric climate models, even with a high spatial resolution, have not been able to decipher the processes controlling isotopic variations in water vapor and therefore to quantify them. Future simulations with Meso-NH-ISO should enable further advances on this aspect with the final objective of better studying and quantifying convective processes from water stable isotopologues. Furthermore, Meso-NH now features a two-moment mixed-phase microphysical scheme LIMA, which does not assume a saturation adjustment for ice. Plans are in place to integrate the stable water isotopologue scheme with LIMA in the near future, in order to benefit from the advantages of a two-moment microphysical scheme and to better account for the fractionation of heavy isotopologues during both the liquid-vapor and vapor-ice transitions.
List of symbols.
SymbolsDescriptionSI unitsaParameter for the mass-diameter relationshipkgm−bAFactor in the expression of ΔrcisoCND/EVA–AiThermodynamical function for diffusional growth of ice particlesAwThermodynamical function for raindrop evaporationbParameter for the mass-diameter relationship–cParameter for the fall-speed-diameter relationshipm1−d s−1c′Factor in the expression of ΔrrEVAc′isoFactor in the expression of ΔrrisoEVACParameter for the N=Cλx relationshipC1Parameter for the relationship (C=C1D)–d-excessDeuterium excessdParameter for the fall-speed-diameter relationship–DHydrometeor diametermDvMolecular diffusivity of light water vapor in airm2s−1DvisoMolecular diffusivity of heavy water vapor in airesi(T)Saturation vapor pressure over icePaesw(T)Saturation vapor pressure over liquid waterPafVentilation factor for light particles–fisoVentilation factor for heavy particles–f0, f1, f2Parameters to compute the ventilation factor–FFactor in the expression of αKg(D)Generalized gamma distribution law–kaThermal conductivity of airkgms−3K−1LsLatent heat of sublimationJkg−1LvLatent heat of vaporizationJkg−1mHydrometeor masskgmrMass of a raindropkgmrisoMass of a raindrop containing heavy isotopeskgM(p)p-order moment of the particle size distribution–MdMolar mass of dry airkgmol−1MvMolar mass of water vaporkgmol−1n(D)Number conc. of hydrometeors with D< diameter <D+dDkg−1m−1NNumber concentration of hydrometeorskg-1NcNumber concentration of cloud dropletskg-1NrNumber concentration of raindropskg-1NReReynolds number–NSc,vSchmidt number for water vapor–NSc,visoSchmidt number for heavy molecules of water vapor–pPressurePap0Standard atmospheric pressure at the ground levelParMixing ratiokgkg-1risoIsotopic mixing ratio for H218O and HD16Okgkg-1rcCloud droplet mixing ratiokgkg-1rcisoHeavy mixing ratio of cloud dropletskgkg-1rrRaindrop mixing ratiokgkg-1rrisoHeavy mixing ratio of raindropskgkg-1
Continued.
SymbolsDescriptionSI unitsrsiSaturation vapor mixing ratio over icekgkg-1rvWater vapor mixing ratiokgkg-1rvisoHeavy mixing ratio of water vaporkgkg-1RIsotope ratio–RcIsotope ratio in cloud water–RiIsotope ratio in ice–RlIsotope ratio in liquid condensate–RwIsotope ratio in water vapor–RVSMOWIsotope ratio in the Vienna Standard Mean Ocean Water–RvSpecific gas constant for water vaporJkg−1K−1SisoSource term for heavy water variablesSiSupersaturation over ice–SlSupersaturation over liquid water–TTemperatureKT0Standard atmospheric temperatureKU3D air velocityms-1vHydrometeor terminal fall speedms-1xParameter for the N=Cλx relationship–αParameter for the hydrometeors size distributions–αKKinetic fractionation coefficient–αi/vEquilibrium fractionation factor between ice and water vaporαl/vEquilibrium fractionation factor between liquid and water vaporδIsotopic composition‰δ18OIsotopic composition in H218O‰δ18Oeδ18O in the evaporation flux‰δ18Opδ18O of rain‰(δ18Op)eqδ18O of rain in equilibrium with water vapor‰δ18Ovδ18O of water vapor‰δDIsotopic composition in HD16O‰ΔrACCMass mixing ratio transfer rate during accretion of cloud droplets by snowkgkg-1s-1ΔrisoACCMass mixing ratio transfer rate during accretion of cloud droplets by snow for heavy isotopeskgkg-1s-1ΔrDEPMass mixing ratio transfer rate during deposition of water vapor on ice particleskgkg-1s-1ΔrisoDEPMass mixing ratio transfer rate during deposition of water vapor on ice particles for heavy isotopeskgkg-1s-1ΔrSUBMass mixing ratio transfer rate during sublimation of ice particleskgkg-1s-1ΔrisoSUBMass mixing ratio transfer rate during sublimation of ice particles for heavy isotopeskgkg-1s-1ΔrCND/EVAMass mixing ratio transfer rate during condensation / evaporation of cloud dropletskgkg-1s-1ΔrisoCND/EVAMass mixing ratio transfer rate during condensation / evaporation of cloud droplets for heavy isotopeskgkg-1s-1ΔrrEVAMass mixing ratio transfer rate during raindrop evaporationkgkg-1s-1ΔrrisoEVAMass mixing ratio transfer rate during raindrop evaporation for heavy isotopeskgkg-1s-1η(T)Dynamic viscosity of airPasχVariable in the expression of the ventilation coefficient for light water–χisoVariable in the expression of the ventilation coefficient for heavy water–Γ()Gamma function–λSlope parameter of the hydrometeors size distributionm-1νParameter for the hydrometeors size distributions–ν(T)Dynamic viscosity of airPasρ0Air density at the reference pressure levelkgm-3ρaDry air densitykgm-3ρwisoDensity of heavy water vapor for the environmentkgm-3ρw,DisoDensity of heavy water vapor on the surface of the raindropkgm-3Code and data availability
The water stable isotopologues scheme has been implemented in the 5.5 version of the Meso-NH code. This reference version is under the CeCILL-C license agreement and freely available at http://mesonh.aero.obs-mip.fr/mesonh55 (last access: 14 October 2026). The complete code of Meso-NH v5-5-0 including the water isotope scheme is available at 10.5281/zenodo.18428400. This repository also contains namelists to run the 2D squall line and Python scripts to reproduce the figures of this manuscript.
The supplement related to this article is available online at https://doi.org/10.5194/gmd-19-9935-2026-supplement.
Author contributions
CB and SF developed the implementation of water stable isotopologues in Meso-NH. FV and CR interpreted the isotopic results. CB, FV and CR wrote the paper. CB realized figures and tables.
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 made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. The authors bear the ultimate responsibility for providing appropriate place names. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.
Acknowledgements
Computations were performed on the 120-node cluster of Laboratoire d'Aérologie.
Financial support
This work was funded by the French CNRS-INSU national program LEFE (project MISO-CYCLO) and the ANR PALEOTEMPESTO proposal 24-CE01-6978. The work benefited from a PhD grant from the CEA.
Review statement
This paper was edited by Simon Unterstrasser and reviewed by two anonymous referees.
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