Science of the Total Environment 544 (2016) 1059–1072

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Isotopic modeling of the sub-cloud evaporation effect in precipitation

V. Salamalikis a,⁎, A.A. Argiriou a, E. Dotsika b

a Laboratory of Atmospheric Physics, Department of Physics, University of Patras, GR 26500 Patras, Greeceb Stable Isotope Unit, Institute of Nanoscience and Nanotechnology, National Center of Scientific Research ‘Demokritos’, Ag. Paraskevi Attikis, 15310 Athens, Greece

H I G H L I G H T S G R A P H I C A L A B S T R A C T

• Modeling the sub-cloud evaporation ef-fect in terms of the isotopic composition.

• Two isotopic modeling approaches useda) isotope-mixing evaporation modeland b) numerical isotope evaporationmodel.

• Model evaluation using data fromMadridand Vienna GNIP stations.

• Vertical distribution of stable isotopesin falling raindrops in terms of isotopi-cally transformed difussive equations.

⁎ Corresponding author.E-mail address: vsalamalik@upatras.gr (V. Salamalikis

http://dx.doi.org/10.1016/j.scitotenv.2015.11.0720048-9697/© 2015 Elsevier B.V. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 17 September 2015Received in revised form 9 November 2015Accepted 14 November 2015Available online xxxx

Editor: D. Barcelo

Keywords:Stable isotopesFalling raindropssub-cloud evaporation effectIsotope evaporation models

In dry and warm environments sub-cloud evaporation influences the falling raindrops modifying their finalstable isotopic content. During their descent from the cloud base towards the ground surface, through the unsat-urated atmosphere, hydrometeors are subjected to evaporation whereas the kinetic fractionation results to lessdepleted or enriched isotopic signatures compared to the initial isotopic composition of the raindrops at cloudbase. Nowadays the development of Generalized Climate Models (GCMs) that include isotopic content calcula-tion modules are of great interest for the isotopic tracing of the global hydrological cycle. Therefore the accuratedescription of the underlying processes affecting stable isotopic content can improve the performance of iso-GCMs. The aim of this study is to model the sub-cloud evaporation effect using a) mixing and b) numerical iso-tope evaporation models. The isotope-mixing evaporation model simulates the isotopic enrichment (differencebetween the ground and the cloud base isotopic composition of raindrops) in terms of raindrop size, ambienttemperature and relative humidity (RH) at ground level. The isotopic enrichment (Δδ) varies linearly with theevaporated raindropsmass fraction of the raindrop resulting to higher values at drier atmospheres and for small-er raindrops. The relationship betweenΔδ and RH is described by a ‘heat capacity’model providing high correla-tion coefficients for both isotopes (R2 N 80%) indicating that RH is an ideal indicator of the sub-cloud evaporationeffect. Vertical distribution of stable isotopes in falling raindrops is also investigated using a numerical isotope-evaporation model. Temperature and humidity dependence of the vertical isotopic variation is clearly describedby the numerical isotopic model showing an increase in the isotopic values with increasing temperature and de-creasing RH. At an almost saturated atmosphere (RH=95%) sub-cloud evaporation is negligible and the isotopic

).

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composition hardly changes even at high temperatureswhile at drier andwarm conditions the enrichment of 18Οreaches up to 20‰, depending on the raindrop size and the initial meteorological conditions.

© 2015 Elsevier B.V. All rights reserved.

1. Introduction

Precipitation is the most important component of the hydrologicalcycle for the determination of the water budget over a certain area.The accurate description of the precipitation patterns as well as the un-derlying mechanisms that modulate precipitation is a crucial issue forthe robust parameterization of climate models and to further improvethe quality of the precipitation forecasts. In arid and semi-arid climatessub-cloud evaporation affects the falling hydrometeors during their de-scent from the cloud base towards the groundmodifying the size of theraindrops reaching the ground. The use of environmental tracers sensi-tive to such changes such as stable water isotopes (18O and 2H) can con-tribute to the better understanding of the presence and the impact ofthe sub-cloud evaporation effect in precipitation. For example,Worden et al. (2007), using satellite data, reported that 20% (and upto 50%) of the rainfall is re-evaporated under tropical convective clouds.

Stable water isotopes have been widely used as tracers since theirvalues reflect the water transport and the various phase changes occur-ring at different spatio-temporal scales in the hydrological cycle. Drivenby their mass and vapor pressure differences, the physical properties ofthe different isotopic species vary according to the environmental con-ditions leading to changes in their abundance due to equilibrium and ki-netic fractionation effects (Dansgaard, 1964). Due to the lower vaporpressures, the heavier isotopic species are preferentially accumulatedin the condensed phases information on the mechanisms related tocloud and precipitation formations (Jouzel, 1986). The isotopic compo-sition of water is expressed via the delta (δ) notation in per mille (‰)which is the fractional deviation from unity of the isotopic ratio of awater sample (RSi ) relative to that of a standard (RVSMOW

i ); here the Vien-na Mean Ocean Water (VSMOW) (Eq. (1)).

δi ‰ð Þ ¼ RiS

RiVSMOW

−1

!� 103: ð1Þ

The symbol i stands for 18O and 2H respectively.The falling raindrops are subject to evaporation during their trip from

the cloud base towards the surface through the unsaturated atmosphere.The impact of below-cloud evaporation on the isotopic composition offalling raindrops is strongly related to the prevailing meteorological con-ditions (temperature and humidity) in the sub-cloud layer, the initialraindrop size and the isotopic composition of the ambient moisture. Incase of isotopic equilibrium between a raindrop and the atmosphere sur-rounding it, the isotopic composition of precipitation is derived by the iso-topic composition of the surrounding water vapor and the equilibriumfractionation factor for the liquid–vapor transition.

The isotopic composition of the ambientmoisture decreaseswith in-creasing altitude, following the water vapor distribution in the tropo-sphere. At any vertical level, the isotopic composition of precipitationdepends on the isotopic composition of the pre-condensed moistureas well as on the isotopic composition of the ambient vapor (Bonyet al., 2008). When RH b 100% and the raindrop surface temperatureis lower than the ambient air temperature, a heat flux towards the rain-drop delivers the latent heat of evaporation and heats the raindrop. Dueto kinetic fractionation an isotopic enrichment is detected in the fallingraindrops and a reciprocal depletion in the water vapor, in relation tothe humidity conditions and the temperature difference between theraindrop and the ambient environment. The evaporation rate of theraindrop is inversely proportional to the raindrop diameter (~1/D2) im-plying that smaller raindrops are more favorable to evaporation. In caseof saturation (RH ≃ 100%), thephenomenon of isotopic exchange occurs.

The falling raindrops tend to attain equilibrium with the ambient airenriching isotopically the condensate phase of water in comparison tothe initial isotopic composition at the cloud base (Stewart, 1975; Leeand Fung, 2008). Isotopic exchange is more pronounced for smallerraindrops. The adjustment/equilibration time - the time a dropletneeds to reach the 1/e of the isotopic composition of the environmentalvapor - is positively related to the raindrop size indicating that a lowerequilibration time and a higher equilibration degree are associated tolower sized raindrops (Friedman et al., 1962; Lee and Fung, 2008). Thereduction of the raindrop size due to evaporation depletes the surround-ing air at any falling step on the assumption that the isotopic compositionof the ambient atmosphere is lower than the isotopic composition of thewater vapor near the raindrop's surface.

The distribution of stable isotopes in precipitation ismodeled via theRayleigh distillation process. The temperature and rainfall amount ef-fects are included in a certain extent in the Rayleigh formula in termsof the equilibrium fractionation factor and the rainout fraction. TheRayleigh distillation assumes isotopic equilibrium between liquidand vapor at any step of the precipitation process. Also, precipita-tion is immediately removed from the cloud base without any inter-action with the surrounding atmosphere neglecting the sub-cloudkinetic fractionation phenomena (Criss, 1999). Despite the stronglimitations, the Rayleigh distillation is widely applied for the deter-mination of the overall isotopic patterns and the isotopic evolution ofprecipitation/water vapor along pre-described moisture trajectories(Sodemann et al., 2008).

The general purpose of this paper is a discussion for the isotopicmodification of falling raindrops due to the sub-cloud evaporation ef-fect. In this work this phenomenon is analyzed using three methods,namely:

1. Meteoric Water Lines (MWLs);2. Isotope-evaporation model (Stewart, 1975; Georgakakos and Bras,

1984); and3. Numerical isotope-evaporation model (Jouzel, 1986; Zhang et al.,

1998).

The numerical isotope-evaporation model involves the vertical var-iations of the raindrop diameter and raindrop temperature due to belowcloud interactions as well as the vertical isotope profile of the atmo-spheric moisture. For the subsequent analysis the increase in the rain-drop size due to coalescence and collision and the decrease due tobreakup, are assumed negligible (Schlesinger et al., 1988). This modelis a simplified and computationally ‘light’ version of the complex isotopiccloud-resolving models applied for the representation of the isotopiccomposition of water vapor and its condensates in convective updrafts(Bolot et al., 2013) and the investigation of the tropical tropopause layer(Blossey et al., 2010).

2. Data

Stable isotopic daily data (18O and 2H) for ground water vapor andrainfall were obtained by the GNIP/ISOHIS database for six stations lo-cated in the Northern Hemisphere (IAEA/WMO, 2013). Due to gaps inthemeteorological data in the GNIP database, missing values of temper-ature, precipitation amount and relative humidity were filled using theECA&D database (Klein Tank et al., 2012). Only two stations (Madrid-Retiro, Spain and Vienna, Austria) have temperature and relative hu-midity values available in the ECA&D database while the temperaturegaps in Rehovot, Israel were filled using themeteorological informationfrom the nearest station in Bet-Dagan, Israel.

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3. Methods

3.1. Meteoric water lines and isotopic enrichment of precipitation

The various fractionation processes in water can be interpretedusing the δ2H-δ18O relationship. Globally, the isotopic composition ofprecipitation (δ18O and δ2Η) lies along the Global Meteoric Water Line(GMWL), δ2H = 8 δ18Ο + 10‰ (Craig, 1961). In smaller spatial scales(areas and stations) and on an event and longer temporal basis, theisotopic composition of the observed rainfall varies due to a variety offactors projecting the water samples along a new straight line, theLocal Meteoric Water Line (LMWL), δ2H = a δ18Ο + b, where both theslope and intercept values may differ from those of the GMWL. In caseof sub-cloud evaporation, the values of a and b are significantly lowerthan those of the GMWL implying that the sub-cloud processes can beidentified through the examination of the LMWL (Gat, 2005). In orderto describe the deviation from equilibrium, the slope of the LMWL iscompared against the Rayleigh equilibrium slope αT (Criss, 1999),

aT ¼aeq;l−v

2H� �

δ2Hp−103� �

aeq;l−v18OÞ δ18Op−103

� �� ð2Þ

with aeq,l − v the equilibrium fractionation factor for the liquid–vaportransition (Table A1). The equilibrium fractionation factors for 18O and2H are calculated using the Majoube (1971) formulas in terms of thesurface air temperaturewhile the δ-values of precipitation areweightedaccording to the respective precipitation amount. According to Eq. (2),the Rayleigh slope assumes isotopic equilibrium during the formationof rainfall, neglecting the super-saturation conditions inside the cloudand the secondary evaporation phenomena beneath the cloud base. Ahigher slope difference (Δα = αT

− α) indicates stronger evaporativeenrichment and deviation from equilibrium.

3.2. Isotope-evaporation model

The detection of the sub-cloud evaporation effect is describedalso by the difference between the isotopic composition of precipita-tion in the ground level and cloud base respectively. According toStewart (1975) the isotopic composition in falling raindrops isgiven by,

Ril ¼ γiRi

v;cb þ Ril;cb−γiRi

v;cb

� �f β

i

r

βi ¼1−aieq;l−v Dva=D

iva

� �n1−RHð Þ

aieq;l−v Dva=Diva

� �n1−RHð Þ

;γi ¼aieq;l−vRH

aieq;l−v Dva=Diva

� �n1−RHð Þ

ð3Þ

where Rli is the isotopic ratio of falling raindrops, Rvcbi and Rlcb

i are theinitial isotopic ratios for the vapor and liquid phases at the cloudbase, aeq , l−v

i is the equilibrium fractionation factor calculated at thecloud base temperature,RH is the fractional relative humidity, Dva/Dva

i is the ratio betweenthe molecular diffusivities of the abundant and the rare isotope i,n = 0.58 (Gat, 2000) and fr is the remaining raindrop mass fractionafter evaporation. The molecular diffusivity ratios for water isotopesare taken to be 1.032 and 1.016 for 18O and 2H respectively (Cappaet al., 2003). The cloud base temperature is calculated through themean moist adiabatic lapse rate

γ ¼ −dΤdz

¼ 6:5� 10−3 K=m ð4Þ

assuming that the cloud base is at about the 850 hPa (~1500 m) iso-baric level. Starting from Eq. (3) and assuming that the falling

raindrops have a uniform spherical shape, the isotopic enrichmentdue to sub-cloud evaporation is (Froehlich et al., 2008),

Δδ ‰ð Þ ¼ δi zg� �

−δi zcbð Þ ¼ 103 � 1−γi

aieq;l−v

!f β

i

r −1� �

f r ¼mg

mcb¼ Dg

Dcb

� �3ð5Þ

with D the raindrop's diameter. The indexes g and cb refer to theground surface and the cloud base respectively. For the determina-tion of the final raindrop mass, a station-precipitation model(Georgakakos and Bras, 1984) is applied,

Dg ¼ Dcb3−

4Dva

C1R�v

esat θwð ÞTw

−esat θdð Þ

Tg

� �zcb

� 1=3ð6Þ

with Rv = 461.51 J.kg−1.K−1 the gas constant for water vapor, Dva

(m2·sec−1) the air diffusivity, esat (Pa) the saturation vapor pressureat the wet-bulb temperature, θw and Tw the wet-bulb temperature in°C and K, θd (°C) the dew point temperature, Tg (K) the air tempera-ture at the ground level, zcb (m) the cloud base elevation and C1 =7 × 105 kg.m−3.s−1 for liquid droplets. The wet bulb and the dewpoint temperatures are calculated in terms of relative humidity andair temperature (Lawrence, 2005; Stull, 2011) while the Magnus-Tetens formula (Lawrence, 2005) is applied for the computation ofthe saturation vapor pressure.

Even if the Stewart's model describes the isotopic enrichment offalling raindrops, it has important limitations. The model assumes ahomogenous sub-cloud layer in terms of temperature and humidity,neglecting their vertical distribution, considering also that the isotopiccontribution in the ambient vapor due to the evaporation of the fallingraindrops is negligible. However, those limitations are expectable dueto the nature of the Stewart's model, since it is a mixingmodel betweenthe starting and the final isotopic composition.

3.3. Numerical isotope-evaporation model

In order to study the temporal evolution of the isotopic compositionin falling raindrops, the rate of change of the isotopic ratio is describedby the following equation,

dRil

dt¼ d mi=m

� �dt

¼ 1m

dmi

dt−Ri

ldmdt

� �¼ 6

πρwD3

dmi

dt−Ri

ldmdt

� �: ð7Þ

In Eq. (7), the raindrops are assumed to have a uniform spherical

shape with diameter D and mass m ¼ πρwD3

6 . The evaporation rate (dm/dt) and the rate of change of the isotopic mass (dmi/dt) for the fallingraindrops are derived using the mass transfer equation by means ofthe vapor concentration,

dmdt

¼ 2πD FvDvað Þ ρva Tað Þ−ρvr Trð Þ½ �dmi

dt¼ 2πD FivaD

iva

� �ρiva Tað Þ−ρi

vr Trð Þh i ð8Þ

with Ta, Tr the ambient temperature and the raindrop surface tempera-ture respectively. The parameters Dva, ρva, ρvr, Fv, Dva

i , ρvai , ρvri ,Fvi are thediffusion coefficient of air, the vapor densities at the ambient atmo-sphere and at the raindrop surface temperature, and the ventilation co-efficients for the normal and the heavy water respectively.

1062 V. Salamalikis et al. / Science of the Total Environment 544 (2016) 1059–1072

Eq. (7) using Eq. (8) can be transformed as,

dRil

dt¼ 3ρvr Trð Þ

ρwD2 f vDvað Þ

� FivDiva

FvDva

!RivaRH

ρva;sat Tað Þρvr Trð Þ −Ri

vr

� �−Ri

l RHρva;sat Tað Þρvr Trð Þ −1

� �" #:

ð9Þ

The isotopic composition of the ambient moisture is given by Riva ¼

ρivaðTaÞ

ρvaðTaÞ while the isotopic composition at the raindrop's surface is Rivr ¼

ρivrðTrÞ

ρvrðTrÞ. At the surface of the raindrop, the vapor and liquid phases are con-

sidered in isotopic equilibrium and the isotopic composition of watervapor can be calculated using the isotopic composition of the liquidphase and the equilibrium fractionation factor at the raindrop tempera-

ture, Rivr ¼ Ri

laieq;l−v

ðTrÞ. The quantityFivD

iva

FvDvalimits to ðDi

vaDva

Þnwith n= 0.58 (Gat,

2000). Themolecular diffusivities are equal to 0.9691 and 0.9839 for 18Oand 2H respectively (Cappa et al., 2003).

The term RH refers to the relative humidity of the ambient air. Underthe assumption that vapor is an ideal gas, the vapor densities and the

relative humiditymay be expressed as,ρvaðTaÞ ¼ evaðθaÞR�vTa

,ρvrðTrÞ ¼ evrðθrÞR�vTr

¼esat ðθrÞR�vTr

and RH ¼ ρvaðTaÞρva;satðTaÞ ¼

evaðθaÞeva;sat ðθaÞ , where eva(θa), evr(θr), esat(θr),

eva ,sat(θa)are the vapor pressure and the corresponding saturated valuesof the ambient atmosphere and the falling raindrop at temperatures θaand θr respectively, and Rv

∗ is the universal gas constant for the watervapor. Since the air is close to saturation at the surface of the raindrop,the vapor concentration is equal to its saturated value at the droplettemperature. The curvature effect depends on the drop size and ismore pronounced for smaller drops (i.e. cloud droplets). Thus it isnot included in the calculation of the saturation vapor pressure forraindrops.

During their descent from the cloud base towards the ground,the raindrops fall at their terminal velocity. Due to its strong depen-dence on the raindrop size, the terminal velocity is higher for largerdrops. Considering a constant updraft velocity w, the overall rain-drop velocity is

dzdt

¼ V ¼ Vr−w ð10Þ

with Vr the raindrop velocity and w the updraft velocity. The nomencla-ture for the parameters used as well as their units and mathematical ex-pressions are given in Table A1 of the Appendix A.

Based on the discussion above and Eq. (1), Eq. (9) is rewritten as,

dδildz

¼ 3esat θrð ÞρwR

�vD

2TrVFvDvað Þ

��

Diva

Dva

!n

δiva þ 103� �

RHeva;sat θað ÞTr

esat θrð ÞTa−

δil þ 103� �

aieq;l−v

0@

1A

− δil þ 103� �

RHeva;sat θað ÞTr

esat θrð ÞTa−1

� �

ð11Þ

Eq. (11) describes the vertical variation of the isotopic compositionof falling raindrops due to evaporation in the sub-cloud layer. The isoto-pic composition varies with the meteorological and isotopic conditionsof the ambient atmosphere (temperature, relative humidity and isoto-pic composition of the atmosphericwater vapor) and the raindrop char-acteristics (raindrop size and temperature).

3.3.1. Vertical variations of raindrop size and temperatureThe raindrop mass is modified due to in-flight evaporation. The

raindrop diameter changes with height following the temperature

and relative humidity vertical profiles. The vertical variation of theair temperature in the atmosphere follows the average moistadiabatic lapse rate. This temporal raindrop mass change is calledevaporation rate and can be expressed using the mass transferequation,

dmdt

¼ 2πD FvDvað Þ ρva Tað Þ−ρvr Trð Þ½ �

¼ 2πD FvDvað ÞR�v

RHeva;sat θað Þ

Ta−

esat θrð ÞTr

� : ð12Þ

Using the Eqs. (9) and (11) the vertical change of the raindrop diam-eter equals

dDdz

¼ 4 FvDvað ÞDVρwR

�v

RHeva;sat θað Þ

Ta−

esat θrð ÞTr

� : ð13Þ

The evaporation process occurs when raindrops and the surround-ing air are not in thermodynamic equilibrium. If the raindrop tempera-ture is lower than that of the ambient air, a conductive heat flux fromthe air to the raindrop is detected while the raindrop looses (latent)heat since its size is reduced. The total rate of temperature change atthe raindrop's surface is determined via the heat balance for the evapo-rating raindrop (Pruppacher and Klett, 1997),

dQdt

¼ −Ldmdt

þ dhdt

ð14Þ

with L the latent heat of vaporization and dh/dt is defined in Eq. (16).The left side of Eq. (14) is defined as the total heat rate gain of theraindrop and it is responsible for the temperature difference betweenthe raindrop and the surrounding air. The above heat gain rate can beexpressed as

dQdt

¼ mwcwdTdt

¼ πρwcwVD3

6dTdz

¼ πρwcwVD3

6dTr

dzð15Þ

with cw the specific heat of water. In the right side of Eq. (14), the firstterm is the latent heat due to mass diffusion, while the second term re-fers to the sensible heat derived from the heat transfer equation (Tardifand Rasmussen, 2010),

Ldmdt

¼ 2πLD FvDvað ÞR�v

RHeva;sat θað Þ

Ta−

esat θrð ÞTr

� dhdt

¼ 2πD Fhkað Þ Tr−Tað Þ:ð16Þ

The parameters fh and ka are the heat ventilation coefficient and thethermal conductivity of air (Table A1). Starting from Eq. (14) the differ-ential equation that describes the vertical variation of raindrop temper-ature is given by,

dTr

dz¼ 12Fhka

D2ρwcwVTr−Tað Þ þ FvDvaL

FhkaR�v

� �RH

eva;sat θað ÞTa

−esat θrð Þ

Tr

� � �: ð17Þ

3.3.2. Vertical profile of the isotopic composition of water vapor and relativehumidity

Schlesinger et al. (1988) studied the sub-cloud evaporation effectin precipitation using two limiting conditions, (a) constant relative hu-midity and (b) constant specific humidity in the sub-cloud layer. Thesetwo assumptions have important disadvantages when studying the iso-topic processes occurring during precipitation. In the lower tropospher-ic levels, Rayleigh distillation is the dominant process that controls thewater vapor isotopic composition while the mid-tropospheric vapor ismainly influenced isotopically by the non-fractionating air mass mixing

1063V. Salamalikis et al. / Science of the Total Environment 544 (2016) 1059–1072

between vapor masses with distinct isotopic signatures (Yoshimuraet al., 2011). According to the Rayleigh distillation formula

δiv−δiv0≈ lnRiv

Riv0

!¼ aeq−1� �

lnqq0

� �ð18Þ

the isotopic composition of water vapor depends on the initial isotopiccomposition of water vapor, the condensation temperature and therainout fraction. Neglecting all other contributions that affect the isoto-pic variation of water vapor such as the plant transpiration, the air massmixing, the soil evaporation etc., and according to the second assump-tion - constant sub-cloud specific humidity - the rainout fraction limitsto unity and the isotopic composition at the ground level is the sameto that of the cloud base. On the other side, the relative humidity canbe altered by changing the amount of water vapor or the temperaturein the atmosphere (Peixoto and Oort, 1996) explaining that a constantrelative humidity (assumption (a)) is also a coarse approach for the iso-topic detection of sub-cloud processes in precipitation.

Under the assumption that the relative humidity is the same at alltropospheric levels, Sonntag et al. (1983) and Deshpande et al. (2010)found an exponential relationship with altitude for the isotopic compo-sition of water vapor in the lower troposphere,

δiva zð Þ ¼ δiva zg� �þ 103

� �exp − aieq;l−v−1

� � zH

� �h i−103 ð19Þ

with δvai (z) and δvai (zg) the isotopic compositions of water vapor at agiven vertical level z and the ground surface zg respectively and H isthe atmospheric scale height. The equilibrium fractionation factoraeq,l − v is expressed at the cloud base temperature. The isotopic compo-sition of water vapor at the cloud base is expected to reach isotopicequilibriumwith precipitation and significantly differs from the isotopiccontent of water vapor and precipitation at the ground level (Eq. (19)).This deviation diminishes at low temperatures due to high equilibriumfractionation factors and also at higher temperatures due to secondaryprocesses, such as below cloud evaporation and isotopic exchange.

The sub-cloud evaporation effect reduces the raindrop size at eachvertical level, depleting also the surrounding water vapor since thelighter isotopologues are distributed in vapor. However the isotopiccontribution of the evaporated raindrops to the surrounding watervapor is negligible in comparison to the vertical composition of watervapor developed in accordance to the tropospheric specific humidityvariation. Thus in Eq. (11) the isotopic composition of water vapor isexpressed by Eq. (19) neglecting the small contribution from the evap-oration of raindrops.

3.3.3. Initial conditions and numerical schemeThe vertical profile of the isotopic composition of falling raindrops

forms a system of differential equations (Eqs. (4), (11), (13), (17))and can be defined as an initial value problem solved numerically.Here, the LSODA algorithm (Petzold, 1983) from the package deSolve(Soetaert et al., 2010) of the R language (R Core Team, 2013) is applied.Initial values for air temperature, raindrop temperature, raindrop diam-eter, evaporated mass fraction and isotopic composition of raindrops atthe cloud base level need to be specified.

The initial isotopic composition of cloud basewater vapor is calculat-ed using Eq. (19) for z= zcbwhile the equilibrium fractionation factor iscomputed at the cloud base temperature. At cloud base, vapor and liq-uid phases are in isotopic equilibrium and the initial isotopic composi-tion of raindrops, δli(zcb), is expressed using the equation,

δil zcbð Þ ¼ aieq;l−v Tr zcbð Þð Þ δiva zcbð Þ−103� �

−103 ð20Þ

with δvai (zcb) the isotopic composition of water vapor at the cloud baseand aeq, l−v

i (Tr(zcb)) the equilibrium fractionation factor at the raindroptemperature. The isotopic composition of water vapor at the ground

level is expressed using real measurements obtained through theGNIP/ISOHIS database where a homogenous relative humidity layer isused for the simulations of the isotopic numerical model.

4. Results and discussions

4.1. δ2Η, δ18O in precipitation/water vapor andwater lines for GNIP stations

Stable isotopic data for water vapor/precipitation on an event basiswere obtained through the GNIP/ISOHIS database for various stationslocated in the Northern Hemisphere. The isotopic data were selectedwithin almost the same time period (2000–2003) except from the sta-tion in Azores where both rainfall and vapor samples were collectedin 1998–1999. Summary statistics for the isotopic composition of pre-cipitation and water vapor are shown in Table 1.

δ18Ο in precipitation or water vapor (values in parentheses) rangesbetween−30.22‰ (−32.93‰) and 3.18‰ (−6.17‰), and δ2Η rangesbetween −235.7‰ (−225.0‰) and 22.1‰ (−15.4‰) showing highvariability. The isotopic values of water vapor reflect the reciprocal de-pletion in comparison to precipitation since the heavier isotopic speciesare preferentially distributed in the condensed phases. The observedhigh isotopic variability indicates that different isotopic signatures areassociated with different meteorological conditions and synoptic circu-lation patterns since the observed isotopic composition is an integratedproduct of the underlying physical processes taking place during thecourse of the water mass from the vapor source to the sampling areaand during the precipitation process.

The sampling sites are divided according to their coastal proximityinto two groups (A-coastal and B-continental stations). As shown inTable 1, the isotopic content for precipitation andwater vapor ismore de-pleted for group B (Ankara,Madrid andVienna) in comparison to groupA(Azores, Lisbon and Rehovot). For the continental group the average iso-topic values (δ18Ο and δ2Η) of rainfall are−7.82‰ (arithmetic)/−8.2‰(weighted) and−54.8‰ (arithmetic)/−56.2‰ (weighted)while the av-erage values for the coastal group are−3.35‰ (−4.47‰) and −13.4‰(−21.2‰). On the other hand, the average δ18Ο and δ2Η for watervapor are −17.98‰ and −125.2‰ for group A and −12.78‰ and−74‰ for group B. The isotopic data in precipitation and water vaporare significantly different at the 99% confidence level for the two groupsaccording to the Wilcoxon rank-sum test (p-value bb 0.01). The isotopicdepletion in continental locations is explained by the ‘continentality ef-fect’ i.e. the progressive rainout when the air masses are moving inlandfrom the moisture source. Continentality is controlled by the latitude ofthe location and the annual temperature range. A higher annual temper-ature range corresponds to higher seasonal temperature amplitude at sta-tions located at similar altitudes and latitudes which in turn affects theequilibrium fractionation factors and the initial isotopic composition ofan air mass prior to the precipitation event, and consequently controlsthe final collected isotopic composition.

Ameasure for thedeviation from the equilibriumstate is also thedif-ference between the isotopic composition of rainfall and water vapor(Δδi=δpi −δvi ). If the isotopic difference is comparable to the equilibri-um enrichment (εi ,∗=103(aeq , l−v

i −1)) then liquid and vapor are inisotopic equilibrium. In order to check the statistical difference betweenΔδi and εi,⁎ the two samples t-test is applied. In case of deuterium the t-test results are consistent for all stations. The t-statistic is stronglynegative (−3.5 b t-statistic b −13.1) and the corresponding p-values are lower than 0.05 indicating that Δδ2Η differs significantlyfrom ε2,⁎. The stations of Madrid and Vienna show that Δδ18O andε18,⁎ are significantly different (respective t-statistic = −2.17 and−2.48 and p-value b 0.05) while for the remaining stations the p-value N0.05 and the null hypothesis of the t-test cannot be rejected.Generally the t-test results show that in rainy days the rainwaterand the water vapor at the ground level are not in isotopic equilib-rium since the results for the deuterium imply the presence of kinet-ic fractionation phenomena.

Table 1Summary statistics of the isotopic and meteorological measurements and Meteoric Water Lines for the GNIP stations used.*

Station Type δ18Ο (‰) δ2H (‰) θ (°C) RH (%)

Min Mean Max wMean⁎ Min Mean Max wMean

Azores Precipitation −9.54 −2.59 (±0.24) 1.47 −3.38 (±0.06) −69.1 −10.1 (±0.9) 12.3 −16 (±0.4) 18.2 N/A⁎⁎

Ankara −30.22 −8.82 (±0.76) 3.18 −8.58 (±0.16) −235.7 −60.4 (±5.1) 13.2 −57.4 (±1.2) 9.5 N/ALisbon −11.85 −3.16 (±0.39) 0.37 −4.44 (±0.09) −80.4 −14.4 (±1.8) 12.8 −24.4 (±0.7) N/A N/AMadrid −17.03 −7.16 (±0.67) 5 −7.82 (±0.15) −129.8 −48.6 (±4.5) 12.1 −53.1 (±1.1) 9.9 81.2Rehovot −9.43 −4.31 (±0.39) 1.8 −5.58 (±0.05) −58.5 −15.9 (±1.6) 22.1 −23.2 (±0.4) 14.4 N/AVienna −24.26 −7.48 (±0.57) 2.1 −8.19 (±0.09) −188.4 −55.3 (±4.2) 14 −58.2 (±0.7) 12.4 76.6Azores Water vapor −16.99 −12.09 (±0.93) −6.17 −88.6 −47.8 (±3.7) −15.4 19.0 N/AAnkara −32.93 −18.66 (±1.29) −11.75 −225.0 −123.9 (±8.3) −19.6 12.3 N/ALisbon −17.29 −13.59 (±2) −11.33 −110.2 −90.4 (±13.3) −70.4 N/A N/AMadrid −24.57 −16.19 (±1.18) −10.40 −161.2 −115.4 (±8.4) −70.5 9.4 70.7Rehovot −18.39 −12.67 (±1.04) −9.25 −118.7 −83.8 (±7.7) −66.3 17.6 N/AVienna −30.27 −19.09 (±2.28) −11.59 −210.5 −136.2 (±16.3) −72.3 10.5 75.2Azores Precipitation &

Water vaporPrecipitation −9.37 −3.17 (±0.54) 0.64 −4.12 (±0.12) −66.9 −12.5 (±2.2) 12.3 −20.1 (±1) 17.3 N/A

Ankara −30.22 −8.86 (±1.54) 1.00 −9.42 (±0.36) −235.7 −61.5 (±10.7) 2 −63.5 (±2.8) 8 N/ALisbon −7.95 −2.96 (±0.62) −0.62 −3.59 (±0.18) −54.1 −12.4 (±2.7) 8.9 −19.3 (±1.5) N/A N/AMadrid −17.03 −6.58 (±0.92) 5.00 −7.40 (±0.24) −129.8 −44.3 (±6.2) 12.1 −50.2 (±1.7) 10.2 82Rehovot −8.56 −4.29 (±0.78) −0.12 −5.44 (±0.07) −47.0 −16.5 (±3.2) 18.7 −23.1 (±0.5) 14 N/AVienna −15.64 −7.21 (±1.5) 0.34 −8.58 (±0.31) −120.0 −52.8 (±11) −2.4 −60.8 (±2.1) 9.8 79.2Azores Water vapor −16.99 −12.93 (±2.22) −6.96 −88.6 −51.0 (±8.7) −16.7 17.3 N/AAnkara −31.67 −19.8 (±3.45) −12.64 −225.0 −139.7 (±24.3) −91.6 8 N/ALisbon −17.29 −13.13 (±2.74) −11.33 −110.2 −88.0 (±18.3) −70.4 N/A N/AMadrid −24.57 −16.11 (±2.26) −11.2 −152.4 −116.2 (±16.3) −77.1 10.2 82Rehovot −16.99 −13.72 (±2.51) −10.93 −115.8 −88.6 (±18.1) −71.5 14 N/AVienna −30.27 −19.09 (±3.98) −11.59 −210.5 −135.7 (±28.3) −72.3 9.8 79.2

Precipitation Water vapor Intersection points

αLMWL bLMWL (‰) R2 αT Δα⁎⁎⁎ αVEL bVEL (‰) R2 δ18Ο (‰) δ2Η (‰)

Azores Meteoric Lines (LMWL & VEL) 7.59 (±0.18) 9.62 (±0.7) 0.94 8.65 1.06/0.41 4.50 (±0.27) 6.88 (±3.37) 0.62 −0.89 (±0.07) 2.9 (±0.2)Ankara 7.57 (±0.1) 6.98 (±0.99) 0.98 8.7 1.13/0.43 6.76 (±0.08) −4.95 (±1.44) 0.97 −14.80 (±1.02) −105.2 (±7.3)Lisbon 7.64 (±0.21) 9.67 (±1.05) 0.96 N/A N/A/0.36 5.65 (±0.57) −13.62 (±7.81) 0.69 −11.73 (±1.73) −79.9 (±11.8)Madrid 7.33 (±0.17) 4.21 (±1.45) 0.94 8.71 1.39/0.68 6.72 (±0.18) −6.69 (±2.88) 0.89 −17.95 (±1.30) −126.7 (±9.2)Rehovot 7.35 (±0.29) 18.21 (±1.75) 0.87 8.77 1.42/0.65 5.79 (±0.26) −10.8 (±3.33) 0.81 −18.57 (±1.71) −127.3 (±9.3)Vienna 7.57 (±0.14) 3.83 (±1.24) 0.94 8.56 0.99/0.43 7.06 (±0.1) −1.47 (±2.01) 0.99 −10.22 (±1.22) −73.6 (±8.8)

⁎ w-Weighted, ⁎⁎N/A- Not Available, ⁎⁎⁎Δα= αΤ − αMWL or Δα= αC − αMWL = 8 − αMWL (in the brackets).

1064 V. Salamalikis et al. / Science of the Total Environment 544 (2016) 1059–1072

The Meteoric Water Line for each station is determined by applyingthe Precipitation Weighted Least Squares Regression (Hughes andCrawford, 2012). The precipitation weighting scheme balances insome extent the contribution of the small precipitation events into thecalculation of the LMWL. The ordinary least squares method is usedfor the determination of the Vapor Evaporation Lines. All stations haveMWL slopes lower than 8 indicating the existence of secondary evapo-ration phenomena beneath the cloud base (Table 1). During sub-cloudevaporation more 18Ο is distributed in the liquid phase reducing theslope (Δδ2Η/Δδ18Ο) of the MWL. In order to check the statistical signif-icance of the difference between the MWLs and the GMWL the follow-ing procedure is applied. First δ2HGMWL data are calculated based on theδ18Ο values for each station and the GMWL equation. Then the ANOVA(Analysis of Variance) and the F-ratio tests are applied taking as null hy-pothesis that δ2H-δ2ΗGMWL = C with C a constant while the alternativehypothesis is δ2H-δ2ΗGMWL = f(δ18Ο). For the station in Rehovot theabove procedure is performed using the Eastern Mediterranean WaterLine (δ2Η=8 δ18Ο+22‰; Gat and Carmi, 1970). The F-ratio ranges be-tween 4.3 and 19.3 with p-values b0.05. This reveals that the isotopiccomposition in each station is far from equilibrium and the GMWL orthe EMWL cannot explain accurately the isotopic variability. The slopesof the MWLs are compared against the theoretical Rayleigh slopes, αT.All αLMWL values are significantly lower than αT suggesting that precip-itation suffers from raindrop evaporation. Rehovot depicts the higherslope difference (aT = 8.77, Δα = α-αΤ = 1.42) indicating the highestdeviation from the equilibrium state and the strongest presence of ki-netic fractionation.

The intercepts vary with low values in Madrid and Vienna, and highvalues in Rehovot while the intercepts in the remaining stations areclose to the global average (10‰). In the case of Rehovot, the intercept

value (18.21‰) reflects themoisture characteristics of the EasternMed-iterranean Basin where the evaporation processes occur within low hu-midity continental air masses. Thus a comparison with an intercept of10‰may give erroneous results for the interpretation of the attributedatmospheric processes. Generally, when the intercept is higher than10‰ the main factor that contributes to this positive difference is thecontinental recycling effect (Gat and Matsui, 1991); additional recycledmoisture from land feeds the precipitation process altering the interceptof the MWL. Finally, the comparison of the intercept value (18.21‰)with the EasternMediterranean average (22‰), it suggests that second-ary evaporation phenomena may contribute to the precipitation inRehovot.

The parameters of the Vapor Evaporation Lines are also shown inTable 1. The δ-pairs are placed on the left side of the GMWL (Fig. S1)exhibiting lower slopes in comparison to the LMWLs and the GMWL(Table 1). The slope of the VEL is an indicator of relative humidityconditions occurring during evaporation. The slopes range between4.50 and 6.72 indicating evaporation under different humidity regimes(RH ≥ 50%). According to Table 1, the Azores station has the lowestslope (αVEL = 4.5) and evaporation at 50% relative humidity(Gonfiantini, 1986). However, the relatively low coefficient of deter-mination (R2 = 0.69) indicates that the Ordinary Least Squaresmethod is unable to describe with high predictive power the δ-relationship since the vapor samples are not solely placed on a straightline but group at an elliptical scheme. The δ18Ο and δ2Η values of watervapor are distributed along a straight line in Ankara and Vienna providinghigh R2 values and low standard errors for the VELs parameters (Table 1).Thus the VELs for those stations can be applied to fill themissing values inthe vapor isotopic time series when one of δ18Ο or δ2H has not beenanalyzed.

1065V. Salamalikis et al. / Science of the Total Environment 544 (2016) 1059–1072

Further information from the Water Lines can be extracted throughthe intersection between the MWL and VEL. The intersection point de-termines the ‘initial’ isotopic composition and it is considered as thestarting point prior to evaporative enrichment. A varying ‘initial’ isoto-pic composition is detected with the highest values in the Azores(δ18O = −0.89‰, δ2H = 2.9‰). This station receives precipitationwith an ‘early’ stage rainout where the isotopic composition is modifiedmainly by local meteorological factors resulting to less depleted ‘initial’isotopic values. The ‘initial’ isotopic data for the remaining stations can-not be clustered to distinct groups according to their isotopic character-istics since low values were found in Ankara, Madrid and Rehovot andintermediate isotopic values in Lisbon and Vienna (Fig. S1; Table 1).

4.2. Isotopic enrichment of falling raindrops using an isotope-evaporationmodel

The isotopic enrichment (Δδ) and the remaining mass fraction (fr)are calculated using the isotope-evaporation model (Eq. (5)) and thestation-precipitation model (Eq. (6)) for each (θi, RHi) pair and for var-ious raindrop sizes (1 mm ≤ D ≤ 3 mm), with i = 1,…,n and n the num-ber of measurements. Since relative humidity data are available only forMadrid and Vienna, the calculation of the isotopic enrichment based onStewart's model is possible only for those two sampling locations. Ac-cording to Table 1 and the previous discussion in Section 4.1, Madridand Vienna belong to the continental isotope group exhibiting similarisotopic characteristics. Therefore, the two datasets can be merged togenerate a new augmented dataset for further analysis. The resultsfrom the isotopic enrichment calculations are represented in Table 2and Fig. 1.

The isotopic enrichment ranges between 0.03‰ and 20.11‰ for 18Owhile for 2H between0.0‰ and 70.3‰depending on the raindrop diam-eter. Higher isotopic enrichment corresponds to lower raindrop sizessince the smaller raindrops are more favorable to evaporation. The re-maining mass fraction is calculated between 0% and 79% where thezero values indicate that the falling raindrops remain unaffected bysub-cloud evaporation, either because they are falling under saturatedenvironmental conditions or because they are large enough and theevaporation process is negligible. The isotopic enrichment is linearly re-lated to the evaporated mass fraction EF = 1 − f, for both stable water

isotopes (Fig. 1 and Fig. S2a, b) according toΔδ ¼ ΔðΔδÞΔðEFÞ EF þ b. The slopes

Δδ/EF are 0.25‰/%–0.29‰/% for δ18O and 0.9‰/%–1.0‰/% for δ2H whilefor the combined dataset the Δδ/EF slopes spans between 0.25‰/% and0.28‰/% for 18O and for 2H the Δδ/EF values are around 0.9‰/%.

According to the lower mass and higher vapor pressure, 1H2H16O ismore favorable to evaporation than 1H2

18O leaving the remaining rain-drops less enriched in deuterium. Therefore the change in respect tothe ‘initial’ isotopic composition for δ18O is expected to be higher than

δ2H. To confirm this fact the quantityAið%Þ ¼ 100� ðδilðzcbÞ−δilðzgÞδil;in

Þis calcu-lated. The numerator represents the opposite of the evaporative enrich-ment while the denominator δl , ini is the ‘initial’ isotopic composition ofliquid phase prior to evaporative enrichment. An initial guess for thestarting isotopic composition (δl , ini ) prior to evaporative enrichment istaken by the intersection between the Meteoric Water line and theVapor Evaporation Line for each station (Section 4.1; Table 1). Highervalues of Ai correspond to 18Ο and smaller raindrop diameterwhich agrees with the previous discussion. The A18O and A2H valuesrange between 0%–57% and 0%–29% respectively. In Vienna the ‘ini-tial’ isotopic composition is relatively enriched compared to that ofMadrid (Table 1) and the corresponding Ai values are higher. AlsoAi is higher for smaller raindrop diameters since the difference be-tween the isotopic composition of the cloud base and the groundgets higher.

In order to compare the above results with published works, thedecrease in deuterium excess d (=δ2Η-8 δ18Ο) per evaporated fraction

is calculated. Following the definition of d, the change in d per evaporat-

ed fraction is derived: ΔdEF ¼ Δδ2H

EF −8 Δδ18OEF , ranging from −1.1‰/% to

−1.3‰/%. The minus sign in the Δd/EF values makes sense since theevaporation process tends to reduce d. Froehlich et al. (2008) examinedthe decrease in the deuterium excess in the humid Alps regions. Theyfound a similar decrease by 1.1‰ per 1% evaporated fraction for moun-tain and plain stations despite of the elevation difference. Similar valuesfor the deuterium excess change (1.1–1.2‰ decrease per 1% evaporatedfraction)where found also by Kong et al. (2013) in the region of EasternTianshan, Central Asia.

As already explained, relative humidity is an excellent indicatorfor the sub-cloud evaporation effect. Generally low relative humiditycorresponds to high evaporation rate and consequently to high isotopicenrichment. This relationship is examined by applying a statisticalmodel; here is the ‘heat capacity’ model, for each raindrop diameterbin. The ‘heat capacity’ model follows the equation y = A + Bx + C/x2

with x the fractional relative humidity, y the isotopic enrichment for18O and 2H and A, B and C the model coefficients. For each station andraindrop diameter the statistical models show high predictive perfor-mance with the coefficient of determination (R2) ranging between81% and 91% for 18O and from 86% to 94% for 2H. Similar results are ob-tained for the combined data set (Table 2) with high R2 values for bothisotopic species (81%–88% for 18O and 86%–92% for 2H).Themodel coef-ficients decrease for higher raindrop diameters since the isotopicenrichment is reducedwith theweaker presence of the sub-cloud evap-oration effect.

Furthermore the isotopic enrichment for each raindrop diameter isgrouped in relative humidity bins ranging from 50% to 100% with astep of 10%. The relative humidity values are rounded to the closest de-cade i.e. the group of RH=90% includes isotopic enrichment datawith-in the range 85% ≤ RH b 95%. The results are summarized using box-plots of isotopic enrichment per raindrop diameter and relative humid-ity bin (Fig. S2). For each case the isotopic enrichment decreases expo-nentially with increasing diameter. In case of RH ≥ 90%, low values ofΔδ18Ο and Δδ2Η are calculated ranging from 0.22‰ - 2.69‰ and 0.9‰- 9.8‰. In case of D = 1 mm the median values are close to 1.54‰(RH = 90%) and 0.39‰ (RH = 100%) for Δδ18Ο, and 5.8‰ (RH =90%) and 1.45‰ (RH = 100%) for Δδ2H. Even if the raindrops are verysmall, the isotopic enrichment approaches zero for almost saturated en-vironments explaining that for RH ≥ 90% the isotopic composition doesnot change significantly by the sub-cloud evaporation effect.

For 50% ≤ RH ≤ 80% the isotopic enrichment follows again the expo-nential decrease with increasing diameter; however the isotopic com-position for each raindrop diameter becomes more variable. A possibleexplanation for this variability could be attributed to temperature. Airtemperature plays a significant role in the sub-cloud evaporation.Higher temperature values enhance evaporation, reducing the remain-ing raindropmass fraction, altering also the isotopic composition in fall-ing raindrops. In order to confirm this fact Δδ18Ο is calculated for RH=70% and θ=10 °C, 20 °C and 30 °C for two raindrop diameters (1.2 mmand 2.8mm). For these calculations the initial elevation is taken equal to1500 m.

For the first raindrop diameter (D = 1.2 mm) the Δδ18O values are7.37‰, 11.16‰ and 16.79‰ respectively. This means that for a temper-ature increase of 10 °C, the isotopic enrichment increases approximatelyby 51% and 50%. On the other hand, the larger raindrop (D = 2.8 mm)provides Δδ18Ο equal to 0.58‰, 0.89‰ and 1.30‰ with an increase of53% and 46% per 10 °C increase. Even if the increase percentage of theisotopic enrichment is almost the same for the two raindrop diameters,the values of the isotopic enrichment are significantly different for thesame temperatures. In order to explain this fact the remaining raindropmass fraction fr is examined. The fr values for D = 1.2 mm and 2.8 mmare 0.75, 0.61, 0.40 and 0.98, 0.97, 0.95 respectively, implying that thesmaller raindrop sizes are more sensitive to temperature changes. Theabove discussion is verified by the examination of the boxplots of the

Table 2Statistical relationship between the isotopic enrichment (Δδ) and the evaporated mass fraction (EF) and relative humidity (RH) for Madrid, Vienna and the merged data set.

Statistical models Raindrop diameter (mm)

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

Madrid-RetiroΔδ = f(EF) Δδ18O/ΔEF 0.27 0.28 0.28 0.28 0.28 0.29 0.29 0.29 0.29 0.29 0.29

Δδ2H/ΔEF 0.98 1.00 1.01 1.01 1.01 1.02 1.02 1.02 1.02 1.02 1.02Δd/ΔΕF −1.14 −1.20 −1.24 −1.25 −1.27 −1.27 −1.28 −1.28 −1.28 −1.28 −1.29

Δδ18O = f(RH) A (±sA) 5 (±3) 6 (±2) 5 (±1) 3.57 (±0.82) 2.65 (±0.59) 2.00 (±0.43) 1.53 (±0.33) 1.20 (±0 ) 0.9 (±0.2) 0.77 (±0.16) 0.63 (±0.13)B (±sB) −9 (±3) −8 (±2) −6 (±1) −4.17 (±0.74) −3.05 (±0.53) −2.28 (±0.39) −1.7 (±0.3) −1.36 (± .23) −1.08 (±0.18) −0.87 (±0.15) −0.71 (±0.12)C (±sC) 3.21 (±0.45) 1.5 (±0.3) 0.8 (±0.2) 0.48 (±0.14) 0.3 (±0.1) 0.22 (±0.07) 0.16 (±0.06) 0.12 (±0 ) 0.09 (±0.03) 0.07 (±0.03) 0.06 (±0.02)R2 0.91 0.89 0.88 0.88 0.87 0.87 0.87 0.87 0.87 0.87 0.87

Δδ2H = f(RH) A (±sA) 22 (±8) 24 (±5) 18 (±4) 14 (±2) 10 (±2) 8 (±1) 5.80 (±0.99) 4.53 (±0 6) 3.6 (±0.6) 2.90 (±0.48) 2.36 (±0.39)B (±sB) −35 (±8) −30 (±5) −22 (±3) −16 (±2) −11 (±2) −9 (±1) −6.52 (±0.89) −5.08 (± .69) −4.02 (±0.55) −3.24 (±0.44) −2.64 (±0.36)C (±sC) 12 (±1) 5.27 (±0.92) 2.78 (±2.61) 1.67 (±0.42) 1.1 (±0.3) 0.76 (±0.22) 0.55 (±0.17) 0.41 (±0 ) 0.3 (±0.1) 0.25 (±0.08) 0.20 (±0.08)R2 0.94 0.93 0.92 0.91 0.91 0.91 0.91 0.91 0.91 0.90 0.90

ViennaΔδ = f(EF) Δδ18O/ΔEF 0.25 0.26 0.27 0.27 0.28 0.28 0.28 0.28 0.28 0.28 0.28

Δδ2H/ΔEF 0.87 0.90 0.91 0.92 0.92 0.92 0.93 0.93 0.93 0.93 0.93Δd/ΔΕF −1.10 −1.19 −1.24 −1.26 −1.28 −1.28 −1.29 −1.29 −1.30 −1.30 −1.30

Δδ18O = f(RH) A (±sA) 1 (±5) 5 (±3) 5 (±2) 4 (±2) 3 (±1) 2.38 (±0.83) 1.86 (±0.63) 1.47 (±0 9) 1.17 (±0.39) 0.95 (±0.31) 0.78 (±0.25)B (±sB) −7 (±4) −8 (±3) −7 (±2) −5 (±1) −4 (±1) −2.88 (±0.76) −2.23 (±0.58) −1.75 (± .45) −1.39 (±0.36) −1.13 (±0.29) −0.92 (±0.23)C (±sC) 5.40 (±0.79) 2.47 (±0.55) 1.32 (±0.37) 0.79 (±0.26) 0.51 (±0.19) 0.36 (±0.14) 0.26 (±0.10) 0.19 (±0 ) 0.12 (±0.05) 0.09 (±0.04) 0.09 (±0.03)R2 0.89 0.86 0.84 0.83 0.83 0.82 0.82 0.82 0.82 0.82 0.81

Δδ2H = f(RH) A (±sA) 1 (±14) 20 (±10) 19 (±7) 15 (±5) 11 (±3) 9 (±2) 7 (±2) 5 (±1) 4 (±1) 3.5 (±0.9) 2.83 (±0.73)B (±sB) −22 (±13) −30 (±9) −24 (±6) −18 (±4) −14 (±3) −10 (±2) −8 (±2) −6 (±1) −5 (±1) −4.01 (±0.82) −3.28 (±0.67)C (±sC) 20 (±2) 8.6 (±2) 4 (±1) 2.60 (±0.75) 1.67 (±0.54) 1.1 (±0.4) 0.8 (±0.3) 0.62 (±0 ) 0.47 (±0.19) 0.37 (±0.15) 0.30 (±0.12)R2 0.92 0.90 0.88 0.88 0.87 0.87 0.87 0.86 0.86 0.86 0.86

MergedΔδ = f(EF) Δδ18O/ΔEF 0.25 0.26 0.27 0.27 0.28 0.28 0.28 0.28 0.28 0.28 0.28

Δδ2H/ΔEF 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9Δd/ΔΕF −1.1 −1.2 −1.2 −1.3 −1.3 −1.3 −1.3 −1.3 −1.3 −1.3 −1.3

Δδ18O = f(RH) A (±sA) 4 (±3) 6 (±2) 5 (±1) 4 (±1) 3.04 (±0.72) 2.32 (±0.53) 1.79 (±0.40) 1.41 (±0 ) 1.12 (±0.25) 0.91 (±0.20) 0.74 (±0.16)B (±sB) −9 (±3) −9 (±2) −6 (±1) −5.0 (±0.9) −3.67 (±0.65) −2.77 (±0.48) −2.13 (±0.37) −1.66 (± .28) −1.32 (±0.22) −1.07 (±0.18) −0.87 (±0.15)C (±sC) 4.52 (±0.52) 2.09 (±0.36) 1.13 (±0.24) 0.69 (±0.17) 0.45 (±0.12) 0.32 (±0.09) 0.23 (±0.07) 0.17 (±0 ) 0.13 (±0.04) 0.11 (±0.03) 0.09 (±0.03)R2 0.88 0.85 0.84 0.83 0.82 0.82 0.82 0.82 0.81 0.81 0.81

Δδ2H = f(RH) A (±sA) 13 (±110) 23 (±7) 19 (±4) 14 (±3) 11 (±2) 9 (±2) 7 (±1) 5.2 (±0.9 4.10 (±0.71) 3.32 (±0.57) 2.71 (±0.47)B (±sB) −32 (±9) −32 (±6) −24 (±4) −18 (±3) −13 (±2) −10 (±1) −8 (±1) −5.97 (± .82) −4.74 (±0.65) −3.82 (±0.52) −3.13 (±0.42)C (±sC) 17 (±2) 7 (±1) 3.8 (±0.7) 2.29 (±0.49) 1.49 (±0.35) 1.03 (±0.26) 0.8 (±0.2) 0.56 (±0 ) 0.43 (±0.12) 0.28 (±0.08) 0.3 (±0.1)R2 0.91 0.89 0.88 0.87 0.87 0.87 0.86 0.86 0.86 0.86 0.86

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.310.05

)0.15

Fig. 1. Isotopic enrichment calculated from the isotope-evaporationmodel using themerged station dataset. a, b) linear relationship betweenΔδi and the evaporatedmass fraction. c, d)Δδi

versus relative humidity. The solid lines correspond to the ‘heat capacity’models. The coefficients for the non-linearmodels are reduced for smaller raindrop sizes and as the raindrop sizeincreases the scattered data are placed almost at a straight line.

1067V. Salamalikis et al. / Science of the Total Environment 544 (2016) 1059–1072

isotopic enrichment in case of 50% ≤ RH ≤ 80% (Fig. S2). The isotopic en-richment looks highly variable for the smaller raindrop sizes providinghigher interquartile ranges in the boxplots.

4.3. Isotopic enrichment using a numerical isotope evaporation model

4.3.1. Initial conditionsThe system of the differential equations used for the interpretation

of the isotopic composition of falling raindrops and its vertical structureis described as an initial value problem. In order to apply a numericalmethod - here the LSODA numerical scheme - initial values for air tem-perature, raindrop temperature, raindrop diameter, isotopic composi-tion of raindrops at the cloud base and evaporation rate have to bespecified. However parameters such as the relative humidity (RH) andthe stable isotopic composition of water vapor at the ground levelmust be provided in advance since they are required for solving theabove differential equations. Also, they are not accounted as initial con-ditions for the differentiation problem since their values are assumedconstant for the overall evaluation.

The air temperature at ground level ranges between 5 °C to 30 °Cwith a step of 5 °C. Assuming that the air temperature follows themean moist adiabatic lapse rate and using a mean cloud base elevationat about 1500 m, the cloud base temperatures are calculated and theyare taken as the initial values of the air temperature for the differentia-tion problem. The relative humidity ranges from 40% to 90% with an in-crement of 10%. In order to investigate the vertical isotopic structure atalmost saturated environmental conditions, a relative humidity equal to95% is also applied. The initial raindrop temperature is calculated by thewet bulb temperature formula (Table A1) using the air temperature atthe cloud base and the relative humidity. The initial raindrop diametervaries between 1 mm and 3 mm with an increment of 0.2 mm whilethe initial evaporated mass fraction is taken equal to zero.

As already explained initial values for the isotopic compositionof raindrops at the cloud base as well as the isotopic composition ofgroundwater vapor are necessary as initial conditions for the numericalsimulations. In Section 4.2, amerged dataset is used for the evaluation ofthe isotope-enrichment model and the calculation of the isotopic en-richment of falling raindrops under various meteorological conditionsand raindrop sizes. The average isotopic composition of ground watervapor is derived for different relative humidity values.Without splittingthe isotopic composition of water vapor into relative humidity binsδ18Οv deviates from the normality case according to the Anderson–Darling test (p-value= 0.0001) under the 99% confidence level. Gener-ally the average isotopic composition is−16.98‰with a standard devi-ation of 3.13‰. Summary statistics for the isotopic composition of theground level water vapor per relative humidity bin are represented inTable S1. δ18O in water vapor per relative humidity class ranges be-tween −16.39‰ and −18.67‰ with a mean value of −17.35‰ (s.d.2.8‰). A first check whether the isotopic samples follow the normal dis-tribution is performed using the Anderson-Darling test while theKruskal–Wallis non-parametric test is applied for the examination ofthe (non-) distinction of the isotopic groups. According to Table S1,δ18Οv is close to normality if separate samples are assumed, providingp-values higher than 0.01 under the 99% confidence level while the nullhypothesis (similar mean values) of the Kruskal-Wallis test cannot berejected comparing the isotopic composition of water vapor for50% ≤ RH ≤ 90% with p-value = 0.53. Thus the isotopic composition ofground level water vapor is coarsely assumed to range between −23‰to−11% centered at−17‰. Following this coarse representation of theisotopic composition of the ground level water vapor, the initial isotopiccomposition of raindrops at the cloud base is derived through a twostage procedure. First the isotopic composition of the cloud basewater vapor is specified using the Eq. (19) and then, under the as-sumption that liquid and vapor phases are in isotopic equilibrium at the

1068 V. Salamalikis et al. / Science of the Total Environment 544 (2016) 1059–1072

raindrop's surface, Eq. (20) is applied for the estimation of the initialisotopic composition of raindrops. Overall the numerical isotope-evaporation model simulates the vertical isotopic structure of a fall-ing raindrop for 2310 different initial conditions.

4.3.2. Numerical simulationsUsing the numerical procedure explicitly described in Section 3.3

and according to the initial meteorological and isotopic conditions de-scribed previously, the vertical variation of stable isotopes of fallingraindrops is determined. Due to the large number of numerical simula-tions, three temperatures (5 °C, 15 °C and 30 °C) and three relative hu-midity (40%, 70% and 95%) cases are selected in order to discuss theimpact of sub-cloud evaporation on the falling raindrops in terms oftheir isotopic composition. Fig. 2 visualizes the δ18O in falling raindropswhile similar findings are expected for deuterium due to the strong cor-relation between the two isotopologues.

For each pair of meteorological conditions the vertical distribution ofstable isotopes of falling raindrops is simulated for various raindropsizes. The solid lines and the confidence bands in Fig. 2 correspond tothe mean and the standard deviation of the numerical simulations,since different isotopic compositions of ground level water vapor andraindrops in the cloud base are used. Generally for each single imagethe isotopic composition is simulated for five isotopic values of groundwater vapor following the three-sigma rule described in the previous sec-tion. Then themean and the standarddeviation of the simulations are cal-culated for every vertical step. The isotopic enrichment is also calculatedin order to investigate the contribution of sub cloud evaporation duringthe descent of the raindrops from the cloud base towards the ground.

Table 3 provides the δ18O and δ2H enrichment in falling raindropsbased on the simulations of the isotopic-numerical model. The isotopicenrichment is defined as the difference between the initial and the finalisotopic composition. Also the falling distance is derived as the overalldistance covered by the falling raindrops during their trip from thecloud base to the ground surface. The cloud base elevation is taken ataround 1500 m above surface. Therefore falling distances lower than1500 m imply that sub cloud evaporation processes occurring beneaththe cloud base can completely evaporate the falling raindrops beforereaching the surface. Generally the isotopic enrichment is higherfor lower humidity and higher temperature values and for smallerraindrops.

Fig. 2 shows the vertical isotopic composition of raindrops for the se-lected meteorological conditions. The three first plots (Fig. 2a, b andc) correspond to RH = 40% and temperatures equal to 5 °C, 15 °C and30 °C respectively. In the case of θ = 5 °C almost all the raindropsreach the ground surface with enriched isotopic signatures. Since thesub-cloud evaporation effect is more pronounced on smaller raindrops,raindrops with D ≤ 1.2 mm are completely evaporated before reachingthe ground surface and their δ18O is up to 20‰ explaining the high iso-topic enrichment in falling raindrops during their descent under lowhumidity conditions. Since higher temperatures enhance the subcloud evaporation effect, raindrops with D ≤ 2.2 mm cannot reach theground surface when θ = 15 °C; when θ = 30 °C they are completelyevaporated after 1000 m beneath cloud base and their isotopic compo-sition is highly enriched. The above findings are also reported in Table 3in terms of the isotopic enrichment and the overall traveling distance ofthe falling raindrops.

The values in Table 3 correspond to the total isotopic enrichment ofthe falling raindrops and not the relative isotopic enrichment per fallingdistance. In case of RH = 40% and θ = 15 °C, Δδ18Ο is 32.72 ± 0.15‰and 29.52 ± 0.13‰ for D= 2.2 mm and 1.4 mm respectively. AlthoughΔδ18Ο is higher for D=2.2mm, the traveling distance of the raindrop islonger, namely 500 m more than the raindrop with D = 1.2 mm. Thisindicates that the kinetic fractionation is more intense for smaller rain-drops; actually the induced isotopic enrichment of falling raindrops iscomparable with that of the biggest raindrop (D=2.2mm) for a small-er falling distance. The relationship between Δδ18O and raindrop size is

more clearly depicted for those raindrops that reach the ground surface.For the same meteorological conditions as above but for D ≥ 2.4 mm,Δδ18O is reduced with raindrop size.

The samebehavior for the isotopic enrichment is observed for the in-termediate humidity conditions of 70%. The isotopic composition of fall-ing raindrops is significantly enriched in comparison to the initialisotopic composition (Fig. 2d, e and f). At low temperatures (θ = 5 °C)all raindrop sizes reach the ground surface whereas the isotopic vari-ability is higher for the smaller raindrop sizes. The isotopic compositionfor raindrops with D ≥ 2 mm follows an almost linear relationship withfalling distance and the below cloud evaporation effect does not play asignificant role on the evolution of the stable isotopic composition. Athigher temperatures, a stronger isotopic enrichment is observed. Inthe case of θ = 15 °C, raindrops with D ≤ 1.2 mm are completely evap-orated covering a distance of about 1300mbelow cloud base. Almost allraindrops (D ≤ 2.6mm) do not reach the ground surfacewhen θ=30 °Cresulting to relatively high isotopic differences compared to the isotopiccomposition at the cloudbase. Also for the same temperature conditionsbut for different relative humidities, the isotopic composition increasesin drier atmospheres while the falling distance decreases.

Finally at RH = 95% the ambient air is almost saturated and no sig-nificant variations of the isotopic composition of falling raindrops areobserved. (Table 3; Fig. 2g, h and i). Δδ18O is very low and this demon-strates that at almost saturated atmospheric conditions the sub cloudevaporation effect is negligible. The differences between the isotopic en-richment for D = 1 mm and 3 mm at the three temperature cases are0.64‰, 0.92‰ and 1.11‰ showing that the isotopic difference is verysmall independently from the raindrop size's increase. The temperaturedependence of the isotopic enrichment is clearly shown but Δδ18Ovalues are comparable for each raindrop size. For example when D =1 mm, Δδ18O is equal to 0.83‰, 1.11‰ and 1.33‰ for θ = 5 °C, 15 °Cand 30 °C respectively. Even in higher temperatures the isotopic compo-sition of the falling raindrops is hardly perturbed by the sub cloud evap-oration effect and the final isotopic composition does not changesignificantly compared to the cloud base isotopic composition (Table 3).

For the selected meteorological conditions the isotopic enrichmentis also derived via the isotope-evaporation model described inSection 3.2. This model calculates the isotopic enrichment based onthe prevailing meteorological conditions, without taking into accountthe vertical variations of temperature and the isotopic composition.Those facts are imprinted in the Δδ18Ο values leading to large differ-ences in comparison to the numerical simulations of Δδ18O (Table 3).The nature of the isotope-evaporation model (two member mixingmodel) describes those significant deviations while only in the case ofthe near-saturated atmospheric conditions the two isotopic enrich-ments are generally comparable (Table 3).

5. Conclusions

In this study the sub-cloud evaporation effect on precipitation is in-vestigated in terms of its isotopic composition. In order to detect thevariability of the isotopic signature due to the sub-cloud evaporation ef-fect, three isotopic approaches are followed namely that of MeteoricWater Lines (MWLs), an isotope-evaporation model and a numericalisotope-evaporation model.

First, the slope and intercept of theMWL aswell as the parameters ofthe Vapor Evaporation Lines are examined in order to detect the pres-ence of the bulk evaporation effect on the isotopic composition of pre-cipitation for various stations located in the Northern Hemisphere. Thedeviation of the equilibrium slope is also calculated to assess the inten-sity of the evaporation phenomena. All stations provide slopes lowerthan 8 revealing the existence of kinetic fractionation beneath thecloud base whereas the lowest slopes are represented in Madrid,Spain (αLMWL = 7.33) and Rehovot, Israel (αLMWL = 7.35). Further-more, the highest deviation from the equilibrium state is found for theRehovot, Israel station (Δα= 1.42).

Fig. 2. Vertical structure of the isotopic composition of falling raindrops for various meteorological conditions and raindrop sizes. a, b, c) RH= 40% T= 5 °C, 15 °C, and 30 °C. d, e, f) RH=70% T = 5 °C, 15 °C, and 30 °C. g, h, i) RH = 95% T = 5 °C, 15 °C, and 30 °C.

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In order to measure the impact of the sub-cloud evaporation effectthe isotopic enrichment is calculated using an isotopic-evaporationmodel. This model takes into account the concurrent meteorologicalconditions (temperature and relative humidity) and the initial raindropsize neglecting the vertical structure of temperature and the isotopiccomposition of precipitation/water vapor. Due to the limited availabilityof meteorological information the datasets from Madrid, Spain and Vi-enna, Austria are merged for further analysis. Both isotopic speciesshow a linear relationship with the evaporated mass fraction withslopes ranging between 0.25‰/% and 0.28‰/% for 18O while for 2H the

Δδ/EF values are around 0.9‰/%. Also the change of d per evaporatedfraction spans −1.1‰/% and −1.3‰/% and depicts similar values withthose presented in the literature (Froehlich et al. 2008; Kong et al.,2013). The isotopic enrichment is highly correlated with the raindropdiameter and relative humidity conditions. Generally, Δδ increaseswith decreasing relative humidity and decreasing raindrop size.Δδ is re-lated to RH through a ‘heat capacity’ model providing high coefficientsof determination (81%–88% for 18O and 86%–92% for 2H) indicating thefact that RH is an excellent indicator for the determination of the sub-cloud evaporation phenomenon. Temperature also contributes to the

Table 3Isotopic enrichment and falling distance for raindrops based on the numerical isotopicmodel. The isotopic enrichment is also provided using the isotope-mixing evaporationmodel. The subscripts (n) and (m) correspond to the isotopic numerical andthe mixing evaporation model respectively.

Cases Raindrop diameter (mm)

RH (%) θ (°C) 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

40 5 Δδ18On (‰) 28.81 (±0.13) 31.97 (±0.14) 23.3 (±0.1) 17.55 (±0.08) 14.56 (±0.07) 12.54 (±0.06) 11.06 (±0.050) 9.91 (±0.04) 8.98 (±0.04) 8.22 (±0.04) 7.57 (±0.03)Δδ2Hn (‰) 129.1 (±4.6) 142.5 (±5.1) 113 (±4) 82.9 (± − 2.9) 68 (± − 2.4) 58.2 (±2.1) 51.1 (±1.8) 45.6 (±1.6) 41.2 (±1.5) 37.6 (±1.3) 34.6 (±1.2)Distance (m) 1150 1380 1500 1500 1500 1500 1500 1500 1500 1500 1500Δδ18Om (‰) 13.77 7.62 4.7 3.12 2.18 1.58 1.18 0.91 0.72 0.57 0.46Δδ2Hm (‰) 55 29.9 18.3 12.1 8.4 6.1 4.6 3.5 2.8 2.2 1.8

15 Δδ18On (‰) 22.3 (±0.1) 24.54 (±0.11) 29.52 (±0.13) 28.31 (±0.13) 29.59 (±0.13) 30.13 (±0.14) 32.72 (±0.15) 24.52 (±0.11) 20.62 (±0.09) 18.13 (±0.08) 16.28 (±0.07)Δδ2Hn (‰) 123 (±4.4) 119 (±4.2) 134 (±4.8) 128 (±4.6) 135.1 (±4.8) 138.2 (±4.9) 152.6 (±5.4) 109.8 (±3.9) 90.9 (±3.2) 79.1 (±2.8) 70.6 (±2.5)Distance (m) 650 810 970 1100 1230 1350 1470 1500 1500 1500 1500Δδ18Om (‰) 23.47 12.36 7.5 4.94 3.43 2.48 1.86 1.43 1.12 0.9 0.73Δδ2Hm (‰) 88.7 45.2 27.1 17.7 12.3 8.9 6.6 5.1 4 3.2 2.6

30 Δδ18On (‰) 23.60 (±0.11) 21.8 (±0.1) 24.13 (±0.11) 23.87 (±0.11) 27.44 (±0.12) 28.04 (±0.13) 30.16 (±0.14) 27.51 (±0.12) 30.69 (±0.14) 29.56 (±0.13) 29.64 (±0.13)Δδ2Hn (‰) 89.6 (±3.2) 82.3 (±2.9) 92.3 (±3.3) 113 (±4) 107.2 (±3.8) 110.1 (±3.9) 120 (±4.3) 108.1 (±3.8) 122.9 (±4.4) 117.8 (±4.2) 118.3 (±4.2)Distance (m) 290 360 440 510 590 660 730 790 860 920 980Δδ18Om (‰) N/A 24.24 13.88 8.93 6.14 4.42 3.3 2.52 1.98 1.58 1.28Δδ2Hm (‰) N/A 80.3 44.8 28.5 19.5 14 10.4 8 6.2 5 4

70 5 Δδ18On (‰) 9.24 (±0.04) 7.58 (±0.03) 6.47 (±0.03) 5.65 (±0.03) 5.02 (±0.02) 4.52 (±0.02) 4.11 (±0.02) 3.77 (±0.02) 3.48 (±0.02) 3.23 (±0.01) 3.01 (±0.01)Δδ2Hn (‰) 64.8 (±2.3) 52.1 (±1.9) 44 (±1.6) 38.2 (±1.4) 33.8 (±1.2) 30.4 (±1.1) 28 (±1) 25.2 (±0.9) 23.2 (±0.8) 21.5 (±0.8) 20.1 (±0.7)Distance (m) 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500Δδ18Om (‰) 4.7 2.86 1.84 1.25 0.89 0.65 0.49 0.38 0.3 0.24 0.19Δδ2Hm (‰) 18.6 11.2 7.2 4.8 3.4 2.5 1.9 1.5 1.1 0.9 0.7

15 Δδ18On (‰) 11.13 (±0.05) 12.04 (±0.05) 10.91 (±0.05) 9.49 (±0.04) 8.47 (±0.04) 7.66 (±0.03) 7.00 (±0.03) 6.44 (±0.03) 5.97 (±0.03) 5.56 (±0.03) 5.20 (±0.02)Δδ2Hn (‰) 73.6 (±2.6) 74.9 (±2.7) 74 (±2.6) 62.9 (±2.2) 55 (±2) 49.8 (±1.8) 45.2 (±1.6) 41.4 (±1.5) 38.2 (±1.4) 35.5 (±1.3) 33.2 (±1.2)Distance (m) 1160 1400 1500 1500 1500 1500 1500 1500 1500 1500 1500Δδ18Om (‰) 6.87 4.32 2.83 1.94 1.38 1.01 0.77 0.59 0.47 0.38 0.31Δδ2Hm (‰) 25.3 15.7 10.2 6.9 4.9 3.6 2.7 2.1 1.7 1.3 1.1

30 Δδ18On (‰) 8.33 (±0.04) 8.93 (±0.04) 9.35 (±0.04) 9.63 (±0.04) 10.05 (±0.05) 10.33 (±0.05) 10.71 (±0.05) 10.95 (±0.05) 11.27 (±0.05) 10.65 (±0.05) 10.02 (±0.05)Δδ2Hn (‰) 47.9 (±1.7) 52.6 (±1.9) 56 (±2) 58.1 (±2.1) 61.4 (±2.2) 63.6 (±2.3) 66.6 (±2.4) 68.4 (±2.4) 70.9 (±2.5) 66.1 (±2.4) 61.4 (±2.2)Distance (m) 540 680 810 930 1050 1160 1270 1370 1470 1500 1500Δδ18Om (‰) 10.57 7.4 5.09 3.58 2.58 1.92 1.46 1.13 0.89 0.72 0.59Δδ2Hm (‰) 35.2 24 16.3 11.4 8.2 6.1 4.6 3.6 2.8 2.3 1.8

95 5 Δδ18On (‰) 0.83 0.66 0.54 0.46 0.39 0.34 0.3 0.26 0.23 0.21 0.19Δδ2Hn (‰) 29 (±1) 25.5 (±0.9) 22.5 (±0.8) 20.1 (±0.7) 18.2 (±0.7) 16.6 (±0.6) 15.2 (±0.5) 14.1 (±0.5) 13.1 (±0.5) 12.3 (±0.4) 11.5 (±0.4)Distance (m) 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500Δδ18Om (‰) 0.31 0.19 0.12 0.08 0.06 0.04 0.03 0.02 0.02 0.02 0.01Δδ2Hm (‰) 1.2 0.7 0.5 0.3 0.2 0.2 0.1 0.1 0.1 0.1 0

15 Δδ18On (‰) 1.11 0.88 0.72 0.59 0.50 0.42 0.35 0.30 0.26 0.22 0.19Δδ2Hn (‰) 37.2 (± − 1.3) 33.6 (±1.2) 30.5 (±1.1) 28 (±1) 25.8 (±0.9) 23.9 (±0.9) 22.2 (±0.8) 20.8 (±0.7) 19.5 (±0.7) 18.4 (±0.7) 17.4 (±0.6)Distance (m) 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500Δδ18Om (‰) 0.8 0.52 0.35 0.25 0.18 0.13 0.1 0.08 0.06 0.05 0.04Δδ2Hm (‰) 2.9 1.9 1.3 0.9 0.6 0.5 0.4 0.3 0.2 0.2 0.1

30 Δδ18On (‰) 1.33 (±0.01) 1.15 (±0.01) 0.99 0.84 0.71 0.60 0.50 0.42 0.34 0.27 0.22Δδ2Hn (‰) 38.9 (±1.4) 37.4 (±1.3) 35.9 (±1.3) 34.4 (±1.2) 32.9 (±1.2) 31.5 (±1.1) 30.2 (±1.1) 29 (±1) 28 (±1) 27 (±1) 25.7 (±0.9)Distance (m) 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500Δδ18Om (‰) 1.37 1.12 0.86 0.65 0.49 0.38 0.29 0.23 0.18 0.15 0.12Δδ2Hm (‰) 4.5 3.6 2.8 2.1 1.6 1.2 0.9 0.7 0.6 0.5 0.4

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Table A1Supplementary equations.

Notation Description Equation Unit

αeq,l-v18 Oαeq,l-v2 H

Equilibrium fractionation factor at temperature T (Majoube, 1971) aeq;l−v18O ¼ ; expð−0:002667− 0:4156

T þ 1137T2 Þ

aeq;l−v2H ¼ ; expð0:052612− 76:248

T þ 24844T2 Þ

–

Dv,a Diffusivity of water vapor in air (Monteith and Unsworth,1990) Dv,a = 21.2 × 10−6(1 + 0.007T) m2 s−1

esat Saturation vapor pressure for temperature θ (Lawrence, 2005) esatðθÞ ¼ C ; expð AθBþθÞ

A = 17.625, B = 243.04 °C, C = 610.94 Pa

Pa

P Air pressure p = 101325 × (1 − 2.25577 × 10−5z)5.2559 Paρa Air density ρa ¼ 1

RdT½p−0:378RHesatðθÞ� kg m−3

ρw Water density (Maidment, 1993) ρw ¼ 1000ð1− ðθrþ288:9414Þðθr−3:9863Þ2508929:2ðθrþ68:12963Þ Þ kg m−3

ka Thermal conductivity of air (Pruppacher and Klett, 1997) ka ¼ 2:43� 10−2 1:832�10−5

1:718�10−5 ð T296:0Þ

1:5ð 416:0T−120Þ J m-1s−1K−1

μair Dynamic viscosity of air (Rogers and Yau, 1989) μairðTÞ ¼ 1:72� 10−5ð 393:0Tþ120Þð T

273:15Þ3=2 kg m−1 s−1

vair Kinematic viscosity of air vair ¼ μairρa

m2 s−1

Sc, Re, Pr Scmidt, Reynonlds and Prandtl numbers Sc ¼ vairDv;a

; Re ¼ VrDvair

; Pr ¼ vairka

–

Vr Fall speed for raindrops (Seifert and Beheng, 2006) Vr≅aD−bDe−cDD

aD = 9.65 m s−1, bD = 9.8 m s−1, cD = 600 m−1m s−1

L Latent heat of vaporization L = (2.501 − 0.02361θ) × 106 J∙kg−1

fv Mass ventilation coefficient (Pruppacher and Klett, 1997)f v ¼ f 1þ 0:108ðSc1=3Re1=2Þ2 for ðSc1=3Re1=2Þb1:4

0:708þ 0:308ðSc1=3Re1=2Þ for ðSc1=3Re1=2ÞN1:4–

fh Heat ventilation coefficient (Pruppacher and Klett, 1997)f h ¼ f 1þ 0:108ð ;Pr1=3Re1=2Þ2 for ð ; Pr1=3Re1=2Þb1:4

0:708 þ 0:308ð ;Pr1=3Re1=2Þ for ð ; Pr1=3Re1=2ÞN1:4–

θw Wet bulb temperature (Stull, 2011) θw ¼ θ ; tan−1½ðRH%þ 8:313659Þ1=2� þ ; tan−1ðθþ RH%Þ− ; tan−1ðRH%−1:676331Þ þ 0:00391838ðRH%Þ3=2 ; tan−1ð0:023101RH%Þ−4:686035

°C

θd Dew point temperature (Lawrence, 2005) θd ¼ B½ ; ln ð RH100Þþ AθBþθ�

A− ; ln ð RH100Þ− AθBþθ

A = 17.625, B = 243.04 °C

°C

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sub-cloud evaporation effect leading to higher isotopic enrichments forhigher temperatures. However the temperature dependence is moredistinguishable for smaller raindrops.

Finally, the vertical variation of the isotopic composition of fallingraindrops and the corresponding isotopic enrichment is investigatedthrough a numerical isotope-evaporation model. This model simulatesthe diffusive fluxes due to evaporation in terms of the isotopic composi-tion of the liquid phase taking into account the temperature variationsof the surrounding air and the falling raindrop, the vertical change ofthe raindrop diameter as well as the vertical isotopic structure of theatmospheric water vapor. The isotopic composition becomes moreenriched when the raindrops travel through drier and warmer atmo-spheres, leading to Δδ18Ο up to 20‰ depending on the raindrop sizeand the initialmeteorological conditions. For near saturated atmospher-ic conditions (RH= 95%) the isotopic composition does not vary signif-icantly indicating the absence of sub-cloud evaporation.

Post condensation processes (rain evaporation and isotopic ex-change) have been incorporated into the isotope enabled GCMs (Bonyet al., 2008; Lee et al., 2008; Yoshimura et al., 2008; Risi et al., 2010;Dee et al., 2015) in order to describe more in detail the multiple stepsof the isotope water cycle and to further improve the comparison within-situ observations. The rain evaporation modules are mostly repre-sented by the Stewart's model exhibiting the weaknesses of the mixingmodel to reproduce the ‘real’ isotopic variability. Therefore, the numer-ical isotope model can be an alternative of the Stewart's model in theGCMs due to its better physical representation of the sub-cloud evapo-ration effect and thus it could be used for validating the iso-GCMs andto perform model-station comparisons.

A possible follow up of this workmay be the investigation of the iso-topic composition of precipitation andwater vapor using high temporalresolution measurements in combination with radiosonde or satellitedata for a more precise retrieval of the vertical variation of temperatureand relative humidity. Together with measurements, the use of rainfallparameters such as the raindrop distribution function, the rainfall rateetc. will be helpful to derive the bulk evaporation effect in terms ofthe isotopic composition.

Supplementary data to this article can be found online at http://dx.doi.org/10.1016/j.scitotenv.2015.11.072.

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