A set of methods to evaluate the below-cloud evaporation effect on local precipitation isotopic composition: a case study for Xi’an, China

. When hydrometeors fall from an in-cloud saturated environment toward the ground, especially in arid and semiarid regions, below-cloud processes may heavily alter the isotopic composition of precipitation through equilibrium and non-equilibrium fractionations. If these below-cloud processes are not correctly iden-tiﬁed, they can lead to misinterpretation of the precipitation isotopic signal. To correctly understand the environmental information recorded in the precipitation isotopes, qualitatively analyzing the below-cloud processes and quantitatively calculating the below-cloud evaporation effect are two important steps. Here, based on 2 years of synchronous observations of precipitation and water vapor isotopes in Xi’an, China, we compiled a set of effective methods to systematically evaluate the below-cloud evaporation effect on local precipitation isotopic composition. The (cid:49) d (cid:49)δ diagram is


Introduction
For the paleoenvironment, the isotopic signal of precipitation recorded in ice cores (Thompson et al., 2000;Yao et al., 1996), tree rings (Liu et al., 2004;Liu et al., 2017b), speleothems (Cai et al., 2010;Tan et al., 2014), and leaf wax of loess-paleosol deposits (Wang et al., 2018b) and lake sediments (Liu et al., 2017a(Liu et al., , 2019) could be used to reconstruct the information of temperature, precipitation, and hydrological regimes in geologic history, as it had participated into the formation or the growth of these geological archives.For the modern environment, it could be used to quantitatively constraint the water vapor contribution from the end-members of advection (Peng et al., 2011), evaporation (Sun et al., 2020;Wang et al., 2016a), transpiration (Li et al., 2016;Zhao et al., 2019), and even anthropogenic activities (Fiorella et al., 2018;Gorski et al., 2015;Xing et al., 2020), as itself is itself an important part of the hydrological cycle.Thus, the hydrogen and oxygen isotopes of precipitation are one some of the most important tools to trace the hydrological cycle and climate change (Bowen et al., 2019;Gat, 1996).However, limited by the sampling and isotopic fractionation theories, there remains large uncertainty (i.e., the below-cloud evaporation intensity, the moisture recycling ratio, water molecules exchange between the droplet and ambient air, etc.) in deciphering the information contained in precipitation whenby using hydrogen and oxygen isotopes (Bowen et al., 2019;Yao et al., 2013).
Below-cloud evaporation is exactly one of the processes that influences the falling raindrops and, modify modifies their final stable isotopic content, and thus needs to be properly evaluated.Over the past decades, to determine whether the a hydrometeor has been evaporated during its falling, most studies have depended on a second-order isotopic parameter (Dansgaard, 1964;Jeelani et al., 2018;Li and Garzione, 2017), deuterium excess (defined as d-excess= δ 2 H-8×δ 18 O).This parameter is representative of the non-equilibrium fractionations, since light isotopes ( 1 H and 16 O) equilibrate faster than heavy isotopes ( 2 H and 18 O) in different phases (Clark and Fritz, 1997;Dansgaard, 1964).For raindrops, the lighter water molecules ( 1 H2 16 O) preferentially equilibrate or diffuse from the liquid phase to the gas phase during their falling through unsaturated ambient air.The eEquilibrium fractionation would does not substantially change the d-excess, while athe non-equilibrium diffusional process would result in a decrease of in d-excess in rain (Fisher, 1991;Merlivat and Jouzel, 1979).Additionally, the slope of the local meteoric water line (LMWL) has also been widely used as a metric to infer the below-cloud evaporation effect according to the theory of water isotope equilibrium fractionation (Chakraborty et al., 2016;Putman et al., 2019b;Wang et al., 2018a).Generally, the LMWL's slope is approximately equal to 8.0 belonging toin equilibrium fractionation, and that a slopeis lower than deviating from 8.0 pointing is related to a non-equilibrium fractionation, such as the reevaporation of raindrops.
However, it is worth noting that the change of in air masses (Guan et al., 2013), the condensation in under supersaturation conditions (Jouzel et al., 2013), or the moisture exchange in the cloud and sub-cloud layers (Graf et al., 2019) also cause large variations in the slopes and d-excess values (Putman et al., 2019a;Tian et al., 2018).Therefore, it is imperative to explore a novel method to more accurately identify the below-cloud evaporation processes.Recently, Graf et al. (2019) Graf's et al. (2019) work was only tested on a cold frontal rain event during a short time, and hence, more works needs to be done for validatingto validate the general applicability of their framework.
The initial signalcloud-base signal of precipitation isotopes is important in hydrological studies, and thus it is necessary to quantitatively evaluate the influence of below-cloud evaporation on its variations.Normally, the isotopic difference of raindrops between ground level and cloud base is determined by the below-cloud evaporation intensity.
Due toBecause it is the difficulty ofdifficult to measuring accurately measure the vapor or precipitation isotopic composition at the cloud base, the model proposed by Stewart (1975) has been widely used to estimate evaluate the below-cloud evaporation effect for a long time.Based on the well-defined laboratory conditions, Stewart (1975) parameterized the change of in the isotopic composition of a falling water drop with the vapor and raindrop isotopic compositions at the cloud base, and the remaining fraction of raindrop mass after evaporation (hereafter referred to as method 1).Froehlich et al. (2008)  In recent years, with the progress in optical laser systems, a relatively portable fielddeployable laser spectroscopic instruments have emerged, which makes theallows online, autonomous, and high-frequency site measurements of the water vapor stable isotope composition to be achieved (Aemisegger et al., 2012;Christner et al., 2018).
Therefore, the vapor or precipitation isotopic composition at the cloud base could be directly measured (Salmon et al., 2019), or be indirectly deduced from the ground-level vapor isotopic composition (Deshpande et al., 2010;Salamalikis et al., 2016).This enables us to directly calculate the influence of below-cloud processes on the precipitation isotopic composition (hereafter referred to as method 2).However, thus far, these have not been systematically compared less work has systematically compared the two methods.
Here, we use the measurements of two-year near-ground water vapor isotope compositions, and 141 precipitation isotope compositions (including event-based snowfall samples) thatwhich were collected in Xi'an (34.23°N, 108.88°E),Shaanxi provinceProvince, located in the Chinese Loess Plateau (CLP).The objectives of this study are to: 1. qualitatively identify the below-cloud processes of falling raindrops by using the ΔδΔd-diagram ; 2. quantitatively evaluate the below-cloud evaporation effect on precipitation isotopic composition by two methods and compare their differences; 3. understand the role of meteorological factors on the below-cloud evaporation and the characteristics of below-cloud evaporation in Xi'an city.Therefore, with the advantages of the paired observations of the vapor and precipitation isotopes near the ground, this study will compile a set of effective methods to evaluate the below-cloud evaporation effect on the local precipitation isotopic composition.

Sampling site
As the capital city of Shaanxi province Province and the largest city in northwest Northwest China, Xi'an is located on the Guanzhong Plain on the southern edge of the CLP at an average elevation of 400 m.The city is located in a semi-arid to arid region and is representative of most cities in the northern and northwestern of China (e.g., Lanzhou and Xining citycities, Fig. 1).The mean annual precipitation is 573.7 mm, and the mean annual evaporation is 426.6 mm from 1951 to 2008 year (Wu et al., 2013).
The notable below-cloud evaporation effect has been reported in many studies for this area (Sun et al., 2020;Wan et al., 2018;Zhu et al., 2016).Therefore, it is an ideal site to study the below-cloud processes.The water vapor in -situ measurement site is located in a residential area, approximately 10 km southeast to of downtown of Xi'an city (Fig. 1).The atmospheric water vapor isotopic composition was observed from 1 January 2016 to 31 December 2017 on the seventh floor of the Institute of Earth and Environment, Chinese Academy of Sciences, about approximately 30 m above ground.The rainfall or snowfall collector was placed on the rooftop of the buildings (1 m above the floor of the roof), about approximately 50 m above ground.

Sampling and isotopic measurement
Rainfall and snowfall samples were collected manually from the beginning of each precipitation event using a polyethylene collector (700 mm × 450 mm × 170 mm).
Before being used, the collector was cleaned with soap and water, rinsed with deionized water, and then dried.When the precipitation event ended, the collector was quickly taken back to minimize water evaporation.The rainfall volume was measured using a graduated flask.After collection, the samples were filtered through 0.40--μm polycarbonate membranes.Then, the rainfall samples were immediately poured into 100 ml polyethylene bottles.The snowfall samples were first melted at room temperature in closed plastic bags, aftersecond the samples were filtrationfiltered, and then immediately poured into 100 ml polyethylene bottles.About Approximately a 2 ml of each filtrate was transferred into a sample vial, and stored at -4 °C until being measuredanalysis.Of the 141 collected 141 samples, during the two-year sampling campaigns, 130 are were rainfall samples, and the other 11 are were snowfall samples (Table S3).
In all cases, the data are reported in the standard delta notation (δ), i.e., the per mil (‰) deviation from Vienna Standard Mean Ocean Water according to, δ= (Rsample/Rreference-1) ×1000, where R is the isotope ratio of the heavy and light isotopes (e.g., 18 O/ 16 O) in the sample and the reference.
The precipitation samples were analyzedmeasured with a Picarro L2130-i (serial number HIDS 2104) wavelength-scanned cavity ring-down spectrometer at ain highprecision mode.Every isotopic standard or sample was injected sequentially 8 times using a 5 μL syringe, and then the arithmetic average of the last 3 injections was accepted as the final result.All the samples were calibrated by three laboratory standards, while the δ 18 O and δ 2 H true values of the three laboratory standards (Laboratory Standard-1 (LS-1): δ 18 O =+0.3‰, δ 2 H =-0.4‰; Laboratory Standard-2 (LS-2): δ 18 O =-8.8‰, δ 2 H =-64.8‰; Laboratory Standard-3 (LS-3): δ 18 O =-24.5‰, δ 2 H =-189.1‰) are calibrated to the scale of two international standards VSMOW-GISP (Vienna Standard Mean Ocean Water -)-GISP(Greenland Ice Sheet Precipitation), with a precision of ±0.2‰ and ±1.0‰, for δ 18 O and δ 2 H, respectively.To correct the instrument drift, the instrument was repeatedly calibrated with the laboratory standards after analyzing 8 samples.the three laboratory standards were repeatedly measured after measuring every 8 samples.
Atmospheric water vapor δ 18 Ov and δ 2 Hv were also measured analyzed by Picarro L2130-i, but at in a liquid-vapor dual mode.The inlet of the gas-phase instrument is connected to the vapor source through an external solenoid valve when measuring vapor samples.This valve can switch the input of the instrument from the vapor sample to dry gas.The instrument is connected to dry gas prior to being connected to the evaporator for measuring liquid water standards so that any traces of the water vapor sample are removed from the measurement cell.The standards are injected into the evaporator with a CTC Analytics autosampler, PAL HTC-xt (Leap Technologies, Carrboro, NC, USA), and measured by the laser spectrometer.The atmospheric water vapor is pumped through a 2 m stainless-steel tube (1/8 inch) using a diaphragm pump at the a speed of 4 L min -1 and also detected by the laser spectrometer.The outside length of the stainless-steel tube is about approximately 0.5 m, and the inside length is approximatelyabout 1.5 m.We covered the stainless-steel tube with a heating tape maintained at 60 °C to prevent water vapor from condensing in the stainless-steel tube.
The air intake was protected with a shield to prevent rainwater from entering the sample line and direct sunlight.
The raw water vapor δ 18 Ov and δ 2 Hv data were obtained at approximately at 1 Hz and then block-averaged into 1 h intervals.As the main usage of this instrument is to measure the liquid water samples in our laboratory, it is used to monitor the water vapor isotopes in its spare time.Thus, the missing data indicate that the instrument is used for measuring liquid samples or being maintained.The event-based water vapor isotopic result is the average value from the start of the precipitation event to the end.
The hourly meteorological data, such as temperature, relative humidity (RH), and surface pressure in Xi'an, are reported by the Chinese meteorological administration, and can be downloaded from the website of http://www.weather.com.cn/.The meteorological station is approximatelyabout 10 km to the north of our sampling site.

The representativeness of the data
In Over 2 years, a total of 514 days of water vapor isotopic composition measurements were carried out.For 141 precipitation samples, of which 100 precipitation samples have corresponding event-based water vapor isotopic results.In this study, the precipitation events mainly occurred in summer and autumn, and less frequently in winter and spring.In summer and autumn, the rainfall amount accounted for more than 70% of the annual rainfall (Fig. S3).This is consistent with the multi-year average precipitation distribution in Xi'an (Fig. 1).Therefore, the collected samples are able to represent the precipitation characteristics in this region.

Water vapor isotopic data correction
Since tThe water vapor concentration effect and isotopic composition dependency of the cavity ringdown spectrometer have been pointed out by many studies (e.g., Bastrikov et al., 2014;Benetti et al., 2014;Steen-Larsen et al., 2013;Weng et al., 2020).,To minimize the uncertainty from the measurement, it is important to determine the isotopic composition-humidity correction response function.The humidity dependency shown in Fig. S1 also shows a dependency on the isotopic composition of the standards as reported by Weng et al. (2020).For example, in Fig. S1a and Fig. S1b, LS-1 shows a decrease in Δδ 18 O and Δδ 2 H with decreasing humidity, while LS-3 shows an increase with decreasing humidity.Therefore, we referred to Weng's et al.'s (2020) correction scheme for the isotope composition-humidity dependency.
The isotopic measurements of ground-level δ 18 Ov and δ 2 Hv were corrected for isotopic composition-humidity dependency using the following: where δiso-hum-cor is for the isotopic composition-humidity dependency corrected water vapor isotopic composition at 20000 ppmv; δmeas is the raw, measured isotopic composition at that humidity; h is the measured humidity; and a, b, and c are fitting coefficients for each water standard and isotope species.The detailed correction processes are provided in the supplementary material (Appendix A).
To calibrate the measured water vapor isotopic composition to the VSMOW-GISP scale, three known-value laboratory standards have beenwere used in the conversion, while these standards were measured analyzed in 24 h intervals to correct for instrument drifts.The 1σ estimated total uncertainties are from 2.1 to 12.4 ‰ for δ 2 Hv, 0.4 to 1.7 ‰ for δ 18 Ov, and 3.8 to 18.4 ‰ for d-excessv over the range of humidity from 30000 to 3000 ppmv on a 10-minutes average through the approach using a Monte Carlo method.

ΔdΔδ-diagram
When the raindrop falls from the cloud base to the ground, it continuously exchanges with the surrounding vapor and may lead to encounter net loss due to evaporation.
However, this process is very hard to bedifficult to quantifyied by observation.Making where δpv-eq and δgr-v are the δ 2 H (δ 18 O) of equilibrium vapor from precipitation and observed vapor near the ground, respectively, and d-excesspv-eq and d-excessgr-v are d-excess values of the equilibrium vapor from precipitation and observed vapor near the ground, respectively.For the detailed calculation processes, please refer to the supplemental material (Appendix B), or Graf et al. (2019).

Below-cloud evaporation calculation: Method 1
As reported by Stewart (1975), the isotopic ratio of a falling water drop is: i Rgr = i γ i Rva + ( i Rcb -i γ i Rva)Fr iβ (eqEq.4) where i Rgr is the isotopic ratio of falling raindrops near the ground; i Rva and i Rcb are the initial isotopic ratios for the vapor and raindrop at the cloud base; i γ and i β are the parameters related to the equilibrium fractionation factor, relative humidity, and molecular diffusivities; and Fr is the remaining fraction of raindrop mass after evaporation.
Assuming that the initial isotopic composition of the raindrop at the cloud base is in equilibrium with the surrounding water vapor, Froehlich et al. (2008) adapted the Stewart model and simplified the equation to evaluate the isotopic enrichment due to below-cloud evaporation by: where α is the equilibrium fractionation factor for hydrogen and oxygen isotopes; the parameters of γ and β are defined by Stewart (1975); Fr is the remaining fraction of raindrop mass after evaporation; ∆δp is the raindrop isotopic variations due to belowcloud evaporation; and Fi is the evaporation proportion.For the detailed calculation processes, please refer to the supplemental material (Appendix C), or Froehlich et al. (2008), Wang et al. (2016b), and Salamalikis (2016).

Below-cloud evaporation calculation: Method 2
Because the isotopic composition of a raindrop is directly influenced by the belowcloud processes during its falling, the below-cloud effects could be directly represented by the difference between the isotopic composition of precipitation at the ground level and cloud base: ∆δp =δgr-p-δcb-p (eqEq.7) where δgr-p and δcb-p are the isotope isotopic compositions of a falling raindrop near the ground and below the cloud base, respectively; , and ∆δp is the raindrop isotopic variation due to below-cloud evaporation.The δgr-p is our observed precipitation isotopic composition, and δcb-p is able tocan be calculated based onby ground-level water vapor isotopic composition according to Deshpande et al. (2010).For the detailed calculation processes, please refer to the supplemental material (Appendix D), or Araguás-Araguás et al. (2000), Deshpande et al. (2010), andSalamalikis (2016).
Here, it should be noted that both methods use an important assumption, which is that the surface water vapor is (moist) adiabatically connected to the cloud-base water vapor.In method 1, this assumption is used to calculate the cloud base height, temperature, and pressure (Appendix C, Eq. 14-16).In method 2, the isotopic composition of the cloud-base water vapor is calculated assuming a moist adiabatic ascent of the measured ground-level water vapor (Appendix C, Eq. 22).In addition, in method 2, we assume that the raindrop isotopic composition (δcb-p) at the cloud base is in equilibrium with the surrounding water vapor, and the observed ground-level precipitation isotopic composition (δgr-p) includes the processes of evaporation, growth, and isotopic equilibrium with the surrounding vapor.Furthermore, the air column is assumed to have no horizontal advection into or out of it and no updraft or downdraft of the air masses during the hydrometeors' falling.That means the vertical column at the observation site is undisturbed by horizontal movement.These assumptions only hold if a single vertical column extends from the ground to the cloud-base height.When the rain events during which the single column is affected by the surrounding air, these assumptions become invalid.it should be noted that in this method we assumed that the raindrop isotopic composition (δcb-p) at the cloud base is in equilibrium with the surrounding water vapor, and the observed ground-level precipitation isotopic composition (δgr-p) includes the processes of evaporation, growth, and isotopically equilibrium with the surrounding vapor.In addition, during the hydrometeors falling we assumed that there is no horizontal advection into or out of the column, and no updraft or downdraft.The equilibrium exchange process is not separated from the evaporation, ; therefore, the Δδ results may underestimate the below-cloud evaporation effect in method 2. To get obtain accurate results, more works is needed to separate the equilibration process from the evaporation in the future.
Actually, method 1 makes use of the mass change of the falling raindrop to evaluate the below-cloud evaporation effect on isotopic composition, while method 2 evaluates its effect by directly measuring the variations of in isotope composition.

Statistical Analysis
To compare the difference between the two methods, the independent t -test was performed on Statistical Package for Social Sciences SPSS 13.0 (SPSS 13.0, Inc., Chicago, US),.followed by setting the A significant statistical difference was set at the p < =0.05 level of confidence.

Relationship between water vapor and precipitation isotopic compositions
Influenced by the below-cloud evaporation, the slope of the local meteoric water line (LMWL) would be lower than 8, the precipitation isotopic composition would become more positive, the d-excess of precipitation would be less than 10, and the equilibrated water vapor isotopic composition would be more positive than the observed one.As shown in Fig. 2, the LMWL is defined as: δ 2 Hp=7.0×δ 18Op+3.0based on the event precipitation isotopic composition, and the local water vapor line (LWVL) is defined as: δ 2 Hv=7.8×δ 18Ov+15.1 based on the per-precipitation-event water vapor isotopic composition.Both the slope and intercept of the LMWL are lower than the Global global Meteoric meteoric Water water Line line (GMWL), which are has a slope of 8.0 and intercept of 10.0 (Dansgaard, 1964;Gat, 1996), respectively, indicating the potentially significant below-cloud evaporation effect on precipitation (Froehlich et al., 2008).In general, the slopes of the meteoric water lines are indicative of kinetic processes superimposed on the equilibrium fractionation, and the little somewhat lower slope of the LWVL (slope=7.8)than the expected equilibrium fractionation (slope=8.0)may also be related to the increasing influence of kinetic processes (Rangarajan et al., 2017).BesidesIn addition, we noted that the water vapor and precipitation isotopic compositions were basically distributed in different ranges values, which with the former is being generally more negative than the latter (Fig. 2).According to the classical isotopic fractionation theory, the heavier isotopes preferentially condense into the liquid phase during the precipitation process, which results in the precipitation isotopic composition being more positive than the water vapor one isotopic composition (Dansgaard, 1964).Hence, the distribution characteristics of water vapor and precipitation on the δ 18 O-δ 2 H plot would make us suppose that their isotopic compositions are in or close to equilibrium in at this study site.To validate our assumption, we plot their relationship in Fig. 3a.As expected, they show a significant positive correlation (R 2 =0.70, p<0.01), and thus, the water vapor isotopic composition can explain 70% of the variation of in the precipitation isotopic composition.
Furthermore, we used the measured precipitation isotopic composition to deduce the water vapor isotopic composition at the ground level according to the liquid-vapor equilibrium isotope fractionation (δ 18 Opv-eq), and compared it with the observed water vapor (δ 18 Ov) in Fig. 3b.The scatterplot of the observed δ 18 Ov against the equilibrated δ 18 Opv-eq also presents a significantly positive relationship (Fig. 3b).In Fig. 3bthe relationship plot, we also noted that the equilibrated δ 18 Opv-eq is relatively more positive than the observed δ 18 Ov (Fig. 3b).Because Xi'an city belongs to the a semi-arid area, the raindrops is are likely to be evaporated in the an unsaturated environment during its falling.Therefore, the positive δ 18 Opv-eq is caused by the nonequilibrium fractionation in low relative humidity, which makes the δ 18 Opv-eq-δ 18 Ov points deviation deviate from the 1:1 line.
The reasonable agreement of observed and equilibrated water vapor isotopic compositions has been reported by Jacob and Sonntag (1991), Welp et al. (2008), and Wen et al. (2010), ); however, they postulated the different relationships underlying the δ 18 Ov and δ 18 Opv-eq.Jacob and Sonntag (1991) suggested that the water vapor isotopic composition is possible tocan be deduced from the corresponding precipitation isotopic composition, but Wen et al. (2010) speculated that the equilibrium method cannot accurately predict the ground-level water vapor isotopic composition in arid and semiarid climates because of two the monthly equilibrated water vapor values in April and November deviating deviate from the observed values.Here, with two -years of continuous observations, the mean difference between the δ 18 Ov and δ 18 Opv-eq is −1.1‰ for δ 18 O, -8.1‰ for δ 2 H, and 0.7‰ for d-excess.Although there is a good relationship between δ 18 Ov and δ 18 Opv-eq in our data, the below-cloud evaporation has a significant influence on the precipitation isotopic composition.Therefore, it cautious should be cautious totaken when derive deriving the water vapor isotopic composition from the precipitation oneisotopic composition.

Below-cloud processes indicated by the ΔdΔδ-diagram
Traditionally, to qualitatively assess the below-cloud evaporation of raindrops, the value of d-excessp is a benchmark.Due to the differences in diffusivities of the individual water molecules in non-equilibrium fractionation, therefore, it will cause dexcessp to will deviate from 0‰, which is a theoretical value under vapor-liquid equilibrium fractionation at temperatures of around approximately 20 °C (Gat, 1996).
The global mean value of 10‰ for the d-excessp in precipitation indicates that evaporation is in general a non-equilibrium process.Normally, below-cloud evaporation will decrease d-excessp, and in comparison, mixing with the recycled water vapor from surface evaporation and plant transpiration will increase d-excessp (Craig, 1961;Dansgaard, 1964).In addition, in the water molecules diffusion process,  In Fig. 4, the slope of Δd/Δδ is -0.36 for the rainfall samples and -0.12 for the snowfall samples.In Graf's et al.'s (2019) study, they reported a Δd/Δδ slope of -0.3.It should be noted that the slope of Graf's et al. ( 2019) is based on intra-event samples (from the start to the end of precipitation, each interval of 10 min to collect one sample), while ours is based on per-event samples (only collect one sample was collected in each precipitation event).Although the time scale is different in the two studies, interestingly, the rainfall slopes are close to each other, while the snowfall slope is obviously different from the rainfall slope.The Δd/Δδ slope of -0.3 could represent a general characteristic of rainfall for continental mid-latitude cold front passages (Graf et al., 2019).Xi'an city is located near the 35°N in inland of China, which just belongs to the scope of continental mid-latitude region.In comparison, the Δd/Δδ slope of our snow samples is less negative.Therefore, the different Δd/Δδ slopes might be related to the different climatic characteristics or precipitation types.Certainly, to validate this assumption, more works needs to be done in future studies.

Comparing and analyzing the two methods
The ΔdΔδ-diagram provides rich valuable information on the below-cloud processes, but it is only a qualitative analysis.In comparison, the quantitative evaluation is more important to identify the below-cloud evaporation effect.Here, we chose two methods to respectively calculate the variations of in Δδ 2 Hp and the evaporation fraction (Fi) on per-event precipitation, and compared their differences.

Quantitatively evaluate evaluation of the below-cloud evaporation effect byderived from the two methods
The Δδ 2 Hp ranges from 0 to 131.1 ‰ with an average and standard deviation of 17.8 ± 23.8 ‰, and the Fi ranges from 0 to 82.7 % with an average and standard deviation of 16.3 ± 21.9 % (n=141) for method 1.The Δδ 2 Hp ranges from -73.8 to 82.5 ‰ with an average and standard deviation of 16.3 ± 24.4‰, and the Fi ranges from 0 to 67.6 % with an average and standard deviation of 22.1 ± 21.7 % (n=100) for method 2. For the 90 rainfall events with corresponding water vapor data, the average ± and standard deviation is are 18.4 ± 21.7 ‰ for Δδ 2 Hp in derived from method 1, and the value is 18.7 ± 20.6 ‰ for Δδ 2 Hp in derived from method 2. For the 10 snowfall events, the average ± and standard deviation of Δδ 2 Hp is are 42.6 ± 43.7 ‰ for method 1 and -6.1 ± 41.6 ‰ for method 2. In the two methods, according to the independent t -test, there are no statistical significant differences in the Δδ 2 Hp of rainfall samples (F=0, p=0.91, n=90), but the Δδ 2 Hp of snowfall shows a large difference (F=0.196, p<0.05, n=10).
As shown in Fig. 5a and Fig. 5b, the Δδ 2 Hp and Fi in the two methods have similar fluctuation trends.The A positive Δδ 2 Hp and high Fi appear from March to July, while thea negative Δδ 2 Hp and low Fi show appear from September to following February.In addition, the most positive Δδ 2 Hp values are captured by method 1, while the most negative values are detected by method 2. In order toTo analyze the underlying reason, we checked the equation used to calculate Δδ 2 Hp.We noted that in eEq.5, the Fr is always lower than 1, and thus (Fr β -1) is negative.Similarly, the γ α is smaller than 1, and thus, (1-γ α ) is also negative.Therefore, the Δδ 2 Hp calculated by method 1 could not be a negative numberis always positive.In method 2, the most negative Δδ 2 Hp values are related to the snowfall events.During the supersaturation process, vapor deposition takes place over ice in the cloud (Jouzel and Merlivat, 1984) with non-equilibrium fractionation (the kinetic fractionation factor αk<1), leading to the effective isotopic fractionation factor (αeff =αeqαk) being smaller than the equilibrium fractionation coefficient (αeq), and resulting in the ground-observed δgr-p of solid precipitation (snow) being more depleted than the calculated δcb-p under equilibrium fractionation (in Eq.

7)
.During the supersaturation process, vapor deposition occurs over ice (Jouzel and Merlivat, 1984), which may cause the snow isotopic composition at the ground to be more depleted than its formation height.In fact, the mass of the snow also increases in theunder supersaturation conditions, ; however, method 1 only considers the evaporation process.The diameter of the raindrop used to determine the terminal velocity and evaporation intensity (Supplemental material, eqEqs.10-13) does not take into account the different relationship of fall velocity to hydrometeor size for snowflakes and raindrops, the snowfall factor which results in great uncertainty in method 1.
Therefore, method 1 is not suitable for evaluating the below-cloud effect on the precipitation isotopic composition when thefor snowfall or low-temperature rainfall events.
Figure 5.The variation of in Δδ 2 Hp for per-event precipitation in method 1 and method 2 (a); the same as (a) but for Fi (b); the relationship between Fi and Δδ 2 Hp in method 1 and method 2 (c) In addition, the influence of the below-cloud evaporation effect on the δ 2 Hp is heavier in method 1 than in method 2, especially at higher Fi conditions (Fig. 5c), because the slope of Fi/Δδ 2 H in method 1 (1.00 ‰/%) is a little slightly steeper than that in method 2 (0.91 ‰/%), and the intercept in method 1 (-1.65) is more positive than that in method 2 (-3.97).Thus, under the same evaporation intensity, the Δδ 2 Hp is more enriched in method 1 than in method 2.
On the seasonal scale, both methods show that the below-cloud evaporation effect is heavier in spring and summer and weaker in autumn and winter (Fig. S4).Their differences are the smallest in spring and the largest in winter.The significant difference in winter might be related to the predominance of solid precipitation, which is not accounted for in method 1.The significant difference in winter might be related to the supersaturation process.
precipitation amount is small.As the precipitation amount is above 10 mm, the value of Δδ 2 Hp tends toward 0 ‰.

Sensitivity test
In method 1, the input physical parameters include temperature, RH, precipitation amount, and surface pressure.In method 2, the same input parameters as for method 1 were used except for the precipitation amount.In method 2, the input parameters include temperature, RH, and surface pressure.Therefore, these parameters are considered in the sensitivity tests.
For the RH test, one case adds 10% to the measured RH, and another case subtracts 10% from the measured RH.If the RH values are above 100%, then they are artificially set to 99% to conform to reality.Two temperature scenarios, plus and minus 10 °C based on the actual temperature, are analyzed.In the sensitivity test of precipitation amount, considering that the amounts are lower than 0.1 mm in some precipitation events, therefore, the reduction lower limit is set at to 0.1 mm, and the enhancement upper limit is set at to 5 mm.On the basic surface pressure condition, a 10 kPa pressure fluctuation is considered for its impact.
As shown in Fig. 7, the increase of in RH and precipitation, and decrease of in temperature have a negative impact, ; that is, the below-cloud evaporation effect on the isotopic composition will be attenuated.On the contraryIn contrast, the decrease of in RH and precipitation, and increase of in temperature have a positive impact, indicating that the below-cloud evaporation effect will be strengthened.The varying surface pressure has no impact on the Δδ 2 Hp for both methods.Moreover, the influencing strength of the different physical parameters on the Δδ 2 Hp is different in the two methods.For example, in method 1, the increase of in temperature basically does not change the evaporation effect on the Δδ 2 Hp, and the influence of decreasing temperature on mitigating evaporation is limited as well.However, the situation is totally different in method 2, where the temperature is a decisive factor.In addition, the influence of RH is over the temperature in method 1, but the condition is reversed in method 2. The precipitation amount is also an important factor, as the influence of precipitation on Δδ 2 Hp even surpasses the RH when it is increased by 5 mm.Because of the limited decrease in precipitation amount, its positive feedback is hard difficult to evaluate.In the calculation process of method 2 (eqEq.7, and supplemental material, eqEq.22), except for the measured ground-level precipitation and water vapor isotopic compositions (δgr-p and δgr-v), the other two controlling factors are the equilibrium fractionation factor (α) and the cloud base height.The α is determined by the temperature variations of the cloud base, while the cloud base height is related to surface temperature and RH (supplemental material, eqEq.14-17).With increasing RH increase, the cloud base heights decrease, and vice versa (Fig. S5).In comparison, the cloud base heights are not sensitive to the changes of in temperature (Fig. S5).
Compared with method 2, the calculation process of method 1 is more complex.Many variables, such as raindrop diameter, evaporation intensity, raindrop falling velocity, and cloud base height, etc., are neededneed to be considered, while they are convoluted with temperature, RH, precipitation amount, and surface pressure.Through the sensitivity test, RH and precipitation amount are the two decisive factors in method 1 for deciding determining the below-cloud evaporation intensity.

Uncertainty estimations
There are many uncertainties in the two methods' estimates.In method 1, the input parameters include the variation of in temperature, RH, precipitation amount, and surface pressure.In method 2, the uncertainty comes from the variations of in the input temperature, RH, surface pressure, ground level water vapor δ 2 Hgr-v, and precipitation δ 2 Hp.However, the variations of in surface pressure show no impact on the Δδ 2 Hp in the sensitivity test, ; therefore, it isthey are not considered in the uncertainty calculation.
To check the influence of temperature, RH, precipitation amount, and precipitation δ 2 Hp on the below-cloud evaporation effect, we assume that the errors are mainly from the measurement uncertainty of the instrument, which is ± 0.3 °C, ± 3%, ± 4% precipitation amount, and ± 1.0 ‰, respectively.Due to the humidity effect (section Sect.2.4), the measured δ 2 Hgr-v for each event has a wide range of uncertainty, which varies from 1.3 to 8.2 ‰.Hence, the lower and upper limits of the above used input parameters in for method 1 and method 2 are used to quantify the uncertainties and add them quadratically to ascertain the total uncertainty (Rangarajan et al., 2017;Wu et al., 2022).We obtain the overall uncertainty varying from 0.71 to 0.72‰ for method 1, and from 0.60 to 1.05‰ for method 2 in the estimates of Δδ 2 Hp values (refer to supplemental material, Appendix E).

The characteristics of below-cloud evaporation effect in Xi'an
Since the below-cloud evaporation is very common in arid and semi-arid regions, before exploring the information contained in the precipitation isotopes, it is important to clearly know the variation of precipitation isotopic composition during its falling.Here, we summarized the seasonal variations of Δδ 2 Hp in Xi'an by two methods (Fig. 8).
Figure 8 The variations of temperature, RH, precipitation amount, and Δδ 2 H in four seasons in Xi'an.In the middle of the figure, the red boxes represent the results from method 1, and the blue boxes represent the results from method 2.
By seasonally dividing the precipitation isotopic composition on the ΔdΔδ-diagram, it shows that samples collected in spring and summer dominate the evaporation phase, reflecting a stronger evaporation influence, while most of the winter precipitation and part of autumn precipitation monopolize the cloud signal phase indicating a weak or no below-cloud evaporation, and even supersaturation on these samples (Fig. S6).
Based on quantitative analysis, the two methods show similar evaporation effect in spring, summer, and autumn, and different trends in winter (Fig. 8).The reasons had been discussed in Section 3.3.1.In addition, method 1 shows a narrower variation provided a new interpretive framework to directly separate the convoluted influences on the stable isotopic composition of vapor and precipitation according to the theoretical fractionation processes, especially the influences of equilibration and below-cloud evaporation.The axes of the new diagram consist of the differences, Δδ 2 H and Δd, between the isotopic composition of precipitation equilibrated vapor from precipitation and near-surface observed vapor, namely, the ΔδΔd-diagram.Compared with the slope of the LMWL or the d-excess, the below-cloud equilibration and evaporation have different spatial distributions in the two-dimensional phase space of the ΔδΔd-diagram, which makes them more easily distinguishable.Although the ΔδΔd-diagram gives us a new guideline to more accurately identify the below-cloud processesevaporation, adapted the Stewart model and then assessed the change in d-excess due to below-cloud evaporation based on a simple frame in the European Alps.Wang et al. (2016b) further refined the calculations of the parameters, which are used to determine the remaining fraction of raindrop mass in the Stewart model, to assess the variation in d-excess of raindrops in central Asia.However, these quantitative evaluations for of the below-cloud evaporation are indirect, because the results are largely dependent on the parameter that is the remaining fraction of raindrop mass after evaporation.

Figure 1 .
Figure 1.Average monthly variations of in temperature and precipitation in Xi'an, Lanzhou, and Xining during 2010-2015.Location of the sampling site in the Yanta Zone, 9 km SE of downtown Xi'an.Water vapor samples are taken on the seventh floor of a twelve-story building, about use of stable water isotopes,Graf et al. (2019) introduced a the ΔdΔδ-diagram to diagnose the below-cloud processes and their effects on vapor and precipitation isotopic composition, since equilibration and evaporation are two different processes and lead to different directions in the two-dimensional phase space of the ΔdΔδdiagram.Here, the differences in the isotopic composition of precipitation-equilibrated vapor relative to the observed ground-level vapor can be expressed as: ∆δ v =δ pv-eq -δ gr-v (eqEq.2) ∆d-excess v =d-excess pv-eq -d-excess gr-v (eqEq.3)

Figure 3 .
Figure 3. Relationship between δ 18 Op of precipitation and δ 18 Ov of water vapor in Xian (a); and the relationship between the equilibrium computed δ 18 Opv-eq based on the precipitation isotopic composition and the near ground observed δ 18 Ov (b).The dashed-dotted line in (b) stands represents for the 1:1 line, and the blue line represents the regression line of the data.
the water vapor d-excessv may be modified, and thiswhich enhances the uncertainty to gaugein gauging the below-cloud evaporation process by solely using d-excessp.In contrast, the ΔdΔδ-diagram introduced by Graf et al. (2019) provides richer more information on the below-cloud processes.Theoretically, on the ΔdΔδ-diagram, Δd<0‰ and Δδ>0‰ indicate the below-cloud evaporation process; Δδ<0‰ represents that the falling raindrop is less influenced by below-cloud evaporation and retains the cloud signals; and Δd and Δδ close to 0‰suggest equilibrium conditions.By projecting our data on the ΔdΔδ-diagram, the evaporation, equilibration, and non-exchange (e.g., a snowfall event, or a transition from rain to snow with a stronger cloud signal) processes could be clearly differentiated.It is apparent from in Fig.4that most of the rainfall samples are located in the fourth quadrant with positive Δδ 2 Hv and negative Δd-excessv, indicating that evaporation is the major below-cloud process.Interestingly, most of the snowfall samples seize the second and third quadrants with negative Δδ 2 Hv, which is suggestive of below-cloud evaporation with less impact on them, and their initial signals are well retained after the cloud-based equilibrium fractionation.

Figure 4 .
Figure 4.The projection of our data on the suggested ΔdΔδ-diagram by Graf et al. (2019).The solid lines stand forrepresent Δd-excessv and Δδ 2 Hv of 0‰.The dashed line corresponds to the linear fit through the samples with the 95% confidence band in shading.The red line is for rainfall samples, and the cyan line is for snowfall samples.The upper Romans numerals represent the category of the quadrant.

Figure 7 .
Figure 7. Sensitivity test of Δδ 2 Hp under different cases.In method 1, the cases include ± 10% RH, ± 10 °C temperature, ± 10 kPa surface pressure, +5 mm precipitation amount, and -0.1 mm precipitation amount.In method 2, the cases include ± 10% RH, ± 10 °C temperature, and ± 10 kPa surface pressure.The Δδ 2 Hp(Sen) represents the results of the sensitivity test, and Δδ 2 Hp(Base) represents the results of the base condition.