Quantitative Analysis of the Sub-Cloud Evaporation of Atmospheric Precipitation and Its Controlling Factors Calculated By D -Excess in an Inland River Basin of China

: Atmospheric precipitation is an important part of the water circle in an inland basin. Based on the analytical results of 149 precipitation samples and corresponding surface meteorological data collected at four sampling sites (Lenglong, Ningchang, Huajian and Xiying) at di ﬀ erent elevations in the Xiying river basin on the north slope of Qilian Mountains from May to September 2017, the sub-cloud evaporation in precipitation and its controlling factors are analyzed by the Stewart model. The results show that sub-cloud evaporation led to d -excess value in precipitation decrease and d -excess variation from cloud-base to near surface ( ∆ d ) increase with decreasing altitude. The remaining evaporation fraction of raindrop (f) decreases with decreasing altitude. The di ﬀ erence of underlying surface led to a di ﬀ erence change of f and ∆ d in the Xiying sampling site. For every 1% increase in raindrop evaporation, d -excess value in precipitation decreased by about 0.99% (cid:24) . In an environment of high relative humidity and low temperature, the slope of the linear relationship between f and ∆ d is less than 0.99. In contrast, in the environment of low relative humidity and high temperature, the slope is higher than 0.99. In this study, set constant raindrop diameter may a ﬀ ect the calculation accuracy. The Stewart model could have di ﬀ erent parameter requirements in di ﬀ erent study areas. This research is helpful to understand water cycle and land–atmosphere interactions in Qilian Mountains.


Introduction
In a cold-alpine region, runoff is mainly fed by Cryosphere meltwater (glaciers, snow, permafrost) and precipitation [1]. Almost all glaciers in the world are shrinking, the thicknesses of permafrost active layers are increasing, and snow cover extent and duration are decreasing [2]. In the alpine region of northwest China, which is the main distribution area of Cryosphere (including glacier, permafrost and snow cover), the annual mean surface temperature has risen by 1.8 • C from 1960 to 2007 [3]. In recent decades, the area of glaciers, permafrost and snow cover in Qilian Mountains has decreased significantly [4][5][6]; on the contrary, precipitation is increasing. In the context of global warming, the contribution of precipitation to runoff has continued to increase, while the contribution of Cryosphere meltwater has gradually decreased [7]. Based on the above background, further research on precipitation can help us better understanding the process of regional water cycle. Hydrogen-and

Data Sources
Precipitation samples (n = 149) were collected at four sampling sites (Lenglong, Ningchang, Huajian and Xiying) from May to September 2017 ( Figure 1, Table 1). The Lenglong sampling site is located at the frozen soil zone in the upper reaches of the Xiying river basin. Ningchang and Huanjian sampling sites are located at the alpine forest zone in the middle reaches of the Xiying river basin. The Xiying sampling site is located at the sub-alpine meadow zone in the lower reaches of the Xiying river basin. Meteorological data are recorded by the automatic weather station there. The sample collector was placed in naturally vegetated land undisturbed, 1.5 m from the surface. Placing a table tennis ball in the collection funnel sealed the collector bottle against evaporation and debris. After each precipitation event, precipitation samples were collected using 50 mL polyethylene bottles. All samples were stored in a refrigerator at −18 • C.

Method
Stewart et al. assumed that the cloud-base vapor reached an isotopic equilibrium state, and the variation of d-excess (∆d) (d-excess values of precipitation at near surface minus d-excess values of precipitation at cloud-base) can be calculated by the following formula [22,26]: where f is the evaporation remaining fraction. 2 γ, 18 γ, 2 β and 18 β are defined by Stewart [22]. 2 α and 18 α are isotope equilibrium fractionation factor and can be calculated by the following formula [31]: where T LCL is air temperature (K) at lifting condensation level (LCL). According to Barnes [32], the calculation method is where T d and T are the dew-point temperature and surface air temperature ( • C). According to Kinzer and Gunn [33], f can be calculated by the following formula: f = m end m end + m ev (6) where m end is the mass of the raindrop fall to surface and m ev is the mass of raindrop evaporated. They can be calculated by the following formula: where E is evaporation intensity, t is falling time of raindrops. r end is raindrop radius at landing, ρ is the density of water. According to Kinzer and Gunn [33], evaporation intensity can be calculated by the following formula: where Q 1 is controlled by temperature (T) and raindrop diameter (D), Q 2 is controlled by temperature (T) and relative humidity (h), and the specific calculation method can be found by Kinzer and Gunn [33]. Based on the calculation method proposed by Best [34], Wang et al. proposed a modified empirical formula to calculate median diameter of the raindrops in a semi-arid cold region [26]: where I is precipitation intensity (mm·h −1 ), the parameter of n, A, and P are defined by Wang et al. [26]. Raindrops quickly reach the state of equal velocity motion in the process of falling, and the falling time is: where H cb is cloud-base height, v end is the end velocity of the raindrop which can be calculated as [31].
In the previous researches, the height of cloud-base is set to a constant [19,35]. However, in many cases, the height of cloud-base is often less than 1500 m, affected by topography and meteorological factors in alpine areas. In this study, the height of cloud-base (H cb ) can be calculated by the following formula [36]: where T mean is average temperature ( • C) between the temperature at lifting condensation level and surface temperature, P 0 is surface pressure (hPa), P LCL is pressure (hPa) at lifting condensation level, and P LCL can be calculated by the following formula [32]: where P is pressure at the sampling site (hPa). Table 1 shows d-excess varied from cloud-base to near surface at each sampling site in the Xiying river basin in summer from May to September. With decreasing altitude, d-excess values at near surface decreased from 19.72% (Lenglong) to 10.23% (Huajian), and then increased to 13.9% (Xiying). ∆d increased from 20.29% to 35.15% , and then decrease to 29.45% . In the upper and middle reaches Water 2020, 12, 2798 6 of 12 of Xiying river basin (Lenglong, Ningchang and Huajian), d-excess values at near surface decreased with decreasing altitude, and ∆d increased with decreasing altitude. In the lower reaches, the change of d-excess at near surface and ∆d show opposite trends compared with those of middle and upper reaches, which may be caused by different underlying surfaces. d-excess values at near surface were much lower than that in the cloud-base, indicating that sub-cloud evaporation plays a significant role in precipitation process in semi-arid cold region.

Variations of ∆d
In the middle and upper reaches (Lenglon, Ningchang and Huajian), the evaporation remaining fraction (f ) decreased with decreasing altitude, but suddenly increased in the lower reaches (Xiying) (Figure 2a,b). The f fluctuated between 9.71% and 95.42% in May to September 2017. As shown in Table 2, f in May was relatively lower than that in other months. This is mainly because relative humidity is lower and evaporation intensity is higher than that in other months. Between June and August, relative humidity change was not obvious at each sampling site. Sub-cloud evaporation is mainly affected by air temperature, f decreases with the increase of air temperature and evaporation intensity. In September, the air temperature and evaporation intensity weakened, which led to the increase of f. ∆d depends on altitude and time. As a whole, ∆d increases gradually with decreasing altitude (Figure 2c), and ∆d was higher in May than that in June to September ( Figure 2d).  In the middle and upper reaches (Lenglon, Ningchang and Huajian), the evaporation remaining 175 fraction (f) decreased with decreasing altitude, but suddenly increased in the lower reaches (Xiying)

The Correlation between f and ∆d
It is clear that there is a significant correlation between f and ∆d, with a slope of about 0.99 ( Figure 3). When f is greater than 95%, the correlation between f and ∆d is highly significant with a slope of 0.81, indicating that f increase by 1% would lead to ∆d decrease about 0.81% . It shows that when sub-cloud evaporation is weak and f is high (higher relative humidity, lower temperature and larger raindrop radius), there is a significant correlation between f and ∆d. The relationship gradually becomes weaker as the f decreases (relative humidity decreases, temperature rises, and raindrop radius decreases). When f is below 40%, there is a stronger scattering around the regression line. Analysis of the relationship between f and ∆d at the middle and upper reaches (Lenglong, Ningchang, Huajian) reflects an increasing trend of slope and decreasing trend of correlation as altitude decreases (Table 3). Previous researches [26,35] suggest that there is a significant correlation between f and ∆d with a slope about 1 in a context of high f. In a semi-arid cold region, f may be much lower than 95%, with most small raindrops disappearing as they fall to the near surface [19]. Researchers usually assume that there are a 1% ·% −1 correlation between f and ∆d [16,37]. However, the results of this paper suggest that this assumption also needs to consider the influence of climate, altitude and other factors.
0.81, indicating that f increase by 1% would lead to Δd decrease about 0.81‰. It shows that when sub-194 cloud evaporation is weak and f is high (higher relative humidity, lower temperature and larger 195 raindrop radius), there is a significant correlation between f and Δd. The relationship gradually 196 becomes weaker as the f decreases (relative humidity decreases, temperature rises, and raindrop 197 radius decreases). When f is below 40%, there is a stronger scattering around the regression line.  (Table 3). Previous researches [26,35] suggest that there is a significant correlation between f and Δd 201 with a slope about 1 in a context of high f. In a semi-arid cold region, f may be much lower than 95%, 202 with most small raindrops disappearing as they fall to the near surface [19]. Researchers usually 203 assume that there are a 1‰·% −1 correlation between f and Δd [16,37]. However, the results of this 204 paper suggest that this assumption also needs to consider the influence of climate, altitude and other 205 factors.

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The f gradually decreased with decreasing altitude and Δd gradually increased with decreasing 213 altitude, the same as the conclusion in the middle and upper reaches of this study [36]. However, the   The f gradually decreased with decreasing altitude and ∆d gradually increased with decreasing altitude, the same as the conclusion in the middle and upper reaches of this study [36]. However, the f suddenly increased and ∆d suddenly decreased at the downstream, reflecting the influence of other factors. Through field investigation, we found that there exists an artificial reservoir (Xiying reservoir) near the Xiying sampling site with a distance of 1.4 km between them. As the largest artificial water body in Xiying river basin, with the total storage capacity of 23.5 million m 3 [38], the difference of underlying surface may lead to different contribution of local moisture recycling. Because large water body (lakes, reservoirs, etc.) will increase local moisture recycling [26], the monthly average evaporation of Xiying reservoir in summer half year (May to September) can reach 133 mm ± 18.6 mm [38]. In addition, strong evaporation of the Xiying reservoir will lead to decreased temperature, increased relative humidity and decreased vapor pressure deficit in the surrounding area. These changes will lead to a weakened sub-cloud evaporation in precipitation, increased f, and decreased ∆d. The temperature, relative humidity and cloud-base height of precipitation at each sampling site were analyzed to verify the above analysis further. As shown in Figure 4, relative humidity, air temperature and cloud-base height show obvious trends of decreasing relative humidity, increasing temperature and cloud-base height corresponding to the decreasing altitude in the middle and upper reaches, but these trends are different downstream. Cloud-base height in precipitation increases with decreasing altitude as mentioned in previous studies [26], further confirming that the sudden increase of f downstream is due to the difference of underlying surface.
Water 2020, 12, x FOR PEER REVIEW 8 of 13 Because large water body (lakes, reservoirs, etc.) will increase local moisture recycling [26], the 220 monthly average evaporation of Xiying reservoir in summer half year (May to September) can reach 221 133mm ± 18.6 mm [38]. In addition, strong evaporation of the Xiying reservoir will lead to decreased 222 temperature, increased relative humidity and decreased vapor pressure deficit in the surrounding 223 area. These changes will lead to a weakened sub-cloud evaporation in precipitation, increased f, and 224 decreased Δd. The temperature, relative humidity and cloud-base height of precipitation at each 225 sampling site were analyzed to verify the above analysis further. As shown in Figure 4, relative

235
When the temperature is between 0 °C to 8 °C, there is an obvious linear correlation between f 236 and Δd, and the slope is slightly lower than 1. When the temperature is between 8 °C to 15 °C, the 237 linear correlation between them weakens, and the slope is slightly higher than 1. When the 238 temperature is above 15 °C, the linear correlation between them is further weakened with the slope 239 up to 1.24 (Figure 5a-c). When the relative humidity is below 75%, the linear correlation between 240 them is low, and the slope is as high as 1.64. When the relative humidity is between 75% to 90%, the 241 linear correlation is gradually increasing, and the slope sharply decreased to 0.69. When the relative 242 humidity is above 90%, the slope decreased to 0.61 (there are only few points in Figure 5c, the 243 conclusions might be subject to high error) (Figure 5d-f). When the precipitation is below 5 mm, the 244 linear correlation is relatively high and the slope is lower than 1. When the precipitation is between 245 5mm~10mm, the linear correlation gradually decreased, and the slope is slightly higher than 1. When 246 the precipitation is above 10mm, the slope increased to 1.13 (Figure 5g,h,i). Therefore, it can be 247 concluded that f is high and Δd is close to 0 in the environment of high relative humidity and low 248 temperature. The correlation is significant with a slope lower than 1. By contrast, f is low and Δd is

Influence of Meteorological Factors
When the temperature is between 0 • C to 8 • C, there is an obvious linear correlation between f and ∆d, and the slope is slightly lower than 1. When the temperature is between 8 • C to 15 • C, the linear correlation between them weakens, and the slope is slightly higher than 1. When the temperature is above 15 • C, the linear correlation between them is further weakened with the slope up to 1.24 (Figure 5a-c). When the relative humidity is below 75%, the linear correlation between them is low, and the slope is as high as 1.64. When the relative humidity is between 75% to 90%, the linear correlation is gradually increasing, and the slope sharply decreased to 0.69. When the relative humidity is above 90%, the slope decreased to 0.61 (there are only few points in Figure 5c, the conclusions might be subject to high error) (Figure 5d-f). When the precipitation is below 5 mm, the linear correlation is relatively high and the slope is lower than 1. When the precipitation is between 5 mm~10 mm, the linear correlation gradually decreased, and the slope is slightly higher than 1. When the precipitation is above 10mm, the slope increased to 1.13 (Figure 5g,h,i). Therefore, it can be concluded that f is high and ∆d is close to 0 in the environment of high relative humidity and low temperature. The correlation is significant with a slope lower than 1. By contrast, f is low and ∆d is high in the environment of low relative humidity and high temperature. The influence of precipitation amount on the correlation between f and ∆d is not obvious. Thus, under different climate background, it is necessary to consider the influence of meteorological factors on sub-cloud evaporation of atmospheric precipitation.

Influence of Raindrop Diameter
Raindrop diameters are an important parameter to calculate f and ∆d in the Stewart model [24]. At present, the field observation and research data of raindrop diameter in Qilian Mountains are very minimal. Limited by technical means and field observation, raindrop diameter is often considered a constant in running the Stewart model [13,14,34]. In order to analyze the influence of raindrop diameter on f and ∆d, we set raindrop diameter as a constant from 0.3 to 3 mm with a step-size of 0.1 mm for each sampling site. In order to calculate the value of f and ∆d once again by Stewart model, the raindrop diameter is <1.5 mm, the influence on f and ∆d is obvious, and the influence is slight when it is more than 2 mm (Figure 6a,b). According to the calculation result of precipitation intensity, the most frequent raindrop diameters in this study are below 1 mm. This was consistent with previous studies which observed the raindrop diameter on the northern slope of Qilian Mountains in 2006 [39], indicating that the raindrop diameter was usually lower than 1 mm with average raindrop diameter of 0.9 mm. In summary, the raindrop diameter, which can reflect spatial variability of precipitation, was a significant parameter for calculating the f and ∆d based on the Stewart model. Therefore, setting raindrop diameter as a constant would affect the calculation accuracy in the study of sub-cloud evaporation in precipitation in the Qilian Mountains. In addition, under the conditions of the raindrop diameter being set as constant, the influence of altitude and underlying surface on f and ∆d should not be ignored. Based on the analysis of this paper, we can assume that the raindrop diameter can be set as a constant input to the Stewart model when average raindrop diameter in the study area is higher than 2 mm. However, in arid and semi-arid areas, as well as mountainous areas and areas with different underlying surfaces, it is necessary to consider the influence of raindrop diameter on the output of the Stewart model. studies, we will quantitatively analyze the intensity of local moisture recycling at different altitudes 299 and compare it with that in the Xiying reservoir. In the environment of high relative humidity and 300 low temperature, when f is high and Δd is close to 0, the slope of linear relationship between f and Δd 301 is less than 0.99. By contrast, in the environment of low relative humidity and high temperature, f is 302 low and Δd is high. The influence of precipitation amount on the relationship between them is not 303 obvious. In semi-arid cold regions, the influence of raindrop diameter on f and Δd should be noticed.

304
Setting raindrop diameter as a constant may affect the calculation accuracy in the study of sub-cloud 305 evaporation of precipitation. The Stewart model has different parameter requirements in different 306 study areas.

307
It is necessary to further improve the parameterization scheme in the simulation of sub-cloud 308 evaporation of precipitation using the isotope method. It involves two points: one is whether the 309 required parameters can be measured by technical means to reduce the uncertainty of estimation.

310
The other is whether the algorithm can be optimized, if the original model is not fully suitable for

Conclusions and Prospect
Using Stewart model, this study has quantitatively simulated the variation of f and ∆d in precipitation from cloud-base to near surface at different elevation. The influence of meteorological factors, raindrop diameter and underlying surfaces has also discussed. Influenced by sub-cloud evaporation, the analytical results show that the d-excess value in precipitation gradually decreased from cloud-base to near surface. ∆d increased with decreasing altitude, and evaporation remaining fraction decreased with decreasing altitude. The change of d-excess and f is most obvious in May. There is an obvious correlation between f and ∆d. When f increases by 1%, ∆d decreases to 0.99% . When f is above 60%, the correlation between f and ∆d is more significant, and that every 1% increase of could lead to ∆d decrease about 0.81% . However, the application of this method is still limited in an arid environment. Whether the linear relationship can be maintained at the environment of strong evaporation and low relative humidity needs further verification. The existence of the Xiying reservoir led to increased intensity of local moisture recycling and resulted in weakened sub-cloud evaporation in precipitation, increased f, and decreased ∆d in the downstream. However, our study didn't quantitatively analyze the influence of Xiying reservoir on local moisture recycling. In future studies, we will quantitatively analyze the intensity of local moisture recycling at different altitudes and compare it with that in the Xiying reservoir. In the environment of high relative humidity and low temperature, when f is high and ∆d is close to 0, the slope of linear relationship between f and ∆d is less than 0.99. By contrast, in the environment of low relative humidity and high temperature, f is low and ∆d is high. The influence of precipitation amount on the relationship between them is not obvious. In semi-arid cold regions, the influence of raindrop diameter on f and ∆d should be noticed. Setting raindrop diameter as a constant may affect the calculation accuracy in the study of sub-cloud evaporation of precipitation. The Stewart model has different parameter requirements in different study areas.
It is necessary to further improve the parameterization scheme in the simulation of sub-cloud evaporation of precipitation using the isotope method. It involves two points: one is whether the required parameters can be measured by technical means to reduce the uncertainty of estimation. The other is whether the algorithm can be optimized, if the original model is not fully suitable for arid environment, then how to debug it. Many parameters such as the raindrop diameter and the cloud-base height are treated by conceptual methods in the model. The differences of these parameters may affect the output results, so it is necessary to further optimize and improve them in the future. Due to the limitation of observation conditions, there are only four sampling sites in this study area, and the observation time is also short (data from May to September). It is necessary to optimize the sampling sites and collect more samples in the future.