Is Annual Recharge Coefficient a Valid Concept in Arid and Semi-Arid Region ?

Deep soil recharge (DSR) (at depth more than 200 cm) is an important part of water 21 circulation in arid and semi-arid regions. Quantitative monitoring of DSR is of great importance 22 to assess water resources and to study water balance in arid and semi-arid regions. This study 23 used a typical bare land on the Eastern margin of Mu Us Sandy Land in the Ordos basin of China 24 as an example to illustrate a new lysimeter method of measuring DSR to examine if the annual 25 recharge coefficient is valid or not in the study site, where the annual recharge efficient is the 26 ratio of annual DSR over annual total precipitation. Positioning monitoring was done on 27 precipitation and DSR measurements underneath mobile sand dunes from 2013 to 2015 in the 28 study area. Results showed that use of an annual recharge coefficient for estimating DSR in bare 29 sand land in arid and semi-arid regions is questionable and could lead to considerable errors. It 30 appeared that DSR in those regions was influenced by precipitation pattern, and was closely 31 correlated with spontaneous strong precipitation events (with precipitation greater than 10 mm) 32 other than the total precipitation. This study showed that as much as 42% of precipitation in a 33 single strong precipitation event can be transformed into DSR. During the observation period, 34 the maximum annual DSR could make up to 24.33% of the annual precipitation. This study 35 provided a reliable method of estimating DSR in sandy area of arid and semi-arid regions, which 36 is valuable for managing groundwater resources and ecological restoration in those regions. It 37 also provided strong evidence that the annual recharge coefficient was invalid for calculating 38 DSR in arid and semi-arid regions. This study shows that DSR is closely related to the strong 39 precipitation events, rather than to the average annual precipitation. 40


Introduction
Recharge is an important source of groundwater budget and it is also a fundamental process that links the surface hydrological processes (e.g.precipitation), vadose zone process (e.g.infiltration and soil moisture dynamics), and the saturated zone process (e.g.groundwater flow) (Sanford, 2002;McWhorter and Sunada, 1977).How to accurately estimate recharge remains a persistent challenge and an active research topic in the hydrological science community over many decades (Gee and Hillel, 1988;Scanlon, 2013;Sanford, 2002).It is generally accepted that recharge is correlated to the precipitation in some fashions, and many studies adopt the concept of a recharge coefficient (Turkeltaub et al., 2015;Kalbus et al., 2006;Allocca et al., 2014), which is the ratio of the actual recharge to the precipitation, to estimate the recharge (Fiorillo et al., 2015;Allocca et al., 2014).The magnitude of such a recharge coefficient is controlled by a complex interplay of multiple factors such as moisture dynamics in the vadose zone (Schymanski et al., 2008), depth to the water table, vegetation, etc., and the recharge coefficient is often regarded as a temporally invariant value at a given location (Fiorillo et al., 2015;Min et al., 2017;Vauclin et al., 1979).Specifically, it is assumed to be primarily controlled by the total precipitation, not too much by the temporal fluctuation of precipitation events (Hickel and Zhang, 2006;Acworth et al., 2016).In this study, we will challenge the concept of using a constant recharge coefficient to estimate the recharge in arid and semi-arid regions based on a multi-year field investigation.
As water tables in many arid and semi-arid regions are relatively deep (greater than 2 meters below ground surface) (Williams, 1999;Soylu et al., 2011), recharge in those regions is named Deep Soil Recharge (DSR), which will be the concern of this study.DSR could ease the demand of sand-fixing vegetation on moisture during extremely dry seasons (Zhang et al., 2001;Shou et al., 2016) , and it reduces water deficit, sustains life activities, and helps the vegetation to live through extreme droughts (Zhang et al., 2004).In this sense, DSR is an important factor of water cycle in arid and semi-arid regions (Adolph, 1947), and it could also provide much needed references for the stability analysis of sand-fixing vegetation (Li et al., 2004;Li et al., 2014).In the following, we will briefly review the existing methods of estimating DSR.
In general, there are three methods of measuring DSR in arid and semi-arid regions.The first is an empirical approach which assigns a constant recharge coefficient associated with a certain precipitation event (Allison et al., 1994;Jiménez-Martínez et al., 2010).The empirical approach is simple to use but it lacks a rigorous theoretical base, and the recharge coefficient has to be calibrated through a groundwater flow model in the region, which is often not available.
The second is a modeling approach involving numerical models such as HYDRUS (Šimůnek et al., 2012), SWAT (Arnold et al., 2012), UNSATH (Fayer, 2000), SWIM (Krysanova et al., 2005), SWAP (van Dam, 2000) to calculate DSR.Detailed water balance models can be used for irrigated agriculture, but they usually cannot predict evapotranspiration accurately, especially when plants suffer seasonal water stress and plants cover is sparse (Gee and Hillel, 1988).When recharge is estimated as residual in water balance models, it can cause miscalculation as much as an order of magnitude (Scanlon, 2013;Voeckler et al., 2014).When using soil water flow models with measured or estimated soil hydraulic conductivities and tension gradients, similar miscalculation can also occur (Nyman et al., 2014;Gee and Hillel, 1988).In addition, the modeling usually involves upscaling of parameter values over a spatially and temporally discretized mesh from measurements which are made on specific moments and locations.Such an upscaling process is not always easy to execute and it could sometimes lead to serious errors.This is particularly true for arid and semi-arid regions where most precipitation may be episodic (occurring in short and unpredictable events) (Modarres and da Silva, 2007;Zhou et al., 2016), and may be confined to restricted portions of the area (Gee and Hillel, 1988).
The third includes a cluster of experimental techniques such as isotopic tracer (Klaus and McDonnell, 2013), water flux (Katz et al., 2016), andlysimeter (Scanlon, 2013).Among them, lysimeters are instruments that directly measure the hydrological cycle in infiltration, runoff and evaporation.Generally, this equipment is located in an open observation field or as a controlled device, working either solely or in groups (Good et al., 2015).In a typical lysimeter, soil are filled into a column surrounded by impermeable lateral boundaries thus water can only enter or leave the column from upper or lower boundaries (Duncan et al., 2016;Fritzsche et al., 2016).A drainage system is usually placed at the bottom (Glenn et al., 2013).The depth of soil in the column depends on the experimental purpose.Experiments can be done with the same type of soil at different depths in a single column, or in different columns but at the same depth.The soil surface can be cultivated with different crops or left alone as bare land.Observation can be recorded with weight or volume of water.
Application of above-mentioned methods for assessing DSR in arid and semi-arid regions has met a variety of challenges, primarily due to the fact that precipitation events often happen in the form of short pulses with highly variable intensity (Collins et al., 2014).The intermittent and unpredictable characteristics of precipitation events lead to highly variable moisture and nutrient levels in the soils (Beatley, 1974;Huxman et al., 2004).It is unclear how the precipitation amount, time, and interval will affect the water moisture of arid and semi-arid regions, especially the change of deep soil water storage.
In this study, a new type of lysimeter is designed to accurately measure the amount of DSR in arid and semi-arid regions.With the help of a three-year (2013-2015) field investigation with this new lysimeter, one can answer the following question: Is the concept of an annual recharge coefficient valid or not for estimating DSR at a given location in an arid and semi-arid region?
Before the introduction of this new type of lysimeter, it is necessary to briefly explain the challenges faced by the conventional lysimeter for studying DSR in arid and semi-arid regions.

Problems with the conventional lysimeter methods in arid and semi-arid regions
Lysimeters have been used to access the amount of water consumed by vegetation for more than three hundred years (Howell et al., 1991).The type of lysimeter that is specifically designed to measure evapotranspiration (ET), called precision weighing lysimeter, has been developed within the past six decades.In order to suit different requirements and needs, there are various designs of weighing lysimeters, with surface areas ranging from 1.0 m 2 to over 29 m 2 (Howell et al., 1991).The stored media mass and the type of scale such as diameter and height, are factors on which the accuracy of ET measurement depends, and many lysimeters have accuracies better than 0.05 mm (Howell et al., 1991).Figure 1A shows the schematic diagram of a conventional lysimeter installation in the field.It is basically a weight meter of soil with an open upper boundary at ground surface and a perforated bottom boundary and impermeable vertical side walls.The typical depth of lysimeters varies from 0.2 m to 2 m, but is rarely greater than 2.5 m (Howell et al., 1991).The horizontal cross-section area is usually in the range of 1 m 2 to 29 m 2 .Precipitated water can freely infiltrate into the soil from the top and downward flow of water at the bottom of the lysimeter is collected (through the perforation) as a function of time to calculate the recharge.Alternatively, the weight of combined water and soil inside the lysimeter can be accurately measured using a weight gauge to reflect any soil moisture change.Such information, combined with infiltration or evaporation at the surface, can yield the information of downward water flux at the depth of lysimeter.
The following issues deserve special attention when applying the conventional lysimeter for measuring recharge.Firstly, soil layers are inevitably disturbed when installing the instrument, so the result may not reflect the actual recharge in native (undisturbed) soils (Weihermüller et al., 2007) .Secondly, the cost is too high to use multiple lysimeters to observe large-scale infiltration (Stessel and Murphy, 1992).Thirdly, when precipitation strength is relatively light and concentrated, a large lysimeter cannot sensitively and rapidly measure DSR (Goldhamer et al., 1999;Farahani et al., 2007).The conventional lysimeter often cannot answer the following questions: To what soil layer can different levels of precipitations infiltrate?How much is the infiltration amount under different levels of precipitation? (Gee and Hillel, 1988;Ogle and Reynolds, 2004).
The conventional lysimeter as shown in Figure 1A may meet additional challenges when applied to arid and semi-arid regions.Firstly, the water table depths in arid and semi-arid regions may be much greater than the maximal depth of a conventional lysimeter (2.5 m).For instance, in Chagan Nur, southeast of Mu Us sandy land in the Ordos basin of China, the water table depth was found to be greater than 4 m.In the Gobi desert, the water table was reported to be at least 2.8 m deep (Ma et al., 2009).Therefore, the infiltration measured at the base of a conventional lysimeter may not represent the actual recharge that eventually enters the groundwater system.
Secondly, the measurement accuracy of lysimeter often declines for soils with deep plant roots because the depth of lysimeter installation is limited and it may be less than the depth of those roots at site, which by itself can be important pathways for water migration.Consequently, the

Design of a new lysimeter for measuring DSR in arid and semi-arid regions
This new lysimeter has a few innovations (see Figure 1B) that can be outlined as follows.
Instead of setting the upper boundary of the lysimeter at ground surface, the new design has its upper boundary at a designed depth (denoted as depth-A in Figure 1B) where infiltration will be measured.A cylindrical container with a diameter of 20 cm to 40 cm with impermeable walls is installed from depth-A downward to a deeper depth-B.The length of AB is determined according to the capillary rise of the in-situ soil, which can be calculated using the average grain size of soils within AB.More specifically, the length of AB is greater than the capillary rise of soils within AB and it is usually great than 0.6 m (Liu et al., 2014).At the base of the instrument (depth B), a water collection device is used to measure the amount of water exit the base.
Before the measurement, one necessary preparation is to inject water from the top of the instrument at depth-A using water pumps, the injection will stop until water starts to drip out from the base at depth-B.One usually has to wait 10 days to allow the water profile in column AB to become equilibrium.When water stops flowing out from depth-B, the soil water in the column is regarded as reaching its equilibrium state, in which the soil moisture at depth-B reaches the maximum field capacity.Under such an equilibrium status, the amount of infiltration entering the upper surface of the lysimeter will be discharged (with the same amount) from the base of the lysimeter after a certain delay time.
The proposed new method has a few innovative features that have not been considered in previous studies.Firstly, it can measure DSR at any given layer of a multi-layer soil system using a single apparatus installed in the field.Secondly, continuous real-time measurements can be recorded over any given time period, thus a time-series of DSR can be obtained, which will be very useful to understand the soil water dynamics at sandy area of arid and semi-arid regions.
Thirdly, the apparatus is portable and easy to install, thus a large amount of data can be collected in various locations of a study area using multiple lysimeters, and spatial recharge distribution can also be obtained straightforwardly.This method is field tested in arid and semi-arid sandy regions of western China.It provides key references for the evaluation of water resources, water balance, and the stability assessment of sand-fixing vegetation in arid and semi-arid areas.It also provides data that are much needed for evaluating soil water contents and groundwater resources of those areas.An important feature of this new lysimeter is that it can provide reliable DSR data to examine the concept of annual recharge coefficient when comparing with the precipitation data.

Description of the study area
Figure 2 shows the location of the study which is located in Ejin Horo Banner, on the Eastern margin of Mu Us Sandy Land in the Ordos basin of China (geographic location: 39°05' N, 109°36' E; altitude: 1070-1556 m above mean sea level).The groundwater table between dunes are 5.3-6.8m below ground surface.The climate is semi-arid continental monsoon climate zone.Precipitation concentrates from July to September, with relatively concentrated rainstorm.
The average annual precipitation from 1960 to 2010 is 296.01 mm.The average annual temperature of this area is 6.5℃, with about 151 days of frost-free season, 1809 mm total evaporation, an average 2900 hours of sunshine, and an average wind speed of 3.24 m/s (Wu and Ci, 2002;Karnieli et al., 2014).The study area is located in relatively gentle mobile dunes, and the soil type is Aeolian sandy soil.area, the percentage of fine sand (0.5-0.1 mm) are 88.56%, 77.88%, 88.23%, 88.89%, 90.28%, 83.90%, and 84.21% at depths of 0 cm, 10 cm, 30 cm, 60 cm, 90 cm, 150 cm, and 200 cm, respectively.The rest parts of the soil are primarily coarse sands.It is evident that the soil at the upper 200 cm is relatively homogeneous.

Statistical analysis of data
Research on the relationship between precipitation and DSR of bare sand land in arid and semi-arid regions is beneficial to understand the soil-water dynamics of those regions.Because vegetation is absent, complexity related to transpiration process by plants is not a concern.
Based on two time series of real-time data of precipitation and DSR, one can examine the relationship between DSR and precipitation.This study can serve as a basis for further study of DSR in semi-fixed and fixed sand lands with different fractional vegetation covers.
The statistics of precipitation and DSR are shown in Table 1, which reveals that there is an obvious difference of precipitation at the experimental plot from 2013 to 2015.The annual precipitation is 83 mm in 2013, 205.6 mm in 2014, and 186.4 mm in 2015.This is to say, the annual precipitations in 2014 and 2015 are 2.48 and 2.25 times of that in 2013, respectively.Such a dramatic fluctuation and uneven distribution of annual precipitation is typical of arid and semi-arid regions.The corresponding annual DSR is 20.2 mm in 2013, 20.6 mm in 2014, and 9.2 mm in 2015.This is say that the annual DSR values in 2014 and 2015 are 1.02 and 0.46 of that in 2013.The annual DSR/precipitation ratios (or the so-called annual recharge coefficient) for 2013, 2014, and 2015 are 24.33%,10%, and 4.94%, respectively.It appears that there is no clear correlation between the annual DSR and the annual precipitation according to the data of 2013-2015.In another word, use of the annual recharge coefficient for the study site becomes questionable as such a coefficient implies that there is a close correlation between the annual DSR and the annual precipitation, which is not supported by the data of 2013-2015.Therefore, we will scrutinize the precipitation pattern and intensity more closely to decipher the connection of precipitation and DSR in the following.

The relationship between precipitation pattern and DSR
Research on bare sandy soil water dynamic process usually focuses on temporal and vertical differences (Ritsema and Dekker, 1994;Postma et al., 1991).In term of temporal soil moisture variation over an annual cycle, the process could be divided as soil moisture replenishment, depletion, and relatively stable periods.In term of vertical soil moisture variation, soil water content usually first increases with depth and then decreases based on an interplay of mutual infiltration and evaporation processes.In general, soil could be divided as a surface dry sand layer, a layer with drastic moisture change, and a layer with relatively stable moisture content.
Specifically, the soil deeper than 160 cm in arid and semi-arid regions would have a relatively stable moisture content.This is because of two reasons.Firstly, soil water will not be up-taken to the surface by capillary force at such depths; secondly, ground water table in arid and semi-arid regions is usually much lower than 160 cm.
In our study site, 2013 is an especially dry year with only 83 mm precipitation compared to 296.01 mm of average annual rainfall calculated over a period from 1960 to 2010.The precipitation and DSR patterns of 2013 are shown in Figure 3.The measurement accuracy of the lysimeter is 0.2 mm.During the observation period from April 1 to November 30, there are totally 25 recorded precipitation events, mostly concentrated in the period from May to August.
There is a one-time strongest precipitation event with a 24-hour precipitation amount reaching 32 mm in August 3.The DSR correlated to this event can be identified from September 21 to November 30 and reaches 17.2 mm.The delay time from precipitation event to the start of DSR is approximately 48 days.The DSR/precipitation ratio for this particular event is as high as 53.75%.Such a DSR/precipitation ratio appears to be the highest in 2013.It is worth to note that although the strongest precipitation event at August 3 contributes the greatest to DSR observed from September 21 to November 30, a few precipitation events with amount of 6.6 mm prior to this strongest precipitation event also contribute a minor part for DSR from July 27 to August 1.
It is also notable that the DSR/precipitation ratio for the strongest precipitation event is substantially higher than the average annual recharge coefficient of 24.33% in 2013.This leads to the conclusion that DSR is closely related to the strong precipitation events, rather than to the average annual precipitation.The strongest single-day precipitation in 2014 is 15 mm (occurred in July 30), which is less than half of the strongest single-day precipitation event of 32 mm occurred in 2013 (August 3), annual DSR/precipitation ratio of 2013 is 24.33% but in 2014 is 10%.This once again supports the conclusion that the strong precipitation events rather than the average annual precipitation are mostly responsible for the average annual DSR.
because annual DSR is not always proportional to the total annual precipitation.Instead, it appears to be more closely related to individual precipitation events stronger than 10 mm.

Discussion
This improved lysimeter is on the real-time dynamic monitoring of DSR, and it provides reliable evidence for an accurate evaluation of precipitation-related recharging capability of bare sand lands in arid and semi-arid regions.However, there are a number of issues that deserves further attention and requires additional investigations in the future.The moisture evaporation, the soil absorption of moisture, and the water infiltration of post-evaporative redistribution, are all very complex processes, especially in arid and semi-arid regions.It is sometimes difficult to clearly distinguish the amount of evaporation and DSR with conventional methods as outlined in the introduction.This study selects precipitation and infiltration data during the period from April 1 to November 30, so the influence of freeze-thaw process during winter is avoided, and the experimental design and data analysis is simplified.For this reasons, the next steps should be a full-term monitoring, a systematic study on DSR, as well as a study on the soil temperature and daily temperature influences on DSR.
Although this experiment does not address the issue of soil temperature effect on DSR in great details, the relationship between DSR and soil temperature is evident.In general, a higher temperature means a stronger evaporation demand, thus an often smaller DSR.
Through the analysis of this study, one can see that the use of an annual recharge coefficient for the study area is not supported by the data collected from the new lysimeter, as the annual recharge is not positively correlated with the annual total precipitation.Instead, we find that the recharge is somewhat positively correlated with a few strong precipitation events (greater than 10 mm), and very closely correlated with the strongest precipitation event (considerably greater than 10 mm).It is probably reasonable to assign different weighting factors for different precipitation strengths to calculate DSR.However, the threshold to define a strong precipitation Figure 1(B).

Figure 1 .
Figure 1.Schematic diagram of conventional lysimeter (A) and the new lysimeter (B).

Figure 2 .
Figure 2. Geographic location of the experimental area.
arid regions, summer evaporation is strong, leading to relatively less DSR during the summer season.While during the period from September 1 to November 30, atmospheric temperature drops and sunshine duration becomes shorter, which results in less surface evaporation and greater DSR during this period.Compares to 2013, there are more summer precipitation events in 2014.That is why precipitation in 2014 (205.6 mm) is greater than 2013 (83 mm) but the overall DSR in 2014 is less than that in 2013.
Under the condition of continuous precipitation, it may be difficult to discretize precipitation into individual events.The following example illustrates a procedure to deal with this situation.As shown in Figure6, there is a 13-days continuous precipitation process in 2013 from July 27 to August 8, and the accumulative precipitation is 43.8 mm.The start of a continuous DSR distribution corresponding to this 13-day continuous precipitation event is observed 3 days after the end of this precipitation process, and the peak value of DSR occurs 46 days after the end of this precipitation process.The DSR distribution gradually recedes to zero around 78 days after the end of the precipitation process.The accumulative DSR amount over a 75-day period is 18.4 mm.The ratio of the 75-day cumulative DSR over the 13-day precipitation event is 42%.

Table 2 :
Percentage of valid precipitation in total precipitation amount.