Characteristics of Recharge in Response to Rainfall in the Mu Us Sandy Land, China

Abstract

Water scarcity is a significant issue in arid and semi-arid regions and improving our understanding of infiltration and recharge processes is crucial for water resource management. In this study, weighing lysimeters were employed in Mu Us Sandy Land, China to continuously monitor soil water content and recharge rates during the non-freezing seasons from April 2021 to October 2023. The performance of three empirical weight functions, including Poisson, Rayleigh, and Gamma distributions in simulating the recharge process was evaluated. The results indicate that: (1) The process of groundwater recharge displays significant interannual and seasonal differences. Due to low initial soil moisture and scarce rainfall, recharge accounts for only 10.9% of the averaged annual rainfall in 2021. Due to extreme rainfall events (126.8 mm), groundwater recharge increased by 649.4% compared to 2021, accounting for 51.2% of the annual rainfall in 2022. Because of relatively high soil moisture, groundwater recharge accounted for 18.3% of the annual rainfall in 2023. (2) The Poisson empirical weight function is more suitable for simulating a gradual increase in recharge rate, while it fails to accurately capture the rapid rise in recharge rates associated with extreme rainfall events. (3) Compared to the Poisson empirical weight function, the Gamma distribution performs better under extreme rainfall conditions. This study provides a detailed analysis of groundwater recharge dynamics in semi-arid regions and offers technical support for a deeper understanding of groundwater recharge processes.

1. Introduction

Water resource issues in arid and semi-arid regions are an important topic of global concern. These regions face increasing challenges in water resource management [1,2,3]. The arid and semi-arid areas of northwestern China account for around one-third of the country’s land area in China [4]. The Mu Us Sandy Land is a typical semi-arid sandy area in China, characterized by scarce rainfall and intense evaporation [5]. Rainfall is one of the main sources of soil water content replenishment and has important impacts on agriculture and socioeconomic development in arid and semi-arid regions [6]. The infiltration process plays an important role in the hydrological cycle, which is crucial in water resource management and ecological environment protection. Therefore, a thorough understanding of soil water dynamics after rainfall is essential for effective water resource management and the development of sustainable agricultural strategies.

In arid and semi-arid regions, where evaporation is high and the rainfall infiltration recharges groundwater significantly only after large rainfall events occur [7]. Liu et al. [8] pointed out that 20–30% of the annual rainfall recharges groundwater through rainfall infiltration in the Horqin Sandy Land, China. In the desert area of Dunhuang, China, only rainfall greater than 20 mm/d can effectively recharge groundwater [9]. In the Badain Jaran Desert, China, rainfall less than 30 mm/d cannot effectively recharge groundwater [10]. Ma et al. found that even when rainfall exceeds 40 mm/d, it does not always infiltrate into deep soil or contribute to groundwater recharge [10]. Zheng et al. [11] highlighted that the extreme rainfall events are a significant source of groundwater recharge, accounting for up to 42% of the total groundwater recharge in Yuanshi County, North China Plain. The response of soil water content to rainfall events at different depths is a complex process influenced by multiple factors, such as rainfall amount and intensity [12,13]. Cheng et al. [14] analyzed the response of soil water content to rainfall in mobile dunes under different initial soil water content conditions in the Mu Us Sandy Land, and their results indicated that initial soil water content is a key factor controlling the depth of infiltration and subsequent groundwater recharge.

Currently, several approaches are available for quantifying groundwater recharge, such as tracers, lysimeters, numerical modeling, and water table fluctuation method [15,16]. However, each technique has inherent limitations. For example, the use of isotopes is not an accurate method for short time periods. Lysimeters provide direct observation of recharge is costly and not feasible for large-scale implementation [17]. To enhance understanding of the infiltration and recharge processes, numerical modeling has been widely used. For instance, Mattern and Vanclooste [18] investigated the effect of unsaturated zone thickness on the lag time of recharge using the HYDRUS-1D model. Zhang et al. [19] explored the importance of non-isothermal flow on simulating the groundwater recharge based on the HYDRUS-1D model in a semi-arid region. Lu et al. [20] conducted numerical simulations at five representative sites to investigate the effects of irrigation and water table depth on groundwater recharge. Their results indicated that the time-lag effect at varying water table depths must be considered when estimating groundwater recharge. Zheng et al. [21] simulated and analyzed the effects of different soil fractions and irrigation conditions on water transport using HYDRUS-1D model. Nevertheless, uncertainties remain in the use of numerical models to simulate water transport in the region, including issues related to model structure and calibration parameters [22,23,24]. Furthermore, when the vadose zone is relatively thick, it becomes challenging to obtain sufficient observed data to calibrate numerical models and accurately estimate groundwater recharge.

To address this limitation, some research has applied weighting functions to calculate groundwater recharge. Wu et al. [25] employed the gamma distribution function to characterize the infiltration process, and the simulation results were found to be in good agreement with the observations. Jie et al. [26] employed an improved transfer function (ITF) to investigate the influence of unsaturated zone thickness on lagged groundwater recharge in an arid zone irrigation area in northwest China. They compared ITF results with Hydrus-1D, but the reliance on models without extensive empirical measurements could limit the robustness of the conclusions, especially in areas with highly variable or extreme hydrological conditions. Because of the lack of sufficient field data, the parameters of the transfer function are affected by the characteristics of the unsaturated zone [27]. As a result, their applicability varies across different study areas. Zhang et al. [28] used Poisson distribution function to simulate recharge dynamics. They found the parameter showed a linear relationship with average soil moisture. However, they only explored a few rainfall scenarios, and there are still uncertainties regarding its ability to accurately describe the recharge process during extreme rainfall events.

In light of the limitations of existing research, this study aims to address the following research questions: (1) to analyze the recharge characteristics under different rainfall events under the bare ground condition and to examine the influence of various factors on recharge; (2) to utilize different empirical weighting functions to illustrate the recharge process of a single rainfall event and to evaluate the suitability of different empirical weighting functions. This study provides accurate theoretical support and practical guidance for water resource management in this region.

2. Materials and Methods

2.1. Study Area

The Mu Us Sandy Land (37°27.5′–39°22.5′ N, 107°20′–111°30′ E, elevation 997–1610 m) is situated in the middle reaches of the Yellow River at the confluence of Shaanxi Province, Inner Mongolia Autonomous Region, and Ningxia Hui Autonomous Region, encompassing an area of approximately 34,500 km² (Figure 1). The boundary of Mu Us Sandy Land was obtained from Zhao et al. [29]. The mean annual temperature ranged from 6.0 °C to 8.5 °C, while the mean annual rainfall ranged from 250 mm to 440 mm. The mean annual potential evapotranspiration of 2200.5 mm. Approximately 60–75% of annual rainfall occurs from July to September [30]; and a soil type of sandy soil [31].

2.2. Experimental Design and Data Collection

A bare soil weighing lysimeter with a diameter of 0.8 m and a depth of 1.5 m was installed in the experimental site. The lysimeter was filled with undisturbed soil and was not subjected to any disturbance from the surrounding vegetation. The weighing system of the lysimeter has a minimum resolution of 20 g. Recharge was observed through a drainage container affixed to the base of the lysimeter. The soil water content was measured by the 5TE sensors (Decagon Inc., Washington, DC, USA) installed in the undisturbed soil at depths of 20, 40, 60, 80, and 100 cm. Rainfall data was measured by a tipping bucket rainfall gauge (Texas Electronics, Inc., Dallas, TX, USA). Rainfall events were classified in accordance with the Classification of Rainfall Levels (GB/T 28592-2012), standard promulgated by the China Meteorological Administration. Rainfall events less than 9.9 mm/d are considered as light rain, those between 10 and 24.9 mm/d are moderate rain, those between 25 and 49.9 mm/d are heavy rain, those between 50 and 99.9 mm/d are torrential rain, and those between 100 and 249.9 mm/d are downpour. All data were recorded every 10 min. This study was conducted over a period of three years, from April 2021 to October 2023. The soil textures of the experimental site is taken from Zhang et al. [28] and is listed in

Table 1. Soil texture along with soil profile.

Depth (cm)	Sand (%)	Silt (%)	Clay (%)
0–20	97	3	0
21–40	99	1	0
41–60	98	2	0
61–80	96.9	3.1	0
81–100	93	7	0

.

2.3. Empirical Weight Functions Describes the Infiltration Process

The Poisson distribution probability density function can be utilized to describe the infiltration process [32]. It can be expressed as follows:

$$\sum _{\tau =0}^{n}f\left(\tau \right)=1$$

(1)

$$f\left(\tau \right)={\displaystyle \frac{{\gamma }^{\tau }}{\tau !}}exp(-\gamma )$$

(2)

where $f\left(\tau \right)$ is the groundwater recharge weight function, $\tau$ is the time step, $\gamma$ is the ratio of the vadose zone thickness to the characteristic parameter of the vadose zone.

The Rayleigh distribution can describe recharge rate, and it is a special case of the Weibull distribution [33]. The Weibull distribution can be expressed as follows:

$$\omega \left(x,\alpha ,\beta ,\delta \right)=\left\{\begin{array}{c}\left({\displaystyle \frac{\alpha }{\beta }}\right){(x-\delta )}^{\alpha -1}exp\left(-{\displaystyle \frac{{(x-\delta )}^{\alpha }}{\beta }}\right) x\ge \delta \\ 0 x<\delta \end{array}\right.$$

(3)

where $x$ is a continuous random variable, $\beta$ is the scale parameter of Weibull distribution, $\alpha$ is the shape parameter, and $\delta$ is the location parameter. When $\alpha$ = 2 and $\delta$ = 0 in Equation (3), the Weibull distribution is called the Rayleigh distribution. The Rayleigh distribution can be expressed as follows:

$$\omega \left(x,2,\beta ,0\right)=\left\{\begin{array}{c}\left({\displaystyle \frac{2}{\beta }}\right)xexp\left(-{\displaystyle \frac{x^2}{\beta }}\right) t\ge T_s\\ 0 t<T_s\end{array}\right.$$

(4)

where $\omega \left(x,2,\beta ,0\right)$ is the probability density function of the Rayleigh distribution, $\beta$ is the is the scale parameter of Rayleigh distribution, $t$ is the cumulative time from the start of infiltration to the end of recharge, and $T_s$ is lag time (d). The parameter $\beta$ is calculated from Equation (5):

$$\beta ={\left({T_i/2T}_s\right)}^2$$

(5)

The equation for the random variable x is:

$$x=\left({t-T}_s\right)/T_s$$

(6)

where $T_i$ is the total time of recharge (d), $\beta$ needs to be determined from the lag time of the recharge curve ($T_s$) and the total time of recharge ($T_i$).

Besbes [34] utilized the Gamma distribution density function to describe the recharge process, and the equation can be described as:

$$f(\tau )={\displaystyle \frac{exp\left(-\tau /k\right)}{k\mathrm{\Gamma }\left(n\right)}}{({\displaystyle \frac{\tau }{k}})}^{n-1}$$

(7)

where $f(\tau )$ is the instantaneous unit hydrograph of the vadose zone, $\mathrm{\Gamma }\left(n\right)$ is the Gamma function, $n$ is the shape parameter of Gamma distribution, and $k$ is the scale parameter of Gamma distribution.

3. Results

3.1. Characterized the Variability of Rainfall and Recharge

Figure 2 shows the dynamics of rainfall and cumulative recharge during the non-freeze–thaw period from April 2021 to October 2023. The cumulative rainfall during the non-freeze–thaw period in 2021 was 249.5 mm, and the cumulative recharge was 27.1 mm, which is 10.9% of the rainfall. The maximum daily recharge rate occurred on 10 October 2021 (1.39 mm/d). There were 61 rainfall events in 2021, 53 of which were light rain. A total of 7 events were moderate rain, accounting for 47.5% of the total rainfall. The maximum rainfall of 28.9 mm/d occurred on 18 August (Figure 2a). Recharge mainly occurred in June, August and October in 2021.

The total rainfall during the period of non-freezing–thaw in 2022 was 397.0 mm, which exceeded the rainfall amount recorded during the same period in 2021. The cumulative recharge was 203.1 mm, representing 51.2% of the total rainfall. The maximum daily recharge and rainfall were 41.4 mm/d and 110.8 mm/d occurred on 11 July 2022. Most of the rainfall occurred during July and August, with 56 days of rainfall recorded. A total of 50 events occurred in which the amount of rainfall was light rain, and 164.4 mm of rainfall was recorded, constituting 41.4% of the total rainfall. Moderate rain and heavy rain accounted for 11.2% and 47.4% of the total rainfall, respectively. In 2022, recharge mainly occurred from July to September.

The cumulative rainfall during the non-freeze–thaw period in 2023 was 279.6 mm, with a cumulative recharge of 51.1 mm (Figure 2c). The maximum daily recharge of 5.01 mm occurred on 5 April. Among the 54 days of rainfall events, 44 events were light rain, and the cumulative rainfall during the period accounted for 36.8% of the total rainfall. Moderate rain and heavy rain occurred for 8 and 2 days, respectively, accounting for 40.3% and 22.9% of the total rainfall. The total rainfall was 95.9 mm from April to May, with a cumulative recharge of 38.5 mm, representing 40.2% of the rainfall and 75.4% of the cumulative recharge. Recharge mainly occurred in April, May and September.

3.2. Characterization of Recharge Under Different Types of Rainfall Events

Figure 3 shows the dynamics of recharge rates following six different rainfall events during the experimental period.

The rainfall was 12.8 mm from 24 to 25 June 2021 with an intensity of 1.83 mm/h and a duration of 7 h. Recharge rates exhibit significant differences in their rising and falling phases under different rainfall events. For example, the daily recharge rate reached a maximum of 0.21 mm/d on the 8th day after the rainfall started. Rainfall of 21.1 mm with an intensity of 0.88 mm/h over 24 h occurred on 15 September 2021. The daily recharge rate reached a maximum on the 6th day after the rainfall started. The maximum recharge rate was 0.31 mm/d. The cumulative rainfall from 2 to 5 April 2023 was 32.2 mm, with an intensity of 0.43 mm/h for 75 h. The daily recharge rate was highest on the 4th day after the rainfall event occurred, with a maximum recharge rate of 5.01 mm/d. The cumulative rainfall from 4 to 6 October 2021 was 36.1 mm, with an intensity of 0.64 mm/h for 56 h. The daily recharge rate was highest on the 7th day after the rainfall event occurred, with a maximum recharge rate of 1.39 mm/d. From 18 to 19 August 2021, the cumulative rainfall was 51.6 mm, with an intensity of 1.66 mm/h and a duration of 31 h. The maximum daily recharge rate was reached on the 5th day after the rainfall event occurred, with a maximum recharge rate of 1.08 mm/d. From 9 to 11 July 2022, the cumulative rainfall was 126.8 mm. The rainfall intensity was 2.25 mm/h over a period of 56 h. The daily recharge rate reached its maximum on the third day after the rainfall event occurred, and the total rainfall on this day reached 110.8 mm, with a maximum recharge rate of 41.43 mm/d.

3.3. Characterization of the Recharge Process Based on Empirical Weight Functions

Figure 4 illustrates the simulation results from the Poisson empirical weight function under different rainfall events. As illustrated in Figure 4a,b, the Poisson empirical weight function effectively reproduces the entire recharge process and the peak recharge rate during rainfall events of 12.8 mm and 21.1 mm, with R² values of 0.97 and 0.91, respectively. Compared with the increasing recharge rates shown in Figure 4a,b, the recharge rate was faster in Figure 4c. However, the Poisson empirical weight function does not fit the rising phase and peak value well. The Poisson empirical weight function can effectively describe the upward process, the peak, and the occurrence time under the 36.1 mm rainfall event condition (Figure 4d) given that the increasing recharge rate was found to be slower than that in Figure 4c. However, the estimations of recharge rate lack accuracy during the rapid decline phase (Figure 4c,d). Figure 4e illustrates that the Poisson empirical weight function can obtain satisfactory results during the infiltration process under a rainfall scenario of 51.6 mm. The rise and decline phases, the peak, as well as timing of peak occurrence can be characterized with a high degree of accuracy (R² = 0.96). For the rainfall of 126.8 mm (Figure 4f), the Poisson empirical weight function is poorly fitted to the peak and rise periods because the increasing recharge rate was too fast.

Figure 5 illustrates the simulated infiltration process based on the Rayleigh empirical weight function under different rainfall events. When the rainfall was 12.8 mm (Figure 5a), the Rayleigh empirical weight function was observed to better describe the rising phase of the recharge process. The peak value and time of occurrence deviated from the measured value, and the R² was 0.87. When the rainfall was 21.1 mm (Figure 5b), the Rayleigh empirical weight function does not reproduce the upward phase and the peak well, but it is able to describe the trend of the downward phase relatively well. When the rainfall was 32.2 mm and 36.1 mm (Figure 5c,d), the Rayleigh empirical weight function fails to adequately characterize both the ascending phase and the peak. However, the Rayleigh empirical weight function was more accurate in describing the recession phase than that of the increasing phase and peak. When the rainfall was 51.6 mm and 126.8 mm (Figure 5e,f), the Rayleigh empirical weight function was unable to characterize the rising process effectively. However, the function provided a superior description of the descending phase and peak arrival time compared to other rainfall events.

Figure 6 shows the results of simulation recharge using the Gamma empirical weight function under different rainfall events. The Gamma empirical weight function demonstrates a good fit to the measured data, with R² ranging from values of 0.86 to 0.98. When the rainfall was 12.8 mm, there was a lag between the simulation peak and observed data (Figure 6a). For the rainfall events of 32.2 mm and 36.1 mm, the simulated peak underestimated the measured data (Figure 6c,d). During the decreasing process, there was slight difference between the simulated recharge and observed values. However, the simulated results of the Gamma empirical weight function were better compared to the results from Poisson empirical weight function and Rayleigh empirical weight function. For the rainfall events of 21.1 mm, 51.6 mm, and 126.8 mm, the gamma empirical weight function accurately represents the entire infiltration process (Figure 6b,e,f).

4. Discussion

Current studies indicate that recharge is subject to many influencing factors, including soil properties, evapotranspiration, initial soil water content, rainfall amount and intensity, as well as the depth to the water table [16,35]. Our results show that groundwater recharge varies significantly between different years. In 2021 (Figure 2a), the recharge concentrated in August (6.1 mm) and October (10.4 mm). The main key driving factors were the two intense rainfall events, which occurred on 18–19, August (total rainfall amount: 51.6 mm) and October 4–6 (total rainfall amount: 36.1 mm). The soil water-content deficit in the unsaturated zone was replenished first and subsequently followed by the recharge of groundwater via piston flow. In 2022 (Figure 2b), recharge predominantly occurred in July (116.4 mm) and August (65.1 mm), with an extreme rainfall event on July 11 (110.8 mm). Our data show that after the extreme rainfall event, the soil water content at 100 cm increased from 0.31 cm³/cm³ to 0.34 cm³/cm³, whereas at 80 cm, it only increased slightly from 0.17 cm³/cm³ to 0.18 cm³/cm³. This finding indicates that extreme rainfall has the potential to facilitate hydraulic connectivity among disparate pore domains, thereby inducing the formation of preferential flow paths [36,37]. Zhang et al. [28] also found that preferential flow may exist if the heavy rainfall occurred in the Mu Us Sandy Land, China. Consequently, recharge was 203.1 mm in 2022, representing a 649.4% increase compared to 2021. In 2023 (Figure 2c), groundwater recharge primarily occurred in April, despite the occurrence of intense rainfall events in June and August, which contributed relatively little to recharge. This can be mainly attributed to the significantly higher evapotranspiration rates in June and August compared to April.

The performance of different empirical weight functions in describing the infiltration process varies significantly. Our results indicate that the Poisson empirical weight function requires careful consideration of rainfall amount, initial soil water content, and recharge rate. Taking the 32.2 mm rainfall event as an example, the average soil water content of the soil profile prior to the rainfall was 0.15 cm³/cm³. The hydraulic connectivity from the surface to the deeper soil layers was relatively high, enabling rapid movement of infiltrated water through the vadose zone and resulting in a swift increase in the recharge rate, which led to a rapid increase in recharge rate (Figure 4c). During the extreme rainfall event of 126.8 mm, water preferentially moved through preferential flow pathways in the vadose zone, resulting in an abrupt increase in groundwater recharge (Figure 4f). Therefore, the Poisson empirical weight function is inadequate in accurately capturing the rapid rise in recharge rate; it performed poorly in simulating the recharge processes in both the 32.2 mm and 126.8 mm rainfall events. This finding was different from the conclusion of Zhang et al. [28], who pointed out that the Poisson empirical weight function effectively reproduced recharge dynamics. This is related to the fact that the extreme rainfall event was not considered in their study.

Compared to the Poisson empirical weight function, the Rayleigh empirical weight function shows a positively skewed distribution and pronounced tailing characteristics. These properties allow it to better capture the recession stage of groundwater recharge (as shown in Figure 5e,f). In contrast, the Gamma empirical weight function demonstrates superior performance under extreme rainfall scenarios, primarily due to its dual-parameter structure (shape parameter and time parameter). By calibrating these two parameters, the model more accurately characterizes the rapidly rising phase of the infiltration recharge process, thereby overcoming the limitations inherent in single-parameter models.

5. Conclusions

A bare soil weighing lysimeter and a weather station were installed in the Mu Us Sandy land, China. The soil water content, recharge rate, and meteorological data were measured during the non-freezing and thawing period from 1 April 2021 to 1 November 2023. The performances of different empirical weight functions in describing the recharge process under different rainfall events were evaluated. The main conclusions can be drawn as follows: (1) There are obvious interannual and seasonal differences in groundwater recharge. In 2022, due to the occurrence of an extreme rainfall event (126.8 mm), groundwater recharge accounted for 51.2% of the annual rainfall, which was higher than in 2021 (10.9%) and 2023 (18.3%). (2) The Poisson empirical weight function requires careful consideration of rainfall amount, initial soil water content, and recharge rate. However, it fails to accurately capture the rapid rise in recharge rates associated with extreme rainfall events. (3) The Rayleigh empirical weight function, characterized by its positively skewed nature and pronounced tail, can better capture the recession stage of groundwater recharge. Conversely, the Gamma empirical weight function, with its shape and time parameters, has been shown to enhance the precision of simulating recharge processes during extreme rainfall events. In summary, this study not only helps us understand the recharge processes and the applicability of empirical weight functions under the bare soil condition in the Mu Us Sandy Land, China, but also offers technical support for groundwater dynamics assessment and sustainable utilization in arid and semi-arid regions.