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Article

Dynamic Response Characteristics of Shallow Groundwater Level to Hydro-Meteorological Factors and Well Irrigation Water Withdrawals under Different Conditions of Groundwater Buried Depth

by
Yi Cai
1,2,*,
Ruoyao Huang
1,
Jia Xu
3,*,
Jingwen Xing
1 and
Dongze Yi
1
1
Department of Hydraulic Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, China
2
The Yangtze River Water Environment Key Laboratory of the Ministry of Education, Tongji University, Shanghai 200092, China
3
China Construction Eight Bureau Smart Technology Co., Ltd., Nanjing 210046, China
*
Authors to whom correspondence should be addressed.
Water 2022, 14(23), 3937; https://doi.org/10.3390/w14233937
Submission received: 25 October 2022 / Revised: 18 November 2022 / Accepted: 29 November 2022 / Published: 3 December 2022
(This article belongs to the Section Hydrogeology)
Browse Figures
Review Reports Versions Notes

Abstract

:
Many irrigation districts along the Yellow River have been suffering shallow groundwater depression and agriculture-use water shortage. For comprehending response relationships of shallow groundwater level and various factors under different conditions of groundwater buried depth, the hydro-meteorological time series and the agricultural production data in Puyang area of Henan Province, China during 2006–2018 were collected for performing wavelet analysis of the relationship between the groundwater level and the four different factors, such as precipitation, air temperature, water stage of the Yellow River, and well irrigation water amount. It is shown that when the burial depth of groundwater varied from 0–10 m to over 10 m, the groundwater level was related with both the precipitation and air temperature from moderately to weakly and the delayed response times of the groundwater level to them extended from 2–4 months to more than 5 months. The groundwater level maintained a medium correlation with the well irrigation water amount as the burial depth increased, but the lag response time of groundwater level to well irrigation dramatically decreased when the burial depth exceeded 10 m. The dynamic response relationship between the groundwater and the water stage of the Yellow River was mainly affected by the distance away from the Yellow River rather than the burial depth and the influence of the river stage on the groundwater level was limited within the distance approximate to 20 km away from the Yellow River. The findings are expected to provide the reference for groundwater level prediction and groundwater resources protection.

1. Introduction

Groundwater is a dominant water resource in arid and semi-arid areas and widely utilized in various fields of social life [1,2]. Owing to a growing population, fast economic development, and frequent extreme drought events, the demand for water resources has been increasing and, consequently, a large amount of groundwater was over exploited to meet daily water supply [3,4,5,6]. Overexploitation is likely to make the water shortage even worse and, consequently, to weaken agricultural drought-resistant capability and ecological resilience in arid and semi-arid areas [7,8,9]. Therefore, the rational development and utilization of groundwater resources is of great significance to the sustainability of water resources in arid and semi-arid areas.
Fully understanding the variation characteristics of groundwater level is a prerequisite for rational development and utilization of groundwater resources [10,11,12]. It is indicated from many previous studies that groundwater level is affected by many factors, such as hydro-meteorological conditions, ground factors, and human activities [13,14,15,16]. Leblanc et al. found that there was a sharp decline in groundwater level in the Murray–Darling basin in Australia from 2000 to 2007 due to the extreme drought [17]. The groundwater withdrawals, the artificial recharge, and the land-use nature change can lead to the variation in groundwater level [18]. The investigation performed by Xiao et al. showed that the average decline rate of groundwater level during 2007–2013 was higher than during 2001–2006 in Beijing piedmont plain and the decline rate of groundwater level in the agricultural irrigation areas was lowest, compared with those in residential and industrial areas [19]. In addition, it was found that the dynamic change in groundwater level was usually of extremely complex nonlinear characteristics, such as periodicity and randomness [20]. Moreover, some influencing factors, e.g., rainfall and irrigation amount, vary periodically [21]. Therefore, it is difficult to quantify the response relationships of groundwater level and influencing factors using traditional correlation analysis methods, e.g., Pearson correlation analysis. Therefore, it is necessary to find a way to determine both cycle characteristics and response time.
With its advantages in multi-scale analysis, wavelet analysis has been extensively employed in image processing, hydro-meteorological sequence recognition, signal diagnosis, etc. [22,23,24]. In contrast to Fourier transform, wavelet transform can perform multi-scale refinement and analysis through the stretching and translation operation on functions or signals. Therefore, wavelet analysis is helpful in finding time-frequency characteristics of non-stationary time series [25,26]. In recent years, wavelet analysis has been used to study the dynamic change in groundwater and a large amount of valuable results have been obtained. Gordu et al. proposed the decades-long groundwater dynamic prediction method by means of multi-scale wavelet analysis and applied it to study the effects of pumping and climate change on groundwater level [27]. Wu et al. combined wavelet analysis with a LSTM model to simulate the temporal and spatial variation of groundwater level [28]. Cui et al. [29] applied wavelet analysis to investigate the response relationship of groundwater depth to precipitation based on the monthly time series data and found that the delayed response time ranged from 8 to 14 months in Baotou, China during the period of 2007–2017. Clyne and Sawyer analyzed the lag response time of riparian groundwater level to stream stage at 17 locations distributed in the United States and found that it varied from days to weeks in the spring and summer [30]. Qi studied the dynamic response of karstic water level to precipitation and water stage of the Yellow River in Jinan area of Shandong Province in China during 2007–2018 [31]. The results showed that the lag response time of karst water level was 110–165 days to precipitation and 105–162 days to the Yellow River stage. Through the wavelet analysis conducted by Dong et al. [32], it was found that the delayed response times of groundwater level to precipitation and river stage were 4–128 days and about 1 year, respectively, in the Yoshino River basin, Japan during 1972–2014 and the lag response times varied significantly with seasons.
It is indicated from the previous studies that the main factors affecting groundwater level vary geographically and the response times of groundwater level to different factors are sensitively influenced by the data available. In view of the shortage of long-term gauged data concerning agriculture-use groundwater withdrawals in most of irrigated areas, there are few reports on the quantification of the response relationship of groundwater level and extracted groundwater water amount in large area of farmland. Furthermore, some studies showed that soil evaporation and groundwater recharge varied with buried depths of groundwater [33]. Groundwater level is governed by groundwater recharge and discharge. Therefore, with the buried depths of groundwater changing, the variation mechanism of groundwater level will vary accordingly. However, the response relationship between groundwater level and driving factors under different buried depths of groundwater is rarely reported. To improve the accuracy of groundwater protection, it is necessary to discover the effect of the buried depths of groundwater on the response relationship between groundwater level and affecting factors.
One of the major objectives of the study is to propose the quantitative method for generating the time series of 5-day irrigation-use groundwater withdrawals based on the meteorological data and agricultural information. The other is to quantify the response relationship between groundwater level and different factors including precipitation, air temperature, river stage, and well irrigation water withdrawals under the different conditions of the buried depth of groundwater by means of wavelet analysis and, consequently, to determine the dominant control factors affecting the shallow groundwater level at various buried depths. The findings are expected to be helpful in fully comprehending the influences of natural factors and anthropogenic disturbance on groundwater resources and in providing some scientific references for groundwater level prediction, management, and protection of groundwater resources.

2. Study Area

Puyang area of Henan Province is located at the junction of Hebei, Shandong and Henan provinces, with a total area of 4188 km2. The terrain of Puyang is relatively flat and concentrated in the elevation of 48 to 58 m above mean sea level (AMSL). The first stratum with a thickness of about 300 m is composed of the Quaternary loose sediment. The shallow aquifer is the dominant aquifer type in the area. The buried depths of the bottom and the top plates of the layer are 86.0–116.0 m and 3.6–20.0 m, respectively. The sediment is mainly composed of silty-fine and medium-fine sand. Due to less aquitard, the groundwater in the area belongs to phreatic water or slightly confined water. The loose loam soil can maintain water and fertilizer and, consequently, provide a suitable environment for crop growth. The mean annual precipitation is about 563.0 mm and the mean evaporation of water surface is approximate to 930.3 mm according to the statistical analysis of the data observed from 1956 to 2016. The rainfall in summer from June to September accounts for more than 70% of the total amount of the whole year.
As illustrated in Figure 1, Puyang area lies along the Yellow River, with three major rivers flowing through it. The Yellow River, with the mean annual runoff of 43.66 billion m3, provides the abundant pass-by water resources for Puyang and the mean annual water diverting quantity reached 0.8 billion m3 during the period of 2015–2019. The Jindi River is an important tributary of the Yellow River and the annual runoff is about 0.17 billion m3 on average. The Jindi River is a seasonal river and its main functions are to receive abandoned water from the irrigated areas and alleviate waterlog disaster. The levee on the north side of the Jindi River cuts Puyang area into two. The north part, consisting of two counties and central urban area, belongs to the Hai River basin and the south covering three counties belongs to the Yellow River basin. The Wei River flows through the northern boundary of Puyang with the mean annual runoff approximate to 1.58 billion m3 and is mainly responsible for flood prevention.
Serving as an important grain-producing area, Puyang, with the well-developed canal system, has large area of farmland, which accounts for about 72% of the total area. Since most of the water diversion from the Yellow River is consumed in the south, the agricultural irrigation in the north mainly depends on groundwater. With the increasing agriculture-use water demand, the groundwater withdrawal amount has been increasing in the study area. The long-term overexploitation of groundwater has resulted in the continuous decline in groundwater level and the formation of funnel-shaped ground water surface. Until the end of 2018, the area of the groundwater depression cones reached 1850 km2 and accounted for 44.2% of the total area [34].
The main crops in Puyang area are winter wheat and summer maize. In the study area, winter wheat has eight growth phases including seeding from mid to late October, stooling from early to mid November, overwintering from late November to mid February, regreening from late February to early March, jointing from mid March to early April, heading from mid April to early May, filling from mid to late May, and maturation from early to mid June. Different from winter wheat, summer maize has six growth phases including seeding from early June to mid June, emergence from mid to late June, jointing from early to late July, tasseling from early to mid August, filling from late August to mid September, and maturation from late September to early October. The irrigation water demand of crops varies with growth phases. For winter wheat, it reaches the peak at heading and the low level at stooling. Due to strong evapotranspiration and uneven distribution of precipitation in time and space, irrigation with appropriate amount and frequency is required for maize even in rainy summer. The Yellow River has three flood seasons including spring flood, summer flood, and autumn flood, in which spring flood and summer flood are very important to the growth of the major crops. The water diversion duration from the Yellow River is usually half a year, from early March to late August.

3. Data and Methodology

3.1. Data Collection

The daily precipitation time series over the 11-year period of 2006–2018 were collected from meteorological stations in Puyang. The planting areas of winter wheat and summer maize were obtained from Puyang statistical yearbooks, 2006–2018. The daily river stage data were collected from the two hydrological stations, i.e., Gaocun station and Sunkou station (see Figure 1). Through correlation analysis, it was found that the water level at Gaocun station was significantly correlated with the Sunkou station, and the Pearson correlation coefficient between them was approximate to 0.97 during the study period. Therefore, it was reasonable to choose the water level at Gaocun station as the Yellow River stage in the study area. The 5-day time series of groundwater buried depth and the elevation data of well heads (AMSL) were obtained from 73 observation wells scattered in Puyang (see Figure 2). Considering the impact of missing data, 55 wells with the missing rates of less than 3% were used as the interpolation points of groundwater depth and the remaining 18 wells as the verification points. Table 1 presents the inter-annual variations of precipitation, water stage (AMSL) at Gaocun station, and crop planting area in Puyang area from 2006 to 2018.

3.2. Estimation of Groundwater Pumpage for Irrigation

The net irrigation water requirement of crops has a relation with effective precipitation, crop evapotranspiration, and deep infiltration [35]. Considering that Puyang is in arid and semi-arid areas, low rainfall, strong evaporation, and large area of crops contribute to the elimination of deep infiltration. Therefore, the net irrigation water requirement in the investigation was defined as the differential value between crop water requirement and effective precipitation. The well irrigation water requirement could be quantified based on the well irrigation coefficient, the crop planting area, and the net irrigation water requirement, as described in Equation (1):
W I R = A β ( E T c - α P ) × 10 − 3
where WIR is the well irrigation water demand in m3; A is the crop planning area in km2; ETc is the crop evapotranspiration in mm during the whole growth period of crops; α is the empirical coefficient of effective precipitation and assigned as 0.7 according to the study conducted by Feng et al. [36]; P is the precipitation in mm; and β is the coefficient of well irrigation. According to Puyang Water Resources Bulletin, β was assigned as 0.7 for the north and 0.2 for the south.
Based on the crop coefficients and the reference crop evapotranspiration values for different growth stages, the crop evapotranspiration can be calculated using Equation (2):
E T c = ∑ E T c i = ∑ ( K c i E T 0 i )
where ETci is the crop evapotranspiration in stage i in mm; Kci is the crop coefficient in stage i; and ET0i is the reference crop evapotranspiration in stage i in mm. According to the research reported by Liang [37], the crop coefficients and the reference crop evapotranspiration values for different growth stages of the two crops are listed in Table 2.

3.3. Spatial Interpolation of Groundwater Depth

The five methods were adopted to carry out spatial interpolation of groundwater depth separately, including Trend Surface, Regular Spline, Ordinary Kriging, Inverse Distance Weight, and Simple Kriging. The three indexes, i.e., mean absolute error (MAE), mean relative error (MRE), and root mean square error (RMSE), were employed to evaluate the interpolation accuracy of the methods mentioned above. It is shown from Table 3 that the Ordinary Kriging was of relatively high accuracy, with the minimum values of MAE, MRE, and RMSE. Therefore, the Ordinary Kriging was chosen in the study as the spatial interpolation method.

3.4. Wavelet Analysis

In the study, continuous wavelet transform (CWT) was used to calculate the period of continuous time series and cross wavelet transform (XWT) to determine the response time of one time series to the other. The calculation formula of CWT is defined as Equation (3) [38]:
W f ( a , b ) = ∫ - ∞ ∞ f ( t ) 1 a ψ ( t - b a ) * d t
where f(t) is a given time series; a is the position of time point t; b is the scale inversely related to frequency; ψ is the mother wavelet; and * is the complex conjugate operator. Since the time series of groundwater level is a continuous and non-stationary signal, the time–frequency localization should be considered when selecting the mother wavelet. The Morlet wavelet can maintain a balance between time and frequency localization and for this reason, it was adopted as the mother wavelet in the study.
The continuous wavelet power spectrum, which can be used to evaluate the relative contribution to the variance of time series at different scales and each time point, is expressed as Equation (4) [39]:
W P S f ( a , b ) = W f ( a , b ) W f * ( a , b ) = W f ( a , b ) 2
The calculation of XWT is represented as Equation (5) [40]:
W X Y ( a , b ) = W X ( a , b ) W Y * ( a , b )
where WX(a,b) and WY(a,b) are the continuous wavelet transform of time series X and time series Y, respectively. |WXY| is defined as the cross wavelet power and can be used to evaluate the correlation of two sequences [41]. The higher the |WXY| values, the more significant the correlation between the two sequences.
The wavelet coherence coefficients of two time series are calculated using Equation (6) [42]:
R 2 ( a , b ) = S ( b - 1 W X Y ( a , b ) ) 2 S ( b - 1 W X ( a , b ) ) S ( b - 1 W Y ( a , b ) )
where R is the coherence coefficient and S is the smoothing operator.
Figure 3 displays the results of wavelet analysis for a case. The lighter shade designates the COI and the thick black contour represents areas that pass the 5% significant level red noise test. The color scale indicates the wavelet power density or the wavelet coherence coefficient, where red and blue represent the peak and the valley, respectively. The arrows characterize the phase relationship between the two time series. Pointing right represents the in-phase and pointing left represents the anti-phase. Pointing straight down indicates the first time series leading the second by 90° and the reverse is the second leading the first by 90°.
In the study, the average wavelet coherence (AWC) was used to analyze the strength of the correlation between two time series. It was calculated by averaging the wavelet coherence coefficient outside the cone of influence (COI). It is generally considered that there is almost no correlation between two time series, if the AWC is less than 0.2. The AWC in the ranges of 0.2–0.4, 0.4–0.6, and over 0.6 indicates weak correlation, medium correlation, and strong correlation, respectively. The percentage area of the significant coherence (PASC), obtained by dividing the area of the region passing the 5% significant level red noise test by the total area of the domain outside the COI, was adopted to assess the significant degree of the correlation between two time series [43]. A greater AWC with a larger PASC indicates the stronger correlation between two time series [44].
As shown in Figure 4a,b, there are no stable oscillation periods for the cross wavelet coherence spectrum and the corresponding power spectrum. Moreover, few high-coherence (coherence coefficient is greater than 0.8) domains and high-power (power density is greater than 8) ones were scattered in the coherence spectrum and the power spectrum, respectively. In this situation, the average phase angle cannot be quantified and as a result, the response time of one time series to the other is not available. Figure 4c,d shows the cross wavelet coherence and power spectrums with stable oscillation periods. If high-coherence and high-power regions exist after superimposing the two spectrums, the average phase angle between two time series can be quantified using the circular mean of the phase over regions with high-coherence and high-power density, as described in Equation (7) [45]. The lag response time between two time series can be finally determined by multiplying the average phase angle and half of the dominant period.
λ m = a r g ∑ j = 1 n c o s ( λ j ) , ∑ j = 1 n s i n ( λ j )
where λm is the average phase angle and λj is a set of angles (j = 1, …, n).

4. Results and Discussion

4.1. Spatio-Temporal Variation of Buried Depth of Shallow Groundwater

It is distinctly seen from Figure 5 that the mean buried depth of the groundwater showed an upward trend in general from south to north for each month during the period of 2006–2018. The buried depth of the groundwater in the southern part ranged from 1.0 to 10.0 m. From July to September, the groundwater level in the south ascended and the area with groundwater buried depth of 5–10 m decreased from 938 to 767 km2. However, from October to June of the following year, the groundwater level descended and the area with the buried depth of 5–10 m increased from 836 to 1010 km2. The buried depth of the groundwater in the northern part ranged from 10.0 to 35.1 m. In contrast to the groundwater in the south, the groundwater in the north of the study area had a clear dynamic funnel area (marked with a black ellipse) and the area varied greatly with seasons. The area of the funnel zone reached the minimum of about 70 km2 in February and peaked in July at about 288 km2. The excess exploitation of the groundwater for irrigation was the main cause of the funnel formation. The distinct spatio-temporal variation in groundwater depth in the study area implied that the dominant control factors of the groundwater level might be different between the north and the south.

4.2. Variation of Well Irrigation Water Amount

Figure 6 shows the 5-day well irrigation water amount estimated in Puyang during the period of 2006–2018. It can be seen from Figure 6a that the well irrigation amount in the northern part showed a stable oscillation period of 1 year. Its variation curve had two peaks within a year, which corresponded to the filling stage of winter wheat in May and the tasseling stage of summer maize in August, respectively. The well irrigation water amount with a 1-year oscillation period showed an upward trend in the south from 2006 to 2018 except for 2010. Due to a dramatic increase by a factor of 46% in summer maize planting area, the well irrigation water amount reached the maximum at about 407 thousand m3 in 2010. Since winter wheat was rarely planted in the south before 2015, the variation curve of the well irrigation amount had possessed a peak (occurred in August) within each year of 2006–2014, as shown in Figure 6b. With the continuous increase in winter wheat planting area, the well irrigation amount peaked in both May and August in the south during the period of 2015–2018. The water amount of well irrigation in the south was less than the north during the study period, owing to the diversion of water from the Yellow River serving as a dominant irrigation water source in the south. The difference in well irrigation water amount between the north and the south contributed to the spatial variability of the groundwater buried depth in the study area.

4.3. Cross Wavelet Coherence Analysis of Groundwater Level and Different Factors

Continuous wavelet analysis was carried out on the groundwater level in each observation well in Puyang, and the results showed that the groundwater level in the study area had an oscillation period of about 12 months. It is clearly found from Figure 7 that there was a continuous and significant oscillation period regardless of groundwater level or other factors studied (i.e., precipitation, air temperature, water stage of the Yellow River, and well irrigation water amount) in Puyang during the period of 2006–2018. The dominant oscillation periods were 361, 373, 360, 368, and 387 days for the groundwater level, the precipitation, the air temperature, the water stage of the Yellow River, and the well irrigation water amount, respectively. It implied that the groundwater level and the other four factors showed clear yearly periodic variations in the study area.
Since the groundwater level and the other four factors had similar oscillation periods, cross wavelet analysis could be carried out between the groundwater level and any of the four factors to obtain the corresponding coherence spectrum. The AWC and PASC were quantified according to each coherence spectrum obtained. To comprehend the correlation between the groundwater level and the four factors under different groundwater buried depths, the four groups of buried depth (i.e., 0–5 m, 5–10 m, 10–20 m, and deeper than 20 m) were adopted for statistical analysis on the AWC and PASC, with the consideration of the distribution of observation wells and groundwater buried depths in the study area.
It is found from Table 4 that the mean AWC and mean PASC describing the correlation between the groundwater level and the four factors changed with groundwater buried depth. When the burial depth was less than 5 m, the mean AWC between the groundwater level and the precipitation was 0.50 and the corresponding mean PASC was 32.71%. If the buried depth increased to 5–10 m, the mean AWC decreased to 0.42 and the mean PASC decreased to 25.40%. The simultaneous decline in the AWC and PASC indicated that the correlation between the groundwater level and the precipitation became weak. With the further increase in burial depth, the mean AWC continued to decline to 0.35, and even to 0.25. Therefore, if the burial depth was less than 10 m, the groundwater level had medium correlation with the precipitation; otherwise, it weakly related to the precipitation.
Similarly, the mean AWC between the groundwater level and the air temperature also showed a gradual downward trend with the increase in burial depth. If the burial depth increased from 0–5 m to 5–10 m, the mean AWC decreased from 0.51 to 0.43. When the depth was greater than 10 m, the mean AWC was about 0.32–0.34. The mean PASC ranged from 26.41% to 29.13% and varied little with burial depth. Therefore, the groundwater level had medium correlation with the air temperature within the burial depth of 10 m. If the depth exceeded 10 m, there was weak correlation between the groundwater level and the air temperature. This implied that the correlation between groundwater level and air temperature diminished with the increase in burial depth, which is consistent with the work of Malik et al. [46].
With the increase in burial depth, the mean AWC between the groundwater level and the Yellow River water stage experienced an initial decrease followed by an increase, while the mean PASC changed a little.When the burial depth was less than 10 m, the mean AWC was greater than 0.40, which implied that the groundwater level had medium correlation with the river stage. However, if the burial depth was beyond 10 m, the mean AWC was less than 0.40 and thus, the groudwater level was weakly related to the river stage. In addition, both the AWC and the PASC between the groundwater level and the well irrigation water amount changed a little with burial depth. The mean AWC was approximate to 0.50 and the PASC was about 30.00%, which indicated that the groundwater level had medium correlation with the well irrigation water amount, regardless of shallow or deep groundwater.
Considering that rivers are distriubted linearly, the influence of distance on the correlation between groundwater level and river stage was analyzed in the investigation. It can be seen from Figure 8 that the correlation between the groundwater level and the Yellow River stage gradually became weak as the distance between the observation well and the Yellow River increased. When the distance was less than 20 km, the groundwater level had medium correlation with the Yellow River water level; otherwise, it was weakly related to the river stage. Therefore, it is clear that the distance had more significant effect on the correlation between groundwater level and river stage than the burial depth. As far as the study area was concerned, the oberservation wells distributed in the northern part were mostly more than 20 km away from the Yellow River and the groundwater buried depth was greater than 10 m in the north. However, the situation in the south was the opposite. Therefore, the groundwater level in the north was significantly affected by the exploitation of well irrigation and less affected by the precipitation, the air temperature, and the Yellow River stage. By comparison, the groundwater level in the south was greatly affected by the four factors mentioned above.

4.4. Response Time of Groundwater Level to Influencing Factors

To estimate the delayed response time of the groundwater level to the four factors in the study area, the cross wavelet power spectrum between groundwater level and any of the four factors for each observation well was depicted and overlapped with the corresponding cross wavelet coherence spectrum. It was found that there were few high-power and high-coherence domains, after the overlapping analysis of the cross wavelet power and coherence spectrum between the groundwater level in the north and the Yellow River water stage. Therefore, the delayed response time of the groundwater level in the north to the river stage could not be computed.
The delayed response times of the groundwater level to the precipitation, to the air temperature, and to the well irrigation water amount varied with burial depth (Figure 9). It is seen from Figure 9a that the lag time of the groundwater level to the precipitation showed an upward trend at first and then a stable trend, as the burial depth increased. When the burial depth was less than 10 m, the median of the lag time ranged from 80 to 110 days; otherwise, it was about 190 days. Figure 9b presents that with the increase in burial depth, the lag time of the groundwater level to the air temperature increased at first and then remained at a relatively high value. When the burial depth is less than 10 m, the median of the lag time was 128–135 days. If the depth exceeded 10 m, it was about 175 days. As illustrated in Figure 9c, the lag time of the groundwater level to the well irrigation water amount showed a downward trend first and then a stable trend, as the burial depth increased. The median of the lag time decreased from 130 to 118 days, if the depth increased from 0–5 m to 5–10 m. When the depth exceeded 10 m, it continuously descended to about 83 days.
It can be found through comparison that when the burial depth of groundwater was shallow (0–5 m), the response of the groundwater level to the precipitation was more than 50 days faster than to the air temperature or to the groundwater withdrawals on average. If the depth changed to 5–10 m, the response of the groundwater level to rainfall was as fast as to the groundwater exploitation, but about 25 days faster than to the air temperature on average. When the depth was greater than 10 m, the response of the groundwater level to groundwater exploitation was about 3 months faster than to rainfall or to air temperature. These could be explained by the hydrological process. An increase in burial depth of groundwater can result in the extension of time taken for rainwater to enter groundwater and the decline in phreatic evaporation capacity. Therefore, the deep groundwater has slow response to meteorological factors. In addition, when groundwater was exploited, it is hard for deep groundwater to be quickly replenished by rainwater and surface water infiltrating and, as a result, the groundwater level responds to exploitation quickly.
The lag response time of the groundwater level in the south to the Yellow River stage was 10–120 days and showed an overall upward trend with the increase in distance away from the Yellow River during the study period (Figure 10). If the distance was less than 20 km, the lag response time of the groundwater level to the Yellow River stage was concentrated in the range of 10–75 days. However, for the observation wells beyond 20 km away from the Yellow River, there was almost no lag response time of the groundwater level to the river stage. It was implied that the influence scope of the lateral seepage of the Yellow River water was up to 20 km, which matches well with the finding obtained using conventional hydrological and isotopic methods [47].
It was found through comparing the lag response times that the groundwater level in the south had faster response times to the Yellow River stage and the precipitation, which is similar to the results received using the sliding window analysis [48]. Since the Puyang reach of the Yellow River was known as “second-level suspended river”, the water level of the Yellow River was higher than the groundwater level throughout the year and, as a result, the Yellow River water continuously recharged the groundwater [49,50]. Furthermore, the burial depth of groundwater was shallow and the irrigation mainly depended on the Yellow river water rather than the groundwater in the south. Therefore, the groundwater level in the south was more significantly affected by the water level of the Yellow River and rainfall. Although the groundwater level had medium correlation with the air temperature in the south, the groundwater level responded to the air temperature slowly. It indicates that air temperature is one of the important factors that can influence phreatic evaporation. In brief, the groundwater in the north was the exploitation type, while in the south, it was the hydro-meteorological type.

5. Conclusions

In the investigation, a simplified method was presented to construct the daily well irrigation water amount time series for arid and semi-arid areas where groundwater withdrawal data were unavailable, with the consideration of crop water requirement during the growth period and the proportion of well irrigation amount. The dynamic response relationships of the groundwater level and the four driving factors including precipitation, air temperature, water stage of the Yellow River, and well irrigation water amount were quantified by employing the CWT method and the XWT method and their variations with groundwater buried depth were finally discussed.
It is indicated from the CWT results that the groundwater level and the four driving factors showed significant yearly periodic variations during the study period. The XWT results show that the correlation between the groundwater level and the precipitation (or the air temperature) and the corresponding lag response time varied with the burial depth of groundwater. If the burial depth exceeded 10 m, the moderate correlation changed to the weak one and the lag response time extended by 1–3 months. Although the groundwater level maintained the medium correlation with the well irrigation water amount as the burial depth increased, the delayed response time was significantly shortened. The correlation between the groundwater and the water stage of the Yellow River and the lag response time were mainly affected by the distance away from the Yellow River. This impact could reach 20 km away from the Yellow River. The findings of the investigation help in comprehending the driving mechanism of groundwater change and in providing the reference for groundwater prediction and control in variable environment. In future study, an investigation of the response relationship between the groundwater level and the phreatic evaporation should be conducted.

Author Contributions

Conceptualization, Y.C.; methodology, J.X. (Jia Xu); validation, J.X. (Jingwen Xing) and D.Y.; investigation, J.X. (Jia Xu) and R.H.; writing—original draft preparation, R.H.; writing—review and editing, Y.C. and R.H.; supervision, Y.C.; project administration, Y.C. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Natural Science Foundation of Shanghai (funder: Shanghai Science and Technology Committee; grant number: 20ZR1459700) and the Planning Project concerning the Joint Governance of Four Water Problems in Puyang (funder: Puyang Water Conservancy Bureau; project number: WZ0190020200086).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data are contained within the article.

Acknowledgments

Special thanks go to the Puyang Hydrology and Water Resources Survey Bureau, Yellow River Institute of Hydraulic Research and the Puyang Meteorological Service for providing the observation data.

Conflicts of Interest

The authors declare no conflict of interest.

References

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Water 14 03937 g001 550
Figure 1. Administrative divisions and water system in Puyang area.
Figure 1. Administrative divisions and water system in Puyang area.
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Figure 2. Distribution of observation wells of shallow groundwater in Puyang area.
Figure 2. Distribution of observation wells of shallow groundwater in Puyang area.
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Figure 3. The results of wavelet analysis for a case: (a) Continuous wavelet power spectrum; (b) Cross wavelet coherence spectrum; (c) Cross wavelet power spectrum.
Figure 3. The results of wavelet analysis for a case: (a) Continuous wavelet power spectrum; (b) Cross wavelet coherence spectrum; (c) Cross wavelet power spectrum.
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Figure 4. Cross wavelet coherence spectrum and its corresponding power spectrum between two time series for different cases: (a) Cross wavelet coherence spectrum without a stable oscillation period; (b) Cross wavelet power spectrum without a stable oscillation period; (c) Cross wavelet coherence spectrum with a stable oscillation period; and (d) Cross wavelet power spectrum with a stable oscillation period.
Figure 4. Cross wavelet coherence spectrum and its corresponding power spectrum between two time series for different cases: (a) Cross wavelet coherence spectrum without a stable oscillation period; (b) Cross wavelet power spectrum without a stable oscillation period; (c) Cross wavelet coherence spectrum with a stable oscillation period; and (d) Cross wavelet power spectrum with a stable oscillation period.
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Figure 5. Distribution of the mean buried depth of the groundwater in Puyang area for each month during the period of 2006–2018.
Figure 5. Distribution of the mean buried depth of the groundwater in Puyang area for each month during the period of 2006–2018.
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Figure 6. Variation of well irrigation water amount in Puyang during the period of 2006–2018: (a) The northern region; (b) The southern region.
Figure 6. Variation of well irrigation water amount in Puyang during the period of 2006–2018: (a) The northern region; (b) The southern region.
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Figure 7. The continuous wavelet power spectrums of different time series during the period of 2006–2018: (a) Groundwater level; (b) Precipitation; (c) Air temperature; (d) Water stage of the Yellow River; (e) Well irrigation water amount.
Figure 7. The continuous wavelet power spectrums of different time series during the period of 2006–2018: (a) Groundwater level; (b) Precipitation; (c) Air temperature; (d) Water stage of the Yellow River; (e) Well irrigation water amount.
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Figure 8. Box plots of the AWC between groundwater level and water stage of the Yellow River in Puyang under different distances away from the Yellow River.
Figure 8. Box plots of the AWC between groundwater level and water stage of the Yellow River in Puyang under different distances away from the Yellow River.
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Figure 9. Box plots of delayed response time of groundwater level to the four factors under different burial depths: (a) Groundwater level to precipitation; (b) Groundwater level to air temperature; (c) Groundwater level to well irrigation water amount.
Figure 9. Box plots of delayed response time of groundwater level to the four factors under different burial depths: (a) Groundwater level to precipitation; (b) Groundwater level to air temperature; (c) Groundwater level to well irrigation water amount.
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Figure 10. Distribution of the lag response time of groundwater level to water stage of the Yellow River in southern Puyang during the period of 2006–2018.
Figure 10. Distribution of the lag response time of groundwater level to water stage of the Yellow River in southern Puyang during the period of 2006–2018.
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Table
Table 1. Inter-annual variation of precipitation, the Yellow River stage, and crop planting area in Puyang from 2006 to 2018.
Table 1. Inter-annual variation of precipitation, the Yellow River stage, and crop planting area in Puyang from 2006 to 2018.
YearPrecipitation/mmWater Level (AMSL) at Gaocun Station/mCrop Planting Area/km2
Winter WheatSummer Maize
NorthSouthAverageNorthSouthNorthSouth
2006434.9443.859.571409.4910.9357.8515.6
2007491.0576.459.411174.6935.7386.7525.6
2008590.7504.659.131193.6943.1410.6527.6
2009542.1582.958.801204.9950.1424.0548.8
2010721.7703.058.921208.6954.6431.1861.6
2011583.9592.958.931213.3958.1448.4570.4
2012438.3348.559.041219.2961.4482.0586.9
2013447.6443.458.721232.0958.4475.9588.1
2014531.3504.158.471241.0961.3505.9588.0
2015543.2556.858.381243.7953.9564.6597.5
2016560.2541.456.591210.7930.4621.4625.4
2017480.0515.956.481298.5983.6778.3701.8
2018594.5625.257.131323.71000.2750.2696.3
Table
Table 2. Crop coefficients and reference crop evapotranspiration of winter wheat and summer maize at different growth stages.
Table 2. Crop coefficients and reference crop evapotranspiration of winter wheat and summer maize at different growth stages.
StageKcET0/mm
Winter WheatSummer MaizeWinter WheatSummer Maize
Seeding stage0.700.6252.2445.87
Stooling stage0.69-44.08-
Emergence stage-0.68-78.64
Overwintering stage0.51-81.14-
Regreening stage0.72-83.28-
Jointing stage0.900.9785.8986.32
Tasseling stage-1.08-100.58
Heading stage1.08-79.68-
Filling stage0.620.68104.2355.65
Maturation stage----
Table
Table 3. Error statistics of the five methods for interpolating shallow groundwater depth in Puyang.
Table 3. Error statistics of the five methods for interpolating shallow groundwater depth in Puyang.
Interpolation MethodMAE/mMRE/%RMSE/%
Trend Surface1.453.133.01
Regular Spline1.653.212.87
Ordinary Kriging0.180.230.63
Inverse Distance Weight0.711.341.58
Simple Kriging0.260.381.29
Table
Table 4. Arithmetical means of average wavelet coherence (AWC) and percentage area of significant coherence (PASC) between the groundwater level and the four factors for different groundwater buried depths.
Table 4. Arithmetical means of average wavelet coherence (AWC) and percentage area of significant coherence (PASC) between the groundwater level and the four factors for different groundwater buried depths.
Depth/mPrecipitationAir TemperatureThe Yellow River Water StageWell Irrigation
AWCPASC/%AWCPASC/%AWCPASC/%AWCPASC/%
0–50.50 32.71 0.51 26.79 0.45 29.92 0.48 30.79
5–100.42 25.40 0.43 26.41 0.42 28.36 0.48 30.74
10–200.35 22.74 0.34 29.13 0.30 28.73 0.47 29.98
>200.25 23.06 0.32 26.81 0.34 28.29 0.51 30.52
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Cai, Y.; Huang, R.; Xu, J.; Xing, J.; Yi, D. Dynamic Response Characteristics of Shallow Groundwater Level to Hydro-Meteorological Factors and Well Irrigation Water Withdrawals under Different Conditions of Groundwater Buried Depth. Water 2022, 14, 3937. https://doi.org/10.3390/w14233937

AMA Style

Cai Y, Huang R, Xu J, Xing J, Yi D. Dynamic Response Characteristics of Shallow Groundwater Level to Hydro-Meteorological Factors and Well Irrigation Water Withdrawals under Different Conditions of Groundwater Buried Depth. Water. 2022; 14(23):3937. https://doi.org/10.3390/w14233937

Chicago/Turabian Style

Cai, Yi, Ruoyao Huang, Jia Xu, Jingwen Xing, and Dongze Yi. 2022. "Dynamic Response Characteristics of Shallow Groundwater Level to Hydro-Meteorological Factors and Well Irrigation Water Withdrawals under Different Conditions of Groundwater Buried Depth" Water 14, no. 23: 3937. https://doi.org/10.3390/w14233937

APA Style

Cai, Y., Huang, R., Xu, J., Xing, J., & Yi, D. (2022). Dynamic Response Characteristics of Shallow Groundwater Level to Hydro-Meteorological Factors and Well Irrigation Water Withdrawals under Different Conditions of Groundwater Buried Depth. Water, 14(23), 3937. https://doi.org/10.3390/w14233937

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