Assessing the Inﬂuence of Precipitation on Shallow Groundwater Table Response Using a Combination of Singular Value Decomposition and Cross-Wavelet Approaches

: Identifying the spatiotemporal change of the groundwater table to precipitation at the river basin scale can be important for regional water resource management. In this study, we proposed a method that combines singular value decomposition and cross-wavelet approaches to analyze the relationship between groundwater level dynamics and precipitation. The method was applied to the Naoli River Basin, Northeast China. Moreover, the method of continuous wavelet using fast Fourier transform was also used to reveal clearly the relationship between groundwater level and heavy precipitation. The results showed that the major mode of relationship between groundwater and precipitation was divided into four patterns in the study area. In general, the lag time is 27.4 (standard deviation: ± 8.1) days in pattern 1, 107.5 (standard deviation: ± 13.2) days in pattern 2, 139.9 (standard deviation: ± 11.2) days in pattern 3, and 173.4 (standard deviation: ± 20.3) days in pattern 4, respectively. In addition, the response of groundwater level dynamics is very sensitive to heavy precipitation in all patterns. Therefore, enhancing the utilization of heavy rainfall and ﬂood resources is an effective way to increase groundwater recharge in this basin.


Introduction
Groundwater is a vital freshwater source for a variety of domestic, agricultural, and industrial uses [1,2]. In the past several decades, depletion of groundwater storage has emerged all over the world because of the excessive increase of groundwater use for rapid development in agriculture, industry, and urbanization [3], for instance, in India [4], the United States [5], Australia [6], Africa [7], and China [8,9]. The situation of groundwater shortage in many countries continues, threatening the long-term sustainability of the regional economy and ecosystem services.
Precipitation infiltration is one of the major sources for local groundwater recharge. Although there have been many studies on groundwater recharge, our knowledge about the direct

Study Area
The Naoli River Basin (45 • 43 -47 • 35 N and 131 • 31 -134 • 10 E) located in China's high-latitude northeast covers a total land area of approximately 24,200 km 2 . It is one of the most important grain production bases in China, as well as a large inland freshwater wetland region ( Figure 1). Climate of this basin can be characterized as temperate humid and semihumid continental monsoon, with a long-term annual average temperature of 3.5 • C and a long-term annual average precipitation of 518 mm, 60-72% of which falls during May and September. The terrain of this area is flat, and most of the area is located in the floodplain with a gradient of 0% to 3%. Land use and land cover (LULC) of the Naoli River Basin have changed considerably in the past decade. The basin used to have a large area of wetlands, but a majority of them (i.e., about 80%) were converted into cultivated land during the past half century [26]. Currently, major LULC types in the basin include paddy field, dry land, forest land, grass land, wetland, construction land, and water body (Figure 1b). The paddy fields occupy 22.7% (or 5500 km 2 ), dry lands 35.1% (or 8500 km 2 ), the forest lands 25.3% (or 6100 km 2 ), the grass lands 2.6% (or 600 km 2 ) [26], wetlands 9.8% (or 2400 km 2 ), and others 4.5% (or 1100 km 2 ). The basin is mainly covered by Quaternary alluvial sediments, where the largest amount of groundwater storage and extraction are located. The lithology and hydraulic conductivities of the aquifers are clay (8 m/day), silty clay (11 m/day), silty sand soil (22 m/day), and gravel soil (35 m/day), respectively ( Figure 1c), which has been investigated by the China Geological Survey [27][28][29]. In addition, the average unsaturated zone thickness in this basin varied from 0.92 to 10.7 m during 2008-2013 (Figure 1d), based on the statistical analysis of groundwater depth.
Groundwater is the most-used water source for agriculture and public supply in the Naoli River Basin. Recent studies have reported that the groundwater level in this region has been dropping at a rate of 0.3 m/year due to the development of large-scale paddy fields in the past decade's

Meteorological Data Collection
We collected data on the shallow groundwater level of 50 wells across the Naoli River Basin during 2008-2013 from the Jiamusi Bureau of Hydrology. Groundwater depths of these wells were recorded with an automatic water level recorder (Odyssey, Dataflow Co., Christchurch, New Zealand). The groundwater depths were recorded on the 1st, 6th, 11th, 16th, 21st, and 26th day of each month for six years during 2008-2013. Daily precipitation data from 45 stations in the Naoli River Basin were obtained for the period of 2008-2013 from the China Meteorological Assimilation Driving Datasets, which is developed based on the China Land Data Assimilation System (CLDAS), which can be download from the website (http://www.cmads.org/) [33]. In order to have the same time scale as the groundwater level, the daily precipitation was accumulated as 5-day precipitation data. All these data were carefully checked before use.

Singular Value Decomposition
The SVD method was used to identify the spatial modes of the relationship between groundwater level and rainfall for the whole basin, assuming that n is the number of records for a single sample (n = 432 in this study), p is the number of precipitation gauges (p = 45 in this study), q is the number of observation wells (q = 50 in this study). The precipitation data is matrix X 45×432 , groundwater data is matrix Y 50×432 , and their covariance matrix is A 45×50 : After that, the matrix A p×q is decomposed into the product of three following matrices: where U and V are orthogonal matrices, U U = I and V V = I, and Λ is a diagonal matrix composed of non-negative singular values. Elements of nonzero elements are singular values in the matrix, and its number is s, which is the rank of the matrix. λ are eigenvalues of the matrix, which are sorted by size to λ 1 ≥ λ 2 ≥ · · · ≥ λ q . The columns of U and V are orthonormal eigenvectors of AA and A A, respectively. The expansion coefficients of matrix X 45×432 and Y 50×432 can be expressed as: where A p×n and B q×n are the expansion coefficients. Contribution rate g(k) of the kth modes to square covariance was defined as followed: Heterocorrelation coefficient (r) of the kth modes was calculated as followed: where < > is the average operation.

Spatial Interpolation
In recent years, many spatial interpolation methods have been applied to study the spatial distributions of groundwater and precipitation. The inverse distance weighting method (IDW) gave the lowest mean error among the three common interpolation methods (spline, ordinary kriging, and inverse distance weighting). In addition, the method has been applied widely all over the world [34,35]. Thus, in this study, the IDW method was applied to analyze the spatial variation of each variable using a minimum of three neighbor points and a maximum of five neighbor points, a distance powered to two. Moreover, the interpolation results was validated using the cross-validation method. The spatial interpolation error is 4.2%.

Cross-Wavelet and Continuous Wavelet Using Fast Fourier Transform
The cross-wavelet was used for demonstrating the temporal association between groundwater level and rainfall. The XWT of the two time series x n and y n can be defined as W XY = W X W Y *, where * stands for their complex conjugation. Their cross-wavelet power is defined as |W XY |. The complex parameter, arg(W xy ), can be considered as the local relative phase between x n and y n Water 2018, 10, 598 5 of 16 in time frequency space. The theoretical distribution of the cross-wavelet power and its background power spectra, p X k and p Y k , for two time series can be referenced to Torrence and Compo [22], which is expressed as follows: where Z v (p) denotes the confidence level associated with the probability p of a probability distribution function which is defined by the square root of the product of two χ 2 distribution. The phase difference between the two time series over the basin with a statistical significance above 5% was calculated as follows: where a m is the circular mean of a set of phase angles (a i , i = 1, 2, . . . , n). The temporal lags (T lag ) were calculated as followed: In order to analyze the temporal change of the different components in multiple time scales, the WTC method was applied to identify the intensity of the covariance of two time series, x n and y n , in time-frequency domains. Ranging from 0 to 1, where 1 represents the highest covariance between x n and y n , the values of the wavelet squared coherency R were calculated as follows [21]: where W x n and W y n are the wavelet transforms of the time series x and y, respectively, according to time t, and W xy n is their cross-wavelet spectrum. S represents a smoothing operator and can be expressed as: where S scale and S time represent the smoothing along the wavelet scale and time, respectively. For the Morlet wavelet, a suitable smoothing operator is given by Torrence and Webster [22] as follows: where c 1 and c 2 are normalized constants and Π is the rectangle function. The factor of 0.6 is the empirically determined scale decorrelation length for the Merlet wavelet [26]. In this study, the wavelet analysis was performed by using the Matlab toolbox developed by Grinsted et al. [21], which is available at http://noc.ac.uk/using-science/crosswavelet-wavelet-coherence.
In addition, original signals of groundwater level and precipitation were decomposed and reconstructed via the continuous wavelet using fast Fourier transform (CWTFT) method, respectively. A more complete process of the methodology was described by Montejo [36]. Furthermore, a conceptual framework of research procedure was shown in Figure 2 to demonstrate the analytical design in this study.
In addition, original signals of groundwater level and precipitation were decomposed and reconstructed via the continuous wavelet using fast Fourier transform (CWTFT) method, respectively. A more complete process of the methodology was described by Montejo [36]. Furthermore, a conceptual framework of research procedure was shown in Figure 2 to demonstrate the analytical design in this study.

Spatial Mode Recognition between Groundwater and Precipitation
One major mode has been identified based on the SVD method, which explains 97.1% of the spatial relationship between the five-day groundwater level and precipitation across the Naoli River Basin during 2008-2013. Based on the heterocorrelation coefficient (r) of the major mode, the relationship between groundwater level and precipitation was divided into four spatial patterns in the entire basin ( Figure 3). The spatial distribution of r represents the correlation between the expansion coefficient of groundwater level and precipitation in space.
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Spatial Mode Recognition between Groundwater and Precipitation
One major mode has been identified based on the SVD method, which explains 97.1% of the spatial relationship between the five-day groundwater level and precipitation across the Naoli River Basin during 2008-2013. Based on the heterocorrelation coefficient (r) of the major mode, the relationship between groundwater level and precipitation was divided into four spatial patterns in the entire basin ( Figure 3). The spatial distribution of r represents the correlation between the expansion coefficient of groundwater level and precipitation in space.

Temporal Patterns Recognition between Groundwater Level and Precipitation
The typical wells were randomly selected in four pattern regions, and the meteorological stations closest to the typical wells were selected, respectively. The comparisons of the time series between groundwater levels and precipitation during 2008-2013 were shown for four patterns ( Figure 4). The groundwater level dynamic is characterized by a periodic change of annual scale in four patterns. In pattern 1 (Figure 4a), the groundwater level is sensitive to changes in precipitation, which quickly increases as precipitation increases, and decreases as precipitation decreases. In pattern 2 (Figure 4b), the sensitivity of groundwater level to precipitation is delayed. When the precipitation occurs, the groundwater level rise will be delayed until after a certain period of time. In pattern 3 (Figure 4c), groundwater level shows a significantly declining trend during 2008-2012. When precipitation occurs, the level rises after a period of time. In pattern 4 (Figure 4d), the dynamic of the groundwater level is significantly delayed by that of precipitation. The groundwater level is in the trough during the wet period and the peak during the dry period of every year.

Temporal Patterns Recognition between Groundwater Level and Precipitation
The typical wells were randomly selected in four pattern regions, and the meteorological stations closest to the typical wells were selected, respectively. The comparisons of the time series between groundwater levels and precipitation during 2008-2013 were shown for four patterns ( Figure 4). The groundwater level dynamic is characterized by a periodic change of annual scale in four patterns. In pattern 1 (Figure 4a), the groundwater level is sensitive to changes in precipitation, which quickly increases as precipitation increases, and decreases as precipitation decreases. In pattern 2 (Figure 4b), the sensitivity of groundwater level to precipitation is delayed. When the precipitation occurs, the groundwater level rise will be delayed until after a certain period of time. In pattern 3 (Figure 4c), groundwater level shows a significantly declining trend during 2008-2012. When precipitation occurs, the level rises after a period of time. In pattern 4 (Figure 4d), the dynamic of the groundwater level is significantly delayed by that of precipitation. The groundwater level is in the trough during the wet period and the peak during the dry period of every year. Based on XWT results, the time-frequency relationships and phase angles between groundwater and precipitation are shown in Figure 5. The dynamic of the groundwater level has a correlation of 5% significance level with that of precipitation for four patterns in a range of 230-480 (46 × 5-96 × 5) days throughout the entire study period, which are the areas surrounded by black lines ( Figure 5). This means that there is a response period of 230-480 days for precipitation in groundwater. In addition, there are also some local significant intervals, such as the significant correlation shown with a range of 20-40 (4 × 5-8 × 5) days for pattern 1 in 2009 (Figure 5a), with a range of up to 30 (0 × 5-6 × 5) days for pattern 2 in 2013 (Figure 5b), and so on. These features indicate that precipitation has a strong effect on groundwater level change in these time scales during the entire study period. In other words, the response of groundwater to precipitation is significant in these time scales. In addition, the phase angles had an increasing trend in all patterns during 2008-2013, which means the response time of groundwater level to precipitation for each pattern was increasing.
As with the XWT, the mean phase angle between groundwater level and precipitation was calculated during 2008-2013. Based on the mean phase angle, the temporal lag of variation of groundwater level relative to precipitation in significant regions for four wells was also calculated. That of other wells also was calculated by the same method (Table 1). In pattern 1, the phase angle between groundwater level and precipitation is the smallest, which is 27° (std: ±8°), and the temporal lag of 27.4 (std: ±8.1) days is also the smallest of the four patterns. In addition, the phase angle of pattern 4, which is 171° (std: ±20°), is the largest of the four patterns. Similarly, the temporal lag of 173.4 (std: ±20.3) days is also the largest of the four patterns. Table 1. Mean phase angles (±std) and temporal lags (±std) over the regions for the four patterns in a period of 365 days.

SVD Patterns
Phase Angles (°) Temporal Lags (day) Based on XWT results, the time-frequency relationships and phase angles between groundwater and precipitation are shown in Figure 5. The dynamic of the groundwater level has a correlation of 5% significance level with that of precipitation for four patterns in a range of 230-480 (46 × 5-96 × 5) days throughout the entire study period, which are the areas surrounded by black lines ( Figure 5). This means that there is a response period of 230-480 days for precipitation in groundwater. In addition, there are also some local significant intervals, such as the significant correlation shown with a range of 20-40 (4 × 5-8 × 5) days for pattern 1 in 2009 (Figure 5a), with a range of up to 30 (0 × 5-6 × 5) days for pattern 2 in 2013 (Figure 5b), and so on. These features indicate that precipitation has a strong effect on groundwater level change in these time scales during the entire study period. In other words, the response of groundwater to precipitation is significant in these time scales. In addition, the phase angles had an increasing trend in all patterns during 2008-2013, which means the response time of groundwater level to precipitation for each pattern was increasing.
As with the XWT, the mean phase angle between groundwater level and precipitation was calculated during 2008-2013. Based on the mean phase angle, the temporal lag of variation of groundwater level relative to precipitation in significant regions for four wells was also calculated. That of other wells also was calculated by the same method (Table 1). In pattern 1, the phase angle between groundwater level and precipitation is the smallest, which is 27 • (std: ±8 • ), and the temporal lag of 27.4 (std: ±8.1) days is also the smallest of the four patterns. In addition, the phase angle of pattern 4, which is 171 • (std: ±20 • ), is the largest of the four patterns. Similarly, the temporal lag of 173.4 (std: ±20.3) days is also the largest of the four patterns.  Except for the relevant time scales mentioned above, more local correlations between groundwater level and heavy rainfall was found based on the WTC method for the four patterns during 2008-2013 ( Figure 6). The correlation with a 5% significance level was shown with a range of 0-10 (0 × 5-2 × 5) days in 2008, 40 (Figure 6d). These features in the results may be explained by the responses of the groundwater level dynamics to heavy rainfalls.
In summary, the response characteristics of groundwater level to precipitation not only were displayed with the annual time scale throughout the entire study period, but also were exhibited with many local time scales in the Naoli River Basin. Figure 5. The cross-wavelet transform (XWT) between precipitation and groundwater in the Naoli River Basin, Northeast China, for pattern 1 (a), pattern 2 (b), pattern 3 (c), and pattern 4 (d), respectively. The significant level of 5% for red noise is displayed as a thick contour, and the relative relationship of phase is denoted as arrows (with anti-phase pointing left, in-phase pointing right).
Except for the relevant time scales mentioned above, more local correlations between groundwater level and heavy rainfall was found based on the WTC method for the four patterns during 2008-2013 ( Figure 6). The correlation with a 5% significance level was shown with a range of 0-10 (0 × 5-2 × 5) days in 2008, 40 (Figure 6d). These features in the results may be explained by the responses of the groundwater level dynamics to heavy rainfalls.
In summary, the response characteristics of groundwater level to precipitation not only were displayed with the annual time scale throughout the entire study period, but also were exhibited with many local time scales in the Naoli River Basin. 2010, 100-165 (20 × 5-35 × 5) days in 2011, and 50-70 (10 × 5-14 × 5) days in 2013 for t pattern 4 (Figure 6d). These features in the results may be explained by the responses of the groundwater level dynamics to heavy rainfalls.
In summary, the response characteristics of groundwater level to precipitation not only were displayed with the annual time scale throughout the entire study period, but also were exhibited with many local time scales in the Naoli River Basin. (c) (d) Figure 6. The wavelet coherence (WTC) between precipitation and groundwater in the Naoli River Basin, Northeast China, for pattern 1 (a); pattern 2 (b); pattern 3 (c); and pattern 4 (d), respectively. The significant level of 5% for red noise is displayed as a thick contour, and the relative relationship of phase is denoted as arrows (with anti-phase pointing left, in-phase pointing right).

The Practical Value of the Method
Previous studies have applied hydrological models to investigate the relationship between groundwater level and precipitation [9,[37][38][39][40][41]. However, these models often require large datasets, such as precipitation, groundwater level, runoff, soil type, land use, topography, DEM, lithology, and aquifer parameters, making their applications difficult to many areas without detailed field measurements and historical information. Not only will it take too much time, but also be costly to collect data. Therefore, a simple and economical way should be used for identifying the spatiotemporal response of groundwater level dynamics to precipitation. A novel method is proposed in this study by combining the SVD and cross-wavelet approaches to identify the spatiotemporal relationship between groundwater level and precipitation for the Naoli River Basin in Northeast China. This method can characterize the features of response based on the measured hydrological signals inherent in the observations. Moreover, in this approach, the temporal lags of groundwater level dynamics to precipitation at different regions can be identified [36,[42][43][44][45][46]. Therefore, the spatiotemporal patterns of characterized results can help to understand hydrological processes, validate the simulated results of a hydrological model, and promote sustainable use of groundwater resources [10,[42][43][44]. In addition, the results can also help assess aquifer vulnerability to climate change [45].

Factors Influencing the Relationship between Groundwater Level and Precipitation
Based on the method combining SVD and cross-wavelet approaches, four spatiotemporal patterns were identified between groundwater level and precipitation in the Naoli River Basin, Northeast China. In space, there are different temporal lags of groundwater level dynamics to precipitation for the four patterns. The reasons for the finding may be explained by: (1) Human activities As mentioned above, land use and land cover in the Naoli River Basin has changed greatly since the 1950s. Almost 80% of wetlands were converted into cultivated land due to rapid economic development [26], of which the sum of the paddy fields occupy 22.7% (or 0.55 × 10 4 km 2 ). The rice is the main plant in the basin and is the largest water user, especially in the growth period from May to August [46]. In the Figure 6. The wavelet coherence (WTC) between precipitation and groundwater in the Naoli River Basin, Northeast China, for pattern 1 (a); pattern 2 (b); pattern 3 (c); and pattern 4 (d), respectively. The significant level of 5% for red noise is displayed as a thick contour, and the relative relationship of phase is denoted as arrows (with anti-phase pointing left, in-phase pointing right).

The Practical Value of the Method
Previous studies have applied hydrological models to investigate the relationship between groundwater level and precipitation [9,[37][38][39][40][41]. However, these models often require large datasets, such as precipitation, groundwater level, runoff, soil type, land use, topography, DEM, lithology, and aquifer parameters, making their applications difficult to many areas without detailed field measurements and historical information. Not only will it take too much time, but also be costly to collect data. Therefore, a simple and economical way should be used for identifying the spatiotemporal response of groundwater level dynamics to precipitation. A novel method is proposed in this study by combining the SVD and cross-wavelet approaches to identify the spatiotemporal relationship between groundwater level and precipitation for the Naoli River Basin in Northeast China. This method can characterize the features of response based on the measured hydrological signals inherent in the observations. Moreover, in this approach, the temporal lags of groundwater level dynamics to precipitation at different regions can be identified [36,[42][43][44][45][46]. Therefore, the spatiotemporal patterns of characterized results can help to understand hydrological processes, validate the simulated results of a hydrological model, and promote sustainable use of groundwater resources [10,[42][43][44]. In addition, the results can also help assess aquifer vulnerability to climate change [45].

Factors Influencing the Relationship between Groundwater Level and Precipitation
Based on the method combining SVD and cross-wavelet approaches, four spatiotemporal patterns were identified between groundwater level and precipitation in the Naoli River Basin, Northeast China. In space, there are different temporal lags of groundwater level dynamics to precipitation for the four patterns. The reasons for the finding may be explained by: (1) Human activities As mentioned above, land use and land cover in the Naoli River Basin has changed greatly since the 1950s. Almost 80% of wetlands were converted into cultivated land due to rapid economic development [26], of which the sum of the paddy fields occupy 22.7% (or 0.55 × 10 4 km 2 ). The rice is the main plant in the basin and is the largest water user, especially in the growth period from May to August [46]. In the Naoli River Basin, the main purpose of groundwater pumping is to meet the need of agricultural irrigation [47]. Wu [48] has shown that the groundwater pumping has increased from 0.94 × 10 8 m 3 in 1988 to 28.4 × 10 8 m 3 in 2013 in the Naoli River Basin (Figure 7). In fact, the pumping has become one of the most important drainage ways of groundwater [49][50][51]. The natural balance of the groundwater is affected, and the dynamics of the groundwater change. If the amount of groundwater extracted is equal to that of the groundwater recharge, and the groundwater level is at a lower level than the original average water level, it will experience larger changes, but it will not continue to decline [52]. However, if the amount is too large and exceeds the groundwater recharge, the groundwater level will continue to decline, resulting in an increase of the unsaturated zone's thickness (Figure 4), which in turn has resulted in an increase of temporal lags in the response of the groundwater level to precipitation ( Figure 5). If the overexploration remains unchanged or continues to increase, the response time of the groundwater level to precipitation will increase further. The correlation between the lag time of two factors and the thickness of the unsaturated zone has been studied in previous research works [53,54]. For example, Yang et al. [54] proved by experiments that when the thickness of the unsaturated zone is greater than the limit of the diving evaporation, the infiltration rate decreases with the increase of the unsaturated zone thickness, and then the temporal lags increase. In this study, the phenomenon can also be observed in Figures 4 and 5. For pattern 1, the groundwater depth is shallow as well as less than 5 m (Figure 1d), the groundwater level variation is very highly sensitive to precipitation, and temporal lags were also reduced compared to other patterns. For the other patterns, the groundwater depths were all more than 5 m (Figure 1d), and the temporal lags were also larger than that of pattern 1. In addition, the phase angles were increasing with the increase of the unsaturated zone thickness. This phenomenon demonstrates that the temporal lags were increasing with the increase of the unsaturated zone thickness for the individual pattern ( Figure 5). This may be a signal of groundwater depletion due to groundwater pumping for agricultural irrigation [55]. large and exceeds the groundwater recharge, the groundwater level will continue to decline, resulting in an increase of the unsaturated zone's thickness (Figure 4), which in turn has resulted in an increase of temporal lags in the response of the groundwater level to precipitation ( Figure 5). If the overexploration remains unchanged or continues to increase, the response time of the groundwater level to precipitation will increase further. The correlation between the lag time of two factors and the thickness of the unsaturated zone has been studied in previous research works [53,54]. For example, Yang et al. [54] proved by experiments that when the thickness of the unsaturated zone is greater than the limit of the diving evaporation, the infiltration rate decreases with the increase of the unsaturated zone thickness, and then the temporal lags increase. In this study, the phenomenon can also be observed in Figures 4 and 5.
For pattern 1, the groundwater depth is shallow as well as less than 5 m (Figure 1d), the groundwater level variation is very highly sensitive to precipitation, and temporal lags were also reduced compared to other patterns. For the other patterns, the groundwater depths were all more than 5 m (Figure 1d), and the temporal lags were also larger than that of pattern 1. In addition, the phase angles were increasing with the increase of the unsaturated zone thickness. This phenomenon demonstrates that the temporal lags were increasing with the increase of the unsaturated zone thickness for the individual pattern ( Figure  5). This may be a signal of groundwater depletion due to groundwater pumping for agricultural irrigation [55]. (2) Lithology of the aquifer Except for the effect of human activities, the lithology of the aquifer is also one of the important factors influencing the relationship between groundwater and precipitation [56,57]. In general, different lithologies of the aquifer have different hydrogeological parameters, that is, the hydraulic conductivity, the recharge coefficient of precipitation infiltration, specific yield, and so on [58,59]. Therefore, the different patterns were shown in space regarding the temporal lags of groundwater level dynamics to precipitation. Previous studies showed that the distribution area of mountainous areas or residual hillocks in the basin belongs to the aquifers of the bedrock fissure, which is also the discharge area of aquifers [31], and the plain area of the basin is the recharge area of the groundwater. In this study, four patterns were identified in the Naoli River Basin. It is worth noting that both the temporal lag and groundwater level (2) Lithology of the aquifer Except for the effect of human activities, the lithology of the aquifer is also one of the important factors influencing the relationship between groundwater and precipitation [56,57]. In general, different lithologies of the aquifer have different hydrogeological parameters, that is, the hydraulic conductivity, the recharge coefficient of precipitation infiltration, specific yield, and so on [58,59]. Therefore, the different patterns were shown in space regarding the temporal lags of groundwater level dynamics to precipitation. Previous studies showed that the distribution area of mountainous areas or residual hillocks in the basin belongs to the aquifers of the bedrock fissure, which is also the discharge area of aquifers [31], and the plain area of the basin is the recharge area of the groundwater. In this study, four patterns were identified in the Naoli River Basin. It is worth noting that both the temporal lag and groundwater level variation are all smallest for pattern 1 of all the patterns (Figure 4a). That demonstrates that the groundwater is easily recharged by precipitation and is quickly discharged into rivers through underground runoff in aquifers of the bedrock fissure. Therefore, the response of groundwater to precipitation is more rapid, but there is no obvious change in water level. However, the temporal lag and groundwater level variation are all largest for pattern 4 of all the patterns (Figure 4d), which indicates that when the groundwater is recharged by precipitation, the hydraulic gradient is not obviously increased because it is far away from the discharge area, and the increased intensity of groundwater runoff is not significant, and then the water level rises.
(3) Intensity of precipitation Precipitation is one of the most important sources for groundwater. Its intensity will have a strong impact on groundwater dynamics [11,60]. However, it is different in the spatiotemporal relationship between groundwater level and precipitation, because of the influence of the factors mentioned above. In addition, it is worth noting that the groundwater level dynamics are very sensitive to extreme rainfall in the Naoli River Basin (Figures 4 and 6).
In order to clearly reveal the relationship between the groundwater level and heavy rainfall, signals of groundwater level and precipitation were reconstructed based on the CWTFT method, respectively ( Figure 8). These reconstructed signals mean the intensity of groundwater level or precipitation change per unit of time. In pattern 1, the amplitude of groundwater level is highly consistent with that of precipitation (Figure 8a). In other patterns, the amplitudes of groundwater levels are relatively gentle (Figure 8b,c), which have weakly responded to levels of precipitation. However, some strong amplitudes are identified during April and May in every year in pattern 4, which may be explained by the fact that groundwater is pumped for the irrigation of paddy fields, resulting in a sharp drop in groundwater levels [28]. This result has been demonstrated by some previous studies [27,46,[61][62][63]. In addition, in order to cope with droughts and floods, the recharge of heavy rainfall on groundwater and the interannual allocation of water resources in underground reservoirs should be carefully studied. Precipitation is one of the most important sources for groundwater. Its intensity will have a strong impact on groundwater dynamics [11,60]. However, it is different in the spatiotemporal relationship between groundwater level and precipitation, because of the influence of the factors mentioned above. In addition, it is worth noting that the groundwater level dynamics are very sensitive to extreme rainfall in the Naoli River Basin (Figures 4 and 6).
In order to clearly reveal the relationship between the groundwater level and heavy rainfall, signals of groundwater level and precipitation were reconstructed based on the CWTFT method, respectively ( Figure 8). These reconstructed signals mean the intensity of groundwater level or precipitation change per unit of time. In pattern 1, the amplitude of groundwater level is highly consistent with that of precipitation ( Figure 8a). In other patterns, the amplitudes of groundwater levels are relatively gentle (Figure 8b,c), which have weakly responded to levels of precipitation. However, some strong amplitudes are identified during April and May in every year in pattern 4, which may be explained by the fact that groundwater is pumped for the irrigation of paddy fields, resulting in a sharp drop in groundwater levels [28]. This result has been demonstrated by some previous studies [27,46,[61][62][63]. In addition, in order to cope with droughts and floods, the recharge of heavy rainfall on groundwater and the interannual allocation of water resources in underground reservoirs should be carefully studied.

Uncertainties of This Study
Some uncertainty may exist in identifying the spatiotemporal patterns by combining the SVD and cross-wavelet approaches, because the accuracy of identification may be greatly influenced by the spatial

Uncertainties of This Study
Some uncertainty may exist in identifying the spatiotemporal patterns by combining the SVD and cross-wavelet approaches, because the accuracy of identification may be greatly influenced by the spatial distribution of observation wells and scarcity of measured precipitation data. In addition, accurate spatial and temporal characterization of groundwater recharge can be difficult, due to its dependence on a multitude of physical factors such as land use and hydrogeological heterogeneity, groundwater pumping, and so on [64,65]. Despite the uncertainties and limitations, this method still sheds some light on an understanding of the spatiotemporal response of groundwater level dynamics to precipitation in some regions lacking basic data. Moreover, future studies are needed to constrain the uncertainties and refine the response of groundwater level dynamics to different intensities of precipitation.

Conclusions
This study identified the spatiotemporal responses of the groundwater table to precipitation in the Naoli River Basin, Northeast China, using a method combining SVD and cross-wavelet approaches. Based on the findings, the following conclusions can be drawn: (1) The new method can be a cost-effective approach for identifying the spatiotemporal responses of the groundwater table to precipitation, especially in areas where hydrological models are difficult to construct due to a lack of basic data. (2) The major mode of the relation between groundwater and precipitation was divided into four patterns in the Naoli River Basin. In general, the lag time is 27.4 (std: ±8.1) days, 107.5 (std: ±13.2) days, 139.9 (std: ±11.2) days, and 173.4 (std: ±20.3) days for the patterns 1-4, respectively. (3) The rapid agricultural development relying on groundwater irrigation has led to an increase of the unsaturated zone thickness, which in turn results in an increase of temporal lags in the groundwater table response to precipitation. (4) The response of the groundwater table in the studied river basin is very sensitive to heavy rainfall.
Thus, enhancing the utilization of the heavy rainfall and flood resources by groundwater may be an effective way to recharge the groundwater. Furthermore, it is possible to make use of the interannual allocation of water resources for the groundwater reservoir to deal with extreme hydrological events of flood and drought.
Author Contributions: P.Q. and Y.J.X. conceived the idea of the study and wrote the manuscript; P.Q. carried out data collection and analysis; G.Z. supervised the research project and contributed to oversight of the data collection; L.W., C.D., and C.C. contributed valuable analysis and manuscript review; all authors approved the final manuscript.