Characteristics in the Spatiotemporal Variation and Periodic Evolution of Groundwater in the Xining Area of China, Eastern Qinghai–Tibet Plateau

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Introduction
The Qinghai-Tibet Plateau, which is the source area for three rivers, namely, Yellow River, Yangtze River, and Lancang River, is known as the great water tower of Asia (Zhang et al. 2013;Huang et al. 2020).The abundant water resources of the Qinghai-Tibet Plateau not only play an important role in the sustainable economic development of the plateau region but also have a strategic significance in ensuring the water resource security of China and Southeast Asia (Zhang et al. 2017).The groundwater resources in the territory are very rich and widely distributed, with good water quality and stable water volume (Cheng and Jin 2013;Xiang et al. 2016).With the implementation of the great development strategy of Qinghai Province in China, Xining, which is the capital city of Qinghai Province, has rapidly risen to be the main grain-producing area and industrial base.The city has concentrated 50% of the population and 35% of the economy in the province (Pan et al. 2021).Groundwater has become an important resource that cannot be ignored in promoting the sustainable development of Xining area with the continuous increase in city scale and population (Qinghai et al. 2018).Since the 1960s, the climate of the Qinghai-Tibet Plateau has undergone significant changes, including increased precipitation, decreased evaporation, rising annual average temperature, melting of glaciers, and serious degradation of permafrost (Xie et al. 2010;Bibi et al. 2018).This situation led to major changes in the spatial and temporal distribution patterns of groundwater.The groundwater dynamics are affected not only by natural factors, such as rainfall and runoff, but also by human activities, such as exploitation and urban expansion (Mendieta-Mendoza et al. 2021).The influence of human factors on groundwater in the Xining area is becoming increasingly serious with the rapid development of social economy, thereby complicating the dynamic change of groundwater (Gao et al. 2019).In addition, the demand for groundwater resources in the Xining region has been increasing in recent decades with the development of the western region, and the exploitation of groundwater resources has been intensified, resulting in the continuous decline of the groundwater level in most areas, the deterioration of water quality, and the increasingly tense contradiction between supply and demand of groundwater resources (Mekonnen and Hoekstra 2016;Sun et al. 2019).This phenomenon seriously effects the social and economic development, agricultural production, and the local people's lives.
According to previous studies, the inter-annual groundwater level has continued to drop since the chronic overexploitation in the 1960s, with a maximum cumulative depth of 15 m (Tan et al. 2012;Xining City 2018).
The reasonable utilization of groundwater resources is directly related to the sustainable development of the Qinghai-Tibet Plateau (Ge et al. 2008).The groundwater problems in the northeastern margin of the Plateau have become increasingly prominent with the increasing water demand and the intensifying water shortage in the middle and lower reaches of the Qinghai-Tibet Plateau (Bibi et al. 2019).Accordingly, the research on the status and variation characteristics of groundwater resources has become a major topic in the field of hydrogeology all over the world (Xu et al. 2018;Liu et al. 2019;Dai et al. 2019).However, the analysis of the characteristics of groundwater resources in the Qinghai-Tibet Plateau has been carried out relatively late due to the limitation of the topographic conditions of the Tibet Plateau, the concealment of groundwater, and the difficulty in obtaining data (Kang et al. 2020;Sun et al. 2020;Gao et al. 2021).Consequently, the study on groundwater resources has been in a difficult exploration in the Qinghai-Tibet Plateau.
Groundwater dynamics not only has annual and inter-annual variation changes but also has extremely complex randomness and periodicity and other nonlinear response characteristics because of the variety of internal and external factors (Lin et al. 2019;Li et al. 2020).Groundwater depth is a key variable in groundwater environment, and multiple time scale is an important feature that must exist in the evolution of groundwater.Time series scale analysis can focus on exploring the distribution characteristics of groundwater in frequency oscillations, variation amplitudes and periodic evolution on different time scales (Lin et al. 2019).This mechanism better reveals the random rule of groundwater sequence and the variation characteristics at different time scales and predicts future evolution of short-term trend, thereby providing scientific reference for the sustainable development and utilization of groundwater resources.At present, few reports have been carried out on the dynamic characteristics and driving factors of groundwater in the Xining area.Most scholars focus on the study of the change characteristics of the single index of groundwater level or water quality in local places (Zhang et al. 2007;Tan et al. 2012).
Meanwhile, the previous research data are mostly old, scattered, and discontinuous.
Moreover, the dynamic evolution of groundwater at different time scales in this area has not been reported.In this work, Xining region was taken as the research area, and the spatiotemporal variation characteristics and periodic scale of groundwater level from 1980 to 2018 were determined using traditional statistical method, geographic information system, and Morlet wavelet analysis.This study aimed to (1) analyze the inter-annual dynamic types and tendency of the groundwater level in the past 40 years, (2) explore the spatial variation range, distribution characteristics, and variation structure in different periods of abundant and dry seasons, (3) study the periodic evolution of groundwater at different time scales, and (4) predict its evolution trend in the short-term future.The results can provide scientific theoretical basis for the rational exploitation of groundwater resources and help government decision-making service in ensuring the safety of groundwater in the eastern Qinghai-Tibet Plateau.

Study Area and Data Source
Xining, the capital of Qinghai Province of China, is the largest city in Qinghai Province and also the largest city on the entire Qinghai-Tibet Plateau (Figure 1a) (Gao et al. 2019).The geographical coordinates are between the east longitude of 100°58'48"-102°01'26" and north latitude of 36°24'40"-37°03'33", with the research area of approximately 700 km 2 .The study area is a typical plateau valley city located in the middle reaches of Huangshui River Basin in the eastern Qinghai-Tibet Plateau (Mao et al. 2019).The terrain is high in the northwest and low in the southeast, with an elevation between 2200 m and 3000 m.The area can be divided into four areas: Beichuan, Xinachuan, Xichuan, and Nanchuan (Figure 1b).The study area has the typical semi-arid plateau continental climate characteristics (mainly cold and dry).The annual average temperature is 5.9 °C, and the annual average evaporation capacity reached 1708.4 mm.The annual average precipitation is 393.6 mm.In particular, the annual distribution of precipitation is uneven with approximately 60% of the precipitation concentrated in July, August, and September (Fan and Fang 2020).
Abundant shallow groundwater is the main water source in Xining area.The aquifer is used for domestic water for urban residents and industrial water for factories and mining

Geographic Information System Method
Groundwater level has the characteristics of randomized regional variable with dual properties of randomness and spatial correlation (Lin et al. 2019).Traditional statistical methods can only evaluate the overall variation of the variables in the region but cannot evaluate the spatial distribution of the variables.Geostatistics method can effectively characterize the spatial distribution of its variables by using variogram as the main tool (Júnez-Ferreira et al. 2019;Ohmer et al. 2019).Kriging interpolation is an interpolation method based on spatial variogram theory and structural analysis (Aryafar et al. 2020).The core principle of this method is to use the semi-variance variogram model to represent the variation of variables in space with distance and estimate the value of each point by fitting to a specific point or all points within a given search radius (Nikroo et al. 2010).The Kriging formula is as follows: where Z′(x0) is the estimated value of groundwater depth (m) at position x0 of the monitoring well, Z(xi) is the measured groundwater depth (m) at the position xi of monitoring well, λi is the unknown weight assigned to Z(xi).n is the number of monitored wells, δ is the error variance of the estimated value (Charizopoulos et al. 2018).
Semi-variance variogram is a formal expression of the spatial structure of regional variables, which can describe the spatial dependence and overall differentiation of groundwater depth in the study area as a whole and can be used to reflect the global spatial variability (Liu et al. 2016).The original variation function is calculated as follows: where γ(h) is a semi-variance function; h is the space interval distance of the monitoring well (m); n is the number of monitoring wells with an interval of h; Z(xi+h) and Z(xi) are the measured depths (m) of the regionalized variable Z(x) at the spatial position xi+h and xi, respectively; C0 is the nugget value; a is the variable range; b is the expression coefficient of different variation functions; and C0+C is the base station value.
Variation function includes three important parameters: nugget value C0, range a, and base station value C0+C (Burgess and Webster 2019).When the distance h is zero, the variation function value is the nugget value C0.The variation function increases with the increase in the distance h until it reaches a stable constant, which is called the base station value C0+C.The larger the base value, the greater the spatial variation of the variable.The distance h at this time is range a, which represents the spatially dependent distance of the regionalized variable and mainly reflects the size of the influence range of the variable (Bachmaier and Backes 2011).The nugget coefficient is the ratio of nugget value C0 to base value C0+C, which is also known as the nugget effect.If the coefficient is less than 0.25, then it shows a strong spatial correlation.If the coefficient is between 0.25 and 0.75, then it has a moderate spatial correlation.If the coefficient is greater than 0.75, then the spatial correlation of this region is weak (Swain and Patra 2019;Zhang and Wang 2020).
Anisotropy is the ratio of short-axis to long-axis range, indicating the magnitude of anisotropy of spatial variation.The more the heterogeneity approaches one, the more the regional variables tend to be isotropic.

Wavelet Analysis
Wavelet analysis has developed into a major research tool for signal analysis and time scale analysis and has been widely used in image processing (He et al. 2019), signal diagnosis (Cheng et al. 2021), and hydrometeorological sequence recognition (Zhang et al. 2019) in recent years.Wavelet analysis is derived from Fourier transform, which can simultaneously reflect the time and frequency domain characteristics of nonstationary time series and analyze its internal fine structure to extract the hidden regularity (Ling et al. 2021).The monitoring data of groundwater level depth are continuous and nonstationary time series.Therefore, the complex Morlet continuous wavelet transform is selected as the wavelet function in this study, and the discrete complex wavelet coefficient function is as follows: further determine the main period in time series (Partal 2017).The larger the variance, the more prominent the periodicity on this scale.The maximum value indicates the strongest periodic oscillation here, and the corresponding scale a is the first main period.Its expression is as follows:

Dynamic Characteristics of Annual Groundwater Level
According to the data of multiple monitoring wells, the groundwater dynamics in study region are mainly restricted by three factors of river water infiltration, groundwater drainage and artificial exploitation.According to the combination relationship of these factors, the groundwater characteristics can be divided into three types: hydrological, hydrological exploitation, and runoff drainage types.
(1) Hydrological type The hydrological type of groundwater dynamic is characterized by an obvious wave peak in the curve of groundwater level change.This type is mainly distributed in the upstream or near the middle reaches of all rivers in the study area, such as the downtown of Xining, and the upper reaches of Huangshui River in Beichuan and Xichuan areas.The groundwater in this area is mainly affected by the river linear vertical infiltration and has the same trend as the river flow.In Figure 2, the dynamic curve of groundwater level has an obvious wave peak, which is basically consistent with the rainy season.The groundwater level from July to September rises with the river flow increase.The groundwater level greatly varies within a year (1-4.5 m).(3) Runoff discharge type Runoff discharge type is mainly distributed in river valley margins and groundwater discharge zones, such as the downstream area of Nanchuan and east of Xining downtown.
These zones are far from the exploitation area, and the uplift of the site leads to the release of groundwater.The dynamic change of groundwater level is relatively stable due to the regulation effect of groundwater runoff and discharge, without obvious rise and fall.The annual variation is less than 1 m, which is also called a stable type.Figure 4 clearly shows that the annual dynamic change curve is flat, with no obvious peaks and valleys.The time of the highest water level is uncertain, mostly from May to September, and the lowest water level of the year mostly occurs at the beginning or end of the year.

Statistical Analysis of Sample Data
In the study area, September is the abundant season in which the groundwater is shallowly buried throughout the year.March is the dry season when the groundwater is deeply buried.First, the sample data are statistically analyzed.Table 1 illustrates  The variation coefficient (Cv) can reflect the degree of spatial variation of groundwater level, which can be divided into strong variability (Cv>1), medium variability (0.1<Cv< 1), and weak variability (Cv<0.1)according to the grade (Burgess and Webster 2019).The variation coefficient of the groundwater in the study area is between 0.1 and 1 (Table 1), which belongs to the medium degree of variation.Therefore, the groundwater depth in different periods has moderate spatial variation intensity.The standard deviation of groundwater depth varies from 7.24 to 10.11 over the years, which indicates that the spatial variation range is large in the dry and abundant seasons, and the difference between the maximum and minimum depth is significant.Therefore, the spatial difference of groundwater depth is great.After logarithmic transformation, the skewness coefficient of the sample data is close to zero, and the kurtosis coefficient is close to two, indicating that the sample data basically conform to lognormal distribution in space.The groundwater depth difference between the dry and the abundant seasons shows a decreasing trend over the years, which is mainly due to the increasing trend of precipitation in recent years and the maintenance of exploitation amount within a stable range, which makes the difference between the compensation and drainage become smaller and smaller.The depth in September was greater than that in March in certain areas because the buried depth difference between the dry and the abundant seasons becomes smaller.Gaussian, spherical, linear and exponential models are common variogram models (Liu et al. 2016).In this study, the Gaussian, spherical, linear, and exponential models of the spatial variation of groundwater depth were established by using Kriging interpolation method in ArcGIS.The best model was selected through the comparison of fitting  4) by GS+ software.Table 2 clearly illustrates that the spherical model has the highest fitting accuracy and the minimum average error of 0.037.
The mean predicted standard deviation is closest to the root mean square, with a difference of 0.07.The mean standard deviation is 0.0019, the closest to zero.The prediction error of mean square error was 0.984, the closest to one.This finding indicates that the fitting results of each index of the spherical model performed good, followed by the fitting accuracy of the Gaussian and exponential models and the linear model.Meanwhile, the cross-validation results in Figure 7 and the variation trend of semi-variance with a step size in Figure 8 show that the spherical model has a higher simulation accuracy and is suitable for the analysis of spatial variability of groundwater depth in the Xining region.Although the increase in rainfall and surface runoff increased the recharge of groundwater resources, the intensity of human exploitation activities also reached the maximum with the arrival of the abundant season, and the amount of groundwater exploitation significantly increased.The imbalance of mining and replenishment and the difference of buried depth between the abundant and the dry seasons significantly increased; accordingly, the spatial correlation of groundwater decreased compared with that during the dry season.The depth in September is greater than that in March in some areas where exploitation of groundwater sources is concentrated.The long-axis range and short-axis range reflect the influencing range and spatial correlation degree in their respective searching directions.The spatial autocorrelation distance of groundwater depth in the Xining area is large over the years, with a long-axis range of 65.1-71.6km and a short-axis range of 37.9-47.Urbanization changes the river hydrological process and the underlying surface environment and destroys the benign recharge and discharge relationship between groundwater and surface water.The continuous decline of the groundwater level in the groundwater source area leads to the regional descent funnel, which changes the local groundwater flow direction, reduces the spatial autocorrelation distance and weakens the overall connectivity of groundwater.The uneven development of each region in the process of urbanization makes the spatial distribution of human activities greatly different, which leads to the enhancement of the spatial anisotropy of groundwater depth.The growth rate of groundwater exploitation has been controlled with the introduction of a series of groundwater development and protection policies by the local government.Moreover, the exploitation amount has been maintained within a stable range, reaching 9.18 million m 3 /a by 2020.The groundwater depth tends to be stable from 2010 to 2020, and the level even rises in some areas, which enhances the groundwater connectivity and makes the groundwater depth transition from strong spatial anisotropy to spatial isotropy.
To fully study the spatial evolution of groundwater depth in the Xining region, this work selects 1985,1997,2001,2010 and 2020 as the typical years and the groundwater depth data after logarithmic transformation and trend to eliminate on the basis of the spherical model of kriging interpolation method by using ARCGIS that mapped the groundwater depth space distribution in different periods.Figure 9 shows the groundwater depth in the Xining region presents a pattern of deep in the south and shallow in the north and deep in the east and shallow in the west, with an island distribution pattern in local areas.The areas with greater groundwater depth are mainly concentrated in the vicinity of groundwater source areas.With the excessive exploitation of groundwater, the natural runoff field of groundwater is destroyed due to the unbalanced exploitation, thus forming the regional fall funnel.In Figure 9 Finally, the contour lines of the real part of the wavelet coefficient, the modulus square with time-frequency parameter variation, and the wavelet variance map of the groundwater depth are drawn by Surfer.Table 4 illustrates the primary cycle of groundwater depth in the wells.The groundwater depth in most wells in the study region exhibits the same time scale of variation characteristics, mainly for 12a, 21a, and 6a main cycles.Furthermore, the groundwater level has significant cycle characteristics and regional consistency under the influence of human activities and climate change.According to the wavelet real part contour map in Figure 12 1986-1993, 1999-2005, and 2011-2017 with the oscillation centers of 1990, 2002, and 2014, respectively.Figure 12 shows that the dashed line of negative value did not completely close after 2017, indicating that the groundwater depth is in the decreasing period from 2017 to 2020.Thus, the rise of groundwater level would occur in the next few years.In the 17-25a time scale, two regional positive/negative value alternating changes were observed.
The two decrease periods of groundwater depth were from 1980 to 1985 and from 1996 to  The energy spectrum of the wavelet can be expressed by the square value of the modulus of the wavelet system, and the oscillating ability of different time scales can be analyzed by the distribution of the modulus square of the wavelet system.Figure 13 shows that the energy distributed in the 9-14a time scale is the strongest, and the strong energy performs well in the whole domain.The shock energy of the 17-25a time scale is the second, and it has remained strong since 1991.However, the energy of 5-7a and other smaller time scales is very weak (close to zero); thus, the periodic effect of those small scales can be ignored.The wavelet variance graph is obtained and drawn according to Equation ( 7).The periodic scale corresponding to each variance peak represents the main period of the time scale.Figure 14 demonstrates two distinct peaks in the time series, of which 12a corresponds to the largest peak, indicating that the signal of groundwater depth oscillates most strongly on the 9-14a time scale.The 21a corresponds to the second peak, followed by signal oscillations on the 17-25a time scale.The 6a corresponds to the third peak, with the weakest signal oscillation, and its periodic effect is negligible.Therefore, two main cycles control the cycle evolution of groundwater in Xining from 1980 to 2020.Given that the oscillation intensity of the first peak is much higher than that of the second and other peaks, the first and second primary periods include 12a and 21a, respectively.According to the evolution law of the main cycle, the development tendency of groundwater level in the short-term future can be predicted.Figure 15 demonstrates that the groundwater depth experienced three periodic changes during 1980 and 2020 under the condition of the first main period of 12a.According to the red dotted line of 12a, the groundwater level in the Xining region will show a rising trend from 2021 to 2023 and will decline from 2024 to 2030.In the case of the second main period of 21a, the groundwater depth experienced two periodic changes from 1980 to 2020.According to the red dotted line of 21a, the groundwater level in the Xining region will show an increasing trend from 2021 to 2026 and a decrease from 2027 to 2030.Given that the first main cycle is the dominant trend, the probability of groundwater level rising is relatively large in the next few years.
Fig. 1 Map of the study area: (a) location map of Qinghai Province in China; (b) location map of the study area in Xining; and (c) distribution of the monitoring wells of groundwater in the Xining 6) where f(t) represents the original sequence, ψ(t) represents the basic wavelet function; a is the scale factor representing the period length of the sequence, b is the time factor indicating the shift in time domain, and t is the time interval.The contours of the real part of the Morlet wavelet coefficients can reflect the energy intensity information at different phases and time scales.The variation process of the wavelet coefficients with time represents the evolution law of alternating high and low values of the time series at this scale (Rahman et al. 2020).The positive and negative changes in contour of the real part of the coefficient represent the evolution process and abrupt characteristics of the given data in the near future: the positive value corresponds to the rise period of the sequence, the negative value corresponds to the reduction phase, and the zero value corresponds to the transition period.The magnitude of the modulus square of the wavelet coefficient reflects the oscillation strength of the signal at different time scales and the energy distribution at the specific time scale (Tsai and Hsiao 2020).The integral of this value with scale factor a is called the wavelet variance function。Variance diagram can Fig. 2 Hydrological type curve Fig. 3 Hydrological exploitation type curve(2) Hydrological exploitation type This type of groundwater dynamics is mainly distributed where groundwater is intensively exploited, such as the groundwater source areas from the upper reaches of Beichuan, Xichuan.The groundwater in these zones is not only affected by river seepage recharge but also controlled by artificial exploitation.When the mining amount increases or decreases, the level shows an obvious trend of decrease or increase of approximately 1.03-6.51m.Figure3demonstrates that the annual dynamic curve of groundwater shows a "concave" shape.The groundwater cannot be replenished in time during the dry season

Fig. 4 Fig. 5
Fig. 4 Runoff discharge type curve that the average, maximum and minimum values of groundwater depth all showed a trend of first increasing and then decreasing in the past 40 years.The average depth increased from 11.99 m in 1985 to 13.6 m in 2001 and then decreased to 11.67 m in 2020.The minimum depth increased from 0.72 m in 1985 to 1.31 m in 2001 and then decreased to 0.19 m in 2020.The minimum depth varies from 0.19 m to 1.97 m with a small fluctuation.The maximum depth increased from 36.05 m in 1985 to 45.62 m in 2001 and then decreased to 44.69 m in 2020.The maximum depth varies from 36.05 m to 45.75 m, which greatly fluctuates.
parameters and cross-validation results to carry out spatial interpolation and variability analysis of groundwater depth.The monitoring data of groundwater depth in the dry and abundant seasons of1985, 1997, 2001, 2010, and  2020 are taken as examples.The models were used to fit the groundwater depth in the study area.First, the depth data is converted to the normal distribution by logarithmic transformation to avoid the phenomenon of enlarging the estimation error and concealing the inherent structure due to the skewness distribution of the sample data, which leads to the larger nugget and base station values in the variation function.The parameter values of the semi-variance function of groundwater depth are calculated using Equation (

Fig. 8
Fig. 7 Cross-validation results of the spherical model 7 km.This result indicates that the groundwater depth in the study area has a good spatial continuity.During the dry and abundant seasons from 1985 to 2020, the long-axis range showed a decreasing trend.This result indicates that the spatial autocorrelation of groundwater depth in the study area was weakened, the influence range of spatial correlation was reduced, the continuity was worse, and the interference of human activities on groundwater depth increased.The spatial anisotropy ratio is 1.474-1.837(much larger than one), indicating that the spatial distribution of groundwater depth has strong anisotropy and large spatial difference.The value increased from 1.474 in March 1985 to 1.801 in March 2001 and then decreased to 1.441 in March 2020.The results show that the anisotropy of groundwater spatial distribution tends to be stable with the decrease in human activities in groundwater exploitation.The included angle of the long-axis is approximately 30°, which is basically consistent with the trend of Huangshui River.This finding indicates that the groundwater depth has a strong correlation with the trend of Huangshui River in the parallel direction.In general, the spatial correlation of groundwater depth in the Xining region from 1985 to 2020 was first weakened and then enhanced.Meanwhile, the spatial anisotropy ratio was first increased and then decreased.During 1985-2001, the correlation of groundwater depth rapidly decreased, the degree of anisotropy increased, and the groundwater connectivity became worse.The main reason is that the groundwater resources in Xining were greatly exploited with the rapid development of social economy from 1980s, and the exploitation amount increased from 0.73 million m 3 /a in 1965 to 8.15 million m 3 /a in 2001.

Fig. 9
Fig. 9 Spatial evolution of the groundwater depth in the Xining region: a. September 1985; b.September 1997; c. September 2001; d.September 2010; e. September 2020; f.March 2020 Figure 9(e) is compared with Figure 9(f).The groundwater depth in the study area has a slight decreasing trend in the abundant season.The main reasons are the increase in , the groundwater depth in the Xining region has different quasi-periodic oscillations at various time scales.During the evolution of the groundwater depth in the past 40 years, three-time scales of 5-7a, 9-14a, and 17-25a are evident.The periodicity fluctuation of groundwater depth in 5-7a and smaller time scales is severe with the local periodic variation.The positive/negative value alternating law was relatively clear before 2010.Thereafter, the regularity disappeared and the signal performance became more chaotic and unstable.However, the time scales of 9-14a and 17-25a were uniformly distributed in the temporal domain and had significant global characteristics.Three complete alternation of high and low values were observed on the 9-14a time scale.The negative value period of each period indicated that the groundwater depth decreased from1980 to 1986, from 1993 to 1999, and from 2005 to    2011.In those decreasing phases, the three oscillation centers were distributed in1983,    1996, and 2008.By contrast, the three increasing periods of groundwater depth are 2007, and the oscillating centers of gravity were 1980 and 2002, respectively.The two negative value periods meant that the groundwater depth increased from 1985 to 1997 and from 2007 to 2017 with the vibration centers of 1992 and 2012, respectively.Figure12also demonstrates that the periodic evolution of 17-25a and 9-14a is consistent after 2017, indicating that the groundwater depth decreased from 2017 to 2020.Furthermore, the negative isolines are still not completely closed until 2020, which fully demonstrates that the groundwater level in the study area will continue to rise in the short-term future, regardless of the time scale.In the evolution of groundwater depth, no specific change period has been recorded; however, the change period changes with the different time scales, which shows that the large time scale and the small scale are nested and contained each other.The decrease or increase of groundwater depth in the 9-14a time scale is mainly reflected in the rise or decline of the groundwater level in the 17-25a time scale.Therefore, the evolution of the groundwater depth in Xining has the characteristics of local change and multi-level time scale structure in the time domain.

Fig. 12
Fig. 12 Time-frequency distribution of real part of the wavelet coefficient in the groundwater depth Fig. 13 Contour map of the wavelet coefficient modulus square of groundwater depth Fig. 15 Periodic evolution of wavelet coefficients at different time scales of groundwater depth

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