Mineral water is the main source of drinking water and is a dominant component of local economic development in Fusong County, Changbai Mountain, Jilin Province of China. Precipitation is the main recharge factor for mineral water in Fusong County; therefore, it is necessary to determine whether precipitation can effectively guarantee the supply of mineral water resources. In this study, precipitation data from the Donggang hydrological station in Fusong County were collected and analyzed to determine annual changes in characteristics and extreme probability. The results show that precipitation is stable and that the probability of extreme precipitation is small. Precipitation and mineral spring discharge in the Mingshui, Baixi, No. 2 Jinjiang, and Laoling springs were then collected and analyzed for separate periods by using a continuous wavelet method. The results show that the main oscillation period of both precipitation and spring discharge is approximately 11 months. Finally, the cross-wavelet method is conducted to analyze the period relationships between spring discharge and precipitation. The results show that both precipitation and spring discharge share the same phase, which indicates spring discharge has an immediate reaction to precipitation changes.

INTRODUCTION

With shortages and intensified pollution levels of global water supplies, potable water safety has attracted increasing attention to become one of the most critical global concerns. Moreover, the market demand for natural mineral drinking water is also increasing daily (Ning et al. 2010). The Changbai Mountains offer a rare area of natural mineral water enrichment. The diverse mineral species in the water in Fusong County include abundant lithium, strontium, vanadium, and 20 microelements that are beneficial to human nutrition (Tao et al. 1992; Ji et al. 2001; Yin et al. 2008). A recent increase in the production of mineral water by the local government has put pressure on mineral water recharge; therefore, studies to evaluate the changing regulation of recharge factors and the relationship between them are urgently needed.

Although numerous studies have been conducted on Changbai Mountain mineral water, few focus on the mineral water problems in Fusong County. Cao (2010) proposed that the mineral water should be marketed under numerous brands; however, this plan was determined to be unfeasible. In addition, the monetary profits were negligible, and proper oversight for exploitation and protection could not be guaranteed. Liu (2007) and Zhang (2013) proposed that the main groundwater recharge source in the mountainous area is infiltration of atmospheric precipitation, by using deuterium and oxygen isotopic methods. Li (2012) and Wei (2014) proposed that the characteristic components of mineral water, and Sr, originate from dissolution of basalt and that CO2 density, temperature, pressure, and water characteristics are controlling factors in the mineral water formation in Changbai Mountain, Jingyu County. Tao (2013) analyzed the factors and occurrence conditions of the natural mineral water supply in Fusong County and evaluated its hydrochemical characteristics, quality, and water quantity. According to the aforementioned academic studies, we can conclude that the atmospheric precipitation infiltrated the groundwater within the hilly area and reacted with the rock mineral composition in the flow path to form the peculiar groundwater composition. In addition, we conclude that precipitation directly affects the abundance of groundwater resources.

Thus far, research has not been conducted on the correlation between precipitation and spring discharge in Fusong County. Therefore, in this paper, we analyze the dynamic relationship between precipitation and spring discharge in this region by using precipitation data from 1960 to 2013 and the dynamic discharge monitoring data of several springs. We applied Matlab (Yu et al. 2007) programming software to analyze precipitation and spring discharge characteristics and their correlation. As a result, we present an important theoretical basis for sustainable exploitation, utilization, and protection of area mineral resources.

MATERIALS AND METHODS

Study area

Fusong County, which covers an area of 6,530 km2, is located in the southeast region of Jilin Province, northeast China, in the center of the Changbai Mountains (Figure 1). This area has a northern temperate continental monsoon climate, with an annual average temperature of 3.3 °C and annual precipitation of 808.9 mm, much of which occurs during the period from June to July. Mineral water is mainly produced by 16 springs located within a 370.18 km2 protected area of Fusong County.
Figure 1

Geographical location of Fusong County, Jilin Province of China.

Figure 1

Geographical location of Fusong County, Jilin Province of China.

Hydrogeological setting

The formation and storage of groundwater in the study area are mainly controlled by regional geology and topography. According to its storage and burial conditions and hydraulic properties, groundwater can be classified as basalt porous fissure water, clastic rock porous fissure water, carbonate fissure soluble water, and bedrock fissure water (Yan et al. 2015), as shown in Figure 2.
Figure 2

Hydrogeological map of Fusong County.

Figure 2

Hydrogeological map of Fusong County.

Figure 2 shows that basalt formed in the Jun Jianshan group is widely distributed in the mineral water source and surrounding areas. Primary and secondary pores with good connectivity are developed in the rock, creating beneficial conditions for groundwater circulation. Moreover, the terrain is relatively low, which is conducive to groundwater recharge and storage and results in rich groundwater (Wei & Sun 2006). However, the various degrees of pore and fissure development in the area's basalt leads to uneven water storage. Therefore, after precipitation is infiltrated, the water is discharged into the valley in the form of springs. Thus, the hydrogeological conditions in the study area provide a good environment for precipitation recharge of groundwater through infiltration (Hu et al. 1997; Zhao 2011).

Data source

We downloaded the quantity of monthly and yearly precipitation from 1960 to 2013 from the Donggang hydrological station in Fusong County, and we analyzed changes in the regulation of precipitation in the area. Moreover, we collected the precipitation and monthly discharge data recorded from July 1981 to November 2008 for four typical springs in the mineral water protected area in Fusong County, including Mingshui, Baixi, No. 2 Jinjiang, and Laoling springs.

ANALYTICAL METHODS

Pearson III distribution

Pearson III distribution is a method widely used to analyze the distribution of extreme precipitation probability. The Pearson III (Zheng et al. 2014) curve is asymmetric with a single peak and a one-sided infinite end, known as a gamma distribution in mathematics. Its probability density function can be expressed as 
formula
1
where is a gamma function of , and are three parameters. The probability density function can be determined when the three parameters are identified. The relationship among the three parameters and the mean value of the three statistical parameters , variation coefficient , and coefficient of skew is 
formula
2
The frequency curve is needed for frequency analysis. The specific frequency of can be obtained from the following formula: 
formula
3
where P is the designated probability.

Continuous wavelet transform theory

Wavelet transform, an effective tool in time-series analysis, was used to obtain the time-frequency characteristics of precipitation and spring discharge. A window function was applied to the wavelet analysis, which is based on Fourier transform. This method has developed rapidly since the mid-1980s and has been applied in signal processing, computer vision, image processing, speech analysis and synthesis, and numerous other fields (Xue et al. 2002; Chowdhury & Nimbarte 2015; Jean et al. 2015; Yao et al. 2015).

Continuous wavelet transform, also known as integral wavelet transform (Mallat 1989; Michele et al. 2003; Delegerima et al. 2014; Liu et al. 2014; Xu 2014), is defined as 
formula
4
where, are coefficients of wavelet transform, is the mother wavelet, and a and b are scaling and time shift factors, respectively.

Cross-wavelet transform theory

Cross-wavelet transform was developed from continuous wavelet transform and is applied to multi-scale analysis involving two time series. We used the cross-wavelet transform method to analyze the correlation of precipitation and spring discharge and to clarify the response mechanism of spring discharge to precipitation. This method assumes that the distribution results of continuous wavelet transform with two time series and are and (Grinsted et al. 2004; Guo et al. 2014). The cross-wavelet spectrum can be defined as 
formula
5
where * is a complex conjugate, and is the cross-wavelet spectrum.

RESULTS AND DISCUSSION

Characteristics of precipitation

We used the China meteorological data-sharing system to download the 1960–2013 precipitation data recorded by Donggang hydrological station. Figure 3 shows that from 1960 to 2013, the annual precipitation change was between 574.2 mm and 1,190.8 mm, which reflects a period change. The precipitation reached the maximum of 1,190.8 mm in 1986 and minimum of 574.2 mm in 1978; the annual average precipitation was 827.88 mm. Annual precipitation less than 600 mm accounted for 1.85% in dry years; that between 600 mm and 800 mm and between 800 mm and 1,000 mm accounted for 38.9% and 48.1%, respectively, in normal years, and that more than 1,000 mm accounted for 11.1% in humid years. The statistical results show that the proportion of dry years and humid years is significantly lower, which indicates that the quantity of precipitation in each year was relatively steady.
Figure 3

Original precipitation data and regression prediction data from 1960 to 2013.

Figure 3

Original precipitation data and regression prediction data from 1960 to 2013.

By calculating the annual precipitation variation coefficient Cv and the ratio of the quantity of greatest and least precipitation, we determined the ratio of maximum and minimum precipitation in 1960–2013 to be 2.07 and the annual precipitation variation coefficient to be 1.017 × 10−17. The small value indicates stable precipitation in Fusong County. In addition, we used the support vector machine method regression technique to determine precipitation in the near future (Ouyang et al. 2014) because this method is reliable for analyzing the regression and prediction of precipitation. First, according to the original precipitation data from 1960 to 2013, we conducted regression fitting and obtained satisfactory results (Figure 3). We next determined the precipitation of the next 2 years to be 846.2 mm and 820.7 mm (Figure 3). Therefore, the precipitation in Fusong County will not undergo obvious changes. Thus, the precipitation will guarantee the sustainable recharge of mineral water for the next 2 years.

Analysis of extreme precipitation probability

For extreme weather events such as torrential rain occurring once every hundred years, the recurrence period is very long, and the probability of occurrence is small. However, this type of disaster is often destructive. Determining the extreme value of the occurrence of this type of disaster can provide a basis for major engineering designs. Many projects with high economic value must consider human life and safety and therefore must be resistant to extreme weather disasters (Bao 2011; Luo & Jin 2014). Because precipitation is the main recharge source of mineral water, it affects the quantity of mineral water. Therefore, it is necessary to analyze the probability of the occurrence of extreme precipitation in order to avoid damage caused by improper exploitation of the natural mineral water.

According to statistics on maximum annual precipitation from 1960 to 2013 in Fusong County, we applied Pearson III distribution to estimate the precipitation probability of the maximum value.

By using the least squares method to define parameter values, we calculated the maximum annual average precipitation according to the precipitation sample data. The results are shown in Figure 4.
Figure 4

Extreme precipitation probabilities in study area obtained by using Pearson III distribution.

Figure 4

Extreme precipitation probabilities in study area obtained by using Pearson III distribution.

According to the results calculated by Pearson III distribution (Table 1), the maximum annual precipitation in a decade was 1,040 mm; that in 50 years was about 1,240 mm; that in 100 was around 1,280 mm; and that in 400 years was 1,400 mm. Overall, the extreme precipitation probability is small; therefore, precipitation will not produce a dramatic change in the supply of mineral water.

Table 1

Maximum annual precipitation design values obtained by using Pearson III distribution (unit: mm)

Probability (P%) 0.17 0.25 0.84 2.55 6.83 15.92 31.81 
Maximum annual precipitation 1,600 1,400 1,300 1,200 1,100 1,000 900 
Probability (P%) 0.17 0.25 0.84 2.55 6.83 15.92 31.81 
Maximum annual precipitation 1,600 1,400 1,300 1,200 1,100 1,000 900 

Period of precipitation and spring discharge

In the basalt regions, the dynamic change in spring discharge depends mainly on the quantity of precipitation. By using the observed data of precipitation and spring discharge in 196 months from July 1981 to November 2008, we analyzed the continuous wavelet precipitation and spring discharge period for Mingshui, Baixi, No. 2 Jinjiang, and Laoling springs and compared the precipitation and spring discharge concussion periods. The spatial distribution characteristics of the four springs are illustrated in Table 2; the continuous wavelet analysis results are shown in Figure 5.
Table 2

Geodetic coordinates of the observed springs within the study area

Geodetic coordinates
SpringsSpring no.XY
Baixi 127 °40′10″ 42 °03′01″ 
No. 2 Jinjiang 127 °37′56″ 41 °54′03″ 
Laoling 127 °44′44″ 41 °53′37″ 
Mingshui 127 °20′50″ 42 °26′15″ 
Geodetic coordinates
SpringsSpring no.XY
Baixi 127 °40′10″ 42 °03′01″ 
No. 2 Jinjiang 127 °37′56″ 41 °54′03″ 
Laoling 127 °44′44″ 41 °53′37″ 
Mingshui 127 °20′50″ 42 °26′15″ 
Figure 5

Continuous wavelet analysis of precipitation (upper part) and spring discharge (lower part) in (a) Baixi spring, (b) No. 2 Jinjiang spring, (c) Laoling spring, and (d) Mingshui spring in the 196-month period.

Figure 5

Continuous wavelet analysis of precipitation (upper part) and spring discharge (lower part) in (a) Baixi spring, (b) No. 2 Jinjiang spring, (c) Laoling spring, and (d) Mingshui spring in the 196-month period.

Figures 5(a)5(d) represent the continuous wavelet analysis results of precipitation (upper part) and spring discharge (lower part) in Baixi spring, No. 2 Jinjiang spring, Laoling spring, and Mingshui spring, respectively. The red and blue colors in the images respectively represent the peaks and troughs of the power density, which reflects local and dynamic characteristics of time-frequency. Dark colors indicate changes in relative energy density. The area enclosed by the thick black line exceeds the 95% red noise test confidence level. The cone parts below the thin black line are wavelet cones of influence, which reflect areas influenced to a greater degree by the continuous wavelet transform edges of the data. Figure 5 shows that the main oscillation period of both precipitation and spring discharge is 11 months, which indicates a certain correlation between the two parameters.

Dynamic correlation between precipitation and spring discharge

By using spring discharge data in Baixi, No. 2 Jinjiang, Laoling, and Mingshui springs from July 1981 to November 2008, including the 196 months, cross-wavelet analysis was used to determine the response relationship between precipitation and spring discharge data during the same period. The results are shown in Figure 6.
Figure 6

Cross-wavelet spring discharges of (a) Baixi spring, (b) Jinjiang No. 2 spring, (c) Laoling spring, and (d) Mingshui spring during the 196-month period.

Figure 6

Cross-wavelet spring discharges of (a) Baixi spring, (b) Jinjiang No. 2 spring, (c) Laoling spring, and (d) Mingshui spring during the 196-month period.

The levels index at the right of the images in Figure 6 indicates the density of the cross-wavelet power spectrum. In addition, the arrow direction reflects the phase relation between precipitation and spring discharge. The arrows from left to right indicate precipitation and spring discharge in the same phase; those from right to left indicate precipitation and spring discharge in the opposite phase. Vertical upward arrows indicate spring discharge changes a quarter of a period ahead of precipitation, whereas vertical downward arrows indicate precipitation changes a quarter of a period ahead of spring discharge.

Figures 6(a)6(d) represent the precipitation and spring discharge cross-wavelet results for Baixi spring, No. 2 Jinjiang spring, Laoling spring, and Mingshui spring, respectively, for the 196-month period. The arrow direction in the figure from left to right indicates that precipitation and spring discharge are in the same phase; that is, spring discharge reacts immediately to changes in precipitation. Owing to the wide distribution of basalt in the study area, the pores and fractures are well developed, which is favorable for precipitation infiltration and groundwater recharge. Therefore, the cross-wavelet results of precipitation and spring discharge are in good agreement with the hydro-geochemical conditions in the study area.

CONCLUSIONS

Through continuous wavelet and cross-wavelet analysis of precipitation and mineral water discharge in Fusong County, the period characteristics and their correlation have been determined. The main conclusions are given in this section.

The continuous wavelet results show that the oscillation period of both precipitation and spring discharge during the 196 months of observation was approximately 11 months, which reflects a certain relationship between precipitation and spring discharge.

The correlation of precipitation and spring discharge for Baixi, No. 2 Jinjiang, Laoling, and Mingshui springs in the 196-month period was made by using cross-wavelet analysis. The results show that precipitation and spring discharge share the same phase; that is, spring discharge change is immediately affected by changes in precipitation. This result indicates a positive correlation.

By analyzing the important influencing factors for mineral water replenishment in the study area, we determined that the precipitation will not undergo abnormal changes and that the probability of extreme precipitation is small. The precipitation for the next 2 years was close to the annual precipitation; thus, abundant precipitation will guarantee an effective and stable resource for mineral water during the next 2 years. Precipitation will not cause dramatic changes in the mineral water supply; rather, it will provide continuous supply for the groundwater in the study area. Therefore, the mineral water in Fusong County is sustainable and can be exploited under the allowable exploitation limit.

ACKNOWLEDGEMENTS

This study was sponsored by the Natural Science Foundation of China (No. 41072255). The authors wish to thank the editor and anonymous reviewers for their constructive comments and suggested revisions.

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