Identification of Strong Karst Groundwater Runoff Belt by Cross Wavelet Transform

Water Resour Manage (2014) 28:2903–2916 DOI 10.1007/s11269-014-0645-8

Jinjie Miao & Guoliang Liu & Bibo Cao & Yonghong Hao & Jianmimg Chen & Tian−Chyi J. Yeh

Received: 12 January 2013 /Accepted: 23 April 2014 / Published online: 5 June 2014 # Springer Science+Business Media Dordrecht 2014

Abstract Karst aquifers are highly heterogeneous and exhibit hierarchical permeability structures or flow paths. Conduits and fractures typically account for less than 1 percent of the porosity of the aquifer, but more than 95 percent of the permeability. For the purposes of karst groundwater resources management, as well as of protection strategies against potential contamination, identifying the strong karst groundwater runoff belt of an entire aquifer system is generally more important than information about a specific spring. In this project, we introduce cross wavelet transform to analyze the relation between precipitation and spring discharge, and then identify the strong karst groundwater runoff belt. In highly concentrated karst areas, the precipitation signal can penetrate an aquifer relatively easily and will readily affect spring discharge. The precipitation and spring discharge are thus closely related, and the cross wavelet transform coefficients are large. Conversely, in areas of low karst concentration,

J. Miao School of Water Resources and Environment, China University of Geosciences (Beijing), Beijing 100083, People’s Republic of China

G. Liu College of Environment and Resources, Shanxi University, Taiyuan 030006 Shanxi Province, People’s Republic of China

B. Cao College of Environmental Science and Engineering, Nankai University, Tianjin 300071, People’s Republic of China

Y. Ha o ( *) Tianjin Key Laboratory of Water Resources and Environment, Tianjin Normal University, Tianjin 300387, People’s Republic of China e-mail: [email protected]

Yonghong Hao e-mail: [email protected]

J. Chen College of Urban and Environmental Science, Tianjin Normal University, Tianjin 300387, People’s Republic of China

T. J. Yeh Department of Hydrology and Water Resources, The University of Arizona, Tucson, AZ 85721, USA 2904 J. Miao et al. the cross wavelet transform coefficients are small. We applied the method to Niangziguan Springs Basin in China to detect the strong karst groundwater runoff belt. Results showed that Pingding County and Yangquan City have a high degree of karstification (i.e. the strong karst groundwater runoff belt), Xiyang County and Shouyang County have a moderate degree of karstification, and Yuxian County, Heshun County, and Zuoquan County have a low degree of karstification. The results agree with the geological structure of Niangziguan Springs Basin.

Keywords Heterogeneity. Strong karst groundwater runoff belt . Cross wavelet transform . Spring discharge . Precipitation . Niangziguan Springs

1 Introduction

In karst terrane, karstification is dominated by geological structure, hydrogeologic condition, and carbonate dissolution (Quinn et al. 2006). The level of karstification can vary greatly throughout a karst aquifer (Hao et al. 2012a). In a well-developed karst area, dendritic or branching networks of conduits and fractures join together as tributaries, increase in size and order, and form a strong karst groundwater runoff belt (Palmer 1991; Yin et al. 2011). Conduits and fractures typically account for less than 1 percent of the porosity of the aquifer, but more than 95 percent of the permeability. The hydraulic conductivity of the conduits and fractures ranges from two to eight orders of magnitude greater than the porosity of the matrix (Worthington et al. 2000; Taylor and Greene 2008). The strong karst groundwater runoff belt affects the hydraulic flow field by capturing groundwater from the surrounding aquifer matrix, the adjoining fractures, and the smaller nearby conduits (Palmer 1991, 1999;WhiteandWhite 1989; Fiorillo and Guadagno 2010). The strong karst groundwater runoff belt is the major focus for groundwater development and management, and groundwater contamination remediation (Hartmann et al. 2012;Eaton2006a; 2006b;Froukh 2002; Mylopoulos et al. 1999). It is important to identify potential recharge zones and groundwater flow system for implementa- tion of appropriate water management (Lin et al. 2013). Amir et al. (2013) simulated the submarine groundwater flow in the coastal aquifer at the Palmahim area, and yielded a basic understanding of the flow system on the consideration of upper and the lower aquifers. Another technical way to assessing the groundwater characteristics is a coupled remote sending and GIS approach (Albuquerque et al. 2013; Singh et al. 2013). The purpose of the project described in this paper is to identify the strong karst groundwater runoff belt by using cross wavelet transforms. Wavelet techniques have been widely applied to various water resources research because of its excellent time-frequency representation (Sang 2012). Cross wavelet transform is a bivariate extension to wavelet transform by combined wavelet transform and cross-spectral analysis for examining relations in time frequency between two time series (Hudgins et al. 1993; Hudgins and Huang 1996;Grinstedetal.2004). Correlation and trend analysis can determine the significance of relation between nonstationary time-series (Xu and Singh 2004). However, these methods may not detect correlations between sinusoidal signals of the same wavelength in two records, if these signals are phase shifted. If the phase shift approaches Φ=π/2 then both time-series appear uncorrelated. Cross-correlation and cross- spectral analysis can detect such phase shifts, but only as average values, and are not able to represent nonstationarities in the signals. On the other hand, cross-wavelet analysis permits detection, extraction, and reconstruction of relations between two nonstationary signals simultaneously in frequency (or scale) and time (or location) (Prokoph and Bilali. 2008; Grinsted et al. 2004). In recent years, Adamowski (2008) used cross wavelet transform in Identification of Strong Karst Groundwater Runoff Belt by Cross Wavelet Transform 2905 geophysics to determine the phase difference values between the river flow and meteoro- logical variables and to develop cross wavelet constituent components on river flow forecasting. Cross wavelet transform is also used to analyze time-frequency correlations between the anomaly series of monthly arctic oscillation indices and monthly precipitation, and temperature (Sun and Cheng 2008), and more recently has been used to quantify the relation between the geomagnetic Ap index and sunspot number (Wang et al. 2011a), and detect the relation between paleoclimate proxy records (Prokoph and Bilali 2008). But scarce articles deal with identification of heterogeneity of aquifer by using cross wavelet transforms. Because of data insufficiency, more cost-effective methods are essential to identify the heterogeneity of a karst aquifer in an extensive karst area with scarce data (Halford 2004; Chebud and Melesse 2011). One of the key components of karst aquifer heterogeneity identification is a good knowledge of the rainfall-discharge process (Dörfliger et al. 2009). The aim of this project is to identify the strong karst groundwater runoff belt based on the spring discharge and precipitation of sub-areas in the Niangziguan Springs Basin China. Different from Hao et al. 2012b who investigated the karst groundwater hydrological processes by Morlet wavelet transforms, this paper focuses on identifying the strong karst groundwater runoff belt by cross wavelet transform.

2 The Hydrogeological Setting of the Niangziguan Karst Springs Basin

The Niangziguan Springs complex, the largest karst springs in northern China, is located in the Mian River Valley, Taihang Mountains, Eastern Shanxi Province, China. The Niangziguan Springs are distributed along 7 km of the Mian riverbank (Fig. 1). The springs discharge at an annual average rate of 9.8 m3/s based on records from 1958 to 2009. The maximum annual recorded spring flow was 18.10 m3/s in September 1964, and the minimum was 4.69 m3/s in March 1995. The Niangziguan Springs receive water from a 7,394 km2 catchment that includes the city of Yangquan, and the counties of Pingding, Heshun, Zuoquan, Xiyang, Yuxian, and Shouyang (Fig. 1). Precipitation is believed to be the primary source of recharge to the aquifer in the Niangziguan Springs Basin (Han et al. 1993). The annual average precipitation is 529.9 mm based on records from 1958 to 2010. The largest recorded annual precipitation was 843.85 mm in 1963, and the smallest was 292.57 mm in 1972. For most years, about 60-70 % of the annual precipitation occurs in July, August, and September. Small basins and gentle sloping river valleys are the primary physiographic features of the Niangziguan Springs Basin, and extensive areas of the basin consist of rough hilly terrain where the altitude ranges from 1,200 to 1,600 m above mean sea level. The western part of the basin is higher than the eastern part, with the general topography of the basin inclining to the east. The Mian River bank, where the Niangziguan Springs discharge, has the lowest altitude in the Niangziguan Springs Basin, ranging from 360 to 392 m above mean sea level (Fig. 1). The Niangziguan Springs Basin is an independent hydrogeological unit. Generally, there are five kinds of natural karst groundwater boundaries in northern China: (a) groundwater divide; (b) surface water divide; (c) tectonic divide; (d) impermeable bed boundary; and (e) low-permeable fault boundary (Han et al. 2006). The perimeter of Niangziguan Springs Basin is also defined by the five boundary types. Northeast boundary is surface water divide, and northwest boundary is a groundwater divide. The west boundary is a tectonic divide where anticlines and faults separate the Niangziguan groundwater system and Taiyuan Dongshan groundwater system. The southwest boundary is an impermeable bed boundary, and the southeast boundary is a groundwater divide. East boundary is a low-permeable fault boundary (Han et al. 1993;Tan1995). The main strata in the Niangziguan Springs Basin are 2906 J. Miao et al.

Fig. 1 Location of Niangziguan Springs, and a simplified geographic map of the Niangziguan Springs Basin

Ordovician carbonate rocks, Carboniferous coal seams, Permian and Triassic detrital formations, and Quaternary deposits (Gao et al. 2011). The main aquifers of the basin are Ordovician karstic limestone. Karst groundwater flows from the north and the south toward Niangziguan Springs in the east (Fig. 1). At the Mian River bank, the springs arise from the occurrence of a geologic unconformity, where groundwater perches on low−permeable strata of dolomicrite, and eventually intersects the ground surface, thus creating the Niangziguan Springs (Hu et al. 2008). Precipitation is the main source of groundwater in Niangziguan Springs Basin. The precipitation infiltration propagates through the conduits and fissures, discharges at Mian River bank. Identification of Strong Karst Groundwater Runoff Belt by Cross Wavelet Transform 2907

3Methods

3.1 The Continuous Wavelet Transform

The basic purpose of the wavelet transform is to achieve a complete shift-scale representation of localized and transient phenomena happening at different time scales (Sahay and Srivastava 2014;Wangetal.2011b). The continuous wavelet transform can provide better temporal resolution characteristics on the high-frequency signal band, while providing better frequency resolution characteristics on the low-frequency band. The continuous wavelet transform CX(a,τ)ofx(t) is defined as: Z þ∞ CX ðÞ¼a; τ xtðÞΨa;τ ðÞt dt ¼ xtðÞ; Ψ a;τ ðÞt ð1Þ −∞ With ‐τ −1=2 t Ψ ;τ ðÞ¼t jja Ψ ; a; τ ∈R; a≠0 ð2Þ a a

Where a and τ are scale and time variables respectively, and Ψa,τ (t) represents the wavelet family generated by continuous translation and dilation of mother wavelet Ψ(t). The complex Morlet wavelet to be implemented in this study is defined as:

− = ω − 2= yðÞ¼t π 1 4ei 0te t 2 ð3Þ

Where ω0 is a constant, the Morlet wavelet can approach the admissible conditions when ω0≥5, its first and second derivative approach zero. It also has good time-frequency resolution. The wavelet spectrum WX(a,τ)ofx(t) is defined as the modulus of its wavelet coefficients:

Ã 2 W X ðÞ¼a; τ CX ðÞa; τ CX ðÞ¼a; τ jjCX ðÞa; τ ð4Þ

* Where CX(a,τ)andCX (a,τ) are the wavelet coefficient, and the complex conjugate of the wavelet coefficient of X, respectively (Labat 2010).

3.2 The Cross Wavelet Transform

When analyzing the relation between two different variables like precipitation and spring discharge, one needs the bivariate extension of wavelet transform (Hudgins et al. 1993). The cross wavelet transform of two time series X and Y is defined as Ã W XY ðÞ¼a; τ CX ðÞa; τ CY ðÞa; τ ð5Þ

* Where CX (a,τ)andCY(a,τ) are the wavelet coefficient of X, and the complex conjugate of the wavelet coefficient of Y, respectively. The cross wavelet spectrum is complex, and hence XY one can define the cross wavelet power as |W (a,τ)|. The complex argument arg (Wxy(a,τ)) can be interpreted as the local relative phase between X and Y in time frequency space. (Torrence and Compo 1998; Grinsted et al. 2004). The wavelet transformation at a point in time t0 always contains information of neighboring data points. The number of these points depends on the chosen wavelet and the scale considered. Thus, if the wavelet is centered close to the beginning or the end of the time series, edge effects occur. The boundary of edge effects forms a wavelength-dependent curve for significantly edge-effect free wavelet coefficients that is called the Cone of Influence 2908 J. Miao et al.

(COI). Here we take the COI as the area in which the wavelet power caused by a discontinuity at the edge has dropped to e−2 of the value at the edge (Torrence and Compo 1998; Maraun and Kurths 2004).

3.3 Data Acquisition

The seven weather stations in Niangziguan Springs Basin which are located in Yuxian County, Shouyang County, Yangquan City, Pingding County, Xiyang County, Heshun County, and Zuoquan County were set up at different times near corresponding gauging stations between 1950–1960 (Table 1). Monthly precipitation data were collected from the weather stations from the time they were set up through December 2010 (Fig. 2a–g). Monthly Niangziguan Springs discharge data from January 1958 to December 2009 were collected from the Niangziguan gauge station, and are illustrated in Fig. 2h.

3.4 Identifying the strong karst groundwater runoff belt

Karst groundwater transport is essentially a process of groundwater pressure waves that propagate through conduits, fractures, and the matrix of a karst aquifer (Williams 1983;Hao et al. 2012b). In response to the pressure wave, the groundwater could intersect with a valley or other topographic depression, and might seep out to become a karst spring. Conduits and fractures typically account for less than 1 percent of the porosity of the aquifer, but more than 95 percent of the permeability. The hydraulic conductivities of the conduits and fractures range from two to eight orders of magnitude greater than the porosity of matrix (Worthington et al. 2000; Taylor and Greene 2008). We defined the conduit and fractured area as a strong karst groundwater runoff belt which acts as master drains that locally alter the hydraulic flow field so as to capture groundwater from the surrounding aquifer matrix, adjoining fractures, and smaller nearby conduits (Palmer 1991, 1999; White and White 1989). In the strong karst groundwater runoff belt, the conduits and fractures are well developed, and the precipitation is closely related to spring discharge. In contrast, in areas of poor karst development, precipitation has a lesser affect on spring discharge. Therefore we can identify the strong karst groundwater runoff belt of a karst aquifer by using cross wavelet transform to analyze the relation between precipitation and spring discharge in different areas of the basin. We analyzed the precipitation and spring discharge to investigate the karst hydrological processes by using Morlet wavelet transform, and then identified the strong karst groundwater runoff belt by using cross wavelet transform. The data we used as input were monthly

Table 1 Time periods of the precipitation data collected at gauging Location of gauging stations Time periods stations in seven different locations Start End

Yuxian County January 1958 December 2010 Shouyang County January 1957 December 2010 Yangquan City January 1955 December 2010 Pingding County January 1955 December 2010 Xiyang County January 1958 December 2010 Heshun County January 1956 December 2010 Zuoquan County February 1959 December 2010 Identification of Strong Karst Groundwater Runoff Belt by Cross Wavelet Transform 2909 precipitation records from the seven gauge stations, staring when the gauging stations were set up, through December 2010, and monthly Niangziguan Springs discharge from January 1958, to December 2009 (Fig. 2; Table 1). Figure 2a–g shows the monthly precipitation of the seven gauging stations, and Fig. 2h shows the monthly spring discharge of Niangziguan Springs. Table 1 shows the time period of precipitation records for each of the seven gauging stations.

3UHFLSLWDWLRQ PP 3UHFLSLWDWLRQ PP

7LPH \U 7LPH˄\U (A) The precipitation of Yuxian County (B) The precipitation of Shouyang County

3UHFLSLWDWLRQ PP 3UHFLSLWDWLRQ PP 7LPH˄\U 7LPH˄\U (C) The precipitation of Yangquan City (D) The precipitation of Pingding County

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7LPH \U 7LPH˄\U (E) The precipitation of Xiyang County (F) The precipitation of Heshun County

V 'LVFKDUJH P

3UHFLSLWDWLRQ PP 7LPH \U 7LPH \U (G) The precipitation of Zuoquan County (H) The spring discharge of Niangziguan Springs

Fig. 2 The monthly precipitation and spring discharge of Niangziguan Springs 2910 J. Miao et al.

Because the seven gauging stations were set up and observations began at different times, the time periods of precipitation are different for each station. When calculating the Morlet wavelet analysis, we used all the observation data. When calculating the cross wavelet transform, we matched the precipitation to spring discharge and used same periods of time between precipitation and spring discharge.

4Results

4.1 Results of Morlet wavelet analysis of precipitation and spring discharge

The modulus of the Morlet wavelet transform coefficients of the precipitation data in Fig. 3a–g and the spring discharge in Fig. 3h are depicted by two-dimensional isograms, respectively. These figures are time-scale plots of the signal, where the x-coordinate represents the signal position over time, the y-coordinate represents a periodicity scale, and the contour at each x-y point represents the magnitude of the modulus of Morlet wavelet transform coefficient at that point. A dark gray shade is assigned to the high value of the modulus of Morlet wavelet transform coefficient, which means that the component of the data with periodicity of that range has high energy density and dominates the temporal behavior of the data. A white shade is assigned to the low value of the modulus of Morlet wavelet transform coefficient where the component has low energy density. The red dashed line indicates the COI. In Fig. 3a–g dark gray shades can be seen with a periodicity of 1 year over the period of the record. Gray shades can be found with periodicity of 5 years, from 1980–2003 in Yuxian County (Fig. 3a), 1975–2003 in Shouyang County (Fig. 3b), 1967–2003 in Yangquan City (Fig. 3c), Pingding County (Fig. 3d), 1967–2003 in Xiyang County (Fig. 3e), 1977–2003 in Heshun County (Fig. 3f), and from 1986–2003 in Zuoquan County (Fig. 3g) respectively. Gray shades also can be found with a periodicity of 17 years, from 1983–1988 in Yuxian County (Fig. 3a), Shouyang County (Fig. 3b), Yangquan City (Fig. 3c), Pingding County (Fig. 3d), Xiyang County (Fig. 3e), Heshun County (Fig. 3f), and Zuoquan County (Fig. 3g). Other components of different periodicities scatter along the time period and appear as lighter shades of gray, which means that they have low energy density. These facts reveal an irregular distribution of energy density of the precipitation signal. In Fig. 3h dark gray shades can be seen with a periodicity of 17 years from 1983–1986. Gray shades can be found with a periodicity of 5 years from 1976–2003. It also revealed an irregular distribution of energy density of the spring discharge.

4.2 Results of cross wavelet analysis between precipitation and spring discharge

Similarly, the modulus of cross wavelet transform coefficients is illustrated by two- dimensional isograms in Fig. 4a–g. The contour at each x-y point represents the magnitude of the modulus of cross wavelet transform coefficient at that point. A dark gray shade is assigned to the high value of the modulus of cross wavelet transform coefficient, which means that the precipitation and the spring discharge are closely related to the periodicity. A white shade is assigned to the low value of the modulus of cross wavelet transform coefficient where the precipitation and the spring discharge are less related. The red dashed line indicates the COI. Dark gray shades can be seen in Fig. 4a–g with periodicities of 1 year over the period of record. Gray shades can be found with a periodicity of 5 years, from 1976–2003 in Yuxian Identification of Strong Karst Groundwater Runoff Belt by Cross Wavelet Transform 2911

20 20

15 15 ) ear Y ( 10 10 d o i eriod (Year) Per P

5 5

0 0 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 Year Year (A) Yuxian County (B) Shouyang County

15 15 r)

ea 10 (Y 10 d o i eriod (Year) er P P

5 5

0 0 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 Year Year (C) Yangquan City (D) Pingding County

20 20

15 15

10 10 Period (Year) Period (Year)

5 5

0 0 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 Year Year (E) Xiyang County (F) Heshun County

15 15 ) r

10 10 iod (Yea r Pe

Period (Year) 5 5

0 0 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 Year Year (G) Zuoquan County (H) Niangziguan Springs discharge

Fig. 3 Morlet Wavelet Transform of the precipitation of different areas and the spring discharge in Niangziguan Springs Basin

County (Fig. 4a), 1973–2003 in Shouyang County (Fig. 4b), 1966–2003 in Yangquan City (Fig. 4c), 1966–2003 in Pingding County (Fig. 4d), 1966–2003 in Xiyang County (Fig. 4e), 1975–2003 in Heshun County (Fig. 4f), and from 1977–2003 Zuoquan County (Fig. 4g). Gray shades also can be found with a periodicity of 17 years, from 1983–1988 in Yuxian County 2912 J. Miao et al.

15 15 r) a e 10 10 od (Y i er Period (Year) P

5 5

0 0 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 Year Year (A) Yuxian County (B) Shouyang County

15 15 ) ar e

Y 10

( 10 d o i r e Period (Year) P

5 5

0 0 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 Year Year (C) Yangquan City (D) Pingding County

15 15 ) r a ear) Y Ye 10 ( 10 od Peri Period (

5 5

0 0 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 Year Year (E) Xiyang County (F) Heshun County

15 ) r ea Y

( 10 d o ri e P

0 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 Year (G)Zuoquan County

Fig. 4 Cross Wavelet Transform of the spring discharge with the precipitation at different areas in Niangziguan Springs Basin

(Fig. 4a), Shouyang County (Fig. 4b), Yangquan City (Fig. 4c), Pingding County (Fig. 4d), Xiyang County (Fig. 4e), Heshun County (Fig. 4f), and Zuoquan County (Fig. 4g). Other components of different periodicities scatter along the time period and appear as lighter shades of gray. These facts reveal that the relation between precipitation and spring discharge is an irregular distribution in the time-frequency domain. Identification of Strong Karst Groundwater Runoff Belt by Cross Wavelet Transform 2913

5Discussion

In a karst basin, precipitation penetrates heterogeneous aquifers, and reaches the subsurface water, which causes local groundwater levels to rise. The pressure wave of groundwater propagates through fractures, conduits and porous media, and emerges as springs. The spring discharge variation is thus a response of the groundwater system to precipitation. Because the hydraulic conductivity of the conduits and fractures ranges from two to eight orders of magnitude greater than the porosity of the matrix (Worthington et al. 2000; Taylor and Greene 2008), the signals of precipitation are easy to propagate and reflect in spring discharge in highly karstified areas (i.e. the strong karst groundwater runoff belt). In poorly karstified areas, the precipitation signal is not clearly propagated. Comparing Fig. 3h and Fig. 3a–g,we find that the contour altitude value in Fig. 3h is much smaller than in Fig. 3a–g, and the profile of contour in Fig. 3h is more flat than in Fig. 3a–g. This suggests that when precipitation transforms into spring discharge by infiltration and propagation through the heterogeneous karst formation, the amplitude of precipitation oscillations is attenuated within the aquifer. In the time-frequency of precipitation coefficients, gray shades can been seen with periodicities of 1, 5, and 17 years, which indicates that they have relative high energy density (Fig. 3a–g). However, only the periodicities of 5 and 17 years can be seen in the time-frequency of spring discharge coefficients, and the periodicities of 1 year are not reflected in spring discharge (Fig. 3h). These facts indicate that 1-year precipitation periodicities cannot penetrate karst formations, and do not exit the aquifer as spring discharge. Figure 4 showed the cross wavelet power for precipitation and spring discharge. The gray shadows can be seen around the periodicities of 1 year for all the sub-areas in Niangziguan Springs Basin (Fig. 4a–g). Although the periodicities of 1 year are not present in Fig. 3h,the precipitation and spring discharge also share a common periodicity of 1 year. Similarly, the gray shadows can be seen around the periodicities of 17 years for all the sub-areas in Niangziguan Springs Basin (Fig. 4). This means that the precipitation and spring discharge are sharing the common periodicity of 17 years in all the sub-areas in Niangziguan Springs Basin. We could not find an obvious difference in the cross wavelet transform coefficients around the periodicities of 1and 17 years among the sub-areas in Fig. 4. These facts demon- strate that the cross wavelet transform coefficients around periodicities of 1and 17 years may not be sensitive to the heterogeneity of karst aquifers. However, the cross wavelet transform coefficients around the periodicities of 5 years are largely different. These differences provide us the opportunity to identify the heterogeneity of a karst aquifer. The rank of relation between precipitation and spring discharge can be determined from Fig. 4a–g based on the cross wavelet transform coefficients around the periodicities of 5 years: Pingding County, Yangquan City, Xiyang County, Shouyang County, Yuxian County, Heshun County, and Zuoquan County. The rank manifests that Pingding County and Yangquan City have a high degree of karstification (i.e. the strong karst groundwater runoff belt), Xiyang County and Shouyang County have a moderate degree of karstification, and Yuxian County, Heshun County, and Zuoquan County have a low degree of karstification. The results agree with the geological structure of Niangziguan Springs Basin (Han et al. 1993). In the Niangziguan Springs Basin, the central and east parts, including Yangquan City and Pingding County have a low altitude, where most overburden is less than 200 m, and karstification is well developed. Belts of strong karst groundwater run-off can be found in this region. Toward the northwest and southwest, the altitude becomes higher. In areas covered with 200–500 m of overburden (i.e. Shouyang County and Xiyang County), the karstification is less developed. In areas covered with 500–1000 m of overburden (i.e. Yuxian County, Heshun County, and Zuoquan County) karstification is weak (Zuo 1987; Han et al. 1993; Hao et al. 2006). 2914 J. Miao et al.

6Conclusions

Spring discharge is determined by the time structure of precipitation and heterogeneity of a karst aquifer. Precipitation and runoff reach the groundwater level via infiltration, and subse- quently propagate and emerge as springs. The processes are nonstationary and nonlinear. The cross wavelet transform of precipitation and spring discharge can reveal the relation between precipitation and spring discharge in the time-frequency domain, and detect the strong karst groundwater runoff belt of a karst aquifer. In the strong karst groundwater runoff belt, the precipitation signal can penetrate the aquifer relatively easily and affect spring discharge. Precipitation and spring discharge are thus closely related, and the values of cross wavelet transform coefficients are large. In contrast, in poorly karstified areas, the values of cross wavelet transform coefficients are small. While precipitation propagates through karst formations and transforms into spring discharge, signals are attenuated. But some cross wavelet transform coefficients may not be sensitive to aquifer heterogeneity. When identifying the strong karst groundwater runoff belt of a karst aquifer, it is important to focus on cross wavelet transform coefficients which are sensitive to aquifer heterogeneity. In Niangziguan Springs Basin, Pingding County and Yangquan City are the strong karst groundwater runoff belt, Xiyang County and Shouyang County have a moderate degree of karstification, and Yuxian County, Heshun County, and Zuoquan County have a low degree of karstification. The strong karst groundwater runoff belt of Pingding County and Yangquan City is the major groundwater pathway of Niangziguan Springs Basin, where groundwater converges and discharges to Niangziguan Springs. Like a large reservoir, the karst aquifer of the strong karst groundwater runoff belt stores a great deal of precious water in this semiarid region. It provides us a primary field for groundwater development and protection. In Niangziguan Springs Basin, China, an enormous karst aquifer easily infiltrates precipitation and transforms highly fluctuating precipitation events into relatively stable groundwater flow. Water resource managers in the basin typically lack sufficient data to support well- informed water management decisions. Fortunately, spring discharge provides a vital indicator that reflects the status of the karst groundwater reservoir system. We can acquire a better understanding of heterogeneity of a karst aquifer and karst hydrological processes by using the cross wavelet transform based on the relation between precipitation and spring discharge. The application to Niangziguan Springs Basin demonstrated that cross wavelet transform is a robust tool for identifying the strong karst groundwater runoff belt of a karst aquifer.

Acknowledgments This work is partially funded by the National Natural Science Foundation of China (41272245, 40972165, 40572150). The authors are also grateful to Professor Xingrui Han for his suggestions in this article, and to Dr. Martha P. L. Whitaker for technical editing. Our gratitude is also extended to the AE and an anonymous reviewer for their efforts in reviewing the manuscript and their very encouraging, insightful, and constructive comments.

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