HYDROLOGICAL PROCESSESHydrol. Process. 26, 3062–3069 (2012)Published online 9 January 2012 in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/hyp.8265
Investigation of karstic hydrological processes of NiangziguanSprings (North China) using wavelet analysis
Yonghong Hao,1* Guoliang Liu,2 Huamin Li,3 Zhongtang Li,4 Jiaojuan Zhao3 and Tian-Chyi J. Yeh51 Tianjin Key Laboratory of Water Resources and Environment, Tianjin Normal University, Tianjin, China
2 College of Environment and Resources, Shanxi University, Taiyuan, Shanxi Province, China3 College of Urban and Environmental Science, Tianjin Normal University, Tianjin, China
4 Department of Environmental Engineering, College of Science and Engineering, Jinan University, Guangzhou, China5 Department of Hydrology and Water Resources, The University of Arizona, Tucson, AZ, USA
KEY WORDS karst aquifer; groundwater; wavelet analysis; Niangziguan Springs
Received 29 August 2010; Accepted 10 August 2011
INTRODUCTION
Karst aquifers are highly heterogeneous. They aredominated by secondary or tertiary porosity (i.e. fracturesor conduits, respectively) and exhibit hierarchical perme-ability structures or flow paths (Atkinson, 1977). In karsthydrological systems, precipitation and runoff reach thegroundwater via infiltration through heterogeneous karstaquifers and, subsequently, propagate and emerge assprings. Accordingly, variations in precipitation andheterogeneity of karst formation strongly affect springflow and cause fluctuations in discharge volume. Labat et al.(2000a) described rainfall–runoff relations using a linearstochastic model and Fourier analysis applied to threekarstic systems (i.e. the Aliou, Baget, and Fontestorbessprings) located in the Pyrenees Mountains, France. Theyfound that linear input–output models were not verysuccessful at characterizing hydraulic behaviour of karstsystems, and their results showed that karst groundwaterwas likely a non-linear and non-stationary system. Then,they applied wavelet transform to the karstic systems
orrespondence to: Yonghong Hao, Tianjin Key Laboratory of Waterources andEnvironment, TianjinNormalUniversity, Tianjin 300387,China.ail: [email protected]; [email protected]/grant sponsor: The National Natural Science Foundation ofina; contract/grant numbers: 40972165, and 40572150, Tianjin ScienceTechnology Developing Strategy Foundation; contract/grant numbers:CYBJC27500, and Opening Fund of Tianjin Key Laboratory of Watersources and Environment; contract/grant numbers: 52XS1015.
(Labat et al., 2000b). The results demonstrated that thewavelet analysis can detect the runoff response to bothnatural recharge processes and human stimuli to thegroundwater system and can possibly give an accurateexplanation of the temporal structure of rainfall and runoffrecords in different timescales. Many scientists haveapplied of wavelet analysis to karst hydrology (Andreoet al., 2005; Massei et al., 2006; Herman et al., 2009;Salerno and Tartari, 2009). Labat et al. (2005a,b) reviewedand summarized the works of wavelet application in thefield of earth science. They applied these methods to themonthly discharge of four large rivers (i.e. Amazon,Parana, Orinoco, and Congo) and two long-term climato-logical indices. The results indicate that wavelet analysiscan help to identify the relation between discharge andclimatological indices. Labat et al. (2005a, 2005b) alsoemphasized that there was great potential in applying thewavelet analysis technique to hydrological systems.
China has some of the largest karst terrain in the world.One quarter of the world’s carbonate rock occurs in China(Hua, 1981; Sweeting, 1995). There is about 470 000 km2
of karst terrains in North China. Because North China is asemiarid area where annual precipitation averages less than800mm, the karstification is less developed compared withthe more humid areas in South China. Yet in northernChina, there are large karst basins, which exceed 1000 km2.The aquifers in these basins are mainly recharged byinfiltration of precipitation and, subsequently, provide an
3063INVESTIGATION OF KARSTIC HYDROLOGICAL PROCESSES USING WAVELET ANALYSIS
inflow of more than 1m3/s to many large karst springs. Thepurpose of this project is to acquire a better understandingof karst hydrological processes by analyzing the relation ofprecipitation to karst spring discharge using waveletanalysis. Different from previous research, this papermainly focuses on the role of karst formation in thehydrological processes, groundwater propagation, andenergy transformation from precipitation to spring dis-charge. As the largest spring in North China, theNiangziguan Springs is representative of the karst springsin semiarid North China and is therefore selected as ourstudy region.
THE HYDROGEOLOGICAL SETTING OF THENIANGZIGUAN KARST SPRINGS
The Niangziguan Springs complex, the largest karst springsin northern China, is located in the Mianhe Valley, TaihangMountains, Eastern Shanxi Province, China (Figure 1). Thesprings discharge at an annual average rate of 9.8m3/sbased on the record from 1958 to 2009. The maximumannual recorded spring flow was 18.10m3/s in September1964, and the minimum was 4.69m3/s in March 1995(Figure 2). The Niangziguan Springs are distributed along7 km of the Mianhe riverbank (Figure 1).
Figure 1. Location of Niangziguan Springs and a simplifi
The Niangziguan Springs receive water from a 7394-km2 catchment that includes the city of Yangquan and thecounties of Pingding, Heshun, Zuoquan, Xiyang, Yuxian,and Shouyang (Figure 1). Precipitation is believed to be theprimary source of recharge to the aquifer in theNiangziguan Springs Basin (Han et al., 1993). The annualaverage precipitation is 529.9mm based on the record from1958 to 2010. The largest recorded annual precipitationwas 843.85mm in 1963, and the smallest was 292.57mmin 1972 (Figure 2). For most years, about 60–70% of theannual precipitation occurs in July, August, and September.
Small basins and gentle sloping river valleys are theprimary physiographic features of the Niangziguan SpringsBasin, and extensive areas of the basin consist of roughhilly terrain where the altitude ranges from 1200 to 1600mabove mean sea level. The western part of the basin ishigher than the eastern part, with the general topography ofthe basin inclining to the east. The Mianhe Valley, wherethe Niangziguan Springs discharges, has the lowest altitudein the Niangziguan Springs Basin, ranging from 360 to392m above mean sea level.
The main outcropping strata in Niangziguan SpringsBasin are Ordovician carbonate rocks, Carboniferous coalseams, Permian and Triassic detrital formations, andQuaternary deposits. The main aquifers of the basin are
ed geographic map of the Niangziguan Springs Basin
Hydrol. Process. 26, 3062–3069 (2012)
Figure 2. Spring discharge, precipitation, and pumping rate in Niangziguan Springs Basin
3064 Y. HAO ET AL.
composed of Cambrian and Ordovician karstic limestoneand Quaternary sandstone and porous sediments (Figure 3).The limestone and Quaternary sediment aquifers arehydraulically connected. Karst groundwater flows fromthe north and the south towards the Niangziguan Springs inthe east (Figure 1). At the Mianhe Valley, the springs arisefrom the occurrence of a geologic unconformity, wheregroundwater perches on low-permeable strata of dolomi-crite and eventually intersects the ground surface, thuscreating the Niangziguan Springs (Hu et al., 2008).Since the 1979, karst groundwater in the Niangziguan
Springs Basin has been exploited for irrigation, municipaluse, and industrial water supply (Figure 2). The usage hasaccelerated since the 1980s. Today, the karst groundwateris a major water source for the Niangziguan Springs Basin,which is one of the heavy industry regions in China forcoal mining, power generation, chemical engineering, andmetallurgy (Hao et al., 2006, 2009).
METHODS
Data acquisition
Monthly precipitation data from January 1958 to December2010 was collected from seven gauging stations (Yuxian,Shouyang, Yangquan, Pingding, Xiyang, Heshun, and
Figure 3. A geologic cross section of Niangziguan Spri
Zuoquan; Figure 1) in the basin. The monthly precipitationover the entire Niangziguan Springs Basin is representedwith Thiessen polygon for the precipitation data from theseven gauging stations (shown in Figure 4A). MonthlyNiangziguan Springs discharge data from January 1958 toDecember 2009 were collected from the Niangziguangauge station and is illustrated in Figure 4B.
Morlet wavelet transform
The basic purpose of the wavelet transform is to achieve acomplete shift-scale representation of localized and transi-ent phenomena happening at different timescales. Thecontinuous wavelet transform can provide better temporalresolution characteristics on the high-frequency signalband, while providing better frequency resolution char-acteristics on the low-frequency band.
The continuous wavelet transform CX(a, t) of x(t) isdefined as follows:
CX a; tð Þ ¼Z þ1
�1x tð ÞΨa;t tð Þdt ¼ x tð Þ;Ψa;t tð Þ� �
(1)
with Ψa;t tð Þ ¼ aj j�1=2Ψt-ta
� �; a; t 2 R; a 6¼ 0 (2)
where a and t are scale and time variables, respectively,and Ψa, t(t) represents the wavelet family generated bycontinuous translation and dilation of mother wavelet Ψ(t).
ngs Basin, corresponding to the A–B line in Figure 1
Figure 4. The monthly precipitation from 1958 to 2010 (A) and springdischarge from 1958 to 2009 (B) in Niangziguan Springs Basin
3065INVESTIGATION OF KARSTIC HYDROLOGICAL PROCESSES USING WAVELET ANALYSIS
The complex Morlet wavelet to be implemented in thisstudy is defined as follows:
Ψ tð Þ ¼ eio0te�t2=2 (3)
where, o0 is a constant; the Morlet wavelet can approachthe admissible conditions while o0≥ 5, its first and secondderivative approach to zero. It also has good time–frequency resolution.The wavelet spectrum WX(a, t) of x(t) is defined as the
where CX(a, t) andC�X a; tð Þ are the wavelet coefficient, and
the complex conjugate of the wavelet coefficient of X,respectively (Labat, 2010).The Morlet wavelet is not an orthogonal wavelet, and its
modulus and the real part of the wavelet transformcoefficients are two important factors. The modulus standsfor the energy density of signal, as the energy is in directratio to the modulus. The real part stands for thedistribution of the signal phase in the time domain. Inhydrological processes, the positive value of the real partcorresponds to the wet period, the negative valuecorresponds to the period of drought, and the zerocorresponds to the transitional area (Zhang et al., 2007).Through an analysis of the Morlet wavelet transformcoefficients, features of the multi-scale evolution and thetransient properties in a hydrological system can bedistinguished (Wang et al., 2005).
The Morlet wavelet transform has edge artifacts becausethe wavelet is not completely localized in time. It istherefore useful to introduce a cone of influence (COI) inwhich the edge effects cannot be ignored. Here, we take theCOI as the area in which the wavelet power caused by adiscontinuity at the edge has dropped to e�2 of the value atthe edge (Torrence and Compo 1998).
Cross wavelet transform
The cross wavelet transform of two time series X and Y isdefine as
WXY a; tð Þ ¼ CX a; tð ÞC�Y a; tð Þ (5)
where CX(a, t) and C�Y a; tð Þ are the wavelet coefficient of X
and the complex conjugate of the wavelet coefficient of Y,respectively. The cross wavelet spectrum is complex, andhence, one can define the cross wavelet power as|WXY(a, t)| (Torrence and Compo, 1998; Grinsted et al.,2004).
We also introduce COI to figure out the boundary effectsof cross wavelet transform.
Global wavelet spectrum
The wavelet variance is the integration of all the squaredvalues of the wavelet coefficients with scale a in the timedomain. The formula for calculating the wavelet variance isas follows:
Var að Þ ¼Z þ1
�1Cx a; tð Þj j2dt (6)
The wavelet variance of a time series can be used todetect the main periods contributing to a signal. The higherthe variance of a period, the greater is the contribution ofthis period to the signal.
RESULTS
The results of Morlet wavelet analysis for precipitation
We analysed the precipitation and spring discharge toinvestigate the karst hydrological processes by usingMorlet wavelet transform. The modulus and the real partof the Morlet wavelet transform coefficients of theprecipitation data are depicted by two-dimensional iso-grams in Figures 5A and B, respectively.
These figures are timescale plots of the signal, where thex-coordinate represents the signal position over time, the y-coordinate represents a periodicity scale, and the contour ateach x–y point represents the magnitude of the modulus orreal part of Morlet wavelet transform coefficient at thatpoint. In Figure 5A, a white shade is assigned to the highvalue of the modulus of Morlet wavelet transformcoefficient, which means that the component of the datawith periodicity of that range has high energy density anddominates the temporal behaviour of the data. A dark greyshade is assigned to the low value of the modulus of Morlet
Figure 5. The time–frequency distribution of module (A) and the real part(B) of Morlet wavelet transform coefficient of the precipitation inNiangziguan Springs Basin. The dashed lines indicate the cone of
influence (COI)
3066 Y. HAO ET AL.
wavelet transform coefficient where the component has lowenergy density. In Figure 5B, a white shade is assigned tothe positive value of the real part of Morlet wavelettransform coefficient, indicative of a wet period; a redshade is assigned to the negative value of the real part ofMorlet wavelet transform coefficient, indicative of a dryperiod; and a zero contour line is assigned to the transitioninterval between wet and dry periods (Zhang et al., 2007).The dashed indicates the COI.Light shades can be seen with periodicity of 1 year over
the period of the record. Grey shades can be found withperiodicity of 5, 12, and 17 years over 1971–2002, 1975–1994, and 1983–1987, respectively (Figure 5A). Othercomponents of different periodicities scatter along theperiod of 1958–2010 and appear as dark grey, which meansthat they have low energy density. For example, thecomponents with periodicity of 7, 8, and 9 years also arenoticeable over these periods: 1979–1988, 1970–1978, and1984–1994 (Figure 5A). These facts reveal an irregulardistribution of energy density of the precipitation signal.The alternating wet–drought cycles, the transition
interval distribution, and phase structure of precipitationcan be observed in Figure 5B. Results of wavelet analysisof the data reveal that the precipitation time series iscomposed of three types of quasi-periodic oscillations,namely, 1, 5, and 12 years. The component of 1-yearperiodicity appears positive–negative alternating changeswithin a year, implying that the precipitation has seasonalvariation in Niangziguan Springs Basin. The componentsof the 5 years’ periodicity are apparent with positive–negative alternate phases. During 1969–1972, 1976–1979,1982–1985, 1988–1991, 1994–1997, and 2001–2004, thecomponents have positive value of the real part of Morletwavelet transform coefficients, indicative of high precipi-tation during these periods. The same component over the1966–1969, 1972–1976, 1979–1982, 1985–1988, 1991–1994, and 1997–2001 time frame has a negative value ofthe real part of Morlet wavelet transform coefficients,
corresponding to low precipitation. The transition intervalsare in 1969, 1972, 1976, 1979, 1982, 1985, 1988, 1991,1994, 1997, and 2001, respectively. Similarly, thecomponents of 12 years’ periodicity, during 1974–1981and 1988–1994 have positive values of the real part ofMorlet wavelet transform coefficients, indicative of highprecipitation during these periods. The same componentsover 1981–1988 have negative values, indicative of lowprecipitation. The transition intervals are at 1981 and 1988.
Results of Morlet wavelet analysis to spring discharge
Similarly, the Morlet wavelet spectrum was calculated forthe monthly Niangziguan Springs discharge data duringthe period from 1958 to 2009, and the modulus and realpart of Morlet wavelet transform coefficients are illus-trated by two-dimensional isograms in Figures 6A and B,respectively.
A grey shades can be seen in Figure 6Awith periodicitiesof 17 years over 1983–1986. Other components of differentperiodicities scatter along the period of 1958 to 2009 andappear as dark grey, which means that these componentshave low energy density. For example, the components of12, 9, 6, and 5 years also are apparent, and the signals existin 1975–1994,1967–1973, 1968–1987, and 1971–2002,respectively. From Figure 6B, we can find the alternatinghigh-low discharge cycles, the transition interval distribu-tion, and the phase structure of Niangziguan Springsdischarge (Figure 6B).
Results of cross wavelet analysis of precipitation andspring discharge
Cross wavelet analysis between precipitation and springdischarge was calculated for identifying the relationsbetween precipitation and spring discharge signals. Thedata used for cross wavelet analysis were monthlyprecipitation and spring discharge from 1958 to 2009.The results are illustrated in Figure 7. Figure 7 shows thataround the periodicities of 17 years, the cross waveletpower has high value.
Results of global wavelet spectrum of precipitation andspring discharge
Wavelet variance was calculated for the precipitation andspring discharge, and the results are illustrated in Figure 8.
Using wavelet variance, we can confirm the dominantperiodicity of precipitation and spring discharge inNiangziguan Springs Basin. The wavelet variance of theprecipitation has four peaks in Figure 8, which are locatedat the timescales of 1, 5, 12, and, 17 years. The waveletvariance of the spring discharge has two peaks, which arelocated at the timescales of 8 and 17 years (Figure 8).
DISCUSSION
In a karst basin, precipitation passes through the unsatur-ated zone and reaches the subsurface water, which causeslocal groundwater level to rise. Then, groundwater
Figure 6. The time–frequency distribution of modulus (A) and the real part (B) of Morlet wavelet transform coefficient of Niangziguan Springsdischarge. The dashed lines indicate the COI
3067INVESTIGATION OF KARSTIC HYDROLOGICAL PROCESSES USING WAVELET ANALYSIS
propagates through fractures, conduits, and porous mediaand emerges as springs. So the spring discharge variation isthe response of groundwater system to precipitationthrough the regulation of karst aquifer. Figures 5 and 6reveal that both precipitation and discharge in NiangziguanSprings Basin are characterized by the multi-timescalefeatures, which indicates that the precipitation and springdischarge always occur in a main periodicity combiningwith other sub-periodicities. Their time–frequency domainshave multi-timescale structures, localization features, andwet–dry cycles. Comparing Figures 5 and 6, we can findthat the contour altitude value in Figure 6 is much smallerthan that in Figure 5 and that the profile of contour inFigure 6 is more flat than that in Figure 5. This suggeststhat when precipitation transforms into spring discharge byinfiltration and propagation through the karst formation, theamplitude of precipitation oscillations is attenuated withinaquifer. In the time–frequency of precipitation coefficient,light and grey shades can been seen with periodicity of 1,5, 12, and 17 years, respectively, which indicates that theperiodicities of 1, 5, 12, and 17 years have relative highenergy density (Figure 5A). However, only the periodicityof 17 years can be seen in the time–frequency of springdischarge coefficient, and the periodicities of 1, 5, and12 years are not reflected in spring discharge (Figure 6A).The facts indicate that the precipitation periodicities havingthe high energy and long scale can only penetrate karstformations and exit the aquifer as spring discharge.Figure 7 shows the cross wavelet power for precipitation
and spring discharge. The light shadows can be seen around
Figure 7. The cross wavelet power for the precipitation and spring disch
the periodicities of 17 years, which have the high crosswavelet power (Figure 7). It means that the precipitation andspring discharge share the common periodicity of 17 years.In other words, although components of 1, 5, and 12-yearperiods of precipitation were visible in Figure 5A, they havenot enough energy to penetrate karst formation and bereflected in spring discharge.
Figure 8 illustrates that the wavelet variance of the springdischarge data is much more attenuated than the waveletvariance of the precipitation data. The wavelet variance ofthe precipitation has four largest peaks that correspond toyears 1, 5, 12, and 17, and the wavelet variance of springdischarge has two high peaks located at 8 and 17 year. Inother words, except the 17 year’s periodicity of precipita-tion, other periodicities cannot penetrate aquifer and bereflected in spring discharge because of low energy. Theyare filtered or merged as new periodicities by the aquifers.This reemphasized that the energy of precipitation oscilla-tions is attenuated within the aquifer, and the precipitationperiodicities with the high energy and long scale can onlyexit the aquifer as spring discharge.
A karst aquifer is highly heterogeneous and has long beenconceptualized as having secondary or tertiary porosity (i.e.intergranular porosity within the matrix rocks, fractures, andconduits) and may exhibit hierarchical permeability struc-tures of flow paths (Labat et al., 1999; Martin and Dean,2001). Conduits and fractures are characterized by lowspecific storage and high hydraulic conductivity, but therock matrix displays much higher specific storage and lowhydraulic conductivity (Liedl et al., 2003; Hao et al., 2008).
arge in Niangziguan Springs Basin. The dashed lines indicate the COI
Figure 8. The wavelet variance of precipitation and discharge in Niangziguan Springs Basin
3068 Y. HAO ET AL.
As a consequence, the outcropped parts in a karst aquiferwith strong karstification are dominated by higher flowvelocity (i.e. quickflow); inversely, buried karst aquifer withweak karstification are dominated by lower flow velocity(i.e. baseflow) (Padilla and Pulido-Bosch, 1995). During thepropagation, groundwater (i.e. quick flow and base flow)always intersects, and merges. From Figures 5–8, we canfind that only 17 periodicity of precipitation is reflected inspring discharge, ; other precipitation periodicities (i.e. 1, 5,and 12 12-years periods of precipitation) intersect, merge,and transform into other timescales to reflect in springdischarge.
CONCLUSIONS
Karst hydrological systems, where precipitation and runoffreach the groundwater level via infiltration and subsequentlypropagate and emerge as springs, are non-stationary andnonlinear systems because karst aquifers are highlyheterogeneous and exhibit hierarchical permeability struc-tures or flow paths. In karst hydrological processes,hydrological signal propagates and transforms through karstformations. The springs discharge is determined by the timestructure of precipitation and heterogeneity of karst aquifer.Precipitation and discharge are characterized by the multi-
timescale features in the time domain. They always occur ina main periodicity combining with other sub-periodicity.Their time–frequency domains have multi-scale structuresand localization features. Time distribution of energy ishighly irregular across different scales. Whereas precipita-tion transforms into spring discharge by infiltration and flowthrough karst formations, signals are attenuated. Thosesignals with high energy and large timescales can penetratethe karst formation and exit as spring discharge. Othersignals are filtered and modified. Therefore, groundwaterflow is the process that causes propagation of hydrologicalsignals through karst formations.Morlet continuous analysis cannot only identify the
components of precipitation and discharge in a hydro-logical system, it also can detect the internal structure ofthe time–frequency, the distribution of the strength of
variation, and the transition interval of each components. Itis therefore appropriate to use it to study karst hydrologicalprocesses.
An enormous karst aquifer infiltrates precipitation andtransforms highly fluctuating precipitation events intorelative stable groundwater flow in Niangziguan SpringsBasin. Like a large reservoir, the karst aquifer stores a greatdeal of precious water in this semiarid region. The springdischarge is an important indicator that reflects the status ofthe karst groundwater reservoir system. We can acquire abetter understanding of karst hydrological processes byanalyzing the relation between precipitation and karstspring discharge. It is very important to conserve karstgroundwater in this semiarid region as it supports bothsocial and regional economic development.
ACKNOWLEDGEMENTS
This work is partially supported by the National NaturalScience Foundation of China (40972165 and 40572150),Natural Science Foundation of Tianjin (09JCYBJC27500),and Opening Fund of Tianjin Key Laboratory of WaterResources and Environment (52XS1015). Many thanks areextended to the four anonymous reviewers who have spentenormous efforts reviewing the manuscript and providedvery encouraging, insightful, and constructive comments.
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