Yi Guo,Fng Wng,D-jun Qin,Zhn-fng Zho,Fu-ping Gn,Bi-kun Yn,Jun Bi,Hji Muhmm

a China Aero Geophysical Survey and Remote Sensing Center for Natural Resources, China Geological Survey, Beijing 100083, China

b Chinese Academy of Environmental Planning, Beijing 100012, China

c Key Laboratory of Shale Gas and Geoengineering, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China

d Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101,China

e School of Applied Natural Science, Adama Science and Technology University, P.O.Box 1888, Adama, Ethiopia

Keywords:Karst spring Karst aquifer Hydrodynamic Time series analysis Correlation analysis Spectral analysis Hydrogeological survey engineering Jinan Shandong Province China

ABSTRACT I n order to study the hydrodynamic characteristics of the karst aquifers in northern China,time series analyses (correlation and spectral analysis in addition with hydrograph recession analysis) are applied on Baotu Spring and Heihu Spring in Jinan karst spring system,a typical karst spring system in northern China.Results show that the auto-correlation coefficient of spring water level reaches the value of 0.2 after 123 days and 117 days for Baotu Spring and Heihu Spring,respectively.The regulation time obtained from the simple spectral density function in the same period is 187 days and 175 days for Baotu Spring and Heihu Spring.The auto-correlation coefficient of spring water level reaches the value of 0.2 in 34-82 days,and regulation time ranges among 40-59 days for every single hydrological year.The delay time between precipitation and spring water level obtained from cross correlation function is around 56 days for the period of 2012-2019,and varies among 30-79 days for every single hydrological year.In addition,the spectral bands in cross amplitude functions and gain functions are small with 0.02,and the values in the coherence functions are small.All these behaviors illustrate that Jinan karst spring system has a strong memory effect,large storage capacity,noticeable regulation effect,and time series analysis is a useful tool for studying the hydrodynamic characteristics of karst spring system in northern China.

1.Introduction

Karst system provides drinking water to nearly 25% of the world population with total karst area of 22×106km2(Ford D and Williams P,2007).In China,the karst area is about 3.44×106km2,and the natural karst water resources are 203.42×109m3/a,accounting for 23.39% of groundwater resources (Lu HP et al.,2018).The obvious differences in topography,climate and geology conditions lead to different karst characteristics between northern China and southern China.In northern China,the outcrop karst area is 150×103km2,accounting for 1/6 of the total area of karst outcrop in China,and karst water has become an important source of water supply due to its large reserves,good water quality and stable flow (Luo Z et al.,2005).However,karst spring discharge in northern China has been declining due to climate changes and anthropogenic activities since the 1950s,even some large karst springs have become dry (Zheng XQ et al.,2018a,2018b; Qin DJ et al.,2017).Therefore,it is important and extremely urgent to understand the hydrodynamic characteristics of karst spring system in northern China.

Karst aquifers are highly heterogeneous with aperture diameters varying over more than five orders of magnitude,from pores and small fractures (less than 1 mm) to large fissures and conduits (more than 10 m) (White WB,2002).The duality of karst aquifer structure leads to the duality of hydrogeological condition in karst system,for example the slow infiltration through matrix and rapid infiltration through swallow holes or dolines (Eisenlohr L et al.,1997); quick flow in conduits with high hydraulic conductivity (K> 10-1m/s) and base flow in matrix with low hydraulic conductivity(10-3m/s

Many methods have been used to discover more about karst system,including tracing test (Smart CC,1988; Ender A et al.,2018),geophysical survey (Bermejo L et al.,2017),hydrograph analysis (Dreiss SJ,1982),hydrochemistry(Massei N et al.,2007),isotope tracing (Sun ZY et al.,2016),numerical modeling (Seyhan E et al.,1985; Chang Y et al.,2017) and remote sensing (Fiaschi S et al.,2017).Correlation and spectral analysis is a signal processing method,which can find the relationship between input (precipitation) and output(flow,water level,electric conductivity,temperature,chemical parameter) to reflect the internal characteristics of aquifer.Mangin A (1975) was the first one to apply correlation and spectral analysis of karst spring discharge to reflect the karstification degree of Pyrenean karst aquifers.Since then,correlation and spectral analysis has been widely used to study the groundwater flow patterns (Pulido-Bosch A et al.,1995),the responses of groundwater system to recharge(Fiorillo F and Doglioni A,2010; Mayaud C et al.,2014),the interactions between groundwater and surface water(Larocque M et al.,1998),and the turbidity phenomenon(Bouchaoua L et al.,2002).

Jinan karst spring system is a famous karst spring system in northern China.However,the springs began to flow intermittently in 1972 due to human activities.The most serious is Baotu Spring,which had the longest dry record of 926 days (from 2 March 1999 to 17 September 2001).In order to maintain the flowing of karst springs,water supply sources have been completely shut down since 2003,and the local people drink the surface water instead of groundwater.Although the springs in city center have continuously flow for decades,but the threat of dry springs has remained.Studies about Jinan karst spring system have been performed in aspects of hydrochemical processes (Zhao ZF et al.,2012; Li BX et al.,2017; Guo Y et al.,2019a,2019b),hydrodynamic characteristics (Chi GYet al.,2017; Hu KZ et al.,2011) and numerical modelings (Qian JZ et al.,2006; Kang F et al.,2011; Qin PR,2018) in the last 40 years.In this study,time series analyses including recession analysis of spring hydrograph,correlation and spectral analysis of spring water level and precipitation are conducted in Jinan karst spring system to contribute the knowledge on the hydrodynamic characteristics of the karst spring system in northern China.

2.Study area

Jinan City,the capital city of Shandong Province,is famous for its springs and has the name of “Spring City”,locates in the central and western part of Shandong Province(116°11′-117°44′E,36°01′-37°32′N) with total area of 8177 km2.Topographically,Jinan is in the north of the Mount Tai anticline,gradually lowers from south to north.The southern part is a mountainous region with average elevation of 500 m above the sea level (m.a.s.l.),and the northern part is an alluvial flood plain with an average elevation of 28 m.a.s.l.(Fig.1).

The climate is semi-arid continental monsoon climate,dry in spring and winter,hot and rainy in summer.Air temperature ranges from −1.4°C in January to 27.4°C in July,with average air temperature of 14.3°C.The average annual precipitation is 641.68 mm (1956-2012),with maximum annual precipitation of 1164 mm in the year of 1964 and minimum annual precipitation of 340.3 mm in the year of 1989.Precipitation is unevenly distributed throughout the year,and the rainy season is concentrated in June to September with precipitation amount of 467 mm,accounting for more than 70% of the annual precipitation.The spatial distribution of precipitation decreases from southeast to northwest,and the average precipitation in the southern mountainous area is greater than that in the northern plain(Chi GY et al.,2017).The average annual evaporation is 1500-1900 mm.

Archaean metamorphic rocks are the base and outcrop in the south of the catchment,and overlaid by Cambrian and Ordovician carbonate strata in the north.The limestone and dolomite are massive and well jointed,with thickness of 1300-1400 m,dip direction of NE20° and dip angle from 5°to 10°.The Cambrian strata are composed of thick-bedded limestone,argillaceous limestone,dolomite limestone,and the Ordovician strata are characterized by the inter-bed of limestone and shale.Intrusive magmatic rocks (diorite and gabbro) of the Yanshan epoch in the Mesozoic are located in the top of the Ordovician strata in the north,and the intrusive rocks are buried mostly by Quaternary sediments (Fig.2).

Jinan karst spring system is located in the central part of Jinan,with Dongwu Fault and Mashan Fault as the eastern and western boundary,respectively,the watershed of surface water and groundwater of Mount Tai as the southern boundary,and the Yellow River as the northern boundary.The total area of Jinan karst spring system is about 1500 km2.Jinan karst spring system is an open fracture karst system,precipitation is the main recharge source with a supply module of more than 20 m3/km2per year.River water is another recharge source.The rivers mainly include Yellow River,Yufu River,Beisha River and Xiaoqing River.Among them,Yufu Rive and Beisha River are losing streams,recharge karst aquifer as long as they have flow.The Cambrian and Ordovician limestone are the main karst aquifers,with the hydraulic conductivity ranging from 0.05 m/day to 120 m/day.The water yield property ranges from 60 m3/day to 3000 m3/day and the transmissivity ranges from 100 m2/day to 4000 m2/day for Ordovician carbonate rocks.Groundwater is flowing from the south toward the north,similar to the dip direction of strata,and rises along the fissures in the lower part of the terrain when blocked by the intrusive rocks and becomes springs.There are 136 springs distributed within 2.6 km2in the center of Jinan City.Among them,Baotu Spring and Heihu Spring are the most famous.

In the early 1960s,the amount of karst water exploitation was less than 100×103m3/d,and the spring discharge was 355.2×103m3/d-335.8×103m3/d,with the maximum of 502×103m3/d observed in 1962.In the early 1970s,the amount of groundwater exploitation increased to 450×103m3/d,and the spring stopped flowing since 1972.In order to restore the flow of karst springs,municipal water supply wells were switched off and river water has been used as replacement since 2003.The springs in city center have been restored since September 2003 and continuous flow out for decades,but the threat of dry springs has remained.

3.Data and Methods

3.1.Data

The daily precipitation data are obtained from Dataset of Daily Climate Data from Chinese Surface Stations for Global Exchange (V3.0) in China Meteorological Data Service Center (https://data.cma.cn).In this study,considering the topographic and geological conditions,the data from Jinan Station (code: 54823; 170.3 m.a.s.l.) and Zhangqiu Station(code: 54727; 121.8 m.a.s.l.) from 2 May 2012 to 31 October 2019 are used.

The daily water level of Baotu Spring and Heihu Spring from 2 May 2012 to 13 November 2020 are obtained from Jinan Water Conservancy Bureau (http://www.jnwater.gov.cn).There is no monitoring for the spring discharge,however,the correlation coefficient between annual spring water level and spring discharge reaches 0.95 (Wang QB et al.,2007).In this study,the water level data of Baotu Spring is converted into the discharge data based on the empirical formula(Q=7.0187×H−179.45) (Zhou J,2016).

3.2.Hydrograph recession analysis

Fig.1.Location and geomorphology map of Jinan karst spring system,Shandong Province.

The recession constant of spring discharge hydrograph is calculated using the Equation:whereQtis the discharge at timet,Q0is the initial discharge in the recession limb,αis the recession coefficient,e−αis the recession constant.

3.3.Auto-correlation and simple spectral analysis

Correlation and spectral analysis is taking into account time (correlation analysis) and frequency (spectral analysis).Auto-correlation function quantifies the linear dependency of successive values over a period of time and the memory effect of a system.The auto-correlation coefficientr(k) is given as:

wherekis the time lag (k= 0 tom),mis the truncation point,which has to be taken as 1/3 of the length of the whole dataset according to Mangin A (1984),nis the length of the time series,xtis a single event,andis the mean of thextvalues.

The simple spectral density function [S(f)] is Fourier transformation of the auto-correlation function,which allows visualization of the frequency content of the time series.

wheref=k/2m,andD(k) ensures that the estimatedS(f)values are not biased.

3.4.Cross correlation and spectral analysis

Cross correlation analysis is a signal processing method based on black-box or gray-box models to find the relationship between input time series (xt) and output time series (yt) by increasing the relative displacement between them.The definition of cross correlation coefficientrxy(k) is as follows:

Fig.2.Geological condition map of Jinan City,Shandong Province.1-Archaean metamorphic rocks; 2-Cambrian limestone; 3-Ordovician limestone; 4-Permian strata; 5-Carboniferous strata; 6-Quaternary sediments; 7-magmatic rocks; 8-fault; 9-river; 10-the range of Jinan karst spring area; 11-meteorological station; 12-spring.

where σxand σyare the standard deviations of the time series.

The cross spectral density functionS xy(f) corresponds to the Fourier transformation of the cross correlation function.In polar coordinates,the cross spectrum can be expressed as a function of the cross amplitudeand phase functions θxy(f) for the frequencyf:

The cross amplitude identifies the periodic components of the input stresses by the system,defined as:

The phase function indicates the dephasing between the input signal and the output signal:

3.5.Other functions

The regulation timeTregobtained from the simple spectral density function defines the duration of the influence of the input signal and gives an indication of the length of the impulse response of the system (Larocque M et al.,1998):

The coherence functionCOxy(f) expresses the linearity of the input-output relationship and depends on the simple spectral functions and cross spectral density function [Sxy(f),S x(f) andSy(f)]:

When a change in the input signal creates a proportional change of the output signal,the system is linear withCOxy(f)≈1.

The gain functiongxy(f) expresses the amplification (>1)or attenuation (<1) of the output signal in comparison with the input signal:

4.Results

4.1.Characteristics of precipitation,spring water level and spring discharge

Fig.3 represents the temporal variations of precipitation,spring water level and spring discharge.The precipitation mostly increases from January to July and decreases from August to December.The average annual precipitation ranges from 423.5 mm to 878.9 mm in the year of 2012 to 2019,without significant inter-annual trend.

Fig.3.Time series of precipitation (a),spring water level (b) and discharge (c).

Influenced by precipitation,both the spring water level and discharge show seasonal variations.In comparison,the annual average and minimum water level of Baotu Spring are higher than that of Heihu Spring.However,the annual water level fluctuation of Heihu Spring is larger than that of Baotu Spring.These behaviors indicate the anisotropy of the aquifer structure and storage space in horizontal direction.The cumulative frequency analyses of water level time series have been performed to highlight that the hydrodynamic behavior of the karst system is different when water level exceed 28.5 m.This behavior characterizes the anisotropy of the aquifer structure and storage space in vertical direction.

4.2.Recession curve of karst spring hydrograph

A relatively long time of recession curve is selected for karst spring hydrograph recession analysis.The beginning time is the date of the highest spring discharge in wet season,and the end time is 31 December.When spring drains a cylindrical tank-reservoir,discharge decreases linearly with a constant slope of the discharge-time plot at any time (Fiorillo F,2014).Under this assumption,except the year of 2015,spring discharge decreases with rate varying from 0.272×103m3/d to 0.547×103m3/d withR2higher than 0.8 (Table 1).

In reality,the karst aquifer is not cylindrical and heterogeneous,the recession curves of spring hydrographs are different from one year to another due to the different hydrological conditions.There are five kinds of recession curves: (1) The recession curves of 2019 and 2020 are linearly decreasing with same recession coefficient of 0.002; (2) the recession curves of 2013,2014 and 2018 could be divided into 2 limbs with different slopes,the first limb decreases quickly,and the second limb decreases gently; (3) the recession curves of 2016 and 2017 could be divided into 3 limbs with different slopes,the first limb decreases quickly,the second limb has stable discharge,and the third limb decreases similarly with the first limb; (4) the recession curve of 2012 could also be divided into 3 limbs with different slopes,the first limb decreases gently,the second limb decreases quickly,and the third limb decreases with slope between the first limb and second limb; (5) the recession curve of 2015 could be divided into 4 limbs,the first limb decreases gently,the second limb decreases quickly,the third limb has stable discharge,and the fourth limb increases (Fig.4).Table 1 shows the recession coefficients range from 0.001 to 0.005,with mostly of 0.002.

Table 1.Results of recession curve analysis of Jinan karst spring system.

4.3.Auto-correlation analysis and simple spectral analysis

To understand characteristics of precipitation and spring water level,the auto-correlation functions of these variables are analyzed.For precipitation,a period of seven hydrological years (2012-2019) with 2741 daily readings,a step of 1 day and a truncation point of 910 days are used for long term auto-correlation analysis.The auto-correlation coefficients of precipitation in Jinan Station are very similar to those of precipitation in Zhangqiu Station (Fig.5a).This is due to the homogeneity in the climatic conditions of the study area.The auto-correlation coefficients of the precipitation decrease quickly,and reache the value of 0.2 within 2 days.This behavior indicates the daily precipitation appears fairly random,could be considered as white noise.

For spring water level,a period of eight hydrological years (2012-2020) with 3118 daily readings,a step of 1 day and a truncation point of 1040 days are used for long term auto-correlation analysis.The auto-correlation coefficients decrease slowly and evenly when the lag days increase (Fig.5a).In the case of Baotu Spring,the auto-correlation coefficient of water level reaches the value of 0.2 in 123 days,and a null value in 216 day.For Heihu Spring,the auto-correlation coefficient reaches the value of 0.2 in 117 days,and a null value in 197 day.This indicates that the Jinan karst aquifer has a large storage capacity which is emptied over a long period of time.

A period of one hydrological year,a step of 1 days and a truncation point of 120 days are considered for short term auto-correlation analysis.Similar with the long term autocorrelation analysis,auto-correlation coefficient of the precipitation in the short term auto-correlation analysis reaches the value of 0.2 immediately (Fig.5b).Opposed to precipitation,spring water level shows obvious differences between long term auto-correlation analysis and short term auto-correlation analysis.Averagely,the auto-correlation coefficient of spring water level in short term analysis reachesthe value of 0.2 in 53 days,and a null value in 68 days for both springs,less than the values in the long term autocorrelation analysis (Fig.5c).

Simple spectral density function determines how the variance is distributed over the different frequencies.The peaks at different frequencies lead to the identification of periodical phenomena.On the case of daily precipitation of 2012-2019,there are four obvious peaks in the frequency of 0.0032967,0.0054945,0.0087912 and 0.010989,indicating the annual and seasonal characteristics,respectively (Fig.6a).For the daily spring water level of 2012-2020,the largest peak at the frequency of 0.0028846 (347 days) confirms the presence of annual cycle.In addition,the peak at the frequency of 0.0009615 (1040 days) confirms the presence of multi-annual cycle,the peaks at the frequency of 0.0057692(173 days) and 0.0086538 (116 days) indicate the seasonal period.

For the period of every hydrological year,the precipitation spectrum is consistent with the results in long term analysis that no structure is distinguished: All the peaks remain very close to the background noise,and the amplitude is distributed homogeneously over the entire frequency range (Fig.6b).In contrast,spring water level shows distinct peaks,which confirm the presence of annual cycle (Fig.6c).

4.4.Cross correlation analysis and spectral analysis

Cross correlation functions are calculated to identify the relationship between the precipitation and spring water level.Similar with auto-correlation analysis,precipitation from May 2,2012 to October 31,2019 as input and spring water level in the same period as the output are used for long term analysis.The highest cross correlation coefficient is 0.15 in the lag of 56 days for both springs when using the precipitation in Jinan Station as input.The highest cross correlation coefficient is 0.13 in the lag of 57 days for both springs when using precipitation in Zhangqiu Station as input (Fig.7).

Fig.4.Recession curve of spring hydrograph in 2019 and 2020 (a),in 2013,2014 and 2018 (b),in 2016 and 2017 (c) and in 2012 and 2015 (d)Jinan spring system.

Fig.5.Auto-correlation functions of precipitation (2012-2019) and spring water level (2012-2020) with truncation point of 910 and 1040 (BTQ-Baotu Spring; HHQ-Heihu Spring; JNS-Jinan station;ZQS-Zhangqiu station).a-Auto-correlation functions of precipitation in Jinan Station for every hydrological years with truncation point of 120; b-auto-correlation functions of water level of Baotu Spring for every hydrological years with truncation point of 120 (c).

A period of one hydrological year,a step of 1 days and a truncation point of 120 days (the truncation points for the year of 2012 and 2019 are 80 days and 100 days,respectively) are considered for short term cross correlation analysis.The cross correlation functions for each hydrological year are different.A summary of the analysis results is presented in Table 2.The small correlation coefficients indicate that the precipitation signal is reduced significantly between the entry of the system and the time when it reaches the spring.

Table 2.The cross correlation coefficients under different input and output conditions.

Fig.8 presents that the cross amplitude functions tend to a null value for frequencies above 0.02 (periods of less than 50 days),indicating the small influences of the conduit flow in Jinan karst spring system.

5.Discussion

5.1.The memory effect and storage capacity of Jinan karst aquifer

Memory effect refers to the influence of the first event on the later events over a period of time,the time required for the system to “forget ” the initial conditions.From the hydrogeological point,the shape of the auto-correlogram gives information about the memory effect and the storage of the karst aquifer.The auto-correlogram shows slightly decreasing slope for karst aquifer with a strong memory effect,vice versa (Panagopoulos G and Lambrakis N,2006).Generally,lag time corresponding to the auto-correlation coefficient of 0.2 is used to reflect the memory effect of karst aquifer (Mangin A,1975; 1984; Padilla A and Pulido-Bosch A,1995).In this study,the auto-correlograms of water level for Baotu Spring and Heihu Spring have gentle slopes and fall slowly,reaching the value of 0.2 after 123 days and 117 days,respectively,for the year of 2012-2020.This indicates that Jinan karst spring system has a high memory effect.

Herman EK et al.(2009) found the memory effects are different when the length of the time series are different,and the memory effects are different for every hydrological year with different hydrological conditions.In this study,the memort effects range 34-82 days for one hydrological year.found the regulation time (Treg) were 14,23,50 and 70 days al.(1998) calculatedTregvalues of 76.4 and 72.9 days for

Fig.6.Simple spectrum density functions of precipitation(2012-2019) and spring water level (2012-2020) (BTQ-Baotu Spring; HHQ-Heihu Spring; JNS-Jinan station; ZQS-Zhangqiu station) (a) ; Simple spectrum density functions of precipitation in Jinan Station for every hydrological years (b); Simple spectrum density functions of water level of Baotu Spring for every hydrological years (c).

Fig.7.Cross correlation function between precipitation in Jinan station (a) and Zhangqiu station (b) with the spring water level for 2012-2019.(BTQ-Baotu Spring; HHQ-Heihu Spring).

The memory effect of the karst aquifer is related with the storage capacity which could be reflected by regulation time(Kovacic G,2010; Li JH et al.,2020).Mangin A (1984)for four karst aquifers in the French Pyrenees,the last one being considered having considerable storage; Larocque M et Foulpougne and Leche Spring in France with large storage capacity; Bouchaoua L et al.(2002) found the regulation time of Ain Asserdoune spring’s discharge was 76 days for a inertial karst system in Beni Mellal Atlas,Morocco.In comparison,the regulation time (Treg) of water level of Baotu Spring and Heihu Spring is 186.96 and 175.16 days,respectively,for the year of 2012-2020.For the single hydrological year,regulation time ranges from 40-59 days for both Baotu Spring and Heihu Spring.The above regulation time both for the long term time series and short term time series is long enough to reflect the high storage capacity of Jinan karst spring system.The high storage capacity could be explained by the presence of many small fissures,which do not directly contribute to the spring flow during the high water period,but store water and release later when the highly transmissivity fractures are unsaturated.

5.2.Delay between precipitation and spring water level in Jinan karst spring system

The spring water level and discharge show seasonal changes,while the relationship between daily,monthly or annual precipitation and spring water level is not obvious(Figs.9a-c).There is also no relationship or negative relationship between precipitation and recession coefficient(Fig.9d).In addition,the correlation coefficients based on the cross correlation analysis is small.All these behaviors indicate that the precipitation signal is reduced significantly,which could be reflected by the delay between recharge from precipitation and spring discharge.

The delay between precipitation and water level produces the observed and unexpected null or negative in lag day of 0.The delay time can be defined as the lag day for the maximum cross correlation coefficient.According to this criterion,the delay time between precipitation and spring water level varies among 30-79 days for single hydrological year and around 57 days for the period of 2012-2019 in Jinan karst spring system.

The phase function can be used complementarily to the cross correlation analysis in term of calculating the mean delay time,concerning different frequencies.According to Padilla A and Pulido-Bosch A (1995),the mean delay can be obtained by the slope of the line of best fit to: θxy(f)=2πd f.The phase functions for Jinan karst spring system are very distorted and incoherent for all frequency bands (Fig.8d),making it impossible to calculate the mean delay time by above functions.

In comparison,the delay time between precipitation and spring water level has time scale effect for Jinan karst spring system.The delay time between spring water level and precipitation event is less than 5 days (Chi GY et al.,2017);the delay time between groundwater level and monthly precipitation is 73-134 days (Qi XF et al.,2012).In addition,the delay time of spring water level to precipitation is 45 day for the period of 2008-2012 and 90 day for the period of 2006-2008 (Wang JL et al.,2016).The distance between precipitation station and spring vent is also an important factor influencing the delay time.In this study,the Jinan Station is located in the indirect recharge area,which is much further than the station used by Chi GY et al.(2017).

Fig.8.Variations of cross amplitudes (a),gain functions (b),coherence functions (c) and phase functions (b) at different frequency in Jinan karst spring system.(JNS-BTQ indicates JNS is input and BTQ is output,the rest are similar (BTQ-Baotu Spring; HHQ-Heihu Spring; JNS-Jinan station; ZQS-Zhangqiu station).

Besides,this study finds the delay time is negative related to annual precipitation,which is also observed in the study of Qi XF et al.(2016) (Fig.10).This may be due to that the water level is higher during the wet year,flooding some highly karstification fractures,which transmit the pressure pulse more rapidly and directly to the output.During the dry year,these channels are unsaturated and the pressure pulse is transmitted more slowly and homogeneously in the saturated zone through deeper and narrower fractures.

5.3.Flow components of Jinan karst spring system

In this part,flow components of Jinan karst spring system are discussed in term of recession curve analysis,coherence function and gain function.Firstly,it is only in rare situations to obtain a recession curve with one recession coefficient in karst aquifer (Bonacci O,1993).More frequently,several distinct slopes are found to fit the recession curve of spring hydrographs (Chang Y et al.,2016).For example,a slope with the highest recession coefficient representing the conduit flow,a slope with least recession coefficient representing the base flow,and a slope indicating the mixing between conduit flow and base flow (Mohammadi Z and Shoja A,2014; Adji TN and Bahtiar IY,2016).For Jinan karst spring system,the recession curves of spring hydrographs are different for every hydrological year with different slopes ranging from one to four.In general,except the second slope in the year of 2012 and 2015,all the slopes have little recession coefficient.The recession coefficients are higher than the results of Xing LT et al.(2017),one reason is discharge is used instead of water level in this study,and another reason is the recession curve dates are different.However,these values are lower than that of karst springs in southern China (Zhao LJ et al.,2015),indicating the fissure flow or base flow dominants in Jinan karst aquifer.

Fig.9.Relationship between daily precipitation with spring water level (a),monthly precipitation with spring water level (b),annual precipitation with spring water level (c),precipitation with recession coefficient (d) (P2,P3,P4,P5 corresponding to the values of Table 1).

Fig.10.Relationship between precipitation and delay time (The dalay time between precipitation in Jinan Station and water level of Baotu Spring (a); The delay time between precipitation in Zhangqiu Station and water level of Heihu Spring (b)).

Secondly,aquifer with substantial conduit flow presents high coherence even at high frequencies (Padilla A and Pulido-Bosch A,1995).In Jinan karst spring system,the coherence function decreases to a null value for frequencies over 0.1 and the average coherence function is very low (Fig.8c),indicating the limited conduit flow in Jinan karst aquifer.

Thirdly,according to the criterion of Padilla A and Pulido-Bosch A (1995),the gain function with value over 1 is due to the base flow component,value of less than 0.4 is due to the conduit flow component,and value between 0.4 and 1 is due to the mixture flow or intermediate flow.For Jinan karst spring system,the gain functions show greater attenuation of the input signal at lower frequencies (Fig.8b).In the case of using precipitation in Jinan Station as input,the value 0.4 occurs at the frequency of around 0.017525 for Baotu Spring and Heihu Spring,corresponding to a period of 57 days,which cannot be considered as conduit flow due to its long duration.And the base flow duration,reflected by the frequency of about 0.009858 for Baotu Spring and Heihu Spring,is 101 days,indicates the dominant of base flow in Jinan karst aquifer.Same results could be conducted in the case of using precipitation in Zhangqiu Station.

The results of early tracer test proved the flow rate ranged from 42-192 m/d in Jinan karst aquifer,indicating the highly connected of karst conduits and high degree karstification(Xing LT et al.,2017),which is different with above results.This is due to the results of trace test is just applicative in limited and specific region,while the results of this study is the response of spring to the whole spring region,and in fact the catchment of Jinan karst spring system is quite large.Based on the results from hydrograph recession analysis,correlation and spectral analysis,the karst aquifer in Jinan karst spring system can be considered as equivalent porous media,fissure flow dominants for the whole system even though there is conduit flow in local area,and groundwater flow follows the law of Darcy.

5.4.Karstification characteristics of Jinan karst spring system

Karst system presents different levels of karstification,from the initial state of a poorly drained aquifer with large storage and final state of a well-developed and connected karst network,without storage capacity,which quickly drains the aquifer (Atkinson TC,1977).Mangin A (1984) used four parameters (memory effect,spectral band breadth,regulation time and transfer function) obtained from the correlation and spectral analysis to classify karst systems into four types,ranging from well drained systems to poorly drained system.In the section of “The memory effect and storage capacity of Jinan karst aquifer”,memory effect and regulation time of Jinan karst aquifer have already been discussed,and Jinan karst aquifer has strong memory effect and high storage capacity.In this part,we mainly discuss the spectral band breadth and transfer function.

Spectral band breadth is the dominant frequency.Beyond this frequency,the spectrum can be considered as a white noise (Jeannin PY and Sauter M,1998).A poorly developed karst system with high storage capacity attenuates the short term (high frequencies) input signals,the signals at low frequencies are correspondingly enhanced.Pulido-Bosch A et al.(1995) found the cross amplitude function remained at about unity even at the highest frequencies for karst system with quick flow dominites.Jinan karst spring system has a small spectral band,the considerable variance exists only at the range of low frequencies,namely lower than 0.02 (more than 50 days),indicating the noticeable regulation effect,the greater inertia of the system and the absence of the quick flow component.

As the precipitation is assumed to be random based on the auto-correlation function,the transfer function of Jinan karst spring system is equal to the cross correlation function.In this study,the transfer function is quite homogeneous and smooth,corresponding to response time of around 100 days and the mean delay time of more than one month for every single hydrological year.Usually,the shorter the delay time,the faster the transfer.Therefore,Jinan karst spring system has a slow reactivity in response to precipitation with non-linear behavior,which means the water level variations are not strongly controlled by the sinkhole-spring system,but rather by the overall aquifer dynamics.

Therefore,based on the criterion of Mangin (1984),Jinan karst spring system belong to the fourth type with strong memory effect,short spectra lengths,flat transformation function and long regulation time and delay time.This is easily understandable considering the hydrogeological condition of karst aquifer in northern China,where the aquifer medium is mainly composed by small fissure,and the movement of groundwater flow in aquifer basically obeys Darcy’s law.In Jinan karst spring system,the karst aquifers are deeply buried under the Quaternary sediments,the huge storage capacity of Cambrian-Ordovician limestone makes the Jinan karst aquifer has strong memory effect.Precipitation recharges groundwater after passing through soil layer and Quaternary sediments mainly in the form of piston,soil layer and sediments filter the information contained in the precipitation,therefore,there is long regulation time and delay time between precipitation and spring discharge.

6.Conclusion

This study applies the correlation analysis in time and spectral analysis in frequency combined with the spring hydrograph recession analysis on two famous karst springs(Baotu Spring and Heihu Spring) to provide information for the hydrodynamic characteristics of Jinan karst spring system,a typical karst system in northern China.The autocorrelogram of water level of Baotu Spring and Heihu Spring in 2012-2020 is uniform with gentle slope.The memory effect of Jinan karst aquifer is more than 100 days,indicating the large storage capacity and great inertia of Jinan karst spring system.The cross correlation analysis between precipitation and spring water level shows long impulsion responses,the delay time is around 56 days for 2012-2019 and 30-79 days for single hydrological year.In addition,the recession coefficients,coherence functions and gain functions indicate the dominance of fissure flow in Jinan karst aquifer and the poorly developed karstification of Jinan karst spring system.In a word,the correlation and spectral analysis can contribute to study the hydrodynamic characteristics of karst system in northern China.

Acknowledgment

The authors would like to acknowledge three reviewers for their constructive comments,which greatly helped to increase the quality of the paper.This study is supported by the geological survey project: National Glacier and Desertification Remote Sensing Geological Survey(DD20190515) and Youth Innovation Fund of China Aero Geophysical Prospecting and Remote Sensing Center for Natural Resources (2020YFL18).

CRediT authorship contribution statement

Feng Wang and Da-jun Qin conceived of the presented idea.Yi Guo,Zhan-feng Zhao,Fu-ping Gan,Bai-kun Yan and Juan Bai wrote the manuscript in consultation.Muhammed Haji polished the language.All authors discussed the results and contributed to the final manuscript.

Declaration of competing interest

The authors declare no conflicts of interest.