Using time series analysis to assess tidal effect on coastal groundwater level in Southern Laizhou Bay,China

She-ming Chen,Hong-wei Liu,Fu-tian Liu,Jin-jie Miao,Xu Guo,Zhou Zhang,Wan-jun Jiang

Tianjin Center of China Geological Survey, Ministry of Natural Resources, Tianjin 300170, China.

Abstract: Sea water intrusion is an environmental problem cause by the irrational exploitation of coastal groundwater resources and has attracted the attention of many coastal countries.In this study,we used time series monitoring data of groundwater levels and tidal waves to analyze the influence of tide flow on groundwater dynamics in the southern Laizhou Bay.The auto-correlation and cross-correlation coefficients between groundwater level and tidal wave level were calculated specifically to measure the boundary conditions along the coastline.In addition,spectrum analysis was employed to assess the periodicity and hysteresis of various tide and groundwater level fluctuations.The results of time series analysis show that groundwater level fluctuation is noticeably influenced by tides,but the influence is limited to a certain distance and cannot reach the saltwater-freshwater interface in the southern Laizhou Bay.There are three main periodic components of groundwater level in tidal effect range (i.e.23.804 h,12.500 h and 12.046 h),the pattern of which is the same as the tides.The affected groundwater level fluctuations lag behind the tides.The dynamic analysis of groundwater indicates that the coastal aquifer has a hydraulic connection with seawater but not in a direct way.Owing to the existence of the groundwater mound between the salty groundwater (brine) and fresh groundwater,the maximum influencing distance of the tide on the groundwater is 8.85 km.Considering that the fresh-saline groundwater interface is about 30 km away from the coastline,modern seawater has a limited contribution to sea-salt water intrusion in Laizhou Bay.The results of this study are expected to provide a reference for the study on sea water intrusion.

Keywords: Groundwater;Time series analysis;Correlation;Spectral analysis;Sea-salt water intrusion

I ntroduction

As the impact of global climate change and human activities on the environment is increasingly significant,sea and land interaction research has become a hot issue in the field of current geological research (Sawyer et al.2016;Jurasinski et al.2018;Purwoarminta et al.2018;Seibert et al.2020).In the interaction area between sea and continent,the problem of sea water intrusion has caused great losses to many coastal countries.Based on the achievements of previous research(Shi and Jiao,2014;Zeng et al.2017;Manivannan and Elango,2019),sea water intrusion is a complex groundwater-seawater interaction process which is influenced by densities of seawater and groundwater,geological structure,evapotranspiration,precipitation,regional topography,while the inland extent of intrusion is normally proportional to the abstraction and corresponding decline in groundwater level.Tidal dynamics is an integral component of coastal hydrology,for which a lot of studies have been conducted for years with focus on periodic effect of tidal pressure on groundwater level in coastal aquifers.The degree of hydraulic connection between groundwater of coastal aquifer and seawater can be studied by time series analysis of coastal groundwater dynamics and tidal fluctuation (Rama et al.2018;Shirahata et al.2022).

Recently,many researchers have used time series analysis interpret the characteristics of hydrogeological processes because the time series data provide useful information about patterns of temporal variations of hydrologic processes and impulse response characteristics of the aquifer system (Lo Russo et al.2015;Heudorfer et al.2019).Keshavarzi et al.(2017),Sánchez et al.(2015),and Schuler et al.(2018) studied groundwater dynamics in karst aquifers.Kopsiaftis et al.(2019) and Rajaveni et al.(2021) developed a variable-density groundwater model to analyze the effects of tidal dynamics on sea-salt water intrusion in an unconfined aquifer.Balacco et al.(2022)and Pastore et al.(2020) used time-series to study the effect of rainfall on groundwater in coastal aquifers.Zhang et al.(2017) monitored and analyzed Muri lagoon (21°15'S,159°44'W) on the American east coast of Rarotonga,Cook Islands,where the groundwater levels typically change with the tidal level cycle.Zhang et al.(2020) analyzed the changing characteristics of groundwater level and conductivity with the tidal level in the coastal area.Auto-correlation analysis and crosscorrelation analysis are important methods to describe the sequence of adjacent data and the degree between two sequences in time series analysis,which are widely used in the field of hydrology(Lo Russo et al.2015;Shi et al.2018;Sivelle and Jourde,2021).Spectral analysis is a significant method for analyzing time series with periodic changes,which decomposes the complex components (waveform) into a simple component (waveform) and then identifies the inherent nature of the sequence.Kim et al.(2005) have made great achievements by using mutual correlation analysis and spectral analysis methods to analyze the change of coastal groundwater level and conductivity with the tidal level.

The southern coast of Laizhou Bay is one of the regions where the sea water intrusion problem is severe.Since the discovery of sea water intrusion during the 1970s,the intrusion rate has increased year by year.Until 2014,the seawater has invaded an area of 2 484 km2,and the longest distance between the coastline and the fresh-saline groundwater interface is close to 30 km (Su et al.2018).According to the source of intrusion,the generalized seawater intrusion can be divided into two basic types: The narrow seawater intrusion from modern seawater and the salt water intrusion from the middle ancient seawater (including general underground salt water and brine) in the shallow Quaternary sedimentary layer (Hu et al.2015).On southern coast of the Laizhou Bay,underground saltwater (brine) is distributed between seawater and underground fresh water.Previous studies have found that there are both seawater intrusion and saltwater intrusion in this area,which has been named sea-salt water intrusion (Hu et al.2015;Su et al.2018).However,no scientific consensus has been established in respect of the impact of modern seawater on the sea-salt water intrusion.In addition,the Laizhou Bay coast consist of muddy clay with low permeability and high degree of uncertainty in its hydraulic connections with different aquifers.It is hence important to study the relationship between the tidal level and groundwater level,which is the basis for determining the boundary of the seawater in the coastal groundwater system and understanding the contribution of modern seawater to the intrusion areas.

Therefore,this study mainly focused on the impact of modern seawater on the sea-salt intrusion boundary in the muddy coastal zone of the Laizhou Bay,via auto-correlation and cross-correlation analyses to determine the groundwater dynamic correlation coefficient with the tidal level and then to confirm the degree and extent of the coastal aquifers that are affected by the seawater intrusion.The spectral analytical method was used to analyse the relationship between the complex groundwater level fluctuation and tidal level,from which simple characteristics of the fluctuation such as the hydrographic cycle and lag were figured out.Finally,the boundary conditions of the coastal groundwater system were determined.The results can provide theoretical support for the prevention and treatment of sea-salt water intrusion,and for the development of a comprehensive reference for rational use of the water resources.

1 Study area

The study area,located on the southern coast of Laizhou Bay in the northwest of Shandong Peninsula,is within the Changyi City,Shandong Province (Fig.1).From alluvial plain in the south to coastal plain in the north,the landforms change from narrow banded alluvial-marine plain to marine plain.The terrain gently dips to the north,with a slope of 1/3 000.There are several rivers flow through the area,including the Weihe,Bailang and Mi rivers.The coastal deposit as silty clay is heavily affected by the sediments transported by the Weihe river.It is typical in the northern China that the coastline is composed of silty clay.The tides and irregular occur in a semidiurnal way,with an average tidal level of 171.7 cm.

Fig.1 Locations of the study area and the monitoring wells C01,C02 and C03

In Laizhou Bay,sedimentary layers driven by sea and land interaction are extensively distributed on the surface,with lithology of the sediments of mainly clayey sand and sandy clay.The thickness of surficial layers range from 3 meters to 5 meters and their permeability is relatively low.The underlying layers are characterized by yellowish brown silty sands,containing small shell fragments.In terms of aquifer composition,the area is dominated by alluvial mid-to coarsegrained sands and alluvial-marine fine-grained sands,clayey silt and silty clay deposited in the Quaternary period (Gao et al.2020).From the south to the north,the thickness of the aquifers gradually increases,while the aquifer grain size gradually decreases,and the aquifer changes from single-layered aquifer to multiple-layered one.

The shallow groundwater in the study area has the conditions of good flow path and strong chemical alternation;the hydrochemical field has an obvious zoning characteristic over the plain.From the areas of inland to the coast,of the groundwater appears as fresh water,via brackish water,to salt water and brine,with its TDS changing from 0.27 g/L to 207.76 g/L.

In this study,brackish water and salt water are collectively referred to as salt water.The distribution of underground brine is basically parallel to the coastline,with a width of 15-25 km and a maximum brine floor depth of about 60-70 m.The brine has been extracted as a resource for salt production and shrimp farming,forming a depression cone of the brine groundwater;and groundwater level in the central area of depression cone is about -20 m,locally less than -30 m.The fresh groundwater in the south has also been extensively exploited,resulting in the water level in the center of depression cone of about -10 m to-15 m.The fresh groundwater has been used for greenhouse irrigation and domestic water supplies.There is almost no exploitation of salt water located between the brine and the fresh groundwater;as a result,a shallow groundwater mound has formed in the salt water where the fresh-saline groundwater interface is located.

2 Materials and methods

2.1 Data selection

To analyze the impacts of tidal fluctuation on water level in the coastal aquifer,three monitoring wells (C01,C02,and C03) were selected from which observed data can be obtained (Fig.1),then the groundwater level dynamic curve was plotted(Fig.2).To facilitate the analysis and comparison,the levels of C02 and C03 were shifted up 15 m and 12 m,respectively.Among them,monitoring well C01 has a TDS of 23.05 g/L and an average water level in February of -4.5 m;monitoring well C02 has a TDS of 2.49 g/L and an average water level in February of -16.39 m.Moreover,the both wells are located in the sea-salt water intrusion area.Monitoring well C03 located 1 km to the south of the intrusion line has a TDS of 1.59 g/L and an average water level in February of -19.09 m.The data of the three monitoring wells were acquired with the CTD-Diver data loggers at the time from 00:00:00 1st February 2013 to 12:00:00 28th February 2013,at a monitoring frequency of once an hour.The number of data from a single monitoring well was 672.Tidal data were acquired from the tidal station in Weifang port at a monitoring frequency of once an hour.

Fig.2 Temporal variations of groundwater level in monitoring wells C01,C02 and C03,and tidal level in Weifang station from February 1 to February 28,2013.(C03-12 m means the water level in the figure minus 12 m,which is the actual water level,and the other relevant symbols have the same meaning.)

2.2 Methods

2.2.1 Auto-correlation

The auto-correlation function describes the relation degree of a random time sequence between the values in any two different time series.Through auto-correlation analysis,we can get a dependent quantitative test of specific events in a given time period.Performing an auto-correlation analysis yields a quantitative measurement of linear dependency of certain process values over a given time range (Kleiner,1977).The calculation process based on the auto-correlation function is as follows:

Where:kis the time delay (k=0 tom),nis the number of time-series measurements,xtis the value of the process,is the mean of the process,andmis the cutting point.The cutting point determines the analysis interval and is usually chosen accordingly to the fundamental components of a given process behavior such as annual or longterm effects.

2.2.2 Cross-correlation

Cross-correlation describes the relationship between the two sequences to reveal the influencing degree of a sequence on another sequence.It shows a lag relationship of the later sequence to the previous sequence (Tran et al.2014).The calculation steps of cross-correlation are as follows:

Where:Cxy(k) is the cross-correlogram.σxand σyare the standard deviations of thexandytime series,respectively.

2.2.3 Spectral analysis

The mathematical model for performing a spectral analysis is on the basis of Fourier transform.The Fourier transform for the time series data calculates the power spectrum and then derives the power spectrum diagram in the frequency domain and the lag domain in order to get a periodicity of the time series (Zhou et al.2006).The maximum of the frequency spectrum is called the “peak”.“Peak” frequency is the most concentrated frequency of wave energy.The cycle of the “ peak”frequency corresponds to the main cycle of the fluctuation.The equations are as follows:

Where:Xi(i=1,2,…,N) is the measured data series andNis the number of the series dates,Xis the time series mean value,F(x) is the Fourier transform of the time series,andshows to take the conjugate toF(ω).S(ω) is the energy spectrum of time series.P(f) is the power spectrum of the data series.Based on the calculation principle of power spectrum,the spectrogram based on the calculation results of frequency against power spectrum can be plot via MATLAB programming.Then we can find out the frequency whose frequency component is major in the power spectrum.The reciprocal of the frequency is the required cycle (Duvert et al.2015) .

3 Results and discussions

3.1 Trend analysis and dynamic characteristics of groundwater level

This study chose six-order polynomial to carry out trend analysis,and the fitting results are shown in Fig.3.The decision coefficients of the trendline for wells C01,C02,and C03 are 0.609,0.977,and 0.703,respectively.According to the results of the trend analysis,the groundwater level in well C01 increased from February 1stto 5thand from February 27thto 28thand fell for the rest of the monitoring time,while the groundwater level of the wells C02 and C03 rose from February 1 to 16 and fell after February 16,with the decreasing rate of C02 much higher than that of C03.As suggested by the daily rainfall and groundwater levels,the precipitation infiltration is the main factor to the groundwater level rise,but the water level fluctuations of monitoring wells are all lagged behind the precipitation.There is not a close correlation between daily evaporation intensity and groundwater level change because the groundwater level is much deeper than the threshold of water table depth.Owing to the lack of daily production data,correlation between the exploitation quantity and water level cannot be exactly analyzed.However,according to the annual exploitation quantity data of the study area,it can be confirmed that exploitation is the main mode of groundwater discharge and the main factor that affects the drop of groundwater level in the study area.

Fig.3 Groundwater level trend line and daily rainfall and evaporation intensity of monitoring wells

From the well hydrographs,it can be seen that groundwater level fluctuation of the well C01 is much stronger than those of the wells C02 and C03.In order to observe the fluctuation range of different monitoring wells,the groundwater level data on February 19 were selected randomly for the analysis (Fig.2).The amplitude of fluctuation between the highest and lowest groundwater level is recorded asD.The value ofD1of the C01 is 40 cm,and there are two peaks and a valley in one day.The value ofD2of the C02 is 3 cm,and there are multiple peaks and multiple valleys.The value ofD3of the C03 is 2 cm,and there are multiple peaks and multiple valleys in one day.The amplitude of fluctuation between the highest and lowest tidal level is recorded asTand the value ofTwas 157 cm on February 19.There are two peaks and a valley on that day.The number of peaks and valleys between monitoring well C01 and tide are consistent,indirectly showing that the groundwater level is influenced by the tides.To amply depict the degree of the tidal effect on groundwater level,the tidal coefficient is introduced (Foster and Brown,2015),which is the ratio of groundwater amplitude to tide amplitude,recorded asD/T.According to previous study results,if groundwater level fluctuation of well C01 is completely caused by tides,the tidal coefficient of the well is 0.255.Groundwater level amplitudes of wells C02 and C03 are smaller than that of C01,and there are multiple peaks and valleys.It is speculated that the fluctuation change was mainly affected by air pressure changes.

3.2 Auto-correlation and cross-correlation analyses

As shown in Fig.4,the auto-correlation coefficient of tidal water level changes with an increase in the lag time,with the oscillations occurring around a horizontal line.There are two sine waves in one day.The auto-correlation function of all periodic signals can obtain a certain value domain or fluctuate around a certain value.As a result,the tidal levels obviously occur in a periodic way and have a clear auto-correlation nature.In addition,the tidal level auto-correlation coefficient does not decay with lag time.The coefficient gradually reduces to 0 with the increase in the delay time for the three monitoring wells.Among them,the lag times are 204.0 h,206.4 h,and 158.4 h for C01,C02,and C03,respectively,when the auto-correlation coefficient decreases to 0.The auto-correlation coefficient value of well C01 show obvious fluctuations with the delay time,and there are two sine modes in one day,which is consistent with the changes of tide levels.This finding indicates that there is a strong linear correlation between the groundwater levels of the C01 and the tidal levels;both are subjected to cyclical variation in the source.The auto-correlation coefficient of the C02 changes little,while that of the C03 tends to be a straight line,suggesting a week correlation between the groundwater level of both wells and the tidal level (Larocque et al.1998).

Fig.4 Auto-correlation coefficient of tidal level and groundwater level in monitoring wells

Cross-correlation analysis was conducted to determine the correlation between groundwater levels in different monitoring wells and the tidal levels (Grose et al.2015).Calculation results are shown in Fig.5,which shows that the monitoring well C01 peaked at 4 h,with a cross-correlation coefficient of 0.35;C02 peaked at 0.2 h,and C03 tended to be linear.Among them,the cross-correlation coefficient values of the monitoring wells C01 and C02 presents an obviously sinusoidal oscillation,except that the amplitude of the C02 is much smaller.The periodic change of C01 is consistent with that of the tide with two peaks and valleys in one day.This result further proves that groundwater levels in the C01 are highly correlated with the tidal levels,as the groundwater fluctuation is controlled by the tides.The groundwater levels of the C02 and C03 are not correlated with the tides,and their cross-correlation coefficients tend to be 0.According to the result of cross-correlation analysis with data derived from well C01 and tidal waves,the phase difference of the C01 is 4 h.

Fig.5 Cross-correlation functions of tidal level and groundwater level in monitoring wells

3.3 Spectral density

As shown in the calculation results (Fig.6),the fluctuation of the tidal level has four periods of tide fluctuation,namely 25.571 h,23.821 h,12.487 h,and 11.910 h.Owing to the short time data series,the long period cannot be reflected.According to tide equilibrium theory,the tides are caused by the superposition of different-frequency fluctuations due to the moon,the sun,and other celestial bodies.The Each frequency fluctuation corresponds to a number of constituents,and each constituent corresponds to the simple harmonic motion of seawater caused by a hypothetical object along a certain path,doing uniform motion around the earth at a certain angular rate (Fu et al.2008).The tidal constituent of O1 is “Main lunar diurnal tide”,the tidal constituent of K1 is “Lunar solar declination day constituent”,the tidal constituent of M2 is“Main lunar semidiurnal tide”,and the tidal constituent of S2 is “Main solar semidiurnal tide”.Among them,the O1 and K1 are full-time constituents,while the M2 and S2 are semidiurnal constituents.The four periods of tide correspond to the constituents O1,K1,M2,and S2.

Fig.6 Spectral density functions of tidal level and groundwater level in monitoring wells

The monitoring well C01 has multicycle characteristics of water level fluctuation,whereas no prominent period occurs in the wells C02 and C03.The periods of C01 are 23.804 h,12.500 h,12.046 h,5.990 h,4.807 h,3.985 h,and 3.425 h.Among them,the first three periods are more prominent than the other two,which respectively correspond to the constituents K1,M2,and S2.This result also shows that the fluctuation of groundwater level is evidently controlled by the tides.The spectral density curve of the monitoring well C02 is smooth,with no apparent peak appeared.The curve of the monitoring well C03 indicates the presence of water level fluctuations,and this curve appears to be smooth with no apparent peak either.It is speculated that the groundwater level fluctuations of the wells C02 and C03 are mainly influenced by atmospheric pressure changes.Therefore,the comparison of periodic components shows that the groundwater level of the monitoring well C01 is heavily affected by the tide flows,which has an obvious correlation with the seawater.

3.4 The influence of tide on coastal groundwater

As discussed above,three main mechanisms cause the tide-induced groundwater level fluctuations in the coastal area.Firstly,the unconfined aquifers connect the sea and the aquifer permeability is high.Secondly,as the tidal level changes,the surface mass loading affected by the underlying confined aquifers changes consequently,so that the hydraulic head in confined aquifers changes with the tides.Finally,the offshore shallow groundwater has a hydraulic connection with the tides,though it does not directly connect with the seawater (Buscombe et al.2014).Through the overlying aquifer,the pressure caused by the tide backwater or compression causes the shallow groundwater to fluctuate.According to the previous analysis,the water level of the monitoring well C01 was influenced the most significantly by tides.The groundwater in the C01 is phreatic water,whose water level is lower than the sea level.The average depth of seawater within 20 km along the coastline is 9.1 m,and the aquifer with the C01 consists of a low-permeability layer with clayey fine sand and fine-grained sandy clay.Therefore,the reason that the tides influence the groundwater level of monitoring well C01 is the third one.The offshore aquifer has a hydraulic connection with seawater,which is under the action of weakly permeable layers and the phreatic water does not directly connect with seawater.Tidal fluctuations can cause the fluctuation of the groundwater level through pressure conduction.Therefore,the coastline is not a given head boundary of a coastal groundwater system but should be generalized as a flow boundary.The flow rate is related to the lithology and hydraulic gradient of the tidal zone.

According to a previous study (Fadili et al.2016),the amplitude of coastal groundwater level fluctuation caused by the tides decreases with the increase in the distance from the coast under normal conditions and generally shows a negative exponent attenuation.In other words,the tidal coefficient and distance from the coast are negatively correlated.

Where:yis the tidal coefficient;xis the distance from the coast;Ais the undetermined parameter.The related data of C01 are calculated based on Equation (9),and the result isA=0.000 238 6.

Assuming that the tidal effect can be ignored if the fluctuation of water level induced by tides is less than 1 cm,the maximum influencing distance is 21.12 km using Equation (9).Apparently,the C01 is in the range of tidal effect,whereas groundwater in the C02 and C03 is out of the influencing range.

To further verify the possible distance of the tidal effect,the hydrogeological profile of the coastal groundwater systems with the monitoring wells is used for overall analysis (Fig.7).Fig.7 shows that there are two groundwater depression cones (funnels) where the well C01 is located in the depression area of salty or brine water.The wells C03 and C02 lie in the freshwater area,where a freshwater funnel has formed since a large amount of groundwater was pumped for irrigation.

Fig.7 Hydrogeological profile of the coastal groundwater system

The shallow groundwater between the two funnels is salt water which cannot be used for irrigation purpose or sea salt production or sea cultivation (Cao et al.2022).The water level is relatively high and forms a groundwater mound in the middle area.Because of the existence of the watershed,the conduction of tidal pressure is further influenced by the hydraulic pressure of the groundwater mound.According to the analysis of the groundwater dynamic field,it is believed that the range of tidal effect has reached the central area of the brine groundwater.As shown in the profile,the brine funnel center is 8.85 km from the coastline,which is also the maximum distance of the tidal effect.

Through the analysis of groundwater flow characteristics on the profile (Fig.7),owing to the existence of the brine funnel,the modern seawater mainly infiltrated through the aquiclude to the lower Paleozoic saltwater brine,and then most of the infiltrated modern seawater departed from underground aquifer with the saltwater (brine)extraction.Based on the above analyses,and considering that the source of the underground salt water (brine) or modern seawater is the sea-salt water intrusion,it is can be speculated that the movement of fresh-saline groundwater interface was mainly affected by the south invasion or north retreat of the salt water in watershed,and the modern seawater infiltration made little contribution to the movement of sea-salt water intrusion surface in the study area.

4 Conclusions

(1) As indicated by the dynamic analysis of the groundwater level,the most significant fluctuations occurred in monitoring well C01,while small fluctuations in monitoring wells C02 and C03.The fluctuation pattern of C01 (number of peaks and valleys) was the same as tides with the largest tidal coefficient.The groundwater level in the study area is closely related to rainfall and groundwater exploitation based on the trend analysis.

(2) According to the result of the auto-correlation and cross-correlation analysis,the tidal level has conspicuous periodicity and auto-correlation.There was a strong linear correlation between the groundwater level of monitoring well C01 and the tidal level,both of which were subjected to the same source with periodic changes.The analysis results show that there is no correlation between groundwater levels and tidal level of the other two monitoring wells (C02 and C03) .These results prove that the groundwater level in coastal aquifers is affected by tidal level at a limited distance,which does not exceed the distance of C02 monitoring well.The maximum distance of the tidal effect to groundwater level is 8.85 km.

(3) The offshore aquifer has a hydraulic connection with seawater but does not directly connect it under the action of aquitards.Groundwater level fluctuates due to pressure conduction from tides.Therefore,the coastline can be generalized into the flow boundary for coastal aquifers.Controlled by the existence of the groundwater divide between freshwater funnel and saltwater (brine) funnel,the modern seawater infiltration contributes little to the movement of sea-salt water intrusion surface in the study area.

Acknowledgements

This study was mainly funded by the “Investigation and Evaluation of Geologic Environment for Laizhou Bay” of the China Geological Survey project (12120113003800).The groundwater level monitoring data in the paper was provided by the project.At the same time,the study was financially supported by National Natural Science Foundation of China (No.42102298) and the program of China Geology Survey (No.DD20221759).