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Seawater intrusion is a global environmental problem that is becoming increasingly severe with the overexploitation of underground freshwater in coastal regions and sea-level rise caused by global climate change. Although a series of achievements has been made on seawater intrusion, the role of tidal effects has not been fully revealed. In this paper, a typical case of tidal effects on seawater intrusion is provided. The high-density resistivity method was applied to the high-frequency continuous measurement of the stratigraphic resistance of the south coast of the Laizhou Bay, followed by the panel data analysis method. The results indicate that the formation resistivity in coastal area was affected by the tidal level significantly, particularly in the seawater intrusion channel. The effect of tide on the intensity distribution of formation resistivity was evaluated using this method. Because of the presence of a brine layer in the section, the trends of the tidal level effect on the formation resistivity in the left and right sides of the section were opposite, and the intensity of the effect increased sideways.

On a global scale, the economy in coastal regions is booming; therefore, the water consumption is increasing. The overexploitation of groundwater in these areas is common. A hydraulic connection exists between the groundwater and seawater; therefore, the balance between the groundwater and seawater in coastal regions would be destroyed because of natural factors and overexploitation [

With increasing exploitation of fresh groundwater resources and sea-level rise due to the global climate change, seawater intrusion has become increasingly severe. Studies on seawater intrusion have been carried out since the late 19^{th} Century. However, most of the studies are based on the assumption of a static sea level, without considering the effect of tidal waves [

In fact, tidal fluctuation is an important driving force for the groundwater flow in coastal areas. Several studies on the effect of tidal fluctuations on ground- water have been conducted since the 1950s [

Seawater intrusion has been investigated using hydrographic survey, environmental isotopes, and geophysical methods [

In this study, a case of seawater intrusion in the southern coastal plain of Laizhou Bay, Shandong, China was investigated. The mechanism of seawater intrusion, numerical analysis of underground water, structure of brine, and prevention of seawater intrusion in this region were mainly studied [

The south bank of the Laizhou Bay coastal area (

China, was formed by the alluviation of the rivers in the mountainous region in the central part of Shandong province. The terrain in this area is flat and slightly inclined to the north, with an altitude of 2 - 7 m. Alluvial and proluvial plains are present in the south and north, respectively. The quaternary sediments are mainly piedmont alluvial and coastal sediments, with an aggregate thickness of 500 m. Since the late Pleistocene epoch, the area was long in the process of settlement activities. Zhang et al. divided the marine and continental strata in the late Pleistocene and Holocene epochs, identified three times seawater intrusion, and found that the multilevel underground brine was formed during seawater intrusion and regression [^{2}, with a general mineralization degree of 50 - 150 g/L (the highest mineralization degree is up to 217 g/L). The general burial depth is 0 - 60 m, and the value reaches to 70 - 80 m in some area. There are 3 - 4 brine layers including diving underground brine and confined underground brine areas [

The Changyi marine special reserve is located in the north of Changyi City, Shandong Province, with a total area of 29.29 km^{2}. The wetland ecological system including tamarix chinensis and marine organisms are protected in this area. Compared to the other regions in the south bank of Laizhou Bay, the primitive natural environment in the Changyi marine special reserve are preserved relatively completely because the effect of human activities is relatively small. Considering that the effect of tidal wave on coastal groundwater is very weak, the effect of human activity was excluded in the earlier study. Human activity will be taken into account in the follow-up study.

A high-density resistivity method profile with a length of 94 m was configured in the Changyi Marine Ecology Specially Protected Areas on December 13, 2013. The equipment used was Geopen E60dn from Jiaopeng Co. China, using the Werner method. There are 48 electrodes in total, with an electrode spacing of 2 m (

The tidal data were obtained from the tidal level information provided by the Weifang City Marine Environment Monitoring Station. The data were measured one time per hour. An interpolation method was applied to match the tidal data with those of the high-density resistivity method [

The term “panel data” refers to the multivariate time series data, which were obtained by observing the sectional individual in different times continuously. The time series and cross-section data can be used simultaneously during the parameter analysis of the model. This technique is usually applied to the analysis of economic data [

The main purpose of this case is to investigate the effect of tide on the formation resistivity in different positions. First, the panel data model was selected. Both the section and time were included in the panel data, and the linear data equation, which is often used to analyze the effects of quantitative and qualitative factors, can be expressed as follows [

where y_{it} is the dependent variable; x_{it} is the k-vector of regression coefficients; _{it} is the random disturbance term, which is independent of each other and also satisfies zero mean and heteroscedasticity.

Equation (1) is only used in the description of some cases theoretically. It neither can be estimated nor can be used to predict. Therefore, before the deduction, a structural constraint should be added to the model. First, we assumed that the parameters do not vary with time, but with the individual variation. Therefore, the regression equations for each of the individual components can be defined as follows:

There are three types of constraint condition for Equation (2) as follows:

1) The regression slope coefficient is the same; however, the intercept is different, namely, individual-mean corrected regression equation:

2) The regression intercept is the same; however, the slope coefficient is different, namely, unrestricted equation:

3) Both the regression slope coefficient and intercept are the same, namely, pooled regression equation:

In this case, the formation resistivity may be obtained by the panel model regression of the observed value of the tidal level. According to the previous study, the effect of tidal fluctuation on the groundwater at different positions varies, leading to different effects on the formation resistivity; the main performance is that the coefficient changes with the cross section. When each of the measuring point of the formation resistivity was treated as a cross section, the 119 measurements were treated as a time series, and the constraint condition (b) was selected. The expectation equation can be expressed as follows:

where, r_{i} is the formation resistivity for measuring point i; α is a constant; α_{i} is the intercept for measuring point i; β_{i} is the slope coefficient for measuring point i; and t is the tide level for measuring point i at some point.

Because there are only two variable quantities, which are the formation resistivity and tidal level, and the formation resistivity is a function of both time and section, while the tidal level only changes with time, the data do not fully meet the requirements of panel data. Therefore, in the foundation of the conventional model verification method of panel data, the relative error r' was used to validate the calculation results as follows:

where r_{i} is the value calculated by Equation (6) for measuring point i, and x_{i} is the measured value for the same point.

A variable coefficient model was applied, and the coefficients in model (6) were calculated using the soft of Eveiws 6.0. The model test results are shown in _{i} were both constants, the effect of tidal change on formation resistivity was only associated to β. If the tidal level changes one unit, the formation resistivity changes β units. Therefore, β was regarded as the influencing strength of tidal change on formation resistivity.

Using the panel data calculation, the β value of each point was obtained, as shown in

Cross-section fixed (dummy variables) | |||
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R-squared | 0.998794 | Mean dependent var | 41.86404 |

Adjusted R-squared | 0.998773 | S.D. dependent var | 63.46484 |

S.E. of regression | 2.223014 | Akaike info criterion | 4.452269 |

Sum squared resid | 156111.1 | Schwarz criterion | 4.593068 |

Log likelihood | −70985.69 | Hannan-Quinn criter. | 4.497299 |

F-statistic | 48525.09 | Durbin-Watson stat | 0.275435 |

Prob (F-statistic) | 0.000000 |

In this study, the high-density resistivity method was applied to measure the formation resistivity, and the results were analyzed by the panel data method. Up to date, the results indicate that 1) the formation resistivity in coastal area was affected by the tidal level significantly, particularly in the seawater intrusion channel, indicating that it is possible to analyze the tide effect on the groundwater in coastal area by formation resistivity; 2) because of the presence of a brine layer in the south bank of Laizhou Bay, the effects of the tidal level on the formation resistivity in the left and right sides of the section were opposite. On the right side of the profile, the tidal level has a negative correlation with the formation resistivity, and the effect strength decreases along the direction of seawater intrusion. On the left side of the profile, the tidal level has a positive correlation with the formation resistivity, and the effect increases along the direction of seawater intrusion. The effect strength of tidal fluctuation on formation resistivity varied between 0.132 and 0.29.

This research was supported by National Natural Science Foundation of China (41406072), “State Oceanic Research Project for Public Benefit” (201105020).

Su, Q., Xu, X.Y., Liu, W.Q., Chen, G.Q. and Fu, T.F. (2017) Effect of Tides on the Stratigraphic Resistance of the South Coast of the Laizhou Bay. Journal of Water Resource and Protection, 9, 590-600. https://doi.org/10.4236/jwarp.2017.96039