Yosuke Kishi

The motion of coastal groundwater in response to the tide

Abstract Problems of seawater intrusion into confined coastal aquifers under the influence of the tide are analysed with the use of two different models; the freshwater-saltwater interface model and the dispersion model. The freshwater-saltwater interface model, which describes the motion of the groundwater level and the freshwater-saltwater interface in response to the tide, is applied to the confined coastal aquifers in the estuary of the Naka River and Yura district of Gogo Island in Japan. The position of the outlet of the confined groundwater into the sea and also the degree of spreading of the aquifers thickness, which is assumed to vary exponentially with horizontal distance, are estimated. From the non-dimensional analysis based on the dispersion model, it is found that salt water intrudes furthest inland at the time at which the sea level reaches the mean sea level in the ebb tide stage, consistent with the result obtained by the freshwater-saltwater interface model, and the transition zone from fresh water to salt water becomes widest at that time.

The regional unsteady interface between fresh water and salt water in a confined coastal aquifer

Abstract An areal two-dimensional model to describe the unsteady motion of the fresh-salt water interface and the groundwater level in a confined coastal aquifer is first presented and then applied to the confined groundwater in the estuaries of the Naka and Kiki rivers in Japan. Starting from the basic equations of the groundwater flow, two equations are derived; one equation of the effective water level and one equation of the interface. The first equation describes a very rapid variation of the effective groundwater level and the second equation describes a very slow variation of the interface with time. In order to find solutions of these equations under the boundary conditions in practical field problems, the numerical scheme based on Galerkin finite-element technique was employed. Using this numerical scheme, transient positions of the groundwater level and the interface were calculated in the above-mentioned two regions and compared with the available field data. It was found that the calculated results agree rather well with the data.

Studies on salinization of groundwater, I: Theoretical consideration on the three-dimensional movement of the salt water interface caused by the pumpage of confined groundwater in fan-shaped alluvium

Abstract A theoretical model is presented on the phenomenon of seawater intrusion into confined groundwater, to make clear the relationship between the amount of pumping of fresh water and the corresponding three-dimensional spatial distribution of salt water. First, differential equations are derived for the fresh and salinized regions, respectively, from the fundamental equation on confined water. The equation in the salinized region, which is a quasilinear differential equation, can be transformed to a linear one and then is continued to the equation in the fresh region, resulting in the two-dimensional Poissons equation which is applicable to the entire region. This equation in steady state is solved in integral form by using the method of Greens functions and is simply expressed in the case of idealized field conditions analogous to a fan-shaped alluvium by the usual method of images. Finally, some numerical examples are shown for the case of uniform pumpage in a circular region.

The behavior of groundwater with dispersion in coastal aquifers

Abstract A three-dimensional steady-state hydrodynamic dispersion model is used to simulate seawater encroachment in the confined aquifers in the estuaries of the Naka and Kiki Rivers in Japan. Two expressions of the dispersion coefficient are considered; one is constant over the entire region of the aquifer and the other is dependent on the flow velocity of the groundwater. The magnitudes of the constant dispersion coefficients in the horizontal and vertical directions, D xx and D zz , as well as the longitudinal and lateral dispersivities, a L and a T , are determined so as to reproduce the regional distributions of salt concentration in the confined aquifers in both estuaries. It is found that D xx = 5 cm 2 s −1 , D zz = 5-0.5 cm 2 s −1 and a L = 1000–1250 m, a T = 100–125 m in the estuary of the Naka River; and D xx = 0.2 cm 2 s −1 , D zz = 0.2–0.02 cm 2 s −1 and a L = 200 m, a T = 200-20 m in the estuary of the Kiki River. Examining the local distributions of the dispersion coefficient computed from the dispersivity and velocity fields of groundwater in both estuaries, the same value as estimated in the analysis with the constant dispersion coefficient is located in the middle layer of the aquifer. In the estuary of the Naka River, the piezometric surface predicted with the dispersion model with the velocity-dependent dispersion coefficient is almost the same as that predicted with the dispersion model with the constant dispersion coefficient and they are 5 10% lower than that predicted with the interface model (Kakinuma et al., 1984). They are, however, about 1.3 times the observed one.

The regional steady interface between fresh water and salt water in a coastal aquifer

Abstract First, a theoretical model is presented which is useful for determining the regional steady interface between fresh water and salt water under the appropriate boundary conditions for both confined and unconfined aquifers. This model is then applied to the confined groundwater in the estuary of the Naka River, Tokushima Prefecture, Japan, and the phenomenon of the seawater intrusion into the aquifer is analyzed. Boundary conditions of the confined aquifer and the parameters necessary for analysis are determined from the data. Calculations using a finite-element method are carried out in various cases, by changing the inflow S R or the total pumping amount Q of the groundwater in this alluvial plain. It is found that the region where salt water is intruding expands rapidly inland when S R approaches Q and vice versa. It is also found that the distributions of chloride ion concentration in groundwater calculated by this model with a simplified assumption are in fairly good agreement with the results observed in deep wells.

Studies on the infiltration-discharge of rain water and translation phenomena in soil

Abstract Infiltration and discharge of rain water and water movement in soil were investigated by a numerical analysis based on a one-dimensional infiltration model. A simple approximate formula for the piezometric head and water content distribution in soil in a steady state was obtained. Computational results in unsteady state indicated that the vertical downward speed of the wetting front is generally much larger than that of a tracer, which is assumed to be injected together with the rain water at the soil surface. Theoretical considerations were then developed to relate the movement of the wetting front and that of the tracer front to water movement in soil. Finally, numerical analyses were performed for various precipitation intensities, under various initial soil moisture conditions and with various soil properties. The speed of the wetting front approaches that of the tracer as the precipitation intensity increases, as the initial soil moisture decreases, and the grain size increases.

The motion of coastal confined groundwater in the presence of various patterns of pumping. (II). Numerical analysis by steady state dispersion model.

A two-dimensional steady state hydrodynamic dispersion model is used, with the fresh-salt water interface model, to investigate the motion of the coastal confined groundwater in the presence of various pumping patterns. Two expressions of the dispersion coefficient are considered; one is constant over the entire region of the aquifer, and the other is dependent on the flow velocity of the groundwater. The main results are as follows : 1) As the groundwater is pumped more inland, salt water intrudes more inland, whereas the pumping in the lower layer of the aquifer near the coast is effective to prevent the seawater intrusion; 2) in the upper layer pumping, the fresh-salt water interface model serves as a convenient method for approximate analyses and predictions of seawater intrusion into the coastal confined aquifers.

Studies on the motion of ground water with dispersion in coastal aquifers. (III). Dispersivities in Naka River and Kiki River estuaries.

A three-dimensional steady state hydrodynamic dispersion model with the velocity-dependent dispersion coefficient was used to simulate seawater encroachment in the confined aquifers in the estuaries of the Naka River, Tokushima Prefecture, and the Kiki River, Ehime Prefecture. The main results are as follows: 1) The longitudinal and lateral dispersivities are 1, 000 to 1, 250 m and 100 to 125 m in the estuary of the Naka River, respectively. In the estuary of the Kiki River, the corresponding values are 200 m and 200 to 20 m, respectively. 2) Examining the local distribution of the dispersion coefficient values computed from the dispersivity and velocity fields of groundwater, the same value as estimated in the analysis with the constant dispersion coefficient (KAKINUMA et al., 1985) is located in the middle layer of the aquifer. 3) In the estuary of the Naka River, the piezometric surface predicted using the dispersion model with the velocity-dependent dispersion coefficient in almost the same as the one predicted with the dispersion model with the constant dispersion coefficient. They are 5 to 10% lower than the one predicted with the interface model (KAKINUMA et al., 1984), but about 1.3 times the observed one.

The motion of coastal confined groundwater in the presence of various patterns of pumping. I Numerical analysis by fresh-salt water interface model.

The motion of the coastal confined groundwater in the presence of various pumping patterns was investigated by numerical analyses, based on one and two-dimensional , unsteady fresh-salt water interface models. Approximate equations describing the temporal variation of groundwater level and freshsalt water interface were utilized in the numerical computations together with appropriate boundary conditions. The results were as follows : 1) Groundwater level varied very quickly in response to sudden change in pumping amount, whereas the interface varied very slowly ; 2) movement of the interface was faster when the groundwater was pumped in the fresh water region as compared to that in the saline water region ; 3) movement of the interface was faster when retreating toward the sea as compared to when it was advancing inland ; 4) artificial recharge through wells in the fresh water region and the saline water region was effective to retreat the toe of the interface and to decrease the thickness of salt water layer, respectively ; 5) in the two-dimensional model, results similar to those in the one-dimensional model were obtained for movement of the interface in the presence of various pumping patterns ; 6) characteristic features of the two-dimensional model in the presence of areal distribution of pumping points were also found, e. g., the speeds of interface toe movement close to and far from pumping points were considerably different.

Studies on the Salinization of Coastal Ground Water

In this paper, we first presenta theoretical model on the phenomena of these a water intrusion into coastal aquifers. Withthe use of this model, the spatial distribution of fresh and salt water interface in steady stateis easily determined either in the confined or unconfined aquifer which has arbitrary plane boundaries. We next apply this model to the confined ground wate rin the estuary of the Naka River, Tokushima Pref. The variation of spatial distribution of fresh and salt water interface is investigated in detail in connection with the changes in pumping amount or in inflow rate of ground water.