Numerical Modelling of Salinity Intrusion: Case Study from Southern Coastal Aquifer in Sri Lanka

A numerical model based on the freshwater-saltwater sharp interface assumption has been developed and it has been applied to estimate the salinity intrusion in the lower part of the Walawe river basin in the southern coastal aquifer, Sri Lanka. Evaluation of the effect of hydro-geological factors on the dynamics of freshwatersaltwater interface has been considered through storage coefficient, porosity and hydraulic conductivity. It concludes that hydraulic conductivity is the main hydrogeological factor affecting the movement of salinity interface. The simulation for groundwater recharge shows that the saltwater intrusion is more sensitive to groundwater recharge than hydro-geological properties. Since storage coefficient and porosity are not much affecting to the change of interface, model was calibrated by adjusting the hydraulic conductivity to match the observed salinity profile in the southern coastal aquifer. The observed long term salinity profile has been compared with the simulation results. It shows that the numerical models can be used to reproduce the salinity profile in the area.


Introduction
The use of coastal aquifers as operational reservoirs in water resources systems requires the development of tools that make it possible to predict the behavior of the aquifer under different conditions. Studies on the freshwatersaltwater interface either in steady or transient conditions have become necessary in designing and planning of groundwater systems in coastal areas. The quantitative understanding of the patterns of movement and mixing between freshwater and saltwater, and the factors that influence these processes, are necessary to manage the coastal groundwater resources.
In nature, the freshwater-saltwater interface seldom remains stationary. Large scale recharging into and withdrawals from the aquifer, result in the movement of the interface from one steady position to another. The main objectives of this study are to develop a numerical model to understand the behavior of the freshwater-saltwater interface and to evaluate the effects of different hydro-geological settings and to apply the model to the lower part of the Walawe river basin in the southern coastal aquifer in Sri Lanka. *~

Modeling of the dynamics of freshwatersaltwater interface
Many models have been developed to represent and to study the problem of saltwater intrusion. They range from relatively simple analytical solutions to complex numerical models. The first concept about freshwater saltwater interface, now widely cited as the Ghyben -Herzberg principle, is based on the hydrostatic equilibrium between fresh and saline water. After introducing the Ghyben -Herzberg principle, several analytical and numerical solutions were developed to describe various forms of boundary conditions of cross sectional systems. Recently, studies involving the movement of fresh groundwater and saltwater in coastal aquifer systems have been classically studied using two different approaches [1]. In the first approach, freshwater and saltwater are assumed completely immiscible and a sharp interface exists between these two phases. In the other approach, the freshwater and saltwater are assumed to be in dynamic equilibrium resulting from the flow and dispersion mechanisms within the aquifer. Normally, this method is used in solute transport evaluations.
Density dependent solute transport models are limited to two dimensional vertical cross sections. Three dimensional cases are limited in their application to regional coastal systems by computational constraints [2]. Sharp interface models are useful for vertical cross sections as well as aerial simulations and can represent the bulk freshwater and saltwater flow characteristics of the system. The sharp interface approach, in conjunction with integration of the flow equations over the vertical, can be applied aerially to large physical systems.
The sharp interface models which solve the coupled freshwater and saltwater flow equations have been developed with different numerical techniques [3,4]. A finite element method solution with indirect toe tracking technique was presented [5]. Polo and Ramis discussed an unconditionally convergent finite difference approach to solve sharp interface problems [6]. A sharp interface model which solves the coupled freshwater and saltwater flow equations has been developed and it was successfully applied to evaluate multilayered aquifer systems [7],

Mathematical development of sharp interface model
Sharp interface models couple the freshwater and saltwater flow based on the continuity of flux and pressure. In this approach, together with Dupuit approximation, for each flow domain the equation of continuity may be integrated over vertical direction and come up with following system of differential equations The location of the interface elevation is given by where p / and p s are specific weight in fresh and salt water respectively, // and, If are the piezometric heads of freshwater and saltwater regions, p^and p s are flow rate in fresh and salt water respectively. K f and, K t represent the hydraulic conductivity in fresh and salt water regions. Storage coefficients in fresh and salt water regions are given by iyand S t respectively. 0is the porosity of the aquifer media. a=l for unconfined aquifer and a-0 for confined aquifer.

Numerical scheme
Except for very simple systems, analytical solutions of those two coupled non linear partial differential equations are rarely possible. Various numerical methods must be employed to obtain approximate solutions. From equations (1) and (2), it is possible to derive a numerical model using implicit finite difference techniques. The continuous system described by above two equations are replaced by a finite set of discrete points in space and time, and the partial derivatives are replaced by terms calculated from the differences in both freshwater and saltwater head values at these points. Spatial discretization is achieved using a block entered finite difference grid which allows for variable grid spacing.

Evaluation of the effect of hydrogeological factors
To investigate the effect of hydro-geologic factors mainly, specific storage, porosity and hydraulic conductivity on the dynamics of the freshwater-saltwater flow systems, a 2km x 2km horizontal strip of an unconfined aquifer has been simulated by changing the hydrogeological properties while

Application to the coastal aquifer in Walawe river basin
Our main consideration for field data collection was the lower part of the Walawe river basin located in the southern coastal region which is in the southern part of Sri Lanka (Fig 4). The Coastal Plains covering a major part of the southern region has an elevation less than 6m above Mean Sea Level (MSL), parallel to the coast [9]. The width of the coastal plains generally ranges from 2 km to 10 km. Coastal alluvial soils as well as laterites cover the area parallel to the coast. It includes the river sediments and fine to medium green quartzite sand, silty sands of the plains and grey to dark grey beach sands [10]. Groundwater within the area is constrained by the unconsolidated alluvial and deltaic sediments, which were deposited by main rivers and their tributaries [11].
£323 Cry»t»liiM tutuit solutions for specific cases [12,13]. Therefore, a verification of results with field data is required to test numerical models. Indeed the availability of such secondary data is not very frequent due to the complexity of measuring and collecting information [14]. Therefore, we assume the 50% seawater salinity "contour as the equivalent sharp interface assuming that the seawater salinity is 32/:-'// and the sharp interface (50% seawater salinity profile) at the location of 16/w/ salinity profile.

Model calibration
The single-layer approach to modeling aquifers allows all minor variations to be incorporated may not be accurately representing the field conditions. Therefore the calibrated model has been used to verify the model for short term changes in freshwater-saltwater interface.
In this study, the groundwater recharge is the main influencing factor for the dynamics of the saltwater-freshwater interface. Recharge of the groundwater system is by a number of different processes. Here, the groundwater recharge has been estimated using water balance approach. Meteorological data of the Walawe river basin has been obtained from the International Water Management Institute (IWMI) database of Walawe benchmark basin. This data base has been used to estimate daily groundwater recharge and corresponding monthly average groundwater recharge. Estimated groundwater recharge shows that groundwater resources in Walawe basin recharges in two seasons per year. The two rainy periods are south-west monsoon season in October -December and north-east monsoon season in April-June. In other months the groundwater recharge is zero. Comparison of the simulated monthly freshwater-saltwater interface profiles and the monthly averaged observed salinity profiles in Walawe river basin are shown in Fig. 7. The results show that the comparisons between the observed and modeled salinity have been quite well predicted. Observations are well matched with model output, especially where there is a lowering of the interface can be observed in October -December and March-June due to positive groundwater recharge. The model also well reproduces these changes.

Fig. 7 Comparison between observations and model output
The correlation between simulated and observed interface have been shown in Fig 8 and  These kind of simulations show that the numerical models can be used to reproduce the salinity profile in the complex hydro-geological settings. It further concludes that any groundwater development activity in the southern coastal aquifer needs to be carefully planned with remedial measures in order to prevent the further intrusion of seawater.

Conclusions
The developed sharp interface model has been applied to the lower part of the Walawe river basin in the southern coastal aquifer, Sri Lanka. Evaluation of the effect of hydro-geological factors on the dynamics of freshwater-saltwater interface concluded that hydraulic conductivity is the main hydro-geological factor affecting the movement of salinity interface. The simulation for groundwater recharge shows that the saltwater intrusion is more sensitive to groundwater recharge than hydro-geological properties. The numerical model was calibrated by adjusting the hydraulic conductivity to match the observed salinity profile in the southern coastal aquifer. The observed long term salinity profile has been compared with the simulation results to verify the model. It shows that the numerical models can be used to reproduce the salinity profile in the southern coastal aquifer.