Modelling sea water intrusion in coastal aquifers using heterogeneous computing

The objective of this PhD research program is to investigate numerical methods for simulating variably-saturated flow and sea water intrusion in coastal aquifers in a high-performance computing environment. The work is divided into three overlapping tasks: to develop an accurate and stable finite volume discretisation and numerical solution strategy for the variably-saturated flow and salt transport equations; to implement the chosen approach in a high performance computing environment that may have multiple GPUs or CPU cores; and to verify and test the implementation. The geological description of aquifers is often complex, with porous materials possessing highly variable properties, that are best described using unstructured meshes. The finite volume method is a popular method for the solution of the conservation laws that describe sea water intrusion, and is well-suited to unstructured meshes. In this work we apply a control volume-finite element (CV-FE) method to an extension of a recently proposed formulation (Kees and Miller, 2002) for variably saturated groundwater flow. The CV-FE method evaluates fluxes at points where material properties and gradients in pressure and concentration are consistently defined, making it both suitable for heterogeneous media and mass conservative. Using the method of lines, the CV-FE discretisation gives a set of differential algebraic equations (DAEs) amenable to solution using higher-order implicit solvers. Heterogeneous computer systems that use a combination of computational hardware such as CPUs and GPUs, are attractive for scientific computing due to the potential advantages offered by GPUs for accelerating data-parallel operations. We present a C++ library that implements data-parallel methods on both CPU and GPUs. The finite volume discretisation is expressed in terms of these data-parallel operations, which gives an efficient implementation of the nonlinear residual function. This makes the implicit solution of the DAE system possible on the GPU, because the inexact Newton-Krylov method used by the implicit time stepping scheme can approximate the action of a matrix on a vector using residual evaluations. We also propose preconditioning strategies that are amenable to GPU implementation, so that all computationally-intensive aspects of the implicit time stepping scheme are implemented on the GPU. Results are presented that demonstrate the efficiency and accuracy of the proposed numeric methods and formulation. The formulation offers excellent conservation of mass, and higher-order temporal integration increases both numeric efficiency and accuracy of the solutions. Flux limiting produces accurate, oscillation-free solutions on coarse meshes, where much finer meshes are required to obtain solutions with equivalent accuracy using upstream weighting. The computational efficiency of the software is investigated using CPUs and GPUs on a high-performance workstation. The GPU version offers considerable speedup over the CPU version, with one GPU giving speedup factor of 3 over the eight-core CPU implementation.

Parametric Studies on Saltwater Intrusion into Coastal Aquifers for Anticipate Sea Level Rise

Saltwater intrusion into coastal aquifers is a global issue, exacerbated by increasing demands for freshwater in coastal regions. This study investigates into the parametric analysis on saltwater intrusion in a conceptual, coastal, unconfined aquifer considering wide range of freshwater draft and anticipated sea level rise. The saltwater intrusion under various circumstances is simulated through parametric studies using MODFLOW, MT3DMS and SEAWAT. The MODFLOW is used to simulate the groundwater flow system under changing hydro-dynamics in coastal aquifer. To simulate solute transport MT3DMS and SEAWAT is used. The saltwater intrusion process has direct bearing on hydraulic conductivity and inversely related to porosity. It may also be noted that increase in recharge rate considered in the study does not have much influence on saltwater intrusion. Effect of freshwater draft at locations beyond half of the width of the aquifer considered has marginal effect and hence can be considered as safe zone for freshwater withdrawals. Due to the climate change effect, the anticipated rise in sea level of 0.88 m over a century is considered in the investigation. This causes increase in salinity intrusion by about 25%. The combined effect of sea level rise and freshwater draft (C) 2015 The Authors. Published by Elsevier B.V.

Cross-validation of geo-electrical and hydrogeological models to evaluate seawater intrusion in coastal aquifers

The validation of variable-density flow models simulating seawater intrusion in coastal aquifers requires information about concentration distribution in groundwater. Electrical resistivity tomography (ERT) provides relevant data for this purpose. However, inverse modeling is not accurate because of the non-uniqueness of solutions. Such difficulties in evaluating seawater intrusion can be overcome by coupling geophysical data and groundwater modeling. First, the resistivity distribution obtained by inverse geo-electrical modeling is established. Second, a 3-D variable-density flow hydrogeological model is developed. Third, using Archie's Law, the electrical resistivity model deduced from salt concentration is compared to the formerly interpreted electrical model. Finally, aside from that usual comparison-validation, the theoretical geophysical response of concentrations simulated with the groundwater model can be compared to field-measured resistivity data. This constitutes a cross-validation of both the inverse geo-electrical model and the groundwater model.
[Comte, J.-C., and O. Banton (2007), Cross-validation of geo-electrical and hydrogeological models to evaluate seawater intrusion in coastal aquifers, Geophys. Res. Lett., 34, L10402, doi:10.1029/2007GL029981.]

Towards groundwater security in coastal East Africa: initiating a regional research network and integrated hydrogeologic, climatic & socio-economic observatories in coastal aquifers of the Comoros Islands, Kenya and Tanzania

African coastal regions are expected to experience the highest rates of population growth in coming decades. Fresh groundwater resources in the coastal zone of East Africa (EA) are highly vulnerable to seawater intrusion. Increasing water demand is leading to unsustainable and ill-planned well drilling and abstraction. Wells supplying domestic, industrial and agricultural needs are or have become, in many areas, too saline for use. Climate change, including weather changes and sea level rise, is expected to exacerbate this problem. The multiplicity of physical, demographic and socio-economic driving factors makes this a very challenging issue for management. At present the state and probable evolution of coastal aquifers in EA are not well documented. The UPGro project 'Towards groundwater security in coastal East Africa' brings together teams from Kenya, Tanzania, Comoros Islands and Europe to address this knowledge gap. An integrative multidisciplinary approach, combining the expertise of hydrogeologists, hydrologists and social scientists, is investigating selected sites along the coastal zone in each country. Hydrogeologic observatories have been established in different geologic and climatic settings representative of the coastal EA region, where focussed research will identify the current status of groundwater and identify future threats based on projected demographic and climate change scenarios. Researchers are also engaging with end users as well as local community and stakeholder groups in each area in order to understanding the issues most affecting the communities and searching sustainable strategies for addressing these.

Automated image analysis for experimental investigations of salt water intrusion in coastal aquifers

A novel methodology has been developed to quantify important saltwater intrusion parameters in a sandbox style experiment using image analysis. Existing methods found in the literature are based mainly on visual observations, which are subjective, labour intensive and limits the temporal and spatial resolutions that can be analysed. A robust error analysis was undertaken to determine the optimum methodology to convert image light intensity to concentration. Results showed that defining a relationship on a pixel-wise basis provided the most accurate image to concentration conversion and allowed quantification of the width of mixing zone between the saltwater and freshwater. A large image sample rate was used to investigate the transient dynamics of saltwater intrusion, which rendered analysis by visual observation unsuitable. This paper presents the methodologies developed to minimise human input and promote autonomy, provide high resolution image to concentration conversion and allow the quantification of intrusion parameters under transient conditions.

Experimental Saltwater Intrusion in Coastal aquifers Using Automated Image Analysis: Applications to Homogeneous Aquifers.

This paper presents the applications of a novel methodology to quantify saltwater intrusion parameters in laboratory-scale experiments. The methodology uses an automated image analysis procedure, minimizing manual inputs and the subsequent systematic errors that can be introduced. This allowed the quantification of the width of the mixing zone which is difficult to measure in experimental methods that are based on visual observations. Glass beads of different grain sizes were tested for both steady-state and transient conditions. The transient results showed good correlation between experimental and numerical intrusion rates. The experimental intrusion rates revealed that the saltwater wedge reached a steady state condition sooner while receding than advancing. The hydrodynamics of the experimental mixing zone exhibited similar
traits; a greater increase in the width of the mixing zone was observed in the receding saltwater wedge, which indicates faster fluid velocities and higher dispersion. The angle of intrusion analysis revealed the formation of a volume of diluted saltwater at the toe position when the saltwater wedge is prompted to recede. In addition, results of different physical repeats of the experiment produced an average coefficient of variation less than 0.18 of the measured toe length and width of the mixing zone.

Dynamics of coastal aquifers: data-driven forecasting and risk analysis

This work is focused on the study of saltwater intrusion in coastal aquifers, and in particular on the realization of conceptual schemes to evaluate the risk associated with it. Saltwater intrusion depends on different natural and anthropic factors, both presenting a strong aleatory behaviour, that should be considered for an optimal management of the territory and water resources. Given the uncertainty of problem parameters, the risk associated with salinization needs to be cast in a probabilistic framework. On the basis of a widely adopted sharp interface formulation, key hydrogeological problem parameters are modeled as random variables, and global sensitivity analysis is used to determine their influence on the position of saltwater interface. The analyses presented in this work rely on an efficient model reduction technique, based on Polynomial Chaos Expansion, able to combine the best description of the model without great computational burden. When the assumptions of classical analytical models are not respected, and this occurs several times in the applications to real cases of study, as in the area analyzed in the present work, one can adopt data-driven techniques, based on the analysis of the data characterizing the system under study. It follows that a model can be defined on the basis of connections between the system state variables, with only a limited number of assumptions about the "physical" behaviour of the system.

A new analytical solution for water table fluctuations in coastal aquifers with sloping beaches

The Boussinesq equation appears as the zeroth-order term in the shallow water flow expansion of the non-linear equation describing the flow of fluid in an unconfined aquifer. One-dimensional models based on the Boussinesq equation have been used to analyse tide-induced water table fluctuations in coastal aquifers. Previous analytical solutions for a sloping beach are based on the perturbation parameter, epsilon(N) = alphaepsilon cot beta (in which beta is the beach slope, alpha is the amplitude parameter and epsilon is the shallow water parameter) and are limited to tan(-1) (alphaepsilon) much less than beta less than or equal to pi/2. In this paper, a new higher-order solution to the non-linear boundary value problem is derived. The results demonstrate the significant influence of the higher-order components and beach slope on the water table fluctuations. The relative difference between the linear solution and the present solution increases as 6 and a increase, and reaches 7% of the linear solution. (C) 2003 Elsevier Ltd. All rights reserved.

Steepness expansion for free surface flows in coastal aquifers

Free surface flow of groundwater in aquifers has been studied since the early 1960s. Previous investigations have been based on the Boussinesq equation, derived from the non-linear kinematic boundary condition. In fact, the Boussinesq equation is the zeroth-order equation in the shallow-water expansion. A key assumption in this expansion is that the mean thickness of the aquifer is small compared with a reference length, normally taken to be the linear decay length. In this study, we re-examine the expansion scheme for free surface groundwater flows, and propose a new expansion wherein the shallow-water assumption is replaced by a steepness assumption. A comparison with experimental data shows that the new model provides a better prediction of water table levels than the conventional shallow-water expansion. The applicable ranges of the two expansions are exhibited. (c) 2004 Elsevier B.V. All rights reserved.

A method of lines approach for modelling saltwater intrusion in coastal aquifiers

The equations governing saltwater intrusion in coastal aquifers are complex. Backward Euler time stepping approaches are often used to advance the solution to these equations in time, which typically requires that small time steps be taken in order to ensure that an accurate solution is obtained. We show that a method of lines approach incorporating variable order backward differentiation formulas can greatly improve the efficiency of the time stepping process.