The main aim of this study is to develop a suitable method for the calibration and validation of mathematical models of large and complex aquifer systems. Since the calibration procedure depends on the nature of the model to be calibrated and since many kinds of models are used for groundwater, the question of model choice is broached first. Various aquifer models are critically reviewed and a table to compare them as to their capabilities and limitations is set up. The need for a general calibration method for models in which the flow is represented by partial differential equations is identified from this table. The calibration problem is formulated in the general mathematical framework as the inverse problem. Five types of inverse problems that exist in modeling aquifers by partial differential equations are identified. These are, to determine (1) parameters, (2) initial conditions, (3) boundary conditions, (4) inputs, and (5) a mixture of the above. Various methods to solve these inverse problems are reviewed, including those from fields other than hydrology. A new direct method to solve the inverse problem (DIMSIP) is then developed. Basically, this method consists of transforming the partial differential equations of flow to algebraic equations by substituting in them the values of the various derivatives of the dependent variable (which may be hydraulic pressure, chemical concentration or temperature). The parameters are then obtained by formulating the problem in a nonlinear optimization framework. The method of sequential unconstrained minimization is used. Spline functions are used to evaluate the derivatives of the dependent variable. Splines are functions defined by piecewise polynomial arcs in such a way that derivatives up to and including the order one less than the degree of polynomials used are continuous everywhere. The natural cubic splines used in this study have the additional property of minimum curvature which is analogous to minimum energy surface. These and the derivative preserving properties of splines make them an excellent tool for approximating the dependent variable surfaces in groundwater flow problems. Applications of the method to both a test situation as well as to real -world data are given. It is shown that the method evaluates the parameters, boundary conditions and inputs; that is, solves inverse problem type V. General conditions of heterogeneity and anisotropy can be evaluated. However, the method is not applicable to steady flows and has the limitation that flow models in which the parameters are functions of the dependent variable cannot be calibrated. In addition, at least one of the parameters has to be preassigned a value. A discussion of uncertainties in calibration procedures is given. The related problems of model validation and sampling of aquifers are also discussed.

Delta islands make up the majority of coastal delta area. However, the groundwater hydrology of young, prograding delta systems and its relationship to surrounding surface water dynamics are poorly understood. Deltas in coastal environments are assumed to function as chemical “buffers”, filtering nutrient-rich terrestrial runoff through the island structures and surface water ecosystems as it travels to the sea, but the magnitude of this effect cannot be accurately quantified without understanding the physical relationships between the surface water and groundwater. This study developed the first conceptual model of the hydrology of prograding delta island groundwater systems. The study was based on field data collected at Pintail Island, a 2 km2 island within the Wax Lake Delta in Louisiana. Hydraulic properties and processes were quantified at multiple depths at locations spanning the island elevation gradient. Groundwater and surface water levels were monitored. A weather station recorded precipitation, air, and wind conditions. The groundwater within Pintail Island was both spatially and temporally dynamic throughout the study period of Sept/9/2013 to Feb/4/2014. The aquifer within the distal limbs of the island responded as a connected, saturated unconfined aquifer. The portions of Pintail Island within the older, proximal, higher elevation apex were found to be a two-layer system with fine sediments and organic matter overlying sandy deposits. The aquifer within this section of the island responded differently during times of elevated surface water (storm events) and times of normal surface water (calm periods) and differently from the distal-island unconfined system. The fine, shallow (roughly 0-60cm depth) sediments capping this older, higher portion of the island appeared to inhibit vertical flow between the surface and subsurface, creating semi-confined conditions within the sands in the deeper island subsurface. High water levels led to overpressurization of the apical aquifer, which was maintained between storms due to the low hydraulic gradient and the low permeability of the porous medium. During inundating storm events, groundwater potentials mimicked surrounding surface water levels. This conceptual model of a prograding coastal delta island now provides a foundation for further, hydrologically-realistic study of delta ecology and nutrient exchange. / text

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In the Wairau Valley 40 km southwest of Blenheim, elevated salinities are present in the groundwater below a depth of approximately 15 m, to the north of the Wairau Fault. Saline water is present very close to the surface between the Southern Hills and the Wairau Fault. Highest concentrations are located in well O28/w/0219 with total dissolved solids concentrations approximately 31,000 mg/L. Only a few wells in the study area have intercepted the saline groundwater. A report by Taylor (2003) has identified the groundwater below the Holocene terrace surface is recharged from Southern Hills runoff, however the Wairau Fault has a significant impact on the groundwater flow on the south bank acting as a semi-permeable barrier to groundwater flow from the southern Hills streams identified by several spring which emerge on the fault trace. The scope of this investigation was to identify the extent of the saline groundwater in the Homelands area and to attempt to define the origin of the highly saline groundwater. Furthermore, to define the groundwater flow path below the upper terrace surface to recharge the Wairau Valley Aquifer. The Multi-Electrode Resistivity technique was used to define the extent of the saline groundwater. This shows the saline groundwater is ubiquitous at depth in the study area. The depth to the freshwater/saline water interface varies laterally in the resistivity profiles. A major control on the presence of the groundwater salinity is considered to be the permeability of the gravel. Gravels with a higher permeability are probably washed of any residual salinity that may have been present in the past. Investigations into the origins of the saline groundwater were completed using stable isotope analysis (¹⁸O, ²H, and ¹³C), hydrochemistry and age dating techniques (³H and ¹⁴C). Due to the complex chemistry a single source could not be identified, however two methods were identified as the most likely. This was evaporative concentration of fresh water in the Wairau Valley, or the upward migration from the Wairau Fault of formation water probably of seawater origin. The stable isotope data fits best with an evaporative concentration of freshwater within the Wairau Valley, however, ratios of chemical constituents are very similar to other formation waters found in other parts of the world. Stream gauging of streams on the south bank show no significant water loss in the reaches north of the Wairau Fault. Therefore, recharge must be crossing the Fault trace as groundwater. Boundary Creek looses all of its surface flow for most of the year upon reaching the valley floor. Bounday Creek has washed out sections of the Wairau Fault and Major terrace riser between Wr 1 and Wr 2 terrace surfaces. It is proposed that groundwater flowing in the gravels reworked by Boundary Creek is the major recharge source for the Wairau Valley Aquifer.

Existing analytical treatments of groundwater flow have mostly been founded on classical hydrodynamics, that groundwater motion is derivable from a velocity potential. This conception is in contradiction with the principle of conservation of energy, although it conforms with the principle of the conservation of mass (Hubbert, 1940, p. 285; Scheidegger, 1960, pps. 74-75; Bear, 1972, pps. 122-123). This dissertation shows that both principles can be utilized, based on the fact that a force potential at a point is equal to the work required to transfer a unit mass from this point to another point. This potential is given the symbol φ - gh - gz + (p/ρ) and is incorporated in the force field E. This potential is related to the flow field (q) by the anisotropic hydraulic conductivity. This relation forms a solid formulation for the theory of the flow of fluids through fractured porous media. This relation is applied to develop two basic equations. One partial differential equation, representing flow in the fracture, depending on the actual geometry of the fracture and incorporating the anisotropic parameter of the hydraulic conductivity based on the thermal induced stress and the force potential. A second partial differential equation (storage equation) in two-dimensions for non-steady groundwater flow in confined and saturated aquifers. This storage equation incorporates time, hydraulic conductivity and the radial coordinates. It is solved analytically using the Bessel's functions Jₒ and Kₒ. The two equations represent two models. Both the potential and the thermal hydraulic conductivity constitute a coupling between the two models to render the models a thermohydromechanical model. This aspect is the essential theme underlying this work and is implemented through a matrix-fracture system based on the slow flow and the fast flow behavior. The evaluation of the transient parameters including the aperture becomes possible and falls in line with the physics of the problem. This comprehensive analytical model is found to satisfy the transient demands of the mathematical physics. The application of the phenomena observed in the field from different sources and from Stripa Granite, rendered the model realistic and appropriate to the fractured porous media.

The influence of geologic factors in controlling flow patterns in hydraulic systems is evaluated by hydraulic models which are constructed as a porous consolidated media that simulates the interstitial geometry of consolidated rocks. Colored inks are injected into the flow system and are observed through the transparent sides of the model case. Visual analysis of the flow system, leads to salient conclusions concerning fundamental aspects of complex flow systems. Empirical experiments were conducted on the following aspects: Refraction of flow lines across lithologic interfaces: The law of streamline refraction, as described by King Hubbert, was found to be correct where boundary conditions do not interfere. Continuity of flow around and through highly permeable and impermeable lenses of different lithologies: The flow system around impermeable lenses indicates the nonexistence of stagnant areas where a hydraulic gradient is imposed on a saturated ground water system. Flow net system caused by a single pumping well: Transient changes of individual flow vectors, within the immediate area of influence, were analyzed at the moment pumping began. The absence of a transition phase indicates a rapid adjustment of the flow system to the pumping condition. Flow net system of mutual interference of depression cones caused by pumping multiple wells: This permitted an analysis of the ground water divide. Flow bands divided into flow paths which moved in opposite directions. Effects of emplacing pumping wells in highly permeable media: The increased area of influence of water movement to wells was clearly illustrated. This analysis demonstrates the capture of partially confined flow from great dths. The relation of the shape of artificial recharge pits to infiltration rate: Variations of flow net systems of rectangular and wedge-shaped pits were analyzed. When all other factors were held constant, the shape of the recharge pit was found to have no important effect upon recharge rate. Flow toward an effluent stream: The potential head of ground water beneath the stream was found to increase with depth. The relationship between hydraulic gradient and flow net configuration: The hydraulic gradient was found to have no effect on the flow net of a confined system, but a definite effect upon unconfined flow systems, in as much as it alters the water table which is the upper flow boundary. Flow pattern through tilted and faulted sedimentary structures: The geometric convergence of the aquifer boundaries caused the convergence of flow lines through a brecciated fault zone. A possible genesis of a hydrothermal vein ore was suggested by this flow pattern. Formation of perched water tables: The mechanisms by which saturated ground water mounds can be formed on a low permeability lens was demonstrated. Evidence was found which indicates that perched ground water probably escapes through the perching body as well as around its extremities. Confluence of gravity water and saturated flow: Unsaturated flow arriving at the water table of the saturated ground water body becomes an integral part of that body which acts as a single hydrodynamic system. Artesian ground water systems: A model illustrating the classic artesian aquifer situation was constructed, andflowing and non-flowing artesian wells were studied. A ground water mound was formed in the water table aquifer by water discharging naturally from the artesian aquifer through a fault in the confining layer. Subsidence around a pumping well: Water was pumped from a simulated artesian well, the piezometric surface in the vicinity of the well was lowered and the overburden was observed to subside while compressing the artesian aquifer. Cone of depression formed around single and multiple well systems: The drawdown at any point within the area of influence of a multiple well system was shown to be equal to the sum of the individual drawdowns of each well in the multiple well system, provided recharge and evaporation are neglected. Information resulting from these studies will provide guides for scientific development and exploitation of ground water supplies. Contributions were made that will advance the use of hydraulic models as exploratory tools in scientific hydrology. Further, this work brought into focus the importance of hydraulic models as couinunication media for interpreting cause-effect relationships in highly complex flow systems, of the type that so often are involved in regional problems of water resource development and management.