Equations of subsurface flow of water, the Richards equation and the Boussinesq equation, have no known exact analytical solutions. Approximate analytical solutions to these equations have been developed under linearizing simplifications. In the first part of the dissertation two commonly used linear methods of computation of groundwater flow are investigated. The equation considered includes a recharge term and slope of an impervious bed. A new method of computation with improved accuracy has been developed. The second part of the dissertation deals with vertical, unsaturated flow of water in a homogeneous soil column of finite length with arbitrary initial conditions. The boundary conditions considered at the soil surface correspond to pre-ponding and post-ponding infiltration. / Ph. D.

Introduction: The movement of moisture and the simultaneous transfer of water and solutes in unsaturated porous media are problems of practical interest in ground water hydrology and soil physics. A large fraction of the water falling as rain on the land surfaces of the earth moves through unsaturated zone of soil during the subsequent processes of infiltration, drainage, evaporation, and absorption of soil -water by plant roots. A soil profile is characteristically nonuniform in its properties, nonisothermal, and may be nonrigid. Microorganisms and the roots of higher plants are a part of the system. This region is characterized by cylic fluctuation of water content as water is removed from the soil profile by evaportranspiration and replenished by recharge, irrigation, or rainfall. In unsaturated porous media the problem of movement and retention of water may be approached from (1) the molecular, (2) the microscopic, or (3) the macroscopic standpoint. In the molecular viewpoint theories of the mechanisms of flow and retention in terms of the behavior of water molecules are devised. At microscopic level a theory of flow treating the fluid in pores as a continuum and applying the principles of continuum mechanics to understand the detailed behavior of fluid within the pores is developed. The complicated pore geometry and consequent impossibility of specifying the boundary conditions on flow, preclude any practical progress by this appraoch. Since the behavior of individual molecules and the distributions of fluid velocity and pressure cannot be observed in porous media, a macroscopic theory of flow is needed. In the macroscopic approach, all variables are treated continuous functions of time and space. Velocity, pressure, and other variables are assumed as point functions. Thus, any theory of water transport to be useful must be developed to the point of describing the transfer of water on the macroscopic level. The coefficients of transport such as permeability and diffusivity can be defined microscopically. In many investigations which involve the transport of pesticides and fertilizes along with water , the simultaneous movement of water and solutes is of primary concern. These pollutants when mixed with water move in the unsaturated soil and finally join the region of saturated soil or water table, resulting in the contamination of fresh water existing below the water table. The scope of this report is to review the available literature, that may be categorized into two parts; one, the movement of water in unsaturated soil, and the other, the simultaneous movement of water and solutes in unsaturated soil. The papers, reviewed in this report, pertain to the theoretical study, laboratory study and field study on the two problems. At the end, an appendix appears which lists the references, categorizing the kind of study by various investigators.

Many hydrologic basins in the southwest have seen their perennial streamflows turn to ephemeral, their riparian communities disappear or be jeopardized, and their aquifers suffer from severe overdrafts. Under -management of ground -water exploitation and of conjunctive use of surface and ground waters are the main reasons for these events.

The use of cross-correlation analysis on spring discharge and precipitation data in karst aquifer basins has been used for many years to develop a conceptual understanding of an aquifer and estimate aquifer properties. However, to this point, the application of these processes has relied on gaged precipitation at discrete locations. The use of spatially varying precipitation data and cross-correlation analysis provides a means of spatially characterizing recharge locations on a karst aquifer. NEXRAD provides a spatial estimate of precipitation based by combining reflectivity measurements from radar stations and traditional precipitation gages. This study combines NEXRAD precipitation data with spring discharge data to develop maps of contributing areas for two karst springs in Central Texas. By calculating the cross-correlation of each NEXRAD measurement to spring flow data for the same period of time a map showing the locations hydraulically connected to the spring can be developed. Both numerical experiments and field applications were conducted as part of the study. The numerical experiments conducted by Padilla and Pulido-Bosch are revisited using the numerical groundwater model MODFLOW. This allowed the introduction of spatially varying parameters into the model. The results show that spatially varying parameters can be inferred based on the results cross-correlation of spatially varying precipitation with respect to a single spring discharge location. Also, contributing area maps are prepared for both Barton Springs and Jacob’s Well. Barton Springs has a precise estimate of the recharge area. The current map of the recharge area and the NEXRAD derived map show good agreement with the cross-correlation results. Conversely, Jacob’s Well has not been sufficiently studied to delineate a contributing area map. This study provides an preliminary estimate of the area contributing to flow at Jacob’s Well. Finally, the development of these maps can also be applied to the construction of regional groundwater models. An application of this methodology with the groundwater availability model for the Barton Springs portion of the Edward’s aquifer is introduced. The application of spatial cross-correlation analysis to constrain recharge in the model showed a reduction in the objective function with respect to discharge at Barton Springs of 15%. / text

MODRSP is program used for calculating drawdown, velocity, storage losses and capture response functions for multi - aquifer ground -water flow systems. Capture is defined as the sum of the increase in aquifer recharge and decrease in aquifer discharge as a result of an applied stress from pumping [Bredehoeft et al., 19821. The capture phenomena treated by MODRSP are stream- aquifer leakance, reduction of evapotranspiration losses, leakance from adjacent aquifers, flows to and from prescribed head boundaries and increases or decreases in natural recharge or discharge from head dependent boundaries. The response functions are independent of the magnitude of the stresses and are dependent on the type of partial differential equation, the boundary and initial conditions and the parameters thereof, and the spatial and temporal location of stresses. The aquifers modeled may have irregular -shaped areal boundaries and non -homogeneous transmissive and storage qualities. For regional aquifers, the stresses are generally pumpages from wells. The utility of response functions arises from their capacity to be embedded in management models. The management models consist of a mathematical expression of a criterion to measure preference, and sets of constraints which act to limit the preferred actions. The response functions are incorporated into constraints that couple the hydrologic system with the management system (Maddock, 1972). MODRSP is a modification of MODFLOW (McDonald and Harbaugh, 1984,1988). MODRSP uses many of the data input structures of MODFLOW, but there are major differences between the two programs. The differences are discussed in Chapters 4 and 5. An abbreviated theoretical development is presented in Chapter 2, a more complete theoretical development may be found in Maddock and Lacher (1991). The finite difference technique discussion presented in Chapter 3 is a synopsis of that covered more completely in McDonald and Harbaugh (1988). Subprogram organization is presented in Chapter 4 with the data requirements explained in Chapter 5. Chapter 6 contains three example applications of MODRSP.

A finite element numerical model is developed for the modeling of coupled surface-water flow and ground-water flow. The mathematical treatment of subsurface flows follows the confined aquifer theory or the classical Dupuit approximation for unconfined aquifers whereas surface-water flows are treated with the kinematic wave approximation for open channel flow. A detailed discussion of the standard approaches to represent the coupling term is provided. In this work, a mathematical expression similar to Ohm's law is used to simulate the interacting term between the two major hydrological components. Contrary to the standard approach, the coupling term is incorporated through a boundary flux integral that arises naturally in the weak form of the governing equations rather than through a source term. It is found that in some cases, a branch cut needs to be introduced along the internal boundary representing the stream in order to define a simply connected domain, which is an essential requirement in the derivation of the weak form of the ground-water flow equation. The fast time scale characteristic of surface-water flows and the slow time scale characteristic of ground-water flows are clearly established, leading to the definition of three dimensionless parameters, namely, a Peclet number that inherits the disparity between both time scales, a flow number that relates the pumping rate and the streamflow, and a Biot number that relates the conductance at the river-aquifer interface to the aquifer conductance. The model, implemented in the Bill Williams River Basin, reproduces the observed streamflow patterns and the ground-water flow patterns. Fairly good results are obtained using multiple time steps in the simulation process.

Thesis (MScAgric)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: Increased pressure on groundwater sources due to increased population size and threats of climate change is driving research to better understand the process of aquifer recharge. Soil pattern is of interest as it serves to partition rainwater into different flowpaths destined for surface runoff, evapotranspiration and deep percolation. The challenges inherent to studying these flowpaths are almost universal as uncertainties concerning spatial and temporal heterogeneity in catchments make the upscaling of models complex. This research addresses these challenges as it aims to improve the catchment scale hydrological models of two aquifer systems: One a fractured bedrock system at the Kogelberg Nature Reserve, Kleinmond, and the other a cover sand system in Riverlands Nature Reserve, Malmesbury. This study focussed on strengthening the link between what is known about a given soil form and the hydrological assumptions that can be drawn from that classification, and formulating the results so that they may ultimately be used to calibrate the recharge prediction models for the respective catchments. The research was done in two parts: The first phase was to conduct soil surveys in both reserves during which soils were classified according to South African Soil Classification. Samples were collected at representative observation points which provided textural data for use in pedotransfer functions (PTFs). These PTFs were used to estimate plant available water (PAW) and hydraulic conductivity (K) for the observed profiles. Infiltration experiments were subsequently done to investigate the infiltration patterns of distinctly different soil forms at two sites from each reserve. The experiments included double ring and mini disc infiltration, volumetric water content determination and flow path visualisation using a staining dye. A statistical comparison between the hydrological properties (K and PAW) of the different soil forms suggest that hydraulic properties differed between the deep sandy soil forms (Fernwood, Pinegrove and Witfontein in Kogelberg and Witfontein, Concordia and Lamotte in Riverlands) and the shallow rocky soil forms (Cartref and Glenrosa in Kogelberg). Thus grouping of hydrological similar units (HSUs) could be done on the basis of the soil forms present within the given catchments. The infiltration study showed that shallow, rocky soils that grade into bedrock would have infiltration rates far greater than those estimated using PTFs in Kogelberg. This is due to the prevalence of continuous preferential flow (PF) of water between coarse fragments in these profiles. Recharge estimates would thus be inaccurate in such soils and calibration using locally derived data is recommended. On the contrary, PTFs produced accurate infiltration estimates relative to measured infiltration rates in deep sandy soils in Kogelberg and Riverlands. The Lamotte soil form is an example of such a soil form. It should however be noted that an increase in PF in these soils had subsequently higher K values than estimated, thus illustrating the link between PF and accelerated infiltration rates. These results confirm that using soil survey information, in the form of a soil map, and calibrated hydrological properties, one can delineate HSUs that encompass a large degree of heterogeneity in a given catchment. / AFRIKAANSE OPSOMMING: Verhoogde druk op grondwaterhulpbronne weens die groeiende bevolking en klimaatsverandering dryf tans navorsing om akwifeer hervulling beter te verstaan. Die grondlaag is van belang sienend dat dit reënwater verdeel in oppervlak afloop, evapotranspirasie en diep dreinering. Die uitdagings in hidrologiese navorsing is universeel as gevolg van onsekerhede oor ruimtelike en tydelike variasie wat lei tot komplekse grondwatermodelle. Diè navorsing mik om die tekortkominge in akwifeer hervulling aan te vul deur groundwatermodelle van twee akwifeersisteme te verbeter: Die een is 'n gebroke rots sisteem in die Kogelberg Natuur Reservaat, Kleinmond, en die ander is 'n sand-bedekde sisteem in Riverlands Natuur Reservaat, Malmesbury. Die navorsing streef om die verhouding tussen 'n spesifieke grondvorm en sy hidroliese vloeipaaie te bestudeer en om die gevolgtrekkings so te formuleer dat dit kan gebruik word om die onderskeie grondwatermodelle te kalibreer. Die eerste fase van die navorsing was om 'n grondopname van die onderskeie reservate te doen waartydens die gronde geklassifiseer was volgens die Suid Afrikaanse Grondklassifikasie Sisteem. Grondmonsters is by verteenwoordigende observasiepunte geneem en geanaliseer om tekstuurdata vir pedo-oordraagbare-funksies (PTFs) te kry. Die PTFs was gebruik om plant beskikbare water (PBW) en hidrouliese geleiding (K) te voorspel vir die verskeie observasiepunte. Infiltrasie eksperimente was daarna gedoen om die infiltrasie patroon van twee verskillende grondvorms van elke reservaat te bestudeer. Die eksperimente sluit dubbel- en minidisk-infiltrasie, volumetriese waterinhoud bepaling en vloeipad visualisering met die gebruik van 'n kleurstof in. Die statistiese vergelyking van die hidrouliese eienskappe (K en PBW) en grondvorm dui aan dat die hidrouliese eienskappe verskil tussen die diep, grondvorms met 'n oorwegende sand tekstuur (Fernwood, Pinegrove en Witfontein in Kogelberg en Witfontein, Concordia en Lamotte in Riverlands) en die vlakker, klipperige grondvorms (Cartref en Glenrosa in Kogelberg). Groepering van hidrologies soortgelyke eenhede (HSE's) kan dus op die basis van die teenwoordige grondvorms in 'n opvangsgebied gedoen word. Die infiltrasie studie het bewys dat vlak, klipperige gronde wat tot die rotsbodem gradueer 'n baie hoër infiltratsie tempo sal hê as die PTF voorspelde waardes. Dit is as gevolg van die voorkoms van aaneenlopende voorkeurvloei (VV) van water tussen die growwe materiaal in die profiele, veral die gebroke rots ondergorond. Voorspellings van akwifeer hervulling sal dus onakkuraat wees en kalibrasie met plaaslike data word dus aanbeveel. In teendeel met die begenoemde, het die PTFs akkurate voorspellings gemaak relatief tot die gemete infiltrasie tempo's in die diep sanderige grondvorms in Kogelberg en Riverlands. Dit was duidelik met metings dat 'n toename in aaneenlopende VV hoër gemete K waardes getoon as die voorspelde waardes. Die verband tussen VV en verhoogde infiltrasie tempo word dus hiermee geillustreer. Die resultate bevestig dus dat grondopname data, in die vorm van 'n grondkaart en gekalibreerde hidrouliese eienskappe gebruik kan word om hidrologies soortgelyke eenhede uiteen te sit wat die meerderheid van die variasie in 'n gegewe opvangsgebied insluit. Die HSE's kan gebruik word om grondwatermodelle meer akkuraat te laat funksioneer en dus beter voorspellings te genereer.

This study, which is to provide information to a settlement over the rights to water resources in the Mesilla Basin, uses a groundwater model to estimate how pumping in the basin affects the hydrologic regime.

published_or_final_version / abstract / Earth Sciences / Doctoral / Doctor of Philosophy

published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy