Water allocation in the upper Klamath Basin of Oregon and California has been challenging. Irrigators have increasingly turned to groundwater to make up for surface water shortages because of shifts in allocation toward in-stream flows for Endangered Species Act listed fishes. The largest increase in groundwater pumping has been in and around the Bureau of Reclamation's Klamath Irrigation Project, which includes the Tule Lake subbasin in the southern part of the upper Klamath Basin. Previous groundwater flow model simulations indicate that water level declines from pumping may result in decreased flow to agricultural drains in the Tule Lake subbasin. Agricultural drains on the Klamath Project are an important source of water for downstream irrigators and for the Tule Lake and Lower Klamath Lake National Wildlife Refuges. To better assess the impact of increased pumping on drain flow and on the water balance of the groundwater system, flow data from agricultural drains were evaluated to investigate the changes that have taken place in groundwater discharge to drains since pumping volumes increased. Additionally, a fine-grid groundwater model of the Tule Lake subbasin was developed based on the existing regional flow model. The fine-grid model has sufficient vertical and horizontal resolution to simulate vertical head gradients, takes advantage of time-series data from 38 observation wells for model calibration, and allows agricultural drains to be more explicitly represented. Results of the drain flow analysis show that the groundwater discharge to agricultural drains has decreased by approximately 4000 hectare-meters from the 1997-2000 average discharge. Most of this decrease takes place in the northern and southeastern portions of the subbasin. Results of the groundwater model show that the initial source of water to wells is groundwater storage. By 2006, approximately 56% of the water from wells is sourced from agricultural drains.

Subject of the dissertation is a probability analysis on creation of embankment subsoil filtration deformations. Out of the broad topic of filtration deformations, the dissertation is focused at initiation of the process. At this phase, the overlying layers downstream of levee get uplifted, and eventually get breached. The process of downstream subsoil failure probability estimation is formulated using mathematical and statistical modelling. Within the scope of parametrical study the suggested method is applied onto a test environment. Results of the probability estimation are compared with results obtained using Limit state design method. The results of stochastic modelling can be used for improvement of Limit state design method precision.

This thesis aimed to evaluate the groundwater discharge distribution in the Krycklan catchment by developing a groundwater flow model using COMSOL Multiphysics and assuming a topography- controlled groundwater surface. Previous research has shown that the groundwater surface can be modeled as a subdued replica of the topography in humid climate regions where the permeability of the subsurface is low and where the groundwater surface is shallow. In earlier studies by Mojarrad (2021), it has been shown that the modeled infiltration becomes higher than the observed infiltration when a topography-controlled groundwater surface boundary is used and that a solution to this is to decrease the resolution in recharge areas. This method was therefore used in the thesis; however, the modeled infiltration was unsuccessfully lowered. This is thought to be due to differences between the model and the previous study and which are discussed further in this thesis. The discharge and recharge areas were identified using the direction of the vertical component of Darcy velocity, and the discharge flow distribution was evaluated in ArcMAP. The discharge flow distribution in the landscape was compared to real geographical data of surface water to identify a discharge threshold value for when the water balance is upheld by surface water flow or by evapotranspiration. The evapotranspiration discharge flow distribution was also evaluated, where the highest flow values were found in riparian zones of the landscape. / Syftet med denna avhandling var att utvärdera föredelningen av grundvattnets utflöde i Krycklans avrinningsområde genom att utveckla en grundvattenflödesmodell i COMSOL Multiphysics med antagandet av en topografikontrollerad grundvattenyta. Tidigare forskning har visat att grundvattenytan kan modelleras som en dämpad kopia av topografin i fuktiga klimatområden där permeabiliteten i underytan är låg och där grundvattenytan är grund. En implikation av att använda en topografikontrollerad grundvattenyta har visat sig vara att den modellerade infiltrationen blir högre jämfört med den observerade infiltrationen. Tidigare studier av Krycklans avrinningsområde har visat att genom att minska upplösningen i infiltrationsområden kan den modellerade infiltrationen framgångsrikt sänkas, därför användes denna mesh-utjämningsmetod i avhandlingen. För validering av modellen jämfördes den modellerade infiltrationen med den observerade infiltrationen i Krycklans avrinningsområde. Valideringen visade att mesh-utjämningen misslyckades med att minska infiltrationen, vilket tros bero på skillnader mellan modellen och den tidigare studien och som diskuteras vidare i denna avhandling. Grundvattnets infiltration- och utflödesområden identifierades med hjälp av riktningen på den vertikala komponenten av Darcy-hastighet, och utflödesfördelningen utvärderades i ArcMAP. Utflödesfördelningen i landskapet jämfördes med verkliga geografiska data för ytvatten för att identifiera ett tröskelvärde för utflödet när vattenbalansen upprätthålls av ytvattenflöde eller av evapotranspiration. Fördelningen av utflöden genom evapotranspirations utvärderades också, där de högsta flödesvärdena återfanns i områden nära ytvattenkroppar i landskapet.

Cette thèse porte sur la modélisation de l’écoulement et du transport en milieu poreux ;nous effectuons des simulations numériques et démontrons des résultats de convergence d’algorithmes.Au Chapitre 1, nous appliquons des méthodes de volumes finis pour la simulation d’écoulements à densité variable en milieu poreux ; il vient à résoudre une équation de convection diffusion parabolique pour la concentration couplée à une équation elliptique en pression.Nous nous appuyons sur la méthode des volumes finis standard pour le calcul des solutions de deux problèmes spécifiques : une interface en rotation entre eau salée et eau douce et le problème de Henry. Nous appliquons ensuite la méthode de volumes finis généralisés SUSHI pour la simulation des mêmes problèmes ainsi que celle d’un problème de bassin salé en dimension trois d’espace. Nous nous appuyons sur des maillages adaptatifs, basés sur des éléments de volume carrés ou cubiques.Au Chapitre 2, nous nous appuyons de nouveau sur la méthode de volumes finis généralisés SUSHI pour la discrétisation de l’équation de Richards, une équation elliptique parabolique pour le calcul d’écoulements en milieu poreux. Le terme de diffusion peut être anisotrope et hétérogène. Cette classe de méthodes localement conservatrices s’applique àune grande variété de mailles polyédriques non structurées qui peuvent ne pas se raccorder.La discrétisation en temps est totalement implicite. Nous obtenons un résultat de convergence basé sur des estimations a priori et sur l’application du théorème de compacité de Fréchet-Kolmogorov. Nous présentons aussi des tests numériques.Au Chapitre 3, nous discrétisons le problème de Signorini par un schéma de type gradient,qui s’écrit à l’aide d’une formulation variationnelle discrète et est basé sur des approximations indépendantes des fonctions et des gradients. On montre l’existence et l’unicité de la solution discrète ainsi que sa convergence vers la solution faible du problème continu. Nous présentons ensuite un schéma numérique basé sur la méthode SUSHI.Au Chapitre 4, nous appliquons un schéma semi-implicite en temps combiné avec la méthode SUSHI pour la résolution numérique d’un problème d’écoulements à densité variable ;il s’agit de résoudre des équations paraboliques de convection-diffusion pour la densité de soluté et le transport de la température ainsi que pour la pression. Nous simulons l’avance d’un front d’eau douce assez chaude et le transport de chaleur dans un aquifère captif qui est initialement chargé d’eau froide salée. Nous utilisons des maillages adaptatifs, basés sur des éléments de volume carrés. / This thesis bears on the modelling of groundwater flow and transport in porous media; we perform numerical simulations by means of finite volume methods and prove convergence results. In Chapter 1, we first apply a semi-implicit standard finite volume method and then the generalized finite volume method SUSHI for the numerical simulation of density driven flows in porous media; we solve a nonlinear convection-diffusion parabolic equation for the concentration coupled with an elliptic equation for the pressure. We apply the standard finite volume method to compute the solutions of a problem involving a rotating interface between salt and fresh water and of Henry's problem. We then apply the SUSHI scheme to the same problems as well as to a three dimensional saltpool problem. We use adaptive meshes, based upon square volume elements in space dimension two and cubic volume elements in space dimension three. In Chapter 2, we apply the generalized finite volume method SUSHI to the discretization of Richards equation, an elliptic-parabolic equation modeling groundwater flow, where the diffusion term can be anisotropic and heterogeneous. This class of locally conservative methods can be applied to a wide range of unstructured possibly non-matching polyhedral meshes in arbitrary space dimension. As is needed for Richards equation, the time discretization is fully implicit. We obtain a convergence result based upon a priori estimates and the application of the Fréchet-Kolmogorov compactness theorem. We implement the scheme and present numerical tests. In Chapter 3, we study a gradient scheme for the Signorini problem. Gradient schemes are nonconforming methods written in discrete variational formulation which are based on independent approximations of the functions and the gradients. We prove the existence and uniqueness of the discrete solution as well as its convergence to the weak solution of the Signorini problem. Finally we introduce a numerical scheme based upon the SUSHI discretization and present numerical results. In Chapter 4, we apply a semi-implicit scheme in time together with a generalized finite volume method for the numerical solution of density driven flows in porous media; it comes to solve nonlinear convection-diffusion parabolic equations for the solute and temperature transport as well as for the pressure. We compute the solutions for a specific problem which describes the advance of a warm fresh water front coupled to heat transfer in a confined aquifer which is initially charged with cold salt water. We use adaptive meshes, based upon square volume elements in space dimension two.

[Truncated abstract] The southwest of Western Australia is an intraplate area classified as a stable continental region. It comprises predominantly Archaean and Proterozoic geology and has generally subdued topography. The region currently experiences significant seismicity in the Southwest Seismic Zone (SWSZ), which is one of the most seismically active areas in Australia and is thought to represent the highest seismic hazard of the region. In recent years, numerous scarps, potentially related to large palaeoearthquakes have been recognised not only within the SWSZ, but also in a broader region of the southwest of Australia. Palaeoseismological investigations of two of these scarps, the Dumbleyung and the Lort River scarps, confirm their association with surface-rupturing palaeoearthquakes and indicate events with likely maximum magnitudes of ~Mw 7.0 on faults of low to medium slip rates. Two trenches across the Dumbleyung Fault scarp revealed a thrust fault in alluvial sediments with two associated earthquakes in the last ca 24-60 ka. A possible Holocene age was recognised for the last recorded earthquake event exposed in these trenches. Two trenches across the Lort River Scarp show that this feature results from thrust faulting in the weathered gneissic country rock. These trenches exposed evidence of two events in the last ca 35 ka, with a likely late Pleistocene age for the last earthquake. On both sites, the earthquakes are interpreted as associated with the last phase of fault activity, which was likely been preceded by a long period of quiescence. Assessment of the earthquake hazard associated with large earthquakes at the Dumbleyung and Lort River Faults resulted in calculated peak ground accelerations of up to 2 g in the near-fault fields. Such earthquakes would significantly affect nearby towns such as Dumbleyung, Wagin, Katanning, and Esperance, but they are unlikely to cause any significant damage in Perth. The palaeoseismological investigations show that the earthquake activity in the southwest of Western Australia is not only confined to the SWSZ, as it has been considered in previous assessments of the seismic hazard, but that there is also potential for strong earthquakes across much of the region. The seismicity in the southwest of Western Australia appears to be transient and migratory. This is suggested by the lack of local relief associated with places of current seismicity and fault scarps, the widespread distribution of the fault scarps across the region, the increase in seismicity in the SWSZ following strong recent events, and the apparent long periods of earthquake recurrence at fault sites. Accordingly, the current seismicity in the SWSZ is inferred to be transient and probably associated with stress changes produced by the recent earthquakes. '...' This uplift could be associated with dynamic topography effects resulting from processes along the plate margins. The uplift is probably enhanced by a flexural response of the lithosphere to local differential loads and density contrast along the southern margin, a mechanism that may also help explain the occurrence of some earthquake activity. The results from this study, complemented by additional palaeoseismological studies must be included in future probabilistic assessments of the seismic hazard of the southwest of Western Australia.

The Walla Walla basin lies in an arid region of Eastern Washington and Oregon. A large portion of the area is devoted to agricultural production, relying on irrigation water diverted from the Walla Walla River and underlying aquifers occurring within Quaternary and Mio-pliocene era gravel deposits, as well as a supplemental source from the Columbia River Basalt formation. Heavy water demand over summer months has resulted in a fully allocated surface water supply and significant drawdown in groundwater levels. The Walla Walla River also hosts two salmonid species listed as threatened under the endangered species act and entitled to federal protection. Specific questions have emerged regarding regional water supply as stakeholders work towards management strategies that meet water user demands, well also addressing concerns such as groundwater depletion and fish habitat. Currently, there are proposals aimed at increasing water use efficiency such as the lining of permeable canal beds and the expansion of a shallow aquifer recharge program. Effective implementation of such strategies, in part, relies on understanding the interactions between surface water and groundwater within this region. This project used the distributed hydrologic model, Integrated Water Flow Model (IWFM), for simulating surface and subsurface flows over a portion of the Walla Walla River basin spanning from Milton Freewater, Oregon to west of Touchet, Washington. This application of IWFM uses a grid with an average spacing of 100 x 100 meters over the 230 square kilometer model area. The model was developed and calibrated using data from 2007 through 2009, with 2010 data to be used as a data set for validation. Data collection has been a collaborative effort between a research team from Oregon State University and the Walla Walla Basin Watershed Council (WWBWC). This thesis provides explanation and documentation of model development. This includes details of data collection and processing for groundwater and surface water conditions, estimation of initial and boundary conditions, parameter calibration, model validation, and error analysis. Data sources include federal and state agencies, a gauge network managed by the WWBWC, and geologic research primarily performed by Kevin Lindsey of GSI Water Solutions with support of the WWBWC. Parameters have been independently determined from field measurements whenever possible. Otherwise they were estimated using established methods of hydrologic analysis, values drawn from previous regional studies, or the process of model calibration. Outputs include detailed hydrological budgets and hydrographs for groundwater and surface water gauges. The calibrated model has an overall correlation coefficient of 0.59 for groundwater and 0.63 for surface water. The standard deviation for groundwater is 3.2 meters at 62 well locations and surface water has a mean relative error of 22.3 percent at 34 gauges. This model intended as a tool for formulating water budgets for the basin under present conditions and making predictions of systemic responses to hypothetical water management scenarios. Scenarios of increased inputs into the Locher Road aquifer recharge site and conversion of irrigation district canals into pipelines are presented. / Graduation date: 2012

Bayesian inference occurs when prior knowledge about uncertain parameters in mathematical models is merged with new observational data related to the model outcome. In this thesis we focus on models given by partial differential equations where the uncertain parameters are coefficient functions belonging to infinite dimensional function spaces. The result of the Bayesian inference is then a well-defined posterior probability measure on a function space describing the updated knowledge about the uncertain coefficient. For decision making and post-processing it is often required to sample or integrate wit resprect to the posterior measure. This calls for sampling or numerical methods which are suitable for infinite dimensional spaces. In this work we focus on Kalman filter techniques based on ensembles or polynomial chaos expansions as well as Markov chain Monte Carlo methods. We analyze the Kalman filters by proving convergence and discussing their applicability in the context of Bayesian inference. Moreover, we develop and study an improved dimension-independent Metropolis-Hastings algorithm. Here, we show geometric ergodicity of the new method by a spectral gap approach using a novel comparison result for spectral gaps. Besides that, we observe and further analyze the robustness of the proposed algorithm with respect to decreasing observational noise. This robustness is another desirable property of numerical methods for Bayesian inference. The work concludes with the application of the discussed methods to a real-world groundwater flow problem illustrating, in particular, the Bayesian approach for uncertainty quantification in practice. / Bayessche Inferenz besteht daraus, vorhandenes a-priori Wissen über unsichere Parameter in mathematischen Modellen mit neuen Beobachtungen messbarer Modellgrößen zusammenzuführen. In dieser Dissertation beschäftigen wir uns mit Modellen, die durch partielle Differentialgleichungen beschrieben sind. Die unbekannten Parameter sind dabei Koeffizientenfunktionen, die aus einem unendlich dimensionalen Funktionenraum kommen. Das Resultat der Bayesschen Inferenz ist dann eine wohldefinierte a-posteriori Wahrscheinlichkeitsverteilung auf diesem Funktionenraum, welche das aktualisierte Wissen über den unsicheren Koeffizienten beschreibt. Für Entscheidungsverfahren oder Postprocessing ist es oft notwendig die a-posteriori Verteilung zu simulieren oder bzgl. dieser zu integrieren. Dies verlangt nach numerischen Verfahren, welche sich zur Simulation in unendlich dimensionalen Räumen eignen. In dieser Arbeit betrachten wir Kalmanfiltertechniken, die auf Ensembles oder polynomiellen Chaosentwicklungen basieren, sowie Markowketten-Monte-Carlo-Methoden. Wir analysieren die erwähnte Kalmanfilter, indem wir deren Konvergenz zeigen und ihre Anwendbarkeit im Kontext Bayesscher Inferenz diskutieren. Weiterhin entwickeln und studieren wir einen verbesserten dimensionsunabhängigen Metropolis-Hastings-Algorithmus. Hierbei weisen wir geometrische Ergodizität mit Hilfe eines neuen Resultates zum Vergleich der Spektrallücken von Markowketten nach. Zusätzlich beobachten und analysieren wir die Robustheit der neuen Methode bzgl. eines fallenden Beobachtungsfehlers. Diese Robustheit ist eine weitere wünschenswerte Eigenschaft numerischer Methoden für Bayessche Inferenz. Den Abschluss der Arbeit bildet die Anwendung der diskutierten Methoden auf ein reales Grundwasserproblem, was insbesondere den Bayesschen Zugang zur Unsicherheitsquantifizierung in der Praxis illustriert.

The subject of the presented thesis is a foundation pit dewatering numerical analysis. The study is introduced with practical examples and the summary of the necessary theory. Individual subtasks are modeled as two or three-dimensional problem on a chosen foundation pit example. A comparison with analytical methods and theoretical knowledge about the problem is made. The studies focus on specifying the pumped water quantity, the shape of the depression curve, determining the size of the numerical model and the influence of the finite element network density. The steady-state flow cases, water table aquifer, a well system, sheet pile wall cutoff effect, surface drained pit and partial penetration cases are analyzed. The work proposes a method of modeling a well by FEM. The main output is a 3D analysis of a submerged excavation dewatered with a partially penetrated well system.

MESHWR / See the attached abstract below

Bayesian inference occurs when prior knowledge about uncertain parameters in mathematical models is merged with new observational data related to the model outcome. In this thesis we focus on models given by partial differential equations where the uncertain parameters are coefficient functions belonging to infinite dimensional function spaces. The result of the Bayesian inference is then a well-defined posterior probability measure on a function space describing the updated knowledge about the uncertain coefficient. For decision making and post-processing it is often required to sample or integrate wit resprect to the posterior measure. This calls for sampling or numerical methods which are suitable for infinite dimensional spaces. In this work we focus on Kalman filter techniques based on ensembles or polynomial chaos expansions as well as Markov chain Monte Carlo methods. We analyze the Kalman filters by proving convergence and discussing their applicability in the context of Bayesian inference. Moreover, we develop and study an improved dimension-independent Metropolis-Hastings algorithm. Here, we show geometric ergodicity of the new method by a spectral gap approach using a novel comparison result for spectral gaps. Besides that, we observe and further analyze the robustness of the proposed algorithm with respect to decreasing observational noise. This robustness is another desirable property of numerical methods for Bayesian inference. The work concludes with the application of the discussed methods to a real-world groundwater flow problem illustrating, in particular, the Bayesian approach for uncertainty quantification in practice. / Bayessche Inferenz besteht daraus, vorhandenes a-priori Wissen über unsichere Parameter in mathematischen Modellen mit neuen Beobachtungen messbarer Modellgrößen zusammenzuführen. In dieser Dissertation beschäftigen wir uns mit Modellen, die durch partielle Differentialgleichungen beschrieben sind. Die unbekannten Parameter sind dabei Koeffizientenfunktionen, die aus einem unendlich dimensionalen Funktionenraum kommen. Das Resultat der Bayesschen Inferenz ist dann eine wohldefinierte a-posteriori Wahrscheinlichkeitsverteilung auf diesem Funktionenraum, welche das aktualisierte Wissen über den unsicheren Koeffizienten beschreibt. Für Entscheidungsverfahren oder Postprocessing ist es oft notwendig die a-posteriori Verteilung zu simulieren oder bzgl. dieser zu integrieren. Dies verlangt nach numerischen Verfahren, welche sich zur Simulation in unendlich dimensionalen Räumen eignen. In dieser Arbeit betrachten wir Kalmanfiltertechniken, die auf Ensembles oder polynomiellen Chaosentwicklungen basieren, sowie Markowketten-Monte-Carlo-Methoden. Wir analysieren die erwähnte Kalmanfilter, indem wir deren Konvergenz zeigen und ihre Anwendbarkeit im Kontext Bayesscher Inferenz diskutieren. Weiterhin entwickeln und studieren wir einen verbesserten dimensionsunabhängigen Metropolis-Hastings-Algorithmus. Hierbei weisen wir geometrische Ergodizität mit Hilfe eines neuen Resultates zum Vergleich der Spektrallücken von Markowketten nach. Zusätzlich beobachten und analysieren wir die Robustheit der neuen Methode bzgl. eines fallenden Beobachtungsfehlers. Diese Robustheit ist eine weitere wünschenswerte Eigenschaft numerischer Methoden für Bayessche Inferenz. Den Abschluss der Arbeit bildet die Anwendung der diskutierten Methoden auf ein reales Grundwasserproblem, was insbesondere den Bayesschen Zugang zur Unsicherheitsquantifizierung in der Praxis illustriert.