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Item Open Access Electrical resistivity tomography (ERT) measurements on date palm stems to support irrigation scheduling(2025) Bukhary, Tarig; Huisman, Johan Alexander (Prof. Dr.)Commercial cultivation of date palms has high economic significance, particularly in arid and hyper-arid regions. In Israel, the commercial cultivation of date palms in the hyper-arid Arava and Jordan valleys (from the Sea of Galilee, along the Jordan valley to the Red Sea) has grown substantially in the past two decades. As such, achieving commercially viable yield of dates amid water scarcity and enforced restrictions on water use requires optimising the amount and timing of irrigation. To that end, better understanding of the temporal dynamics of the water use of date palm is of great importance. Traditionally, this can be achieved through sap flow estimates obtained using heat dissipation probes. However, such measurements lack the ability to provide information on the spatial distribution of sap flow, which is important considering that date palms transport water in the entire stem cross-section. Electrical resistivity tomography (ERT), a long established and widely used geophysical method for the imaging and characterisation of sub-surface structures may allow for obtaining improved estimates of transpiration from sap flow measurements and the assessment of stem water dynamics. The aim of this thesis is thus to explore the potential of combining sap flow and electrical measurements to obtain a better understanding of the transpiration and the spatiotemporal dynamics of water flow and storage in date palm trunks. In a first step, a suitable ERT set-up and data acquisition strategies were developed starting from ERT measurements on a sand column as a proof-of-concept, where ERT was used to monitor the progress of a tracer solution through a sand column. The results showed that the adopted strategy for ERT measurement acquisition was successful in capturing the development and breakthrough of the introduced tracer solution, not only in terms of the average real part of the electrical conductivity at each electrode plane, but also in terms of the spatial distribution of the real part of the electrical conductivity. The outcome of the flow experiment on a sand column was used as a starting point to further develop the ERT set-up and data acquisition strategies for measuring on date palm stems, which were then tested on a date palm stem segment. For this, flow was induced through a stem segment that was obtained from a felled date palm tree. ERT measurements were continuously obtained throughout a cycle of flow and no-flow periods. The results showed that the mean bulk electrical conductivity varied strongly due to changes in the flow conditions. In addition, it was found that the electrical conductivity of the outflow was much higher than that of the inflow, which indicates the release of stored salt from the stem segment. Analysis of the spatial distribution of the electrical conductivity suggested that flow mainly occurred in a limited part of the cross-sectional area of the stem. Extending from the flow experiment on a date palm stem segment, the electrical properties were further investigated using a multi-step outflow experiment on a smaller stem fragment. The results showed a slow water release from the date palm stem segment with increasing applied pressure, which suggests that the water is tightly bound in the stem as in a clay soil. The real part of the bulk electrical conductivity of the stem segment showed a declining pattern, which is generally in agreement with the decreasing water content in the stem segment. The real part of the electrical conductivity decreased with the saturation of the stem segment in a pattern that closely resembled that of a clay soil. From the laboratory experiments, it was concluded that ERT is a promising tool to investigate the spatial variability of water flow in date palm stems. In a second step, two field experiments involving irrigation deprivation were conducted on living date palms. In both experiments, ERT measurements were obtained at high temporal resolution following the established set-up and data acquisition strategies from the experiments in the laboratory. Sap flow estimates were obtained from heat dissipation probes in conjunction with continuous ERT measurements. The first experiment involved a juvenile date palm growing in a lysimeter, while the second experiment involved a mature date palm. The combined sap flow and ERT measurements were continuously obtained for a baseline period, followed by an induced water stress period. The monitoring was continued during the recovery period following the restoration of the irrigation treatment for a few days. It was found that the diurnal variations in the electrical properties of the date palm stem during the baseline period were consistent with the expected diurnal variation in transpiration and stem water storage. The findings also made clear that capturing those diurnal variations would not be possible without following a measurement acquisition strategy utilising a high temporal resolution. During the irrigation deprivation period, the juvenile date palm showed a strong response to water stress, as observed in the temporal dynamics of the average real part of the electrical resistivity over the plane as well as the average real part of the transfer impedances. The mature palm, on the other hand, showed no clear signs of water stress during the irrigation deprivation period. This finding was consistent with the results obtained on soil water content, which showed that the loss in water was superficial (above 60 cm depth). Furthermore, the observed spatial variation in the real part of the electrical resistivity showed that some regions of the stem cross-sectional area were more active than others, and that the distribution of areas with high and low electrical resistivity was dynamically changing throughout the day and night. This observation suggests an on-going redistribution of the stem water content and continuous changes in stem water storage. It was further observed that the areas with high electrical resistivity noticeably increased following the suspension of the irrigation treatment. A closer examination of this finding indicated that this was more evident for the juvenile date palm than for the mature date palm. The obtained sap flow estimates and ERT data showed no signs of quick recovery in case of the juvenile date palm after the irrigation was restored. However, subsequent monitoring showed that the juvenile date palm did eventually recover after a few weeks. The results further showed that the mature date palm did not experience significant water stress and by extension recovery. A long-term monitoring on a bi-monthly basis on the mature date palm showed a temporally stable spatial distribution of the real part of the electrical resistivity for measurements made at the same time for a period of several months. This finding provides further confidence in the established ERT set-up and data acquisition strategies as an approach to support irrigation scheduling for date palms and detecting early signs of water stress. In conclusion, the work presented in this thesis provides an important contribution to the establishment of a combined approach in which sap flow estimates obtained from heat dissipation probes and continuous ERT measurements are jointly used to obtain improved monitoring and interpretation of water flow and storage in date palm stems. It was shown that the proposed set-ups, ERT data acquisition protocols and inversion strategies allow for reliably obtaining representative ERT measurements on date palm stems that enabled monitoring of spatiotemporal variability in water flow and storage in date palm stems. The proposed approach also allows for improved estimation of daily variation in transpiration requirements, and detecting of early signs of water stress, which can make a valuable contribution to the planning and scheduling of irrigation treatments that account for transpiration requirements of date palms while adhering to imposed limitation in water use.Item Open Access Bayesian inversion and model selection of heterogeneities in geostatistical subsurface modeling(Stuttgart : Eigenverlag des Instituts für Wasser- und Umweltsystemmodellierung der Universität Stuttgart, 2021) Reuschen, Sebastian; Nowak, Wolfgang (Prof. Dr.-Ing.)Item Open Access Nonlinear finite volume schemes for complex flow processes and challenging grids(Stuttgart : Eigenverlag des Instituts für Wasser- und Umweltsystemmodellierung der Universität Stuttgart, 2019) Schneider, Martin; Helmig, Rainer (Prof. Dr.-Ing.)Item Open Access Coupling free flow and flow in porous media in biological and technical applications : from a simple to a complex interface description(2014) Baber, Katherina; Helmig, Rainer (Prof. Dr.-Ing.)The objective of this work is the development of model concepts and methods for the coupling of free flow and flow in porous media. Coupling concepts of varying complexity ranging from a simple to a pore-scale to a complex interface approach are derived. The main focus is the development and testing of an REV-scale coupling concept that accounts for drop dynamics at the interface. The developed coupling concepts are based on the assumption of thermodynamic equilibrium and on flux balances. The formulation of mechanical equilibrium in the pore-scale and complex interface concept is challenging due to the scale-dependent definition of pressure. The combination of microscopic and macroscopic pressure formulations causes pressure jumps at the interface and non-physical pressure gradients. Hence, an extensive discussion of the pressure conditions is given. The coupled model is implemented in the C++ simulator DuMux (Flemisch et al., 2011) using the mortar method. The applicability of the developed concepts is assessed on the basis of two applications: transvascular exchange and drop dynamics in PEM fuel cells. In Mosthaf et al. (2011) and Baber et al. (2012), we develop a simple interface concept for coupling non-isothermal compositional two-phase flow in the porous-medium with a non-isothermal compositional single-phase system in the free-flow region. The concept is based on the two-domain approach with a simple interface devoid of thermodynamic properties. In this work, the simple interface concept is applied to model transvascular exchange. The simulations reproduce filtration and reabsorption and reveal the influence of wall and tissue parameters on the final distribution of therapeutic agents. However, the complex structure of the micro-vascular wall and the influence of the different pathways cannot be resolved by the presented approach. In some applications, the complex structure of the interface and the processes happening therein cannot be described by a simple interface devoid of thermodynamic properties. In such cases, it might be beneficial to resolve the interface layer or interface region on the pore-scale. We present a first step towards a resulting coupled pore-/REV-scale model where the interface is described by a bundle-of-tubes approach. The coupling concept between the one-phase free-flow, the pore-scale and the two-phase porous-medium model is based on flux continuity and the assumption that pore-and REV-scale pressure are equal. We develop an REV-scale interface concept - the complex interface concept - that describes drop formation, growth and detachment on hydrophobic interface between free and porous-medium flow. The interface stores the mass and energy of the drops without resolving them. The direct exchange between free-flow and porous-medium region next to the drop is also part of the coupling concept since it preserves the exchange processes described by the simple interface concept. The fraction of the interface which is covered by drops is used to obtain an area-weighted average of the coupling conditions with and without drop so that coupling conditions for the whole interface are obtained. The complex interface concept captures drop formation, growth and detachment. These processes are influenced by the conditions of both the free-flow and porous-medium region. The temporal evolution of the drop volume is an outcome of the model. The number of drops that can form on the interface is defined a priori by choosing the size of a drop REV. Neither the influence of the drops on the free-flow conditions nor film flow or sliding and merging of drops is included since the focus is on the interface description. The model is applied to simulate drop formation in the cathode of PEM fuel cells. In fuel cells, water is generated by the electro-chemical reaction in the catalyst layer and flows through the hydrophobic porous fibre structure of the GDL. Reaching the GC, water forms drops on the hydrophobic interface between GC and GDL. The drops significantly influence the water management in fuel cells which must be optimised to achieve good performance and durability. The numerical results show that it is possible to include drop dynamics in the REV-scale coupling conditions between free and porous-medium flow. Drop formation, growth and detachment are represented correctly, if the evaporation from the drop surface is neglected. The interface-coverage ratio, which is an indicator for the quality of the water management, can be predicted. The simulations for a higher number of drops suggest that the interface conditions dominate the system. A parameter study shows that interface wettability and free-flow velocity have a significant influence on the drop growth and detachment. In summary, this work reveals the potential of the developed coupling concepts to deal with realistic problems and exposes the need for further improvement and development.Item Open Access A surrogate-assisted Bayesian framework for uncertainty-aware validation benchmarks(Stuttgart : Eigenverlag des Instituts für Wasser- und Umweltsystemmodellierung der Universität Stuttgart, 2023) Mohammadi, Farid; Flemisch, Bernd (apl. Prof. Dr. rer. nat.)Over the last century, computational modeling in geoscience, especially in porous media research, has witnessed tremendous improvement. After decades of development, the state-of-the-art simulators can now solve coupled partial differential equations governing the complex subsurface multiphase flow system within a practically large spatial and temporal domain. Given the importance of computational modeling, quality assessment of these models in light of the purpose of a given simulation is of paramount importance to engineering designers and managers, public officials, and those affected by the decisions based on the predictions. Users and developers of computational simulations deal with a challenging question: How should confidence in modeling and simulation be critically assessed? Validation is one of the primary methods for building and quantifying confidence in modeling and simulation. It investigates the degree to which a model accurately represents reality from the perspective of the intended application of the model. Usually, this comparison between model outputs and experimental data constitutes plotting the model results against data on the same axes to provide a visual assessment of agreement or lack thereof. While comparisons between model and data are at the heart of any validation procedure, there are several concerns with such naive comparisons. First, these comparisons tend to provide qualitative rather than quantitative assessments and are clearly insufficient as a basis for making decisions regarding model validity. Second, naive comparisons often disregard or only partly account for existing uncertainties in the experimental observations or the model input parameters. Third, such comparisons can not reveal whether the model is appropriate for the intended purposes, as they mainly focus on the agreement in the observable quantities. These pitfalls give rise to the need for an uncertainty-aware framework that includes a validation metric. This metric shall provide a measure for comparison of the system response quantities of an experiment with the ones from a computational model while accounting for uncertainties in both in a rigorous way. To address this need, we developed a statistical framework incorporating a probabilistic modeling technique using a fully Bayesian approach. The dissertation aims to help modelers perform uncertainty aware model validation benchmarks. A two-stage Bayesian multi-model framework is discussed for modeling tasks where a set of models are at hand. To make this framework applicable for computationally demanding models, it is extended to a surrogate-assisted framework, keeping the computational costs at a reasonable level. Moreover, correction factors were introduced to compensate for the surrogate error in the Bayesian hypothesis testing and Bayesian model selection, as using surrogate representations instead of the full-fidelity computational models introduces additional errors to the validation metrics. In this dissertation, I show how the Bayesian formalism could be materialized by employing the concept of polynomial chaos expansion to achieve more accurate surrogates with a sparse representation and account for the uncertainty in the surrogate’s predictions. I also highlight how such surrogate models could be constructed with as few simulations as the computational budget allows. To this end, sequential adaptive sampling strategies are discussed, in which one attempts to augment the initial design iteratively. By doing so, informative regions in the parameter space are adequately explored. These regions are more likely to provide valuable information on the behavior of the original model responses. Using a sequential sampling strategy avoids the waste of computational resources, as opposed to the so-called one-shot designs. A series of benchmark studies are conducted to investigate the predictive capabilities of different sparsity and sequential adaptive sampling methods. Moreover, I introduce BayesValidRox, an open-source, object-oriented Python package that provides an automated workflow for surrogate-based sensitivity analysis, Bayesian calibration, and validation of computational models with a modular structure. The uncertainty-aware validation framework was applied to a range of cases in the field of subsurface hydro-system modeling, mainly to flow and transport in porous media, such as flow simulation models in fractured porous media, coupling free flow and porous medium flow, and microbially induced calcite precipitation. However, this validation framework can be transferred to other disciplines in which models are used for prediction.Item Open Access Development and parameter estimation of conceptual snow-melt models using MODIS snow-cover distribution(Stuttgart : Eigenverlag des Instituts für Wasser- und Umweltsystemmodellierung der Universität Stuttgart, 2023) Gyawali, Dhiraj Raj; Bárdossy, András (Prof. Dr. rer. nat. Dr.-Ing.)Due to a high spatio-temporal variability observed in the inherent snow-related processes in snow-dominated regimes, reliable representation of spatial distribution of seasonal snow has remained a critical challenge for effective monitoring of seasonal evolution of snow and subsequently hydrological estimations, in mountainous regions around the world. This issue, coupled with the crucial relevance to climate change, is further exacerbated by data scarcity in these regions. To address this issue, this thesis presents a novel standalone calibration technique employing the pixel-wise binary (’snow’, ’no snow’) information from MODIS snow-cover images to calibrate independent conceptual snow-melt models, thereby estimating model parameters from individual or sets of MODIS images. This methodology exploits the pertinent information of snow-cover distribution from the freely available remote sensing images, to reliably simulate snow-processes in data scarce regions. Switzerland and Baden-Württemberg were selected as study snow regimes, with the former representing partly longer duration snow and the latter associated with a shorter duration. Different extensions of parsimonious conceptual snow-melt models were developed and used to simulate the snow-cover distribution, with all models showcasing an adept and robust simulation. The selection of binary snow-cover information as calibration variable permits relatively complex snow-melt modules to be calibrated with more robustness because of reduced uncertainty associated with the calibration data. This work further identifies and recommends different simulation thresholds for defining the calibration data (NDSI thresholds), selecting the images for calibration (cloud cover thresholds), and reclassifying the snow water equivalent (SWE) outputs to snow-cover information (SWE thresholds). Furthermore, validation of the MODIS based snow-melt model calibration and the simulated melt outputs was carried out using a modified hydrological model (modified HBV variant) without the snow-routine. This hydrological performance was contrasted with the standard HBV model calibrated solely on discharge. The melt output provided as standalone inputs to the modified HBV was observed to impart an enhanced discharge prediction. As compared with the discharge calibrated standard HBV, a reduction in uncertainty in terms of model performance was observed along with reduced parameter compensation. The increase in model performance is deemed for ‘the right reason’ as the snow processes are adeptly represented by process-informed parameters. The estimation of the parameters solely from MODIS information not only eliminates the reliance on a single calibration variable ’discharge’ which is already an availability constraint in the higher altitudes but also preserves the spatial heterogeneity at a more regional level. This methodology holds a crucial relevance for discharge simulation in areas with episodic days of snow, where the snow processes can be calibrated quickly on images without having to calibrate the entire hydrological model. The study approach shows that the addition of freely available snow-cover information in estimating the parameters of snow-melt models utilizing the snow/no-snow information and a modest and globally available input data demand, facilitates a simple, spatially flexible approach to calibrate snow-cover distribution in mountainous areas with reasonably accurate precipitation and temperature data, especially in data scarce regions.Item Open Access Modeling fixed-bed reactors for thermochemical heat storage with the reaction system CaO/Ca(OH)2(Stuttgart : Eigenverlag des Instituts für Wasser- und Umweltsystemmodellierung der Universität Stuttgart, 2021) Seitz, Gabriele; Class, Holger (apl. Prof. Dr.-Ing.)Item Open Access Analyse des Zuppinger-Wasserrades : hydraulische Optimierungen unter Berücksichtigung ökologischer Aspekte(Stuttgart : Eigenverlag des Instituts für Wasser- und Umweltsystemmodellierung der Universität Stuttgart, 2018) Harten, Matthias von; Wieprecht, Silke (Prof. Dr.-Ing.)Das Zuppinger-Wasserrad stammt in seiner Form aus der Mitte des 19. Jahrhunderts und stellt für Standorte mit großem Durchfluss und niedriger Fallhöhe weiterhin den Stand der Technik dar. Seine Bauart ermöglicht zudem einen Einsatz an Standorten mit stark veränderlichen Durchflüssen und Unterwasserständen. Charakteristisch für diesen Typ Wasserrad ist die Schaufelform: die Form der weit ins Radinnere gezogene Wasserradschaufel entspricht einer Evolvente mit anschließender Geraden. In der Literatur werden Wirkungsgrade von Zuppinger-Wasserrädern von ca. 80% erwähnt. Im Zentrum der vorliegenden Arbeit stehen Optimierungspotentiale, um den Wirkungsgrad erhöhen und damit die Leistungsausbeute steigern sowie Optimierungspotentiale, um die Durchgängigkeit für Fische zu verbessen. Zunächst werden die Entwicklung sowie die Konstruktion und Dimensionierung des Zuppinger-Wasserrades beschrieben. Im Anschluss daran warden Optimierungspotentiale einerseits durch neue Forschungsansätze und andererseits durch einen Technologietransfer aus anderen Energiewandlern abgeleitet. Die Durchführung und Analyse der Optimierungspotentiale erfolgte an einem Versuchsstand an der Hochschule Darmstadt mit einem maßstabsgetreuen Wasserradmodell, welches im Rahmen der vorliegenden Arbeit entwickelt und aufgebaut wurde. Die systematischen hydraulischen Versuche zeigen, dass der Wirkungsgrad durch Änderungen im Betrieb des Wasserrades und dessen Bauweise auf über 85% und die Leistung um bis zu 30% zu steigern sind. Besonders hervorzuheben sind die Schaufelteilung sowie ein Radboden, da diese die größten Zuwächse generieren. Eine Veränderung der Drehzahl kann ebenfalls die Leistungsausbeute steigern und möglicherweise die Durchgängigkeit verbessern. Ein Betrieb über einen Drehzahlbereich würde den Wirkungsgrad über ein breiteres Durchflussspektrum auf einem höheren Niveau halten. Aus den ökologischen Optimierungen werden hinsichtlich der Leistungsausbeute folgende Erkenntnisse gezogen: geringe Auswirkungen auf die Leistungsausbeute durch ein erhöhtes Spaltmaß; Leistungseinbußen durch die Demontage von äußeren Latten und die Reduzierung der Schaufelanzahl.Item Open Access Analysis of real-world spatial dependence of subsurface hydraulic properties using copulas with a focus on solute transport behaviour(2011) Haslauer, Claus; Bárdossy, András (Prof. Dr. rer.nat. Dr.-Ing.)Copulas are a novel tool in geostatistics that allows modelling of pure spatial dependence independently of the marginal distribution and without an assumption of multivariate Gaussian dependence. By using a transformation via the marginal distribution, the effect of extreme values is substantially decreased compared to traditional Gaussian based geostatistical measures such as Kriging. Additionally, the dependence is not described as an average variance as in Kriging, but a different degree of dependence can be modelled for different quantiles of the marginal distribution. Two data-sets from field sites at Borden and North Bay, both in Ontario, Canada, were used to test the performance of copulas as stochastic models for spatial dependence. Furthermore, this thesis explores possible effects of modelling spatial dependence using non-Gaussian copulas on physical properties that are based on such heterogeneous fields. For comparison, the effects of Gaussian structures are evaluated. The Gaussian- and non-Gaussian structures can not be distinguished by their variograms. It was shown that neither of the two data-sets exhibits Gaussian dependence – despite the fact that the Borden aquifer is commonly thought of as a relatively homogeneous porous medium with a small variance of hydraulic conductivity. Two non-Gaussian copula models, v-copulas and maximum Gaussian copulas were fitted to the hydraulic conductivity data, to be compared with a Gaussian copula model. The theoretical copula models were subsequently used for spatial interpolation and simulation. In addition to evaluating the spatial dependence structure of the hydraulic conductivity data-sets, fitting theoretical copula models and using them for interpolation and simulation, the goal of this thesis is to explore if the structure of the hydraulic conductivity field influences a physical property, such as plume evolution as evaluated by second central moments of concentration fields. Despite the fact that Borden is a relatively homogeneous porous medium, and despite the fact that both types of spatial fields are not distinguishable by their variograms, the solute transport characteristics based on these two types of fields differ significantly in two- dimensional settings. The difference is less pronounced in three-dimensions. Non-Gaussian dependence can lead to a non-symmetric distribution of variance of concentration along the main direction of flow. Increasing the variance of a marginal distribution by a certain factor does not necessarily lead to a dispersivity increased by the same factor in the case of non-Gaussian fields. It is postulated that non-Gaussian spatial dependence of hydraulic conductivity and a more skewed marginal distribution of hydraulic conductivity will have significant implications in the other more heterogeneous aquifers.Item Open Access Numerical modelling of bedload transport in rivers using implicit time discretisation to realise full and sequential coupling with shallow water flow(Stuttgart : Eigenverlag des Instituts für Wasser- und Umweltsystemmodellierung der Universität Stuttgart, 2025) Utz, Martin; Flemisch, Bernd (apl. Prof. Dr. rer. nat.)