In arid regions, mountain catchments are the major contributor to the total natural water yield. Due to generally low groundwater tables, subsurface underflow - referred to as mountain-front recharge - is important in distinction to the surface runoff at the mountain front. The extent of the groundwater basin is hereby often vague. Approaches to assess mountain-front recharge are mostly based on groundwater data and integrate over time and space. This, however, cannot provide prognostic and time-dependent estimates of subsurface inflow to the adjacent alluvial basin aquifer. Consequently, the proposed strategy builds on rainfall based approaches. Temporal and spatial resolution is in this case mostly limited by data scarcity regarding hydrological characteristics of the catchment area and high-resolution rainfall data. The proposed novel strategy combines three approaches to tackle these challenges. A newly developed conceptual hydrologic model provides time-dependent estimates based on fully distributed monthly rainfall. For distinct response units and seasons, non-linear relationships between rainfall and recharge describe the hydrogeologic response. The derivation of the response functions is based on a mass balance and considers the principal recharge mechanisms. Parameterisation makes use of available expert knowledge on geomorphology and seasonal rainfall characteristics. As an efficient tool to assess uncertainties, fuzzy arithmetic is used for complementary long-term average water balance estimates. This technique allows considering fuzziness in rainfall input, crop water use in mountain oases, and best available assumptions on recharge as portion of rainfall. Uncertainty regarding the potential, albeit unknown extent of groundwater basins is portrayed based on continuous surfaces which represent the degree of membership to a distinct geographical entity (termed as fuzzy regions). Distinct subsets of these fuzzy regions represent potential groundwater basins for water balance assessment. The proposed strategy was applied on the large scale in an arid karst mountain range in northern Oman. The two complementary assessment approaches result in similar ranges of values. They are in good agreement with inversely computed inflow to a steady state groundwater model for the adjacent basin aquifer. The results of the conceptual hydrologic model are confirmed by the plausibility of average recharge rates for distinct response units and seasons. This shows that less intense winter rainfall contributes mainly to groundwater recharge. Uncertainties due to the vague extent of the groundwater basin are about 30 % of the total mean annual value. An option to mitigate this uncertainty is the complementary consideration of adjacent aquifer systems in future studies. Hydrogeologic survey and observation of groundwater levels in the alluvial basin aquifer in near distance to the mountains is a way to underpin these findings in future studies. This recommenddation applies not only to the discussed study area, but also to mountain block systems in general. / In ariden Gebieten haben Gebirgseinzugsgebiete einen wesentlichen Anteil am gesamten natürlichen Wasserdargebot. Aufgrund i. Allg. tief liegender Grundwasserspiegel ist - in Abgrenzung zum Oberflächenabfluss am Gebirgsrand - auch der unterirdische Abstrom (mountain-front recharge) von besonderer Bedeutung. Die Ausdehnung des unterirdischen Einzugsgebiets ist dabei oft vage. Ansätze zur Abschätzung des mountain-front recharge basieren meist auf Grundwasserdaten und integrieren in Zeit und Raum. Damit können allerdings keine prognostischen oder zeitabhängigen Schätzungen für den Zustrom zur benachbarten alluvialen Aquifer gemacht werden. Daher wird im folgenden ein niederschlagsbasierter Ansatz vorgeschlagen. Das vorgeschlagene neue Konzept kombiniert drei Ansätze, um den genannten Herausforderungen zu begegnen. Mit einem neu entwickelten konzeptionellen hydrologischen Modell auf Basis verteilter Niederschläge werden monatliche Werte für die Grundwasserneubildung bereitgestellt. Es basiert auf nicht-linearen Beziehungen zwischen Niederschlag und Grundwasserneubildung für definierte hydrologisch homogene Einheiten und Jahreszeiten. Deren Ableitung basiert auf einer Massenbilanz und berücksichtigt die wesentlichen Neubildungsmechanismen. Die Parametrisierung basiert auf Expertenwissen zu Geomorphologie und Niederschlagscharakteristika. Fuzzy Arithmetik wird zur Berücksichtigung von Unsicherheiten in einer ergänzenden mittleren jährlichen Wasserbilanz verwendet. Damit können Unschärfen im Niederschlagsinput, beim Pflanzenwasserbedarf in Gebirgsoasen und best verfügbaren Schätzungen der Neubildung als Bruchteil des Niederschlags effizient berücksichtigt werden. Mittels kontinuierlicher Oberflächen, die den Grad der Zugehörigkeit zu einer bestimmten geographischen Entität anzeigen (fuzzy regions) werden Unsicherheiten in der räumlichen Ausdehnung der unterirdischen Einzugsgebiete beschrieben. Definierte Teilmengen dieser fuzzy regions werden dann bei den Wasserhaushaltsbetrachtungen als potentielle Grundwassereinzugsgebiete verwendet. Der vorgeschlagene Ansatz wurde in einer ariden, teils verkarsteten Gebirgsregion im Norden des Sultanats Oman angewendet. Die beiden sich ergänzenden Ansätze zur Abschätzung der Grundwasserneubildung ergaben im langjährigen Mittel vergleichbare Werte. Diese stimmten auch gut mit den Ergebnissen einer inversen Grundwassermodellierung überein. Die Plausibilität der Neubildungsraten für bestimmte hydrologisch homogene Einheiten und Jahreszeiten spricht für die Verlässlichkeit der Ergebnisse des konzeptionellen hydrologischen Modells. Offensichtlich tragen insbesondere die weniger intensiven Winterniederschläge wesentlich zur Grundwasserneubildung bei. Die Unsicherheiten bezüglich der Ausdehnung des Grundwassereinzugsgebiets belaufen sich auf ca. 30 % des mittleren jährlichen Dargebots. Die komplementäre Betrachtung benachbarter Grundwassereinzugsgebiete ist ein denkbarer Weg, diese Unsicherheit in Zukunft zu reduzieren. Ein wesentlicher Beitrag um die Ergebnisse dieser Studie zukünftig weiter zu untermauern wären hydrogeologische Erkundung und Beobachtung von Grundwasserständen im alluvialen Aquifer, insbesondere nahe dem Gebirgsrand. Diese Empfehlung gilt über dieses Fallbeispiel hinaus für vergleichbare Systeme, in denen ein Gebirgseinzugsgebiet den Aquifer in der angrenzende Ebene speist.

In arid regions, mountain catchments are the major contributor to the total natural water yield. Due to generally low groundwater tables, subsurface underflow - referred to as mountain-front recharge - is important in distinction to the surface runoff at the mountain front. The extent of the groundwater basin is hereby often vague. Approaches to assess mountain-front recharge are mostly based on groundwater data and integrate over time and space. This, however, cannot provide prognostic and time-dependent estimates of subsurface inflow to the adjacent alluvial basin aquifer. Consequently, the proposed strategy builds on rainfall based approaches. Temporal and spatial resolution is in this case mostly limited by data scarcity regarding hydrological characteristics of the catchment area and high-resolution rainfall data. The proposed novel strategy combines three approaches to tackle these challenges. A newly developed conceptual hydrologic model provides time-dependent estimates based on fully distributed monthly rainfall. For distinct response units and seasons, non-linear relationships between rainfall and recharge describe the hydrogeologic response. The derivation of the response functions is based on a mass balance and considers the principal recharge mechanisms. Parameterisation makes use of available expert knowledge on geomorphology and seasonal rainfall characteristics. As an efficient tool to assess uncertainties, fuzzy arithmetic is used for complementary long-term average water balance estimates. This technique allows considering fuzziness in rainfall input, crop water use in mountain oases, and best available assumptions on recharge as portion of rainfall. Uncertainty regarding the potential, albeit unknown extent of groundwater basins is portrayed based on continuous surfaces which represent the degree of membership to a distinct geographical entity (termed as fuzzy regions). Distinct subsets of these fuzzy regions represent potential groundwater basins for water balance assessment. The proposed strategy was applied on the large scale in an arid karst mountain range in northern Oman. The two complementary assessment approaches result in similar ranges of values. They are in good agreement with inversely computed inflow to a steady state groundwater model for the adjacent basin aquifer. The results of the conceptual hydrologic model are confirmed by the plausibility of average recharge rates for distinct response units and seasons. This shows that less intense winter rainfall contributes mainly to groundwater recharge. Uncertainties due to the vague extent of the groundwater basin are about 30 % of the total mean annual value. An option to mitigate this uncertainty is the complementary consideration of adjacent aquifer systems in future studies. Hydrogeologic survey and observation of groundwater levels in the alluvial basin aquifer in near distance to the mountains is a way to underpin these findings in future studies. This recommenddation applies not only to the discussed study area, but also to mountain block systems in general.:1 Mountains - 'water towers' for water resources systems in arid regions 2 Mountain hydrology and water resources assessment 2.1 Mountain hydrology and mountain-front recharge 2.2 Essential aspects to advance mountain hydrology 2.2.1 Rainfall characteristics and options for data acquisition 2.2.2 Groundwater-surface water interactions and availability of reference values 2.3 Approaches to the assessment of mountain-front recharge 2.3.1 Options to assess groundwater recharge 2.3.2 Arid zone water balance modelling - options and limitations 2.3.3 Key components for assessing mountain-front recharge 2.4 Linear reservoir models to describe base flow recession 3 Approaches to deal with uncertainty with a special focus on fuzzy sets 3.1 Probability based uncertainty assessment versus fuzzy reasoning 3.2 Fuzzy sets and related methods 3.3 Ranges of application in hydrology and water resources management 4 A novel strategy for estimating groundwater recharge in arid mountain regions 5 Fuzzy-based tools to portray uncertainties in water balance assessment 5.1 Fuzzy Recharge Areas: From qualitative data to quantitative conclusions 5.1.1 The concept of the Fuzzy Recharge Areas 5.1.2 Consideration of adjacent basins 5.2 Water balance assessment based on fuzzy arithmetic 5.2.1 Outline of the calculation procedure 5.2.2 Implementation of the fuzzy arithmetic operators 5.2.3 Implementation of the regionalisation approach APLIS 6 A conceptual hydrologic model to assess mountain-front recharge 6.1 Basic idea 6.2 Model structure 6.3 Calculation procedure using histograms of rainfall depths 6.4 Non-linear seasonal rainfall-recharge relationships 6.4.1 Derivation of the rainfall-recharge relationships 6.4.2 Sensitivity analysis 6.4.3 Response functions based on extreme parameter sets 6.5 Subsurface routing based on linear reservoir models 7 Case Study: Groundwater recharge assessment for the Barka Region (Oman) 7.1 Study area 7.1.1 Topography 7.1.2 Climate 7.1.3 Evapotranspiration 7.1.4 Rainfall characteristics 7.1.5 Geology and Hydrogeology 7.1.6 Soils 7.1.7 Runoff characteristics 7.1.8 Vegetation and irrigated agriculture in mountain oases 7.2 Recharge mechanisms in the study area 7.3 Assessment of mountain-front recharge - Methodology 7.3.1 Data Processing of Fuzzy Recharge Areas 7.3.2 Determining response units 7.3.3 Water use in mountain oases 7.3.4 Long-term average considerations based on fuzzy arithmetic 7.3.5 Time-dependent assessment using the conceptual hydrologic model 7.4 Assessment of mountain-front recharge - Results 7.4.1 Long-term average considerations 7.4.2 Time-dependent estimates 7.5 Consideration of uncertainties 7.6 Discussion & Conclusions 7.6.1 Water resources assessment in the study area 7.6.2 Modelling approaches 8 Summary 9 Prospects for future work List of Figures List of Tables List of Symbols List of Abbreviations Appendix A: Sensitivity of the response function to variations of the different model parameters B: Histograms of subsurface outflow at the mountain front QMFR based on different parameterisations of the conceptual hydrologic model References / In ariden Gebieten haben Gebirgseinzugsgebiete einen wesentlichen Anteil am gesamten natürlichen Wasserdargebot. Aufgrund i. Allg. tief liegender Grundwasserspiegel ist - in Abgrenzung zum Oberflächenabfluss am Gebirgsrand - auch der unterirdische Abstrom (mountain-front recharge) von besonderer Bedeutung. Die Ausdehnung des unterirdischen Einzugsgebiets ist dabei oft vage. Ansätze zur Abschätzung des mountain-front recharge basieren meist auf Grundwasserdaten und integrieren in Zeit und Raum. Damit können allerdings keine prognostischen oder zeitabhängigen Schätzungen für den Zustrom zur benachbarten alluvialen Aquifer gemacht werden. Daher wird im folgenden ein niederschlagsbasierter Ansatz vorgeschlagen. Das vorgeschlagene neue Konzept kombiniert drei Ansätze, um den genannten Herausforderungen zu begegnen. Mit einem neu entwickelten konzeptionellen hydrologischen Modell auf Basis verteilter Niederschläge werden monatliche Werte für die Grundwasserneubildung bereitgestellt. Es basiert auf nicht-linearen Beziehungen zwischen Niederschlag und Grundwasserneubildung für definierte hydrologisch homogene Einheiten und Jahreszeiten. Deren Ableitung basiert auf einer Massenbilanz und berücksichtigt die wesentlichen Neubildungsmechanismen. Die Parametrisierung basiert auf Expertenwissen zu Geomorphologie und Niederschlagscharakteristika. Fuzzy Arithmetik wird zur Berücksichtigung von Unsicherheiten in einer ergänzenden mittleren jährlichen Wasserbilanz verwendet. Damit können Unschärfen im Niederschlagsinput, beim Pflanzenwasserbedarf in Gebirgsoasen und best verfügbaren Schätzungen der Neubildung als Bruchteil des Niederschlags effizient berücksichtigt werden. Mittels kontinuierlicher Oberflächen, die den Grad der Zugehörigkeit zu einer bestimmten geographischen Entität anzeigen (fuzzy regions) werden Unsicherheiten in der räumlichen Ausdehnung der unterirdischen Einzugsgebiete beschrieben. Definierte Teilmengen dieser fuzzy regions werden dann bei den Wasserhaushaltsbetrachtungen als potentielle Grundwassereinzugsgebiete verwendet. Der vorgeschlagene Ansatz wurde in einer ariden, teils verkarsteten Gebirgsregion im Norden des Sultanats Oman angewendet. Die beiden sich ergänzenden Ansätze zur Abschätzung der Grundwasserneubildung ergaben im langjährigen Mittel vergleichbare Werte. Diese stimmten auch gut mit den Ergebnissen einer inversen Grundwassermodellierung überein. Die Plausibilität der Neubildungsraten für bestimmte hydrologisch homogene Einheiten und Jahreszeiten spricht für die Verlässlichkeit der Ergebnisse des konzeptionellen hydrologischen Modells. Offensichtlich tragen insbesondere die weniger intensiven Winterniederschläge wesentlich zur Grundwasserneubildung bei. Die Unsicherheiten bezüglich der Ausdehnung des Grundwassereinzugsgebiets belaufen sich auf ca. 30 % des mittleren jährlichen Dargebots. Die komplementäre Betrachtung benachbarter Grundwassereinzugsgebiete ist ein denkbarer Weg, diese Unsicherheit in Zukunft zu reduzieren. Ein wesentlicher Beitrag um die Ergebnisse dieser Studie zukünftig weiter zu untermauern wären hydrogeologische Erkundung und Beobachtung von Grundwasserständen im alluvialen Aquifer, insbesondere nahe dem Gebirgsrand. Diese Empfehlung gilt über dieses Fallbeispiel hinaus für vergleichbare Systeme, in denen ein Gebirgseinzugsgebiet den Aquifer in der angrenzende Ebene speist.:1 Mountains - 'water towers' for water resources systems in arid regions 2 Mountain hydrology and water resources assessment 2.1 Mountain hydrology and mountain-front recharge 2.2 Essential aspects to advance mountain hydrology 2.2.1 Rainfall characteristics and options for data acquisition 2.2.2 Groundwater-surface water interactions and availability of reference values 2.3 Approaches to the assessment of mountain-front recharge 2.3.1 Options to assess groundwater recharge 2.3.2 Arid zone water balance modelling - options and limitations 2.3.3 Key components for assessing mountain-front recharge 2.4 Linear reservoir models to describe base flow recession 3 Approaches to deal with uncertainty with a special focus on fuzzy sets 3.1 Probability based uncertainty assessment versus fuzzy reasoning 3.2 Fuzzy sets and related methods 3.3 Ranges of application in hydrology and water resources management 4 A novel strategy for estimating groundwater recharge in arid mountain regions 5 Fuzzy-based tools to portray uncertainties in water balance assessment 5.1 Fuzzy Recharge Areas: From qualitative data to quantitative conclusions 5.1.1 The concept of the Fuzzy Recharge Areas 5.1.2 Consideration of adjacent basins 5.2 Water balance assessment based on fuzzy arithmetic 5.2.1 Outline of the calculation procedure 5.2.2 Implementation of the fuzzy arithmetic operators 5.2.3 Implementation of the regionalisation approach APLIS 6 A conceptual hydrologic model to assess mountain-front recharge 6.1 Basic idea 6.2 Model structure 6.3 Calculation procedure using histograms of rainfall depths 6.4 Non-linear seasonal rainfall-recharge relationships 6.4.1 Derivation of the rainfall-recharge relationships 6.4.2 Sensitivity analysis 6.4.3 Response functions based on extreme parameter sets 6.5 Subsurface routing based on linear reservoir models 7 Case Study: Groundwater recharge assessment for the Barka Region (Oman) 7.1 Study area 7.1.1 Topography 7.1.2 Climate 7.1.3 Evapotranspiration 7.1.4 Rainfall characteristics 7.1.5 Geology and Hydrogeology 7.1.6 Soils 7.1.7 Runoff characteristics 7.1.8 Vegetation and irrigated agriculture in mountain oases 7.2 Recharge mechanisms in the study area 7.3 Assessment of mountain-front recharge - Methodology 7.3.1 Data Processing of Fuzzy Recharge Areas 7.3.2 Determining response units 7.3.3 Water use in mountain oases 7.3.4 Long-term average considerations based on fuzzy arithmetic 7.3.5 Time-dependent assessment using the conceptual hydrologic model 7.4 Assessment of mountain-front recharge - Results 7.4.1 Long-term average considerations 7.4.2 Time-dependent estimates 7.5 Consideration of uncertainties 7.6 Discussion & Conclusions 7.6.1 Water resources assessment in the study area 7.6.2 Modelling approaches 8 Summary 9 Prospects for future work List of Figures List of Tables List of Symbols List of Abbreviations Appendix A: Sensitivity of the response function to variations of the different model parameters B: Histograms of subsurface outflow at the mountain front QMFR based on different parameterisations of the conceptual hydrologic model References

Nowadays society strongly depends on its available resources and the long term stability of the surrounding ecosystem. Numerical modelling has become a general standard for evaluating past, current or future system states for a large number of applications supporting decision makers in proper management. In order to ensure the correct representation of the investigated processes and results of a simulation, verification examples (benchmarks), that are based on observation data or analytical solutions, are utilized to evaluate the numerical modelling tool. In many parts of the world, groundwater is an important resource for freshwater. While it is not only limited in quantity, subsurface water bodies are often in danger of contamination from various natural or anthropogenic sources. Especially in arid regions, marine saltwater intrusion poses a major threat to groundwater aquifers which mostly are the exclusive source of freshwater in these dry climates. In contrast to common numerical groundwater modelling, density-driven flow and mass transport have to be considered as vital processes in the system and in scenario simulations for fresh-saltwater interactions. In the beginning of this thesis, the capabilities of the modelling tool OpenGeoSys are verified with selected benchmarks to represent the relevant non-linear process coupling. Afterwards, variable-density application and process studies on different scales are presented. Application studies comprehend regional groundwater modelling of a coastal aquifer system extensively used for agricultural irrigation, as well as hydro-geological model development and parametrization. In two process studies, firstly, a novel method to model gelation of a solute in porous media is developed and verified on small scale laboratory observation data, and secondly, investigations of thermohaline double-diffusive Rayleigh regimes on medium scale are carried out. With the growing world population and, thus, increasing pressure on non-renewable resources, intelligent management strategies intensify demand for potent simulation tools and development of novel methods. In that way, this thesis highlights not only OpenGeoSys’ potential of density-dependent process modelling, but the comprehensive importance of variable-density flow and transport processes connecting, both, avant-garde scientific research, and real-world application challenges.

Nowadays society strongly depends on its available resources and the long term stability of the surrounding ecosystem. Numerical modelling has become a general standard for evaluating past, current or future system states for a large number of applications supporting decision makers in proper management. In order to ensure the correct representation of the investigated processes and results of a simulation, verification examples (benchmarks), that are based on observation data or analytical solutions, are utilized to evaluate the numerical modelling tool. In many parts of the world, groundwater is an important resource for freshwater. While it is not only limited in quantity, subsurface water bodies are often in danger of contamination from various natural or anthropogenic sources. Especially in arid regions, marine saltwater intrusion poses a major threat to groundwater aquifers which mostly are the exclusive source of freshwater in these dry climates. In contrast to common numerical groundwater modelling, density-driven flow and mass transport have to be considered as vital processes in the system and in scenario simulations for fresh-saltwater interactions. In the beginning of this thesis, the capabilities of the modelling tool OpenGeoSys are verified with selected benchmarks to represent the relevant non-linear process coupling. Afterwards, variable-density application and process studies on different scales are presented. Application studies comprehend regional groundwater modelling of a coastal aquifer system extensively used for agricultural irrigation, as well as hydro-geological model development and parametrization. In two process studies, firstly, a novel method to model gelation of a solute in porous media is developed and verified on small scale laboratory observation data, and secondly, investigations of thermohaline double-diffusive Rayleigh regimes on medium scale are carried out. With the growing world population and, thus, increasing pressure on non-renewable resources, intelligent management strategies intensify demand for potent simulation tools and development of novel methods. In that way, this thesis highlights not only OpenGeoSys’ potential of density-dependent process modelling, but the comprehensive importance of variable-density flow and transport processes connecting, both, avant-garde scientific research, and real-world application challenges.:Abstract Zusammenfassung Nomenclature List of Figures List of Tables I Background and Fundamentals 1 Introduction 1.1 Motivation 1.2 Structure of the Thesis 1.3 Variable-Density Flow in Literature 2 Theory and Methods 2.1 Governing Equations 2.2 Fluid Properties 2.3 Modelling and Visualization Tools 3 Benchmarks 3.1 Steady-state Unconfined Groundwater Table 3.2 Theis Transient Pumping Test 3.3 Transient Saltwater Intrusion 3.4 Development of a Freshwater Lens II Applications 4 Extended Inverse Distance Weighting Interpolation 4.1 Motivation 4.2 Extension of IDW Method 4.3 Artificial Test and Regional Scale Application 4.4 Summary and Conclusions 5 Modelling Transient Saltwater Intrusion 5.1 Background and Motivation 5.2 Methods and Model Setup 5.3 Simulation Results and Discussion 5.4 Summary, Conclusion and Outlook 6 Gelation of a Dense Fluid 6.1 Motivation 6.2 Methods and Model Setup 6.3 Results and Conclusions 7 Delineating Double-Diffusive Rayleigh Regimes 7.1 Background and Motivation 7.2 Methods and Model Setup 7.3 Results 7.4 Conclusions and Outlook III Summary and Conclusions 8 Important Achievements 9 Conclusions and Outlook Bibliography Publications Acknowledgements Appendix