Over recent years, political, technological, environmental and economic factors have combined to increase interest in distributed energy resources (DER), and flexibility in the power system. As a resource which is both distributed and flexible, flexible demand (FD) can be considered to be particularly of interest. However, due to many facets of its nature, understanding the available flexibility, and potential value of that flexibility, is difficult. Further, understanding the effects of FD exploitation on other multi-energy system actors, given the complex nature of modern liberalised energy systems, complicates the picture further. These factors form material obstructions to the assessment of FD, for example, for the construction of business cases. To address these gaps this thesis first assesses the nature and value of various applicable current and potential markets and charging/incentive regimes, before detailing a novel multi-energy domestic demand simulation model, capable of modelling, in detail, domestic FD resources. Subsequently, a multi-commodity stochastic energy/reserve optimisation model, capable of modelling various DERs and taking into account price signals related to various energy-related commodities and services (including user utility) is specified. The separation of price components for application at different aggregation levels, which is applied in the optimisation model, also informs the described value mapping methodology, which illustrates the impacts of any, particularly demand-side, intervention on the wider multi-energy system. The power of the above detailed contributions are demonstrated through various studies, which show the physical and economic impact of various demand side interventions and of greater market participation by FD resources.

La question de l'accès au soin est cruciale dans notre société moderne. Un effet évident de la demande accrue de services de santé est l'augmentation du taux d'occupation dans les hôpitaux. La principale différence entre la dispensation de soins à l'hôpital et au domicile est la suivante: le patient doit se déplacer et toutes les ressources nécessaires à son traitement se trouvent dans le même endroit, tandis que dans les soins délivrés au domicile, les ressources doivent être déplacées au chevet du patient. Il existe plusieurs défis afin de pouvoir réaliser ce changement. Dans cette thèse nous traitons trois problèmes importants dans la conception des structures de soins à domicile. D’abord, la localisation des structures en minimisant les coûts logistiques, où nous développons trois modèles incluant différentes caractéristiques comme du système de santé comme les coûts liés aux déplacements des ressources, la variation de la demande dans le temps et l’existence et évolution des ressource libérales. Ces modèles nous permettent de proposer des localisations robustes dans le temps tout en assurant une couverture maximale et en minimisant les coûts. La deuxième problématique consiste au choix des activités et couverture épidémiologique et spatiale en tenant compte différentes activités et types de ressources, les autorisations pour réaliser les pathologies et la couverture. Deux modèles développés nous ont permis montrer les effets sur l’affectation de la demande et le dimensionnement de ressources induits par changements dans les coûts des libéraux, salaires et d’autorisation de servir la demande. Le troisième problème et celui du dimensionnement de ressources avec incertitudes de demande (volume, épidémiologique et géographique) et le modèle proposé tient compte du problème sous-jacent de déplacement des ressources à l’aide d’une estimation de la tournée réalisée. / The issue of access to heamthcare is crucial in our modern society. One obvious effect of the augmentation of healthcare services demand is the increasing occupancy rates in hospitals. The main difference between the provision of care at the hospital and at home is as follows: the patient is at hospital and all the resources necessary for its treatment are in the same place, while in the care delivered at home, resources must be moved to the bedside. There are several challenges in order to achieve this change. In this thesis we address three important issues in the design of structures of home care. First, the location of structures minimizing logistics costs, where we develop three models with different features such as traveling costs of resources, changes in demand over time and evolution of freelance resources. These models allow us to provide robust location over time while ensuring maximum coverage and minimizing costs. The second issue is the choice of activities, epidemiological and spatial coverage, taking into account different types of activities and resources, permissions to serve some pathologies and coverage. Two models developed allow us to show the effects on the demand allocation and resources planning induced by changes in the costs of freelance professionals and authorization to serve some pathologies. The third problem is the dimensioning of resources with demand uncertainty (volume, epidemiological and geographical) and the proposed model takes into account the underlying problem of moving resources using an estimate of the routes performed.

Dans cette thèse, nous cherchons à répondre à une problématique formulée par la DGA Techniques navales pour surveiller une zone stratégique : planifier le déploiement spatial et temporel optimal d’un ensemble de capteurs de façon à maximiser les chances de détecter une cible mobile et intelligente. La cible est dite intelligente car elle est capable de détecter sous certaines conditions les menaces que représentent les capteurs et ainsi de réagir en adaptant son comportement. Les déploiements générés pouvant aussi avoir un coût élevé nous devons tenir compte de ce critère lorsque nous résolvons notre problématique. Il est important de noter que la résolution d’un problème de ce type requiert, selon les besoins, l’application d’une méthode d’optimisation mono-objectif voire multiobjectif. Jusqu’à présent, les travaux existants n’abordent pas la question du coût des déploiements proposés. De plus la plupart d’entre eux ne se concentrent que sur un seul aspect à la fois. Enfin, pour des raisons algorithmiques, les contraintes sont généralement discrétisées.Dans une première partie, nous présentons un algorithme qui permet de déterminer le déploiement spatio-temporel de capteurs le plus efficace sans tenir compte de son coût. Cette méthode est une application à l’optimisation de la méthode multiniveau généralisée.Dans la seconde partie, nous montrons d’abord que l’utilisation de la somme pondérée des deux critères permet d’obtenir des solutions sans augmenter le temps de calcul. Pour notre seconde approche, nous nous inspirons des algorithmes évolutionnaires d’optimisation multiobjectif et adaptons la méthode multiniveau généralisée à l’optimisation multiobjectif. / In this work, we propose a solution to a problem issued by the DGA Techniques navales in order to survey a strategic area: determining the optimal spatio-temporal deployment of sensors that will maximize the detection probability of a mobile and smart target. The target is said to be smart because it is capable of detecting the threat of the sensors under certain conditions and then of adapting its behaviour to avoid it. The cost of a deployment is known to be very expensive and therefore it has to be taken into account. It is important to note that the wide spectrum of applications within this field of research also reflects the need for a highly complex theoretical framework based on stochastic mono or multi-objective optimisation. Until now, none of the existing works have dealt with the cost of the deployments. Moreover, the majority only treat one type of constraint at a time. Current works mostly rely on operational research algorithms which commonly model the constraints in both discrete space and time.In the first part, we present an algorithm which computes the most efficient spatio-temporal deployment of sensors, but without taking its cost into account. This optimisation method is based on an application of the generalised splitting method.In the second part, we first use a linear combination of the two criteria. For our second approach, we use the evolutionary multiobjective optimisation framework to adapt the generalised splitting method to multiobjective optimisation. Finally, we compare our results with the results of the NSGA-II algorithm.

There is a growing societal concern about excessive water and fertilizer use in agricultural systems. High water productivity while maintaining high crop yields can be achieved with appropriate irrigation scheduling. Moreover, freshwater pollution through nitrogen (N) leaching due to the widespread use of N fertilizers demands for an efficient N fertilization management. However, sustainable crop management requires good knowledge of soil water and N dynamics as well as of crop water and N demand. Crop growth models, which describe physical and physiological processes of crop growth as well as water and matter transport, are considered as powerful tools to assist in the optimization of irrigation and fertilization management. It is of a general nature that the reliability of simulation based predictions depends on the quality and quantity of the data used for model calibration and validation which can be obtained e.g. in field experiments. A lack of data or low data quality for model calibration and validation may cause low performance and large uncertainties in simulation results. The large number of model parameters to be calibrated requires appropriate calibration methods and a sequential calibration strategy. Moreover, a simulation based planning of the field design saves costs and expenditure while supporting maximal outcomes of experiments. An adjustment of crop growth modeling and experiments is required for model improvement and development to reliably predict crop growth and to generalize predicted results. In this research study, a new approach for simulation based optimal experimental design was developed aiming to integrate simulation models, experiments, and optimization methods in one framework for optimal and sustainable irrigation and N fertilization management. The approach is composed of three steps: 1. The preprocessing consists of the calibration and validation of the crop growth model based on existing experimental data, the generation of long time-series of climate data, and the determination of the optimal irrigation control. 2. The implementation comprises the determination and experimental application of the simulation based optimized deficit irrigation and N fertilization schedules and an appropriate experimental data collection. 3. The postprocessing includes the evaluation of the experimental results namely observed yield, water productivity (WP), nitrogen use efficiency (NUE), and economic aspects, as well as a model evaluation. Five main tools were applied within the new approach: an algorithm for inverse model parametrization, a crop growth model for simulating crop growth, water balance and N balance, an optimization algorithm for deficit irrigation and N fertilization scheduling, and a stochastic weather generator. Furthermore, a water flow model was used to determine the optimal irrigation control functions and for simulation based estimation of the optimal field design. The approach was implemented within three case studies presented in this work. The new approach combines crop growth modeling and experiments with stochastic optimization. It contributes to a successful application of crop growth modeling based on an appropriate experimental data collection. The presented model calibration and validation procedure using the collected data facilitates reliable predictions. The stochastic optimization framework for deficit irrigation and N fertilization scheduling proved to be a powerful tool to enhance yield, WP, NUE and profit. / In der heutigen Gesellschaft gibt es zunehmend Bedenken gegenüber übermäßigem Wasser- und Düngereinsatz in der Landwirtschaft. Eine hohe Wasserproduktivität kann jedoch durch geeignete Bewässerungspläne mit hohen landwirtschaftlichen Erträgen in Einklang gebracht werden. Die mit der weitverbreiteten Stickstoffdüngung einhergehende Gewässerbelastung aufgrund von Stickstoffauswaschung erfordert zudem ein effizientes Stickstoffmanagement. Eine entsprechende ressourceneffiziente Landbewirtschaftung bedarf präzise Kenntnisse der Bodenwasser- und Stickstoffdynamiken sowie des Pflanzenwasser- und Stickstoffbedarfs. Als leistungsfähige Werkzeuge zur Unterstützung bei der Optimierung von Bewässerungs-und Düngungsplänen werden Pflanzenwachstumsmodelle eingesetzt, welche die physischen und physiologischen Prozesse des Pflanzenwachstums sowie die physikalischen Prozesse des Wasser- und Stofftransports abbilden. Hierbei hängt die Zuverlässigkeit dieser simulationsbasierten Vorhersagen von der Qualität und Quantität der bei der Modellkalibrierung und -validierung verwendeten Daten ab, welche beispielsweise in Feldversuchen erfasst werden. Fehlende Daten oder Daten mangelhafter Qualität bei der Modellkalibrierung und -validierung führen zu unzuverlässigen Simulationsergebnissen und großen Unsicherheiten bei der Vorhersage. Die große Anzahl an zu kalibrierenden Parametern erfordert zudem geeignete Kalibrierungsmethoden sowie eine sequenzielle Kalibrierungsstrategie. Darüber hinaus kann eine simulationsbasierte Planung des Versuchsdesigns Kosten und Aufwand reduzieren und zu weiteren experimentellen Erkenntnissen führen. Die Abstimmung von Pflanzenwachstumsmodellen und Versuchen ist zudem für die Modellentwicklung und -verbesserung sowie für eine Verallgemeinerung von Simulationsergebnissen unabdingbar. Im Rahmen dieser Arbeit wurde ein neuer Ansatz für ein simulationsbasiertes optimales Versuchsdesign entwickelt. Ziel war es, Simulationsmodelle, Versuche und Optimierungsmethoden in einem Ansatz für optimales und nachhaltiges Bewässerungs- und Düngungsmanagement zu integrieren. Der Ansatz besteht aus drei Schritten: 1. Die Vorbereitungsphase beinhaltet die auf existierenden Versuchsdaten basierende Kalibrierung und Validierung des Pflanzenwachstumsmodells, die Generierung von Klimazeitreihen und die Bestimmung der optimalen Bewässerungssteuerung. 2. Die Durchführungsphase setzt sich aus der Erstellung und experimentellen Anwendung der simulationsbasierten optimierten Defizitbewässerungs- und Stickstoffdüngungspläne und der Erfassung der relevanten Versuchsdaten zusammen. 3. Die Auswertungsphase schließt eine Evaluierung der Versuchsergebnisse anhand ermittelter Erträge, Wasserproduktivitäten (WP), Stickstoffnutzungseffizienzen (NUE) und ökonomischer Aspekte, sowie eine Modellevaluierung ein. In dem neuen Ansatz kamen im Wesentlichen folgende fünf Werkzeuge zur Anwendung: Ein Algorithmus zur inversen Modellparametrisierung, ein Pflanzenwachstumsmodell, welches das Pflanzenwachstum sowie die Wasser- und Stickstoffbilanzen abbildet, ein evolutionärer Optimierungsalgorithmus für die Generierung von defizitären Bewässerungs- und Stickstoffplänen und ein stochastischer Wettergenerator. Zudem diente ein Bodenwasserströmungsmodell der Ermittlung der optimalen Bewässerungssteuerung und der simulationsbasierten Optimierung des Versuchsdesigns. Der in dieser Arbeit vorgestellte Ansatz wurde in drei Fallbeispielen angewandt. Der neue Ansatz kombiniert Pflanzenwachstumsmodellierung und Experimente mit stochastischer Optimierung. Er leistet einen Beitrag zu einer erfolgreichen Pflanzenwachstumsmodellierung basierend auf der Erfassung relevanter Versuchsdaten. Die vorgestellte Modellkalibrierung und -validierung unter Verwendung der erfassten Versuchsdaten trug wesentlich zu zuverlässigen Simulationsergebnissen bei. Darüber hinaus stellt die hier vorgestellte stochastische Optimierung von defizitären Bewässerungs- und Stickstoffplänen ein leistungsfähiges Werkzeug dar, um Erträge, WP, NUE und den Profit zu erhöhen.

Constraint handling is difficult in model predictive control (MPC) of linear differential inclusions (LDIs) and linear parameter varying (LPV) systems. The designer is faced with a choice of using conservative bounds that may give poor performance, or accurate ones that require heavy online computation. This thesis presents a framework to achieve a more flexible trade-off between these two extremes by using a state tube, a sequence of parametrised polyhedra that is guaranteed to contain the future state. To define controllers using a tube, one must ensure that the polyhedra are a sub-set of the region defined by constraints. Necessary and sufficient conditions for these subset relations follow from duality theory, and it is possible to apply these conditions to constrain predicted system states and inputs with only a little conservatism. This leads to a general method of MPC design for uncertain-parameter systems. The resulting controllers have strong theoretical properties, can be implemented using standard algorithms and outperform existing techniques. Crucially, the online optimisation used in the controller is a convex problem with a number of constraints and variables that increases only linearly with the length of the prediction horizon. This holds true for both LDI and LPV systems. For the latter it is possible to optimise over a class of gain-scheduled control policies to improve performance, with a similar linear increase in problem size. The framework extends to stochastic LDIs with chance constraints, for which there are efficient suboptimal methods using online sampling. Sample approximations of chance constraint-admissible sets are generally not positively invariant, which motivates the novel concept of ‘sample-admissible' sets with this property to ensure recursive feasibility when using sampling methods. The thesis concludes by introducing a simple, convex alternative to chance-constrained MPC that applies a robust bound to the time average of constraint violations in closed-loop.

There is a growing societal concern about excessive water and fertilizer use in agricultural systems. High water productivity while maintaining high crop yields can be achieved with appropriate irrigation scheduling. Moreover, freshwater pollution through nitrogen (N) leaching due to the widespread use of N fertilizers demands for an efficient N fertilization management. However, sustainable crop management requires good knowledge of soil water and N dynamics as well as of crop water and N demand. Crop growth models, which describe physical and physiological processes of crop growth as well as water and matter transport, are considered as powerful tools to assist in the optimization of irrigation and fertilization management. It is of a general nature that the reliability of simulation based predictions depends on the quality and quantity of the data used for model calibration and validation which can be obtained e.g. in field experiments. A lack of data or low data quality for model calibration and validation may cause low performance and large uncertainties in simulation results. The large number of model parameters to be calibrated requires appropriate calibration methods and a sequential calibration strategy. Moreover, a simulation based planning of the field design saves costs and expenditure while supporting maximal outcomes of experiments. An adjustment of crop growth modeling and experiments is required for model improvement and development to reliably predict crop growth and to generalize predicted results. In this research study, a new approach for simulation based optimal experimental design was developed aiming to integrate simulation models, experiments, and optimization methods in one framework for optimal and sustainable irrigation and N fertilization management. The approach is composed of three steps: 1. The preprocessing consists of the calibration and validation of the crop growth model based on existing experimental data, the generation of long time-series of climate data, and the determination of the optimal irrigation control. 2. The implementation comprises the determination and experimental application of the simulation based optimized deficit irrigation and N fertilization schedules and an appropriate experimental data collection. 3. The postprocessing includes the evaluation of the experimental results namely observed yield, water productivity (WP), nitrogen use efficiency (NUE), and economic aspects, as well as a model evaluation. Five main tools were applied within the new approach: an algorithm for inverse model parametrization, a crop growth model for simulating crop growth, water balance and N balance, an optimization algorithm for deficit irrigation and N fertilization scheduling, and a stochastic weather generator. Furthermore, a water flow model was used to determine the optimal irrigation control functions and for simulation based estimation of the optimal field design. The approach was implemented within three case studies presented in this work. The new approach combines crop growth modeling and experiments with stochastic optimization. It contributes to a successful application of crop growth modeling based on an appropriate experimental data collection. The presented model calibration and validation procedure using the collected data facilitates reliable predictions. The stochastic optimization framework for deficit irrigation and N fertilization scheduling proved to be a powerful tool to enhance yield, WP, NUE and profit.:Contents Nomenclature ..............................................................................................................................xii 1 Introduction..................................................................................................................................1 I Fundamentals and literature review ........................................................................................5 2 Water productivity in crop production ....................................................................................7 2.1 Water productivity .................................................................................................................7 2.2 Increase of crop yield ..........................................................................................................9 2.3 Irrigation ...............................................................................................................................10 2.3.1 Irrigation methods ...........................................................................................................10 2.3.2 Irrigation scheduling and irrigation control ................................................................11 2.3.3 The influence of the field design on profitability .......................................................12 2.4 The concept of controlled deficit irrigation ...................................................................14 3 Nitrogen use efficiency in crop production .........................................................................17 3.1 Nitrogen use efficiency ....................................................................................................18 3.2 N fertilization management .............................................................................................18 3.3 Combination of controlled deficit irrigation and deficit N fertilization ......................19 4 Crop growth modeling ............................................................................................................21 4.1 Physiological crop growth models ..................................................................................21 4.1.1 Model description of SVAT model Daisy ....................................................................22 4.1.2 Model description of crop growth model Pilote .........................................................24 4.2 Optimal experimental design for model parametrization ...........................................25 4.2.1 Experimental design ......................................................................................................25 4.2.2 Model parameter estimation ........................................................................................26 4.2.3 Model parameter estimation based on greenhouse data .......................................27 5 Irrigation and N fertilization scheduling ..............................................................................29 5.1 Irrigation scheduling .........................................................................................................29 5.2 N fertilization scheduling .................................................................................................30 5.3 Combination of irrigation and N fertilization scheduling ............................................30 II New approach for simulation based optimal experimental design ................................33 6 Preprocessing steps ...............................................................................................................37 6.1 Model parametrization and assessment .......................................................................37 6.1.1 Calibration of the soil parameters ...............................................................................38 6.1.2 Calibration of the plant parameters ............................................................................39 6.1.3 Model assessment .........................................................................................................41 6.1.4 Preliminary simulations for an optimal experimental layout ..................................43 6.2 Generation of long time-series of climate data ............................................................44 6.3 Determination of the optimal irrigation control functions ...........................................44 7 Stochastic optimization framework ......................................................................................47 7.1 Stochastic optimization framework .................................................................................47 7.1.1 Optimization algorithm ...................................................................................................47 7.1.2 Generation of the crop water (nitrogen) production functions ................................48 7.1.3 Application of the stochastic optimization framework ..............................................48 7.1.4 Crop growth model requirements ................................................................................49 8 Data collection during the experimentation .......................................................................51 9 Postprocessing steps .............................................................................................................55 9.1 Evaluation of the experimental results ...........................................................................55 9.1.1 Yield and total dry matter ..............................................................................................55 9.1.2 Water productivity and nitrogen use efficiency .........................................................55 9.1.3 Economic aspects ..........................................................................................................55 9.1.4 Evaluation of the model results ....................................................................................56 III Application of the new approach to three case studies ...................................................57 10 Evaluation of model transferability ....................................................................................59 10.1 Objectives and summary ................................................................................................59 10.2 Experimental site and experimental setup .................................................................61 10.3 Data collection during the experimentation ................................................................63 10.4 Calibration and validation of the model parameters .................................................63 10.4.1 Model setup and soil parametrization ......................................................................64 10.4.2 Plant parameter calibration and validation .............................................................67 10.5 Application of the stochastic optimization framework ...............................................75 10.5.1 Generation of the climate data ...................................................................................75 10.5.2 Estimation of the yield potential of wheat ................................................................75 10.5.3 Estimation of the water productivity potential of barley .........................................77 10.6 Discussion and conclusions ..........................................................................................81 11 Real-time irrigation scheduling ..........................................................................................83 11.1 Objectives and summary ................................................................................................83 11.2 Experimental site and field design ...............................................................................85 11.3 Data collection during the experiment ........................................................................86 11.4 Calibration and setup of the crop growth model Pilote .............................................87 11.5 Derivation of optimal irrigation control functions for different drip line spacings 88 11.5.1 Initial Hydrus 2D/3D simulations ...............................................................................88 11.5.2 Determination of the irrigation control functions .....................................................89 11.5.3 Verifying measurements ..............................................................................................92 11.6 Real-time deficit irrigation scheduling .........................................................................93 11.7 Evaluation of the experimental results .........................................................................96 11.7.1 Crop yields .....................................................................................................................96 11.7.2 Water productivity .........................................................................................................97 11.7.3 Prognostic simulations ................................................................................................98 11.7.4 Economic aspects ........................................................................................................99 11.8 Discussion and conclusions ........................................................................................100 12 Multicriterial optimization...................................................................................................103 12.1 Objectives and summary .............................................................................................103 12.2 Experimental site and experimental setup ...............................................................105 12.3 Data collection during the experiment ......................................................................105 12.4 Experimental layout ......................................................................................................106 12.5 Calibration and validation of the model parameters ..............................................107 12.5.1 Calibration of the soil parameters ...........................................................................107 12.5.2 Calibration and validation of the plant parameters .............................................107 12.5.3 Setup of SVAT model Daisy .....................................................................................108 12.6 Generation of the climate data ....................................................................................109 12.7 Optimized irrigation and N fertilization scheduling .................................................109 12.8 Evaluation of the experimental results .......................................................................111 12.8.1 Observed plant variables and weather data .........................................................111 12.8.2 Water productivities and nitrogen use efficiencies ...............................................111 12.8.3 Chlorophyll Meter values ..........................................................................................112 12.8.4 Recalculation of soil parameters .............................................................................113 12.9 Postprocessing simulations of yield and water and N dynamics..........................114 12.9.1 Yield predictions using Daisy 1D ............................................................................114 12.9.2 Yield predictions using Daisy 2D ............................................................................119 12.10 Discussion and conclusions .....................................................................................121 IV General discussion, conclusions and outlook ...............................................................123 13 General discussion ............................................................................................................125 14 General conclusions and outlook ....................................................................................133 Appendix ....................................................................................................................................134 A Tables and Figures ...............................................................................................................137 B Model setup and weather files ...........................................................................................145 List of Tables .............................................................................................................................153 List of Figures ............................................................................................................................153 References ................................................................................................................................159 / In der heutigen Gesellschaft gibt es zunehmend Bedenken gegenüber übermäßigem Wasser- und Düngereinsatz in der Landwirtschaft. Eine hohe Wasserproduktivität kann jedoch durch geeignete Bewässerungspläne mit hohen landwirtschaftlichen Erträgen in Einklang gebracht werden. Die mit der weitverbreiteten Stickstoffdüngung einhergehende Gewässerbelastung aufgrund von Stickstoffauswaschung erfordert zudem ein effizientes Stickstoffmanagement. Eine entsprechende ressourceneffiziente Landbewirtschaftung bedarf präzise Kenntnisse der Bodenwasser- und Stickstoffdynamiken sowie des Pflanzenwasser- und Stickstoffbedarfs. Als leistungsfähige Werkzeuge zur Unterstützung bei der Optimierung von Bewässerungs-und Düngungsplänen werden Pflanzenwachstumsmodelle eingesetzt, welche die physischen und physiologischen Prozesse des Pflanzenwachstums sowie die physikalischen Prozesse des Wasser- und Stofftransports abbilden. Hierbei hängt die Zuverlässigkeit dieser simulationsbasierten Vorhersagen von der Qualität und Quantität der bei der Modellkalibrierung und -validierung verwendeten Daten ab, welche beispielsweise in Feldversuchen erfasst werden. Fehlende Daten oder Daten mangelhafter Qualität bei der Modellkalibrierung und -validierung führen zu unzuverlässigen Simulationsergebnissen und großen Unsicherheiten bei der Vorhersage. Die große Anzahl an zu kalibrierenden Parametern erfordert zudem geeignete Kalibrierungsmethoden sowie eine sequenzielle Kalibrierungsstrategie. Darüber hinaus kann eine simulationsbasierte Planung des Versuchsdesigns Kosten und Aufwand reduzieren und zu weiteren experimentellen Erkenntnissen führen. Die Abstimmung von Pflanzenwachstumsmodellen und Versuchen ist zudem für die Modellentwicklung und -verbesserung sowie für eine Verallgemeinerung von Simulationsergebnissen unabdingbar. Im Rahmen dieser Arbeit wurde ein neuer Ansatz für ein simulationsbasiertes optimales Versuchsdesign entwickelt. Ziel war es, Simulationsmodelle, Versuche und Optimierungsmethoden in einem Ansatz für optimales und nachhaltiges Bewässerungs- und Düngungsmanagement zu integrieren. Der Ansatz besteht aus drei Schritten: 1. Die Vorbereitungsphase beinhaltet die auf existierenden Versuchsdaten basierende Kalibrierung und Validierung des Pflanzenwachstumsmodells, die Generierung von Klimazeitreihen und die Bestimmung der optimalen Bewässerungssteuerung. 2. Die Durchführungsphase setzt sich aus der Erstellung und experimentellen Anwendung der simulationsbasierten optimierten Defizitbewässerungs- und Stickstoffdüngungspläne und der Erfassung der relevanten Versuchsdaten zusammen. 3. Die Auswertungsphase schließt eine Evaluierung der Versuchsergebnisse anhand ermittelter Erträge, Wasserproduktivitäten (WP), Stickstoffnutzungseffizienzen (NUE) und ökonomischer Aspekte, sowie eine Modellevaluierung ein. In dem neuen Ansatz kamen im Wesentlichen folgende fünf Werkzeuge zur Anwendung: Ein Algorithmus zur inversen Modellparametrisierung, ein Pflanzenwachstumsmodell, welches das Pflanzenwachstum sowie die Wasser- und Stickstoffbilanzen abbildet, ein evolutionärer Optimierungsalgorithmus für die Generierung von defizitären Bewässerungs- und Stickstoffplänen und ein stochastischer Wettergenerator. Zudem diente ein Bodenwasserströmungsmodell der Ermittlung der optimalen Bewässerungssteuerung und der simulationsbasierten Optimierung des Versuchsdesigns. Der in dieser Arbeit vorgestellte Ansatz wurde in drei Fallbeispielen angewandt. Der neue Ansatz kombiniert Pflanzenwachstumsmodellierung und Experimente mit stochastischer Optimierung. Er leistet einen Beitrag zu einer erfolgreichen Pflanzenwachstumsmodellierung basierend auf der Erfassung relevanter Versuchsdaten. Die vorgestellte Modellkalibrierung und -validierung unter Verwendung der erfassten Versuchsdaten trug wesentlich zu zuverlässigen Simulationsergebnissen bei. Darüber hinaus stellt die hier vorgestellte stochastische Optimierung von defizitären Bewässerungs- und Stickstoffplänen ein leistungsfähiges Werkzeug dar, um Erträge, WP, NUE und den Profit zu erhöhen.:Contents Nomenclature ..............................................................................................................................xii 1 Introduction..................................................................................................................................1 I Fundamentals and literature review ........................................................................................5 2 Water productivity in crop production ....................................................................................7 2.1 Water productivity .................................................................................................................7 2.2 Increase of crop yield ..........................................................................................................9 2.3 Irrigation ...............................................................................................................................10 2.3.1 Irrigation methods ...........................................................................................................10 2.3.2 Irrigation scheduling and irrigation control ................................................................11 2.3.3 The influence of the field design on profitability .......................................................12 2.4 The concept of controlled deficit irrigation ...................................................................14 3 Nitrogen use efficiency in crop production .........................................................................17 3.1 Nitrogen use efficiency ....................................................................................................18 3.2 N fertilization management .............................................................................................18 3.3 Combination of controlled deficit irrigation and deficit N fertilization ......................19 4 Crop growth modeling ............................................................................................................21 4.1 Physiological crop growth models ..................................................................................21 4.1.1 Model description of SVAT model Daisy ....................................................................22 4.1.2 Model description of crop growth model Pilote .........................................................24 4.2 Optimal experimental design for model parametrization ...........................................25 4.2.1 Experimental design ......................................................................................................25 4.2.2 Model parameter estimation ........................................................................................26 4.2.3 Model parameter estimation based on greenhouse data .......................................27 5 Irrigation and N fertilization scheduling ..............................................................................29 5.1 Irrigation scheduling .........................................................................................................29 5.2 N fertilization scheduling .................................................................................................30 5.3 Combination of irrigation and N fertilization scheduling ............................................30 II New approach for simulation based optimal experimental design ................................33 6 Preprocessing steps ...............................................................................................................37 6.1 Model parametrization and assessment .......................................................................37 6.1.1 Calibration of the soil parameters ...............................................................................38 6.1.2 Calibration of the plant parameters ............................................................................39 6.1.3 Model assessment .........................................................................................................41 6.1.4 Preliminary simulations for an optimal experimental layout ..................................43 6.2 Generation of long time-series of climate data ............................................................44 6.3 Determination of the optimal irrigation control functions ...........................................44 7 Stochastic optimization framework ......................................................................................47 7.1 Stochastic optimization framework .................................................................................47 7.1.1 Optimization algorithm ...................................................................................................47 7.1.2 Generation of the crop water (nitrogen) production functions ................................48 7.1.3 Application of the stochastic optimization framework ..............................................48 7.1.4 Crop growth model requirements ................................................................................49 8 Data collection during the experimentation .......................................................................51 9 Postprocessing steps .............................................................................................................55 9.1 Evaluation of the experimental results ...........................................................................55 9.1.1 Yield and total dry matter ..............................................................................................55 9.1.2 Water productivity and nitrogen use efficiency .........................................................55 9.1.3 Economic aspects ..........................................................................................................55 9.1.4 Evaluation of the model results ....................................................................................56 III Application of the new approach to three case studies ...................................................57 10 Evaluation of model transferability ....................................................................................59 10.1 Objectives and summary ................................................................................................59 10.2 Experimental site and experimental setup .................................................................61 10.3 Data collection during the experimentation ................................................................63 10.4 Calibration and validation of the model parameters .................................................63 10.4.1 Model setup and soil parametrization ......................................................................64 10.4.2 Plant parameter calibration and validation .............................................................67 10.5 Application of the stochastic optimization framework ...............................................75 10.5.1 Generation of the climate data ...................................................................................75 10.5.2 Estimation of the yield potential of wheat ................................................................75 10.5.3 Estimation of the water productivity potential of barley .........................................77 10.6 Discussion and conclusions ..........................................................................................81 11 Real-time irrigation scheduling ..........................................................................................83 11.1 Objectives and summary ................................................................................................83 11.2 Experimental site and field design ...............................................................................85 11.3 Data collection during the experiment ........................................................................86 11.4 Calibration and setup of the crop growth model Pilote .............................................87 11.5 Derivation of optimal irrigation control functions for different drip line spacings 88 11.5.1 Initial Hydrus 2D/3D simulations ...............................................................................88 11.5.2 Determination of the irrigation control functions .....................................................89 11.5.3 Verifying measurements ..............................................................................................92 11.6 Real-time deficit irrigation scheduling .........................................................................93 11.7 Evaluation of the experimental results .........................................................................96 11.7.1 Crop yields .....................................................................................................................96 11.7.2 Water productivity .........................................................................................................97 11.7.3 Prognostic simulations ................................................................................................98 11.7.4 Economic aspects ........................................................................................................99 11.8 Discussion and conclusions ........................................................................................100 12 Multicriterial optimization...................................................................................................103 12.1 Objectives and summary .............................................................................................103 12.2 Experimental site and experimental setup ...............................................................105 12.3 Data collection during the experiment ......................................................................105 12.4 Experimental layout ......................................................................................................106 12.5 Calibration and validation of the model parameters ..............................................107 12.5.1 Calibration of the soil parameters ...........................................................................107 12.5.2 Calibration and validation of the plant parameters .............................................107 12.5.3 Setup of SVAT model Daisy .....................................................................................108 12.6 Generation of the climate data ....................................................................................109 12.7 Optimized irrigation and N fertilization scheduling .................................................109 12.8 Evaluation of the experimental results .......................................................................111 12.8.1 Observed plant variables and weather data .........................................................111 12.8.2 Water productivities and nitrogen use efficiencies ...............................................111 12.8.3 Chlorophyll Meter values ..........................................................................................112 12.8.4 Recalculation of soil parameters .............................................................................113 12.9 Postprocessing simulations of yield and water and N dynamics..........................114 12.9.1 Yield predictions using Daisy 1D ............................................................................114 12.9.2 Yield predictions using Daisy 2D ............................................................................119 12.10 Discussion and conclusions .....................................................................................121 IV General discussion, conclusions and outlook ...............................................................123 13 General discussion ............................................................................................................125 14 General conclusions and outlook ....................................................................................133 Appendix ....................................................................................................................................134 A Tables and Figures ...............................................................................................................137 B Model setup and weather files ...........................................................................................145 List of Tables .............................................................................................................................153 List of Figures ............................................................................................................................153 References ................................................................................................................................159

The initiative by the EU to combat global warming through the introduction of a cap-and-trade system for greenhouse gas emissions in 2005, known as the EU Emissions Trading System (ETS), resulted in the inception of a new financial market. The right to emit one tonne of CO2-equivalents, as well as derivatives on this right, have become commodities, traded both through exchanges and over the counter. A relevant question thus becomes how a market maker trading these derivatives should hedge their exposures. This thesis examines how stochastic optimisation can be used to hedge a portfolio of futures, forwards, and emissions rights in the EU ETS, while taking into account market microstructre effects such as transaction costs. This is done through the implementation of a Stochastic Programming (SP) model that weights portfolio risk against transaction costs,where the entire term structure of futures is Monte Carlo-simulated. The term structure of the futures is analysed by decomposing futures prices into the spot price, the term structure of the risk free interest rate, and the term structure of the convenience yield, as was first done by Working (1948). These are estimated using the non-parametric optimisation framework of Blomvall (2017), where EUROIS contracts and ICE EUA futures are used as benchmark instruments. It was found that the method results in smooth yield curves with small repricing errors, thanks to suitable parameter calibration through 3-fold Cross Validation for both curves. From day-to-day changes in the resulting curves, three systematic risk factors for each curve, that capture more than 98% of the variance during the analysed period from October 2012 to March 2018, were found with PCA. These factors were then fitted to univariate GARCH-models, and normal mixture copulas. This model allows for the hedging problem to be solved with SP. For the out-of-sample period from March 2018 to April 2022, the results show promise, as the portfolios hedged with SP are considerably less volatile than both a statically hedged and an unhedged portfolio. Furthermore, for some values of the parameter weighting risk and costs, these portfolios yield mean variance efficiency.