Nonlocal operators are used in a wide variety of models and applications due to many natural phenomena being driven by nonlocal dynamics. Nonlocal operators are integral operators allowing for interactions between two distinct points in space. The nonlocal models investigated in this thesis involve kernels that are assumed to have a finite range of nonlocal interactions. Kernels of this type are used in nonlocal elasticity and convection-diffusion models as well as finance and image analysis. Also within the mathematical theory they arouse great interest, as they are asymptotically related to fractional and classical differential equations. The results in this thesis can be grouped according to the following three aspects: modeling and analysis, discretization and optimization. Mathematical models demonstrate their true usefulness when put into numerical practice. For computational purposes, it is important that the support of the kernel is clearly determined. Therefore nonlocal interactions are typically assumed to occur within an Euclidean ball of finite radius. In this thesis we consider more general interaction sets including norm induced balls as special cases and extend established results about well-posedness and asymptotic limits. The discretization of integral equations is a challenging endeavor. Especially kernels which are truncated by Euclidean balls require carefully designed quadrature rules for the implementation of efficient finite element codes. In this thesis we investigate the computational benefits of polyhedral interaction sets as well as geometrically approximated interaction sets. In addition to that we outline the computational advantages of sufficiently structured problem settings. Shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations. Here we consider a class of shape optimization problems constrained by nonlocal equations which involve interface-dependent kernels. We derive the shape derivative associated to the nonlocal system model and solve the problem by established numerical techniques.

This study aims to estimate the cotton yield at the field and regional level via the APSIM/OZCOT crop model, using an optimization-based recalibration approach based on the state variable of the cotton canopy - the leaf area index (LAI), derived from atmospherically corrected Landsat-8 OLI remote sensing images in 2014. First, a local sensitivity and global analysis approach was employed to test the sensitivity of cultivar, soil and agronomic parameters to the dynamics of the LAI. After sensitivity analyses, a series of sensitive parameters were obtained. Then, the APSIM/OZCOT crop model was calibrated by observations over a two-year span (2006-2007) at the Aksu station, combined with these sensitive cultivar parameters and the current understanding of cotton cultivar parameters. Third, the relationship between the observed in-situ LAI and synchronous perpendicular vegetation indices derived from six Landsat-8 OLI images covering the entire growth stage was modelled to generate LAI maps in time and space. Finally, the Particle Swarm Optimization (PSO) and general-purpose optimization approach (based on Nelder-Mead algorithm) were used to recalibrate four sensitive agronomic parameters (row spacing, sowing density per row, irrigation amount and total fertilization) according to the minimization of the root-mean-square deviation (RMSE) between the simulated LAI from the APSIM/OZCOT model and retrieved LAI from Landsat-8 OLI remote sensing images. After the recalibration, the best simulated results compared with observed cotton yield were obtained. The results showed that: (1) FRUDD, FLAI and DDISQ were the major cultivar parameters suitable for calibrating the cotton cultivar. (2) After the calibration, the simulated LAI performed well with an RMSE and mean absolute error (MAE) of 0.45 and 0.33, respectively, in 2006 and 0.46 and 0.41, respectively, in 2007. The coefficient of determination between the observed and simulated LAI was 0.83 and 0.97, respectively, in 2006 and 2007. The Pearson- correlation coefficient was 0.913 and 0.988 in 2006 and 2007, respectively, with a significant positive correlation between the simulated and observed LAI. The difference between the observed and simulated yield was 776.72 kg/ha and 259.98 kg/ha in 2006 and 2007, respectively. (3) Cotton cultivation in 2014 was obtained using three Landsat-8 OLI images - DOY136 (May), DOY 168 (June) and DOY 200 (July) - based on the phenological differences in cotton and other vegetation types. (4) The yield estimation after the assimilation closely approximated the field-observed values, and the coefficient of determination was as high as 0.82, after recalibration of the APSIM/OZCOT model for ten cotton fields. The difference between the observed and assimilated yields for the ten fields ranged from 18.2 to 939.7 kg/ha. The RMSE and MAE between the assimilated and observed yield was 417.5 and 303.1 kg/ha, respectively. These findings provide scientific evidence for the feasibility of coupled remote sensing and APSIM/OZCOT model at the field level. (5) Upscaling from field level to regional level, the assimilation algorithm and scheme are both especially important. Although the PSO method is very efficient, the computational efficiency is also the shortcoming of the assimilation strategy on a regional scale. Comparisons between the PSO and general-purpose optimization method (based on the Nelder-Mead algorithm) were implemented from the RSME, LAI curve and computational time. The general-purpose optimization method (based on the Nelder-Mead algorithm) was used for the regional assimilation between remote sensing and the APSIM/OZCOT model. Meanwhile, the basic unit for regional assimilation was also determined as cotton field rather than pixel. Moreover, the crop growth simulation was also divided into two phases (vegetative growth and reproductive growth) for regional assimilation. (6) The regional assimilation at the vegetative growth stage between the remote sensing derived and APSIM/OZCOT model-simulated LAI was implemented by adjusting two parameters: row spacing and sowing density per row. The results showed that the sowing density of cotton was higher in the southern part than in the northern part of the study area. The spatial pattern of cotton density was also consistent with the reclamation from 2001 to 2013. Cotton fields after early reclamation were mainly located in the southern part while the recent reclamation was located in the northern part. Poor soil quality, lack of irrigation facilities and woodland belts of cotton fields in the northern part caused the low density of cotton. Regarding the row spacing, the northern part was larger than the southern part due to the variation of two agronomic modes from military and private companies. (7) The irrigation and fertilization amount were both used as key parameters to be adjusted for regional assimilation during the reproductive growth period. The result showed that the irrigation per time ranged from 58.14 to 89.99 mm in the study area. The spatial distribution of the irrigation amount is higher in the northern part while lower in southern study area. The application of urea fertilization ranged from 500.35 to 1598.59 kg/ha in the study area. The spatial distribution of fertilization was lower in the northern part and higher in the southern part. More fertilization applied in the southern study area aims to increase the boll weight and number for pursuing higher yields of cotton. The frequency of the RSME during the second assimilation was mainly located in the range of 0.4-0.6 m2/m2. The estimated cotton yield ranged from 1489 to 8895 kg/ha. The spatial distribution of the estimated yield is also higher in the southern part than the northern study area.

Global change, i.e. climate and land use changes, severely impact natural ecosystems at different scales. Poikilothermic animals as butterflies, amphibians and reptiles have proven to be useful indicators for global change impacts as their phenology, spatial distribution, individual fitness and survival strongly depend on external environmental factors. In this aspect, phenological changes in terms of advanced flight or breeding periods, immigrations of foreign species, range shifts concomitant with temperature increases and even local population declines have been observed in both species groups. However, to date much attention has been paid to global change impacts on the species or population level and analyses concerning entire ecosystems are scarce. Applying a novel statistical modelling algorithm we assessed future changes in the extent and composition of terrestrial ecoregions as classified by the World Wide Fund for Nature (WWF). They are defined as coarse-scale conservation units containing exceptional assemblages of species and ecological dynamics. Our results demonstrate dramatic geographical changes in the extent and location of these ecoregions across all continents and even imply a repriorisation of conservation efforts to cope with future climate change impacts on biodiversity. On the local scale, climate change impacts become unequivocal. Comparing historical to contemporary butterfly assemblages on vineyard fallows of the Trier Region, a significant decline in butterfly richness, but also a severe depletion in trait diversity was observed. Comparisons of community temperature indices reveal a striking shift in community composition leading to a replacement of sedentary and monophagous habitat specialists by ubiquitous species. Similar changes have been observed in nature reserves in the Saar-Mosel-area. Monitoring data reveal strong losses of species diversity and remarkable shifts of community compositions at the expense of habitat specialists. Besides climatic variability, these findings are largely attributed to changes in habitat structures, mostly due to eutrophication and monotonisation. Management activities are unlikely to counterbalance these effects, thus severely questioning current conservation strategies. Most dramatic global change impacts are suspected on closely associated species and disruptions of biotic interactions are often hold responsible for species declines. A strong host-parasite association has developed in Myrmica ants and Maculinea butterflies, the later crucially depending on specific host ants for their larval survival. Applying environmental niche models we determined considerable niche dynamics in the observed parasite-host relation with a pronounced niche plasticity in the butterfly species adapting to previous evasive niche shifts in their host ants. Moreover, the new emergence of species continuously expanding their northernmost range borders concomitant with global warming like the Short-tailed blue (Cupido argiades) is attributed to climate change. However, species distribution models predict a severe habitat loss and shifts of potentially suitable habitats of this species towards north-eastern Europe and higher altitudes under several IPCC scenarios making the presence of this species in the Trier region a contemporary phenomenon. Species distribution models have emerged as powerful tools to predict species distributions over spatial and temporal scales. However, not only the presence of a species, but also its abundance have significant implications for species conservation. The ability to deduce spatial abundance patterns from environmental suitability might more efficiently guide field surveys or monitoring programs over large geographical areas saving time and money. Although the application of species distribution models to deduce vertebrate abundances is well recognized, our results indicate that this method is not an adequate approach to predict invertebrate abundances. Structural and ecological factors as well as climatic patterns acting at the microscale are key drivers of invertebrate occurrence and abundances limiting conclusions drawn from modeling approaches. Population declines should be interpreted with care as in butterflies and amphibians various reasons are debated. Both species groups are acknowledged to be highly susceptible to land use changes and variations in landscape structure. Moreover, climate and land use are not independently operating factors. The combined impact of both is demonstrated in our study linking climate-driven changes in amphibian phenologies to temporal advanced applications of pesticides and fertilizers. Both environmental factors already represent severe threats to amphibians when standing alone, but linking their combined impacts may result in an potentiated risk for amphibian populations. As all amphibians and numerous butterfly species are legally protected under the Federal Nature Conservation Act, intensifications of agricultural land use in large parts of Germany as well as new agrarian practices (including genetically manipulated plants accompanied by new herbicide technologies) might severely challenge regional conservation activities in the future.

Aus dem Wunsch, die zentralen Prozesse im System Boden"Pflanze"Atmosphäre einschließlich der Auswirkungen verschiedener Bewirtschaftungspraktiken zu verstehen und nachzubilden, resultiert die Entwicklung verschiedener Pflanzenwachstumsmodelle. Ziel der vorliegenden Untersuchung ist zum einen, die im Realsystem auftretenden räumlichen Ertragsmuster zu identifizieren und zu charakterisieren. Mithilfe der Semivariogramm-Analyse ist eine räumliche Autokorrelation der Ertragsdaten von maximal 48 Meter abzuleiten. Die räumliche Analyse (GIS) zeigt, dass die Sommergerste ein leicht abweichendes Verhalten im Vergleich zu den Winterkulturen (Winterweizen, Winterraps) aufweist. Schließlich werden mithilfe der selbstorganisierenden Merkmalskarten die primär und sekundär für das Ertragsverhalten verantwortlichen Ursachen identifiziert. Eine abschließende hierarchische Clusteranalyse gliedert die in die Untersuchung eingehenden Standorte in vier spezifische Cluster mit charakteristischen Eigenschaften. Ein zweites Ziel ist die Klärung der Frage, ob die Pflanzenwachstumsmodelle STICS und DAISY bei entsprechender Parametrisierung in der Lage sind, das für ein detektiertes Muster charakteristische Verhalten von Pflanzenwachstum und Ertrag realitätsnah abzubilden. Den Modellanwendungen gehen eine Sensitivitätsanalyse und verschiedene Parametrisierungsansätze zur Erfassung des jeweiligen Modellverhaltens voraus. In beiden Modellen übt der Bodenwasserhaushalt einen starken Einfluss auf die Ertragsbildung aus. Des weiteren kommt in beiden Modellen den Stressfaktoren eine zentrale Bedeutung zu. Die Parametrisierung der Modelle auf der Grundlage der im Feld erhobenen Daten führt bei beiden Modellen nicht zu einem dem Realsystem entsprechenden Bild. Eine über die Sensitivitätsanalyse hinausreichende, vertiefte Modellkenntnis ist erforderlich, um die in die Modelle eingehenden Parameter bzw. deren spezifischen Einfluss auf das Modellverhalten beurteilen und interpretieren zu können. Dies betrifft insbesondere die Modellgrößen der Bodenmodule. Dieser Aspekt erschwert eine einfache räumliche Übertragung der Modelle STICS und DAISY.

Auf der Grundlage von bodenphysikalischen Standortdaten wurden mit dem physikalisch basierten Modell CATFLOW Bodenwassergehalte und Abflussprozesse von verschiedenen Standorten im Mesozoikum der Trierer Bucht auf der Plotskale simuliert. Die Standorte unterscheiden sich durch das Ausgangssubstrat der Bodenbildung (lehmig-tonig, schluffig-sandig) und die Landnutzung (Acker, Grünland, Wald). Für die Modellvalidierung standen wöchentliche Bodenwassergehaltsmessungen, monatliche Sickerwassersummen aus Lysimetermessungen und Oberflächen- und Zwischenabflusskurven von Beregnungsversuchen zur Verfügung. Ziel der Arbeit ist es zu untersuchen, inwieweit Retentionseigenschaften, Abflussprozesse und Abflussmengen aus Standortdaten ohne eine weitere Kalibrierung des Modells abgeleitet werden können. Besonderer Wert wird dabei auf die Parametrisierung des Bodens gelegt. Das Modell simuliert den Wassertransport in der Bodenmatrix über die zweidimensionale Richardsgleichung und den schnellen Wassertransport in Makroporen über ein einfaches Bulk-Modell. Daneben werden Oberflächenrauhigkeit, Durchwurzelungstiefe und Vegetationsbedeckung im Jahresgang berücksichtigt. Um den Einfluss von unterschiedlichen Parametrisierungen des Bodens aufzuzeigen, werden verschiedene Parametrisierungsvarianten untersucht. Die van Genuchten/Mualem-Parameter, welche die Retentions- und Leitfähigkeitseigenschaften der einzelnen Bodenhorizonte beschreiben, wurden zum einen über die Bodenart und Trockenrohdichte bestimmt und zum anderen über die Anpassung von Retentionskurven an im Labor bestimmte Punkte der Wasserspannungskurve ermittelt. Die Ergebnisse der Simulationen für die Standorte mit Bodenfeuchtemessung zeigen, dass mit dem Modell der Jahresgang der Bodenfeuchte prinzipiell nachvollzogen werden kann. Jedoch führt keine der drei Parametrisierungsvarianten zu einer eindeutigen Überlegenheit bei der Simulationsgüte. Um neben den üblichen Gütemaßen ein weiteres Kriterium für den Erfolg oder Misserfolg einer Standortsimulation zu gewinnen, wurden die Simulationsergebnisse mit den Messwerten der anderen Standorte verglichen. An vier von zehn Standorten führt der Vergleich der Messwerte mit den Simulationen von anderen Standorten zu einer deutlich besseren Übereinstimmung als die Simulation für diesen Standort. Die Ergebnisse der Simulationen der Lysimeterstandorte zeigen, dass mit dem Makroporenansatz ein schneller Wasserfluss im Sommer nicht simuliert werden kann, da das "Anspringen" der Makroporen im Modellkonzept an den Bodenwassergehalt geknüpft ist. Auch hier wurden die Simulationsergebnisse mit den Messwerten der anderen Standorte verglichen. Für fünf von acht Standorten konnte mit den simulierten Sickerwassermengen von anderen Standorten eine bessere Übereinstimmung erzielt werden. Die Simulation der Sickerwassermenge aus Lysimetern scheint daher auf Grundlage der vorliegenden Datenbasis den jeweiligen Standort nicht in seiner Einzigartigkeit charakterisieren zu können. Die mit den Beregnungsversuchen bestimmten Abflussprozesse konnten für die Mehrheit der 18 Standorte mit dem Modell abgebildet werden. Der Oberflächenabfluss konnte für Standorte, die nicht zur Verschlämmung neigen, unter Berücksichtigung von Infiltrationsdaten sehr gut nachgezeichnet werden. Zwischenabfluss wird zwar simuliert, bleibt aber auf der Plotskale in Dynamik und Abflussmenge hinter dem Realsystem zurück. Mit der Untersuchung konnte gezeigt werden, dass sich sowohl die zeitliche Entwicklung des Bodenwassergehaltes, als auch die gemessenen Abflussprozesse allein über die Standortdaten, ohne eine weitere Kalibrierung des Modells, abbilden lassen. Die Trennschärfe der Modellierung ist bei Standorten mit relativ ähnlicher bodenphysikalischer Ausstattung begrenzt. Andererseits müssen aber auch Messungenauigkeiten, besonders bei der thermogravimetrischen Bestimmung des Bodenwassergehaltes, berücksichtigt werden. Eine standortbezogene Aussage über Retentions- und Abflussverhalten ist über eine Simulation möglich, jedoch bleibt die quantitative Aussagekraft begrenzt.