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Process-based hydrological models, which simulate nitrogen load from its sources to the receiving waterbody, play an important role in supporting catchment management. The reliability of those models, such as the representative model SWAT used in this study, is determined by a sound calibration and the analysis of the prediction uncertainty. The multi-objective calibration approach prevails the classic single-objective calibration on the spatial parameterization of specific processes. However, the requirement of additional observations and practical procedures limits its application. Moreover, the prediction uncertainty of nitrogen load is inevitable and should also be quantified. This study is a scientific contribution to catchment management by overcoming the challenge with a systematic, well-founded concept of multi-objective calibration and uncertainty analysis for nitrogen load simulation in data-scarce catchments. The concept is tested and proofed by its practical applicability on the Yuan River Catchment (YRC) in China and leads to a generalized, recommended procedure for catchment management application as valuable progress in this field.
The study proposed to apply three groups of objectives, multi-site, multi-objective-function, and multi-metric. The applicability and the advantages of two multi-objective calibration approaches, Euclidean Distance and Non-Dominated Sorting Genetic Algorithm-II were analyzed. To quantify the prediction uncertainty, the study proposed to use the simulations with the highest or the lowest percent bias to represent the uncertainty band of the nitrogen load from the critical source areas (CSAs) and to the stream. The data-scarcity of the YRC was overcome by metrics obtained from open-access satellite-based datasets and metrics extracted from the existing discharge observations. Results show that multi-objective calibration has ensured the model’s better performance in terms of the spatial parameterization, the magnitude of the output time-series and the water balance components, in comparison to single-objective calibration. The predicted CSAs showed that 50% of the total nitrogen (TN) loading to the stream was from 26.3% to 37.1% of the area in the YRC. Meanwhile, over 50% of those TN were from the paddy field. Recommendations for application go to the multi-objective calibration considering all three groups of objectives. Approaches to obtain multi-metric objectives in the YRC are also applicable for catchments with data-scarcity. Recommendations for nitrogen management in the YRC is to emphasize the CSAs identified, especially the paddy field.
From Gleason's theorem we know that in principle every probability measure can be expressed by Hermitian operators in a separable Hilbert space and the Born rule as part of a quantum mechanical system. However, that theorem is not constructive. For a given discrete and additive probability measure based on a σ-algebra we construct a quantum system with projectors expressing that probability measure.
Eines der am intensivsten untersuchten Probleme aus dem Bereich der Optimierung stellt das sogenannte Traveling Salesman Problem (TSP, in deutsch: Handlungsreisendenproblem) dar. Die Aufgabe hinter dem Handlungsreisendenproblem besteht darin, für eine gegebene Anzahl an Orten eine Route zu entwickeln, sodass die Gesamtlänge der Route minimal ist. Zudem darf kein Ort, bis auf den ersten, mehrmals besucht werden. Ziel der vorliegenden Bachelorarbeit ist es, statistische Untersuchungen bezüglich der Tourlänge des TSP in Abhängig der Anzahl der besuchten Städte vorzunehmen, wobei der Fokus auf einer kleinen Anzahl von Städten liegt. Dazu wurde das Problem einerseits numerisch gelöst und die Verteilung der Lösungen analysiert. Für Teilaspekte wurden analytische Lösungen berechnet.