The role of organic farming for food security: local nexus with a global view

A convergence of factors has made food security one of the most important global issues. It has been the core concept of the Milan Expo 2015, whose title, Feeding the Planet, Energy for Life, embodied the challenge to provide the world’s growing population with a sustainable, secure supply of safe, nutritious, and affordable high-quality food using less land with lower inputs. Meeting the food security agenda using current agricultural production techniques cannot be achieved without serious degradation to the environment, including soil degradation, loss of biodiversity and climate change. Organic farming is seen as a solution to the challenge of sustainable food production, as it provides more nutritious food, with less or no pesticide residues and lower use of inputs. A limit of organic farming is its restricted capability of producing food compared to conventional agriculture, thus being an inefficient approach to food production and to food security. The authors maintain, on the basis of a scientific literature review, that organic soils tend to retain the physical, chemical and biological properties over the long term, while maintaining stable levels of productivity and thereby ensuring long-term food production and safety. Furthermore, the productivity gap of organic crops may be worked out by further investment in research and in particular into diversification techniques. Moreover, strong scientific evidence indicates that organic agricultural systems deliver greater ecosystem services and social benefits.

Deterministic Genericity and the Computation of homological Invariants

The main goal of this thesis is to discuss the determination of homological invariants of polynomial ideals. Thereby we consider different coordinate systems and analyze their meaning for the computation of certain invariants. In particular, we provide an algorithm that transforms any ideal into strongly stable position if char k = 0. With a slight modification, this algorithm can also be used to achieve a stable or quasi-stable position. If our field has positive characteristic, the Borel-fixed position is the maximum we can obtain with our method. Further, we present some applications of Pommaret bases, where we focus on how to directly read off invariants from this basis. In the second half of this dissertation we take a closer look at another homological invariant, namely the (absolute) reduction number. It is a known fact that one immediately receives the reduction number from the basis of the generic initial ideal. However, we show that it is not possible to formulate an algorithm – based on analyzing only the leading ideal – that transforms an ideal into a position, which allows us to directly receive this invariant from the leading ideal. So in general we can not read off the reduction number of a Pommaret basis. This result motivates a deeper investigation of which properties a coordinate system must possess so that we can determine the reduction number easily, i.e. by analyzing the leading ideal. This approach leads to the introduction of some generalized versions of the mentioned stable positions, such as the weakly D-stable or weakly D-minimal stable position. The latter represents a coordinate system that allows to determine the reduction number without any further computations. Finally, we introduce the notion of β-maximal position, which provides lots of interesting algebraic properties. In particular, this position is in combination with weakly D-stable sufficient for the weakly D-minimal stable position and so possesses a connection to the reduction number.

A probabilistic approach to the estimation of regional photovoltaic power generation using meteorological data

In Germany the upscaling algorithm is currently the standard approach for evaluating the PV power produced in a region. This method involves spatially interpolating the normalized power of a set of reference PV plants to estimate the power production by another set of unknown plants. As little information on the performances of this method could be found in the literature, the first goal of this thesis is to conduct an analysis of the uncertainty associated to this method. It was found that this method can lead to large errors when the set of reference plants has different characteristics or weather conditions than the set of unknown plants and when the set of reference plants is small. Based on these preliminary findings, an alternative method is proposed for calculating the aggregate power production of a set of PV plants. A probabilistic approach has been chosen by which a power production is calculated at each PV plant from corresponding weather data. The probabilistic approach consists of evaluating the power for each frequently occurring value of the parameters and estimating the most probable value by averaging these power values weighted by their frequency of occurrence. Most frequent parameter sets (e.g. module azimuth and tilt angle) and their frequency of occurrence have been assessed on the basis of a statistical analysis of parameters of approx. 35 000 PV plants. It has been found that the plant parameters are statistically dependent on the size and location of the PV plants. Accordingly, separate statistical values have been assessed for 14 classes of nominal capacity and 95 regions in Germany (two-digit zip-code areas). The performances of the upscaling and probabilistic approaches have been compared on the basis of 15 min power measurements from 715 PV plants provided by the German distribution system operator LEW Verteilnetz. It was found that the error of the probabilistic method is smaller than that of the upscaling method when the number of reference plants is sufficiently large (>100 reference plants in the case study considered in this chapter). When the number of reference plants is limited (<50 reference plants for the considered case study), it was found that the proposed approach provides a noticeable gain in accuracy with respect to the upscaling method.