A three-pillar approach to assessing climate impacts on low flows

The objective of this paper is to present a framework for assessing climate impacts on future low flows that combines different sources of information, termed pillars. To illustrate the framework three pillars are chosen: (a) extrapolation of observed low-flow trends into the future, (b) rainfall–runoff projections based on climate scenarios and (c) extrapolation of changing stochastic rainfall characteristics into the future combined with rainfall–runoff modelling. Alternative pillars could be included in the overall framework. The three pillars are combined by expert judgement based on a synoptic view of data, model outputs and process reasoning. The consistency/inconsistency between the pillars is considered an indicator of the certainty/uncertainty of the projections. The viability of the framework is illustrated for four example catchments from Austria that represent typical climate conditions in central Europe. In the Alpine region where winter low flows dominate, trend projections and climate scenarios yield consistently increasing low flows, although of different magnitudes. In the region north of the Alps, consistently small changes are projected by all methods. In the regions in the south and south-east, more pronounced and mostly decreasing trends are projected but there is disagreement in the magnitudes of the projected changes. The process reasons for the consistencies/inconsistencies are discussed. For an Alpine region such as Austria the key to understanding low flows is whether they are controlled by freezing and snowmelt processes, or by the summer moisture deficit associated with evaporation. It is argued that the three-pillar approach offers a systematic framework of combining different sources of information aimed at more robust projections than that obtained from each pillar alone

Classical and robust regression for compositional data analysis

Diese Diplomarbeit befasst sich mit der Entwicklung von klassischer und robuster Regression mit Kompositionsdaten. Um die Ergebnisse auch interpretieren zu können, wurden zuerst geeignete Transformationen vom Raum der Kompositionen, dem Simplex, in den euklidischen Raum angewandt. Aufgrund der theoretischen Eigenschaften ist die "isometric log-ratio"-Transformation dabei zu bevorzugen. Die daraus resultierenden, transformierten Daten heißen Koordinaten. Ein Spezialfall davon sind die sogenannten "balances", die die Interpretation erleichtern sollen. Bei der Regressionsanalyse wurden schließlich drei verschiedene Fälle betrachtet. Zuerst beschäftigte man sich mit einem Modell, wo nur die zu erklärenden Variablen kompositionell waren. Weiters wurde ein Modell mit kompositionellen erklärenden Variablen untersucht und schließlich untersuchten wir auch noch den Fall von einem Modell, wo sowohl abhängige, als auch unabhängige Variable von kompositioneller Struktur waren. In allen Fällen wurden Regressionsschätzer mit Hilfe von klassischen und robusten Verfahren berechnet, im multivariaten Fall wurde der MLTS (multivariate least-trimmed squares) Schätzer verwendet.Implementiert wurde dieser durch einen schnellen MLTS Algorithmus. Schlussendlich wurden die beschriebenen Verfahren auf Daten aus der Geochemie angewandt, um Schlüsse von Anteilen von Elementen im Boden auf gewisse abhängige Variable (wie zum Beispiel das Wetter) zu ziehen.Inferenzstatistiken über geschätzte Parameter und Ausreißerdiagnostik sollten zur Beschreibung der Daten helfen.In this diploma thesis, classical and robust multivariate regression for compositions is developed. Therefore, proper transformations from the simplex to the usual Euclidean space have to be applied on the compositional variables for being able to interpret the results in terms of coordinates. Consequently, special kinds of balances are proposed to obtain reasonable results, that are easy to interpret.The regression analysis is divided into three parts. A model with just a compositional response is considered, as well as a model with compositional explanatory variables and finally a model with both, compositional response and compositional explanatory variables is taken into account. Special attention has to be paid to the ilr transformations of the original variables as well as to the resulting models given in coordinates. Further, classical and robust regression analysis can be applied and coefficients are computed. In the robust case, the multivariate least-trimmed squares estimator is used and a fast mlts algorithm has been used for the computations. Geochemical data was available to present the results. Inference statistics on the one hand and diagnostic plots on the other hand are used to display the properties of the data and the models that have been observed.8