Statistical and stochastic post-processing of regional climate model data: copula-based downscaling, disaggregation and multivariate bias correction

In order to delineate management or climate change adaptation strategies for natural or technical water bodies, impact studies are necessary. To this end, impact models are set up for a given region which requires time series of meteorological data as driving data. Regional climate models (RCMs) are capable of simulating gridded data sets of several meteorological variables. The advantages over observed data are that the time series are complete and that meteorological information is also provided for ungauged locations. Furthermore, climate change impact studies can be conducted by driving the simulations with different forcing variables for future periods. While the performance of RCMs generally increases with a higher spatio-temporal resolution, the computational and storage demand increases non-linearly which can impede such highly resolved simulations in practice. Furthermore, systematic biases of the univariate distributions and multivariate dependence structures are a common problem of RCM simulations on all spatio-temporal scales. Depending on the case study, meteorological data must fulfill different criteria. For instance, the spatio-temporal resolution of precipitation time series should be as fine as 1 km and 5 minutes in order to be used for urban hydrological impact models. To bridge the gap between the demands of impact modelers and available meteorological RCM data, different computationally efficient statistical and stochastic post-processing techniques have been developed to correct the bias and to increase the spatio-temporal resolution. The main meteorological variable treated in this thesis is precipitation due to its importance for hydrological impact studies. The models presented in this thesis belong to the classes of bias correction, downscaling and temporal disaggregation techniques. The focus of the developed methods lies on multivariate copulas. Copulas constitute a promising modeling approach for highly-skewed and mixed discrete-continuous variables like precipitation since the marginal distribution is treated separately from the dependence structure. This feature makes them useful for the modeling of different meteorological variables as well. While copulas have been utilized in the past to model precipitation and other meteorological variables that are relevant in hydrology, applications to RCM simulations are not very common. The first method is a geostatistical estimation technique for distribution parameters of daily precipitation for ungauged locations, so that a bias correction with Quantile Mapping can be performed. The second method is a spatial downscaling of coarse scale RCM precipitation fields to a finer resolved domain. The model is based on the Gaussian Copula and generates ensembles of daily precipitation fields that resemble the precipitation fields of fine scale RCM simulations. The third method disaggregates hourly precipitation time series simulated by an RCM to a resolution of 5 minutes. The Gaussian Copula was utilized to condition the simulation on both spatial and temporal precipitation amounts to respect the spatio-temporal dependence structure. The fourth method is an approach to simulate a meteorological variable conditional on other variables at the same location and time step. The method was developed to improve the inter-variable dependence structure of univariately bias corrected RCM simulations in an hourly resolution

On the metric upper density of Birkhoff sums for irrational rotations

This article examines the value distribution of $S_{N}(f, \alpha) := \sum_{n=1}^N f(n\alpha)$ for almost every $\alpha$ where $N \in \mathbb{N}$ is ranging over a long interval and $f$ is a $1$-periodic function with discontinuities or logarithmic singularities at rational numbers. We show that for $N$ in a set of positive upper density, the order of $S_{N}(f, \alpha)$ is of Khintchine-type, unless the logarithmic singularity is symmetric. Additionally, we show the asymptotic sharpness of the Denjoy-Koksma inequality for such $f$, with applications in the theory of numerical integration. Our method also leads to a generalized form of the classical Borel-Bernstein Theorem that allows very general modularity conditions.Comment: 34 pages, comments are welcom

КОН ’ЮНКТУРА РИНКУ ПРАЦІ В УКРАЇНІ

Головним механізмом забезпечення інноваційного розвитку економіки і сус пільства є збільшення взаємодії між освітою , наукою , бізнесом і владою на основі їх взаємної зацікавленості у співпраці . Зокрема , вища освіта повинна не тільки забез печувати відтворення висококваліфікованих професійних кадрів , а й відігравати значну роль у соціальної мобільності , нарощуванні інтелектуального потенціалу суспільства , розповсюдженні найбільш соціально значущих культурних норм і т. д. Ринок праці все більше поповнюють фахівці з вищою освітою , хоча попит на них не зажди адекватний . Подолання диспропорцій , виявлених на ринку праці , можливе наразі лише на інноваційних принципах . Інноваційна складова в трудовій поведінці працюючих передбачає необхідність поліпшення професійно -кваліфіка ційної структури персоналу , розширення номенклатури спеціальностей працюючих , зростання серед останніх фахівців з вищою освітою , а також з високим кваліфікаційним розрядом