Title: Frequency analysis of precipitation amounts Author: Mgr. Zuzana Rulfová Department: Department of Atmospheric Physics Supervisor: RNDr. Jan Kyselý, Ph.D., Institute of Atmospheric Physics CAS Abstract: This thesis deals with analysing characteristics of mean and extreme precipitation in observations and regional climate models (RCMs) with respect to their convective and stratiform origin. An algorithm for subdivision of precipitation amounts into predominantly convective and stratiform using station weather data is proposed and evaluated. The time series of convective and stratiform precipitation from the Czech Republic over 1982-2010 are used for analysing basic climatological characteristics of precipitation, including extremes, and evaluating RCMs from the ENSEMBLES project. Projected changes of convective and stratiform precipitation in Central Europe (the Czech Republic) are analysed using data from RCM simulations from the EURO-CORDEX project. The last part of the thesis introduces a new statistical model for analysing precipitation extremes. This model takes advantage from knowledge of origin of precipitation extremes. In future climate we could expect more convective and stratiform precipitation amounts in all seasons except summer, when climate models project decline in amounts of stratiform...

The statistical modeling of extreme natural hazards is becoming increasingly important due to climate change, whose effects have been increasingly visible throughout the last decades. It is thus crucial to understand the dependence structure of rare, high-impact events over space and time for realistic risk assessment. For spatial extremes, max-stable processes have played a central role in modeling block maxima. However, the spatial tail dependence strength is persistent across quantile levels in those models, which is often not realistic in practice. This lack of flexibility implies that max-stable processes cannot capture weakening dependence at increasingly extreme levels, resulting in a drastic overestimation of joint tail risk. To address this, we develop new dependence models in this thesis from the class of max-infinitely divisible (max-id) processes, which contain max-stable processes as a subclass and are flexible enough to capture different types of dependence structures. Furthermore, exact simulation algorithms for general max-id processes are typically not straightforward due to their complex formulations. Both simulation and inference can be computationally prohibitive in high dimensions. Fast and exact simulation algorithms to simulate max-id processes are provided, together with methods to implement our models in high dimensions based on the Vecchia approximation method. These proposed methodologies are illustrated through various environmental datasets, including air temperature data in South-Eastern Europe in an attempt to assess the effect of climate change on heatwave hazards, and sea surface temperature data for the entire Red Sea. In another application focused on assessing how the spatial extent of extreme precipitation has changed over time, we develop new time-varying $r$-Pareto processes, which are the counterparts of max-stable processes for high threshold exceedances.

In many environmental and climate applications, extreme data are spatial by nature, and hence statistics of spatial extremes is currently an important and active area of research dedicated to developing innovative and flexible statistical models that determine the location, intensity, and magnitude of extreme events. In particular, the development of flexible sub-asymptotic models is in trend due to their flexibility in modeling spatial high threshold exceedances in larger spatial dimensions and with little or no effects on the choice of threshold, which is complicated with classical extreme value processes, such as Pareto processes. In this thesis, we develop new flexible sub-asymptotic extreme value models for modeling spatial and spatio-temporal extremes that are combined with carefully designed gradient-based Markov chain Monte Carlo (MCMC) sampling schemes and that can be exploited to address important scientific questions related to risk assessment in a wide range of environmental applications. The methodological developments are centered around two distinct themes, namely (i) sub-asymptotic Bayesian models for extremes; and (ii) flexible marked point process models with sub-asymptotic marks. In the first part, we develop several types of new flexible models for light-tailed and heavy-tailed data, which extend a hierarchical representation of the classical generalized Pareto (GP) limit for threshold exceedances. Spatial dependence is modeled through latent processes. We study the theoretical properties of our new methodology and demonstrate it by simulation and applications to precipitation extremes in both Germany and Spain. In the second part, we construct new marked point process models, where interest mostly lies in the extremes of the mark distribution. Our proposed joint models exploit intrinsic CAR priors to capture the spatial effects in landslide counts and sizes, while the mark distribution is assumed to take various parametric forms. We demonstrate that having a sub-asymptotic distribution for landslide sizes provides extra flexibility to accurately capture small to large and especially extreme, devastating landslides.

In this project warm extreme temperature events in the Arctic region during the spring months March, April and May were identified and analysed. In the analysis daily average NCEP reanalysis data from NOAA/OAR/ESRL PSL format was used. The extreme events were retrieved as the highest positive temperature anomalies from the climatological mean, and the synoptic scale plots for the 50 most extreme events were created to identify what patterns caused the extreme warming over the Polar region. By contouring the areas of statistical significance, the regions with a reoccuring pattern were identified. The results conclude that cyclonic activity over the high Arctic extending down over Greenland and northern Canada combined with anomalously high geopotential height over the north Pacific ocean, over the Arctic, and towards Siberia cause the high temperatures over the pole. A weaker Polar Vortex causes perturbations in the jet stream, ridges in these Rossby waves can act as a pathway for warm and moist air from the oceanic regions which has a warming effect in the Arctic. Further analysis can be done to investigate what teleconnections these spring-time extreme events have on a global scale. / Under detta projekt har extremt varma temperaturevent i Arktisområdet under vårmånaderna Mars, April och Maj identifierats samt analyserats, genom att använda daglig medelvärdes NCEP reanalys data från NOAA/OAR/ESRL PSL i NetCDF format. De extrema händelserna identifierades genom att ta de största positiva temperaturavvikelserna från ett klimatologiskt medelvärde, storskaliga avvikelseplottar skapades för de 50 mest extrema händelserna för att kunna identifiera meteorologiska mönster som ovanligt varma Arktisdagar. De områden med mest återkommande mönsterna var statistiskt signifikanta  och markerades med svarta konturer. Resultaten visar att lågtrycksaktivitet i Arktis som sträcker sig ner över Grönland samt norra Kanada kombinerat med höga geopotentialhöjdavvikelser över Stilla havet och Sibirien som sträcker sig upp mot Nordpolen orsakar ovanligt höga temperaturer i Arktis. En svag polarvirvel orsakar störningar i jetströmmen, dessa ryggar i jetströmmen kan transportera varm fuktig luft från haven mot polen vilket kan ha en värmande effekt. Vidare forskning kan utföras för att identifiera de exakta kopplingarna och konsekvenserna som dessa varma extrema Arktishändelser har globalt.

Angesichts ihrer unüberschaubaren Ausdifferenzierung scheint es heute kaum noch möglich, eine allgemeingültige Definition von Musik zu finden. Ausgehend von diesem Problem nimmt dieser Text ihre Randbereiche in den Fokus: Die Grenzen des Hörens, wie sie in extremen Formen experimenteller Musik, etwa im Harsh Noise Wall, ausgelotet werden und die Grenzen des Vernehmens, wie sie sich im stets metaphorischen Sprechen über Musik abzeichnen. Als unüberschreitbare Grenze dieser beiden Randzonen bildet die Klangfarbe das Zentrum der Argumentation und den Abschluss der Überlegungen. / Today it seems nearly impossible to find a universally valid definition of music due to its vast differentiation. Ensuing from this problem, this text focuses on music’s borders: the hearing limits as they are explored in extreme forms of experimental music (like Harsh Noise Wall) and the margins of understanding as they are shown in the use of metaphors in speaking about music. Timbre is discussed as an uncrossable border of these two aspects. These thoughts form both the focus and the conclusion of this text.

Warming climate will affect communities across Canada. Many of these communities do not have the adaptive capacity to deal with climate change related challenges. Indigenous communities are believed to be disproportionally affected by climate change because of the lack of adequate infrastructure, and historical and political obstacles that limit their overall adaptive capacity. Therefore, climate change data and information are required to understand the full extent to which these communities are exposed to climate risks. Many past studies in the literature have outlined the effects of climate change at large spatial scales. While these studies are important for understanding the broad effects of climate change, they are not useful for community or local adaptation planning. Ultimately, climate change impacts will be felt at a local level. Hence, high resolution climate change impact studies are urgently needed to capture the realities of these effects in greater detail and to provide relevant data and information at local and community levels, in particular for marginalized and Indigenous communities. Using observed meteorological and hydrologic data, high-resolution downscaled future climate simulations, and a process-based hydrologic model, this thesis explored the physical impacts of climate change on the Six Nations of the Grand River (Six Nations) reserve, which is the largest (by population) Indigenous community in Canada and the seventh largest in the United States and Canada. Changing climate conditions and extreme climate trends in the Six Nations reserve were explored using the widely used ETCCDI (Expert Team on Climate Change Detection and Indices) extreme climate indices. Results indicated a warming and wetting trend in Six Nations, with the temperature rising by 3°C to 6°C by the end of the century and changes in seasonal precipitation. Extreme high temperature and precipitation indices will increase, causing potential human health impacts and increased flooding hazards for the community. A warming climate directly impacts the hydrological cycle and patterns. Analysis conducted using the Coupled Groundwater and Surface-Water Flow Model (GSFLOW) found that the McKenzie Creek - an important water provider for Six Nations - is sensitive to climate change due to its reliance on precipitation. Furthermore, study results showed that winter precipitation and streamflow are projected to increase, and snowpack water content is expected to decrease. These changes in streamflow will cause earlier winter-spring flooding events. Furthermore, agricultural production may be affected by reduced spring soil moisture recharge. Additionally, GSFLOW projected little to no change in late spring and summer streamflow which resulted in low water availability (Ptot-ET) during the growing season. Water availability was further examined by assessing future Blue Water (BW) and Green Water (GW) scarcity in the McKenzie Creek watershed. The water footprint method was used to calculate BW and GW scarcity. Study results showed that under current levels of water usage, BW scarcity would be “low” in the future. However, BW scarcity would increase to “significant” levels in the future, if water users started to withdraw more water for consumption, assuming maximum water withdrawal allocation (i.e., 0.47 m3s-1). This level of BW scarcity has the potential to cause ecological degradation and exacerbate water quality issues in the McKenzie Creek watershed. GW scarcity showed a steadily increasing trend throughout the 21st century due to climate warming. Spatial analysis showed that the western portion of the McKenzie Creek watershed may experience slightly higher levels of GW water scarcity in the future because of the lower water holding capacity of the soil. This may cause water users to withdraw more BW resources in western upstream areas, thereby decreasing BW available for downstream communities, including the Six Nations. Such disparity in water use among Indigenous and non-Indigenous communities may affect community relationships and social cohesion in the area. This thesis provides decision makers in Six Nations and more broadly in the McKenzie Creek watershed area with relevant climate change impact data and information that can be used in future climate change adaptation planning, disaster risk mitigation, and water resources management. Moreover, the results highlight the need for a comprehensive climate change vulnerability assessment of the Six Nations. / Thesis / Doctor of Philosophy (PhD)

Approved for public release; distribution in unlimited. / MEMS technology is rapidly taking an important role in today's and future military systems. MEMS are able to lower the device size from millimeter to micrometer and maintain and sometimes surpass the performance of conventional devices. This thesis encompasses the knowledge acquired throughout the MEMS courses to design a two-axis capacitive accelerometer. The required acceleration and operating temperature range were Š50g in each axis and -40ʻC to +80 ʻC, respectively. The accelerometer was also needed to survive within a dynamic shocking environment with accelerations of up to 225g. The parameters of the accelerometer to achieve above specifications were calculated using lumped element approximation and the results were used for initial layout of it. A finite element analysis code (ANSYS) was used to perform simulations of the accelerometer under various operating conditions and to determine the optimum configuration. The simulated results were found to be within about 5% of the calculations indicating the validity of lumped element approach. The response of the designed accelerometer was 7 mV/g and with sensitivity of 1.3g at 3dB. It was also found that the accelerometer was stable in the desired range of operation including under the shock. Two axes sensing can be achieved using two identical accelerometers having their sensing axes perpendicular to each other. / Major, Taiwan Army

A análise de freqüência de cheias através da distribuição de probabilidade generalizada de valores extremos-GEV tem crescido nos últimos anos. A estimação de altos quantis de cheias é comumente praticada extrapolando o ajuste, representado por uma das 3 formas inversas de distribuição GEV, para períodos de retorno bem superiores ao período dos dados observados. Eventos hidrológicos ocorrem na natureza com valores finitos, tal que, seus valores máximos seguem a forma assintótica da GEV limitada. Neste trabalho estuda-se a estimabilidade da distribuição GEV através de momentos LH, usando séries de cheias anuais com diferentes características e comprimentos, obtidas de séries de vazões diária gerada de diversas formas. Primeiramente, sequências estocásticas de vazões diárias foram obtidas da distribuição limitada como subjacente da distribuição GEV limitada. Os resultados da estimação dos parâmetros via momentos-LH, mostram que o ajuste da distribuição GEV as amostras de cheias anuais com menos de 100 valores, pode indicar qualquer forma de distribuição de valores extremos e não somente a forma limitada como seria esperado. Também, houve grande incerteza na estimação dos parâmetros obtidos de 50 séries geradas de uma mesma distribuição. Ajustes da distribuição GEV às séries de vazões anuais, obtidas séries de fluxo diários gerados com 4 modelos estocásticos disponíveis na literatura e calibrados aos dados dos rio Paraná e dos Patos, resultaram na forma de Gumbel. Propõe-se um modelo de geração diária que simula picos de vazões usando a distribuição limitada. O ajuste do novo modelo às vazões diárias do rio Paraná reproduziu as estatísticas diárias, mensais, anuais, assim como os valores extremos da série histórica. Além disso, a série das cheias anuais com longa duração, foi adequadamente descrita pela forma da distribuição GEV limitada. / Frequency analysis of floods by Generalized Extreme Value probability distribution has multiplied in the last few years. The estimations of high quantile floods is commonly practiced extrapolating the adjustment represented by one of the three forms of inverse GEV distribution for the return periods much greater than the period of observation. The hydrologic events occur in nature with finite values such that their maximum values follow the asymptotic form of limited GEV distribution. This work studies the identifiability of GEV distribution by LH-moments using annual flood series of different characteristics and lengths, obtained from daily flow series generated by various methods. Firstly, stochastic sequences of daily flows were obtained from the limited distribution underlying the GEV limited distribution. The results from the LH-moment estimation of parameters show that fitting GEV distribution to annual flood samples of less than 100 values may indicate any form of extreme value distribution and not just the limited form as one would expect. Also, there was great uncertainty noticed in the estimated parameters obtained for 50 series generated from the some distribution. Fitting GEV distribution to annual flood series, obtained from daily flow series generated by 4 stochastic model available in literature calibrated for the data from Paraná and dos Patos rivers, indicated Gumbel distribution. A daily flow generator is proposed which simulated the high flow pulses by limited distribution. It successfully reproduced the statistics related to daily, monthly and annual values as well as the extreme values of historic data. Further, annual flood series of long duration are shown to follow the form of asymptotic limited GEV distribution.

La protection des zones littorales contre les agressions naturelles provenant de la mer, et notamment contre le risque de submersion marine, est essentielle pour sécuriser les installations côtières. La prévention de ce risque est assurée par des protections côtières qui sont conçues et régulièrement vérifiées grâce généralement à la définition du concept de niveau de retour d’un événement extrême particulier. Le niveau de retour lié à une période de retour assez grande (de 1000 ans ou plus) est estimé par des méthodes statistiques basées sur la Théorie des Valeurs Extrêmes (TVE). Ces approches statistiques sont appliquées à des séries temporelles d’une variable extrême observée et permettent de connaître la probabilité d’occurrence de telle variable. Dans le passé, les niveaux de retour des aléas maritimes extrêmes étaient estimés le plus souvent à partir de méthodes statistiques appliquées à des séries d’observation locales. En général, les séries locales des niveaux marins sont observées sur une période limitée (pour les niveaux marins environ 50 ans) et on cherche à trouver des bonnes estimations des extrêmes associées à des périodes de retour très grandes. Pour cette raison, de nombreuses méthodologies sont utilisées pour augmenter la taille des échantillons des extrêmes et réduire les incertitudes sur les estimations. En génie côtier, une des approches actuellement assez utilisées est l’analyse régionale. L’analyse régionale est indiquée par Weiss (2014) comme une manière très performante pour réduire les incertitudes sur les estimations des événements extrêmes. Le principe de cette méthodologie est de profiter de la grande disponibilité spatiale des données observées sur différents sites pour créer des régions homogènes. Cela permet d’estimer des lois statistiques sur des échantillons régionaux plus étendus regroupant tous les événements extrêmes qui ont frappé un ou plusieurs sites de la région (...) Cela ainsi que le caractère particulier de chaque événement historique ne permet pas son utilisation dans une analyse régionale classique. Une méthodologie statistique appelée FAB qui permet de réaliser une analyse régionale tenant en compte les données historiques est développée dans ce manuscrit. Élaborée pour des données POT (Peaks Over Threshold), cette méthode est basée sur une nouvelle définition d’une durée d’observation, appelée durée crédible, locale et régionale et elle est capable de tenir en compte dans l’analyse statistique les trois types les plus classiques de données historiques (données ponctuelles, données définies par un intervalle, données au-dessus d’une borne inférieure). En plus, une approche pour déterminer un seuil d’échantillonnage optimal est définie dans cette étude. La méthode FAB est assez polyvalente et permet d’estimer des niveaux de retour soit dans un cadre fréquentiste soit dans un cadre bayésien. Une application de cette méthodologie est réalisée pour une base de données enregistrées des surcotes de pleine mer (données systématiques) et 14 surcotes de pleine mer historiques collectées pour différents sites positionnés le long des côtes françaises, anglaises, belges et espagnoles de l’Atlantique, de la Manche et de la mer du Nord. Enfin, ce manuscrit examine la problématique de la découverte et de la validation des données historiques / The protection of coastal areas against the risk of flooding is necessary to safeguard all types of waterside structures and, in particular, nuclear power plants. The prevention of flooding is guaranteed by coastal protection commonly built and verified thanks to the definition of the return level’s concept of a particular extreme event. Return levels linked to very high return periods (up to 1000 years) are estimated through statistical methods based on the Extreme Value Theory (EVT). These statistical approaches are applied to time series of a particular extreme variable observed and enables the computation of its occurrence probability. In the past, return levels of extreme coastal events were frequently estimated by applying statistical methods to time series of local observations. Local series of sea levels are typically observed in too short a period (for sea levels about 50 years) in order to compute reliable estimations linked to high return periods. For this reason, several approaches are used to enlarge the size of the extreme data samples and to reduce uncertainties of their estimations. Currently, one of the most widely used methods in coastal engineering is the Regional Analysis. Regional Analysis is denoted by Weiss (2014) as a valid means to reduce uncertainties in the estimations of extreme events. The main idea of this method is to take advantage of the wide spatial availability of observed data in different locations in order to form homogeneous regions. This enables the estimation of statistical distributions of enlarged regional data samples by clustering all extreme events occurred in one or more sites of the region. Recent investigations have highlighted the importance of using past events when estimating extreme events. When historical data are available, they cannot be neglected in order to compute reliable estimations of extreme events. Historical data are collected from different sources and they are identified as data that do not come from time series. In fact, in most cases, no information about other extreme events occurring before and after a historical observation is available. This, and the particular nature of each historical data, do not permit their use in a Regional Analysis. A statistical methodology that enables the use of historical data in a regional context is needed in order to estimate reliable return levels and to reduce their associated uncertainties. In this manuscript, a statistical method called FAB is developed enabling the performance of a Regional Analysis using historical data. This method is formulated for POT (Peaks Over Threshold) data. It is based on the new definition of duration of local and regional observation period (denominated credible duration) and it is able to take into account all the three typical kinds of historical data (exact point, range and lower limit value). In addition, an approach to identify an optimal sampling threshold is defined in this study. This allows to get better estimations through using the optimal extreme data sample in the FAB method.FAB method is a flexible approach that enables the estimation of return levels both in frequentist and Bayesian contexts. An application of this method is carried out for a database of recorded skew surges (systematic data) and for 14 historical skew surges recovered from different sites located on French, British, Belgian and Spanish coasts of the Atlantic Ocean, the English Channel and the North Sea. Frequentist and Bayesian estimations of skew surges are computed for each homogeneous region and for every site. Finally, this manuscript explores the issues surrounding the finding and validation of historical data

A análise de freqüência de cheias através da distribuição de probabilidade generalizada de valores extremos-GEV tem crescido nos últimos anos. A estimação de altos quantis de cheias é comumente praticada extrapolando o ajuste, representado por uma das 3 formas inversas de distribuição GEV, para períodos de retorno bem superiores ao período dos dados observados. Eventos hidrológicos ocorrem na natureza com valores finitos, tal que, seus valores máximos seguem a forma assintótica da GEV limitada. Neste trabalho estuda-se a estimabilidade da distribuição GEV através de momentos LH, usando séries de cheias anuais com diferentes características e comprimentos, obtidas de séries de vazões diária gerada de diversas formas. Primeiramente, sequências estocásticas de vazões diárias foram obtidas da distribuição limitada como subjacente da distribuição GEV limitada. Os resultados da estimação dos parâmetros via momentos-LH, mostram que o ajuste da distribuição GEV as amostras de cheias anuais com menos de 100 valores, pode indicar qualquer forma de distribuição de valores extremos e não somente a forma limitada como seria esperado. Também, houve grande incerteza na estimação dos parâmetros obtidos de 50 séries geradas de uma mesma distribuição. Ajustes da distribuição GEV às séries de vazões anuais, obtidas séries de fluxo diários gerados com 4 modelos estocásticos disponíveis na literatura e calibrados aos dados dos rio Paraná e dos Patos, resultaram na forma de Gumbel. Propõe-se um modelo de geração diária que simula picos de vazões usando a distribuição limitada. O ajuste do novo modelo às vazões diárias do rio Paraná reproduziu as estatísticas diárias, mensais, anuais, assim como os valores extremos da série histórica. Além disso, a série das cheias anuais com longa duração, foi adequadamente descrita pela forma da distribuição GEV limitada. / Frequency analysis of floods by Generalized Extreme Value probability distribution has multiplied in the last few years. The estimations of high quantile floods is commonly practiced extrapolating the adjustment represented by one of the three forms of inverse GEV distribution for the return periods much greater than the period of observation. The hydrologic events occur in nature with finite values such that their maximum values follow the asymptotic form of limited GEV distribution. This work studies the identifiability of GEV distribution by LH-moments using annual flood series of different characteristics and lengths, obtained from daily flow series generated by various methods. Firstly, stochastic sequences of daily flows were obtained from the limited distribution underlying the GEV limited distribution. The results from the LH-moment estimation of parameters show that fitting GEV distribution to annual flood samples of less than 100 values may indicate any form of extreme value distribution and not just the limited form as one would expect. Also, there was great uncertainty noticed in the estimated parameters obtained for 50 series generated from the some distribution. Fitting GEV distribution to annual flood series, obtained from daily flow series generated by 4 stochastic model available in literature calibrated for the data from Paraná and dos Patos rivers, indicated Gumbel distribution. A daily flow generator is proposed which simulated the high flow pulses by limited distribution. It successfully reproduced the statistics related to daily, monthly and annual values as well as the extreme values of historic data. Further, annual flood series of long duration are shown to follow the form of asymptotic limited GEV distribution.