Climate models are common tools for developing design standards in the hydrologic field; however, these models contain uncertainties in multi-model and scenario selections. Along with these uncertainties, biases can be attached to the models. Such biases and uncertainties can present difficulties in predicting future extremes. These hydrologic extremes are believed to be non-stationary in character. Only in the recent past have model users come to terms that the current hydrologic designs are no longer relevant due to their assumption of stationarity. This study describes a systematic method of selecting a best fit model in relationship to location and time, along with the use of that best fit model for evaluation of future extremes. Rain gage stations throughout Florida are used to collect daily precipitation data used in extreme precipitation and quantitative indices. Through these indices conclusions are made on model selection and future extremes, as they relate to hydrologic designs. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2013.

Three major teleconnections, Atlantic Multidecadal Oscillation (AMO), North Atlantic Oscillation (NAO), and the Pacific Decadal Oscillation (PDO), in warm and cool phases, effect precipitation in Florida. The effects of the oscillation phases on the precipitation characteristics are analyzed by using long-term daily precipitation data, on different temporal (annual, monthly, and daily) and spatial scales, utilizing numerous indices, and techniques. Long-term extreme precipitation data for 9 different durations is used to examine the effects of the oscillation phases on the rainfall extremes, by employing different parametric and non-parametric statistical tests, along with Depth-Duration- Frequency analysis. Results show that Florida will experience higher rainfall when AMO is in the warm phase, except in the panhandle and south Florida, while PDO cool phase is positively correlated with precipitation, except for the southern part of the peninsula. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2013.

The west coast of Vancouver Island is located at the northern end of the California Current System, one of the world’s Eastern Boundary Current Systems. The region is characterized by wind driven coastal upwelling and high productivity, which supports fisheries and related industries. Climate change poses a challenge to these industries by increasing seawater acidity and decreasing dissolved oxygen levels, which are two of the multi-stressors of marine organisms. This thesis explores the relative importance of different physical and biological mechanisms that affect oxygen and carbon extremes in the region. The relatively weak local wind in the region is not well-correlated with local currents and temperature. Results of coherence analyses between multi-depth current and temperature measured at a single mooring site (48.5 ◦ N, 126 ◦ W) in the west coast of southern Vancouver Island and coincident time series of North America Regional Reanalysis (NARR) 10 m wind stress in the geographic domain 36 – 54 ◦ N, 120 – 132 ◦ W are presented. The two-decade long (1989 – 2008) current records from the three shallowest depths (35, 100 and 175 m) show a remote response to winds from as far south as 36 ◦ N. In contrast, temperature only at the deepest depth (400 m) show strong coherences with remote winds. The frequency window of maximum coherence and the estimated average time-lags are consistent with the frequencies and pole-ward propagating phase speeds of coastal trapped waves. Lack of coherence between remote winds and the 400 m currents suggests that the temperature variations at that depth are driven by vertical motion resulting from poleward travelling coastal trapped waves (CTWs). In order to study the relative roles of physical and biological processes on controlling oxygen and carbon tendencies, oxygen cycle has been successfully added to an existing biogeochemical model of the west coast of Vancouver Island. This idealized model then was forced with a long synthetic record of present-day conditions, specifically 1017 years of stochastically generated daily resolved forcing including local and remote winds. The seasonal cycles of the modelled DIC and O2 compare well with depth averaged observational data. They are also found to be strongly coupled in the lower layers, where biological processes are more important. In the upper layer, physical processes such as the differing gas exchange rates partially decouple DIC and O2 . Robust statistics on DIC and oxygen extreme events were calculated by using the long realizations of the model baseline experiment. In the upper mixed layer, O2 extreme events occur 2–3 times more frequently than DIC extreme events. Both extreme events show a much larger interannual variability in the lower layer. In this layer, oxygen extreme events events occur late in the summer, following intense upwelling events early in the upwelling season. Counter-intuitively, within the summer upwelling season, when sporadic upwelling events are expected to cause extreme conditions, the fraction of days with joint DIC–O2 extreme events is negligible. Sensitivity analysis shows that increased primary production, via increased phytoplankton growth rate, decreases the small fraction of days with joint DIC-O2 extreme events in the upper layers during the summer upwelling season but increases it in the winter downwelling season. Lowering upwelling intensities lowers the fraction of days with joint DIC–O2 extreme events. Increasing the upwelling intensities had the opposite effect on this fraction. Changes in up/downwelling intensity did not change this fraction within the summer upwelling season. A non-monotonic response by oxygen extreme events in the lower layer is observed when phytoplankton growth rate was increased. Generally, a moderate decrease in growth rate increases the chances of model lower layer O2 extreme events, while near-zero growth rate does not. In some cases, the same parameter perturbation results in different responses by the mean and the extreme events of DIC and O2 , suggesting that results of studies focusing on physical and biological forcing of the mean state may not directly translate result to extremes. This thesis has identified relative locations within the study domain of priority for effective monitoring of dissolved oxygen and carbon extremes in the study region. Finally, joint DIC- O2 extreme events are found to be common at the end of the summer. This information can be used to inform adaptation and mitigation plans aimed at protecting the economic and bequest value of the coast from potential hazards associated with oxygen and carbon extremes. / Graduate

Shaped by countless influences from the atmosphere, biosphere, hydrosphere, and anthroposphere acting across a wide spectrum of spatiotemporal scales, spatial variations in climate are ubiquitous. Meanwhile, the warming signal from anthropogenically elevated greenhouse-gas concentrations is emerging as an overriding determinant for more and more aspects of the climate system, extreme heat among them. In this dissertation, I explore the interaction of these two effects, and the implications of the patterns they create. A key finding is that rapid increases in extreme heat are already occurring, by some metrics having already doubled in the past 40 years, and further nonlinear increases are expected. Another is the strong dependence of extreme heat-humidity combinations on atmospheric moisture, creating subseasonal and interannual patterns dictated by the principal source of regional warm-season moisture — pre-monsoonal advection in some cases, local evapotranspiration in others. These relationships lead to the demonstrated potential for improvements in predictive power, on the basis of sea-surface temperatures and other canonical modes of large-scale climate variability. In contrast to this overall confidence in current temporal patterns and long-term projections, I show that extreme heat at small spatial scales is much more poorly characterized in gridded products, and that these biases are especially acute along coastlines. While summer daytime temperature differences between the shoreline of the Northeast U.S. and locations 60 km inland are often 5°C or more, I find that recent high-resolution downscaled Earth-system models typically represent no more than 25% of this difference. Across the globe, ERA-Interim reanalysis similarly underestimates extreme humid heat by >3°C, a highly significant margin given the large sensitivity of health and economic impacts to marginal changes in the most extreme conditions. I find that these biases propagate into projections, and their importance is also amplified by the large populations living in the affected areas. Rapid mean warming is pushing the climate system to more and more frequently include extreme heat-humidity combinations beyond that which the human species has likely ever experienced. Such conditions, which had not been previously reported in weather-station data, are described in detail and some of the associated characteristics examined. Several channels of analysis highlight that these events are driven primarily by rising sea-surface temperatures in shallow subtropical gulfs, and the subsequent impingement of marine air on the coastline. Given the severity of potential impacts on infrastructure and agriculture, and the size of the populations exposed, this result underscores that major research and adaptation efforts are needed to avoid calamitous outcomes from the emergence of extreme heat-humidity combinations too severe to tolerate in the absence of artificial cooling. This dissertation discusses strategies for advancing knowledge of extreme heat’s natural variations and its behavior under climate change, in order to design metrics, models, methodologies, and presentation types such that essential findings are translated into tangible action in the most effective way possible. Sustained and integrated efforts are necessary to transition to a climate-system management style encompassing more foresight than the effectively unplanned experiment which has been pursued so far, and which has already exacerbated extreme heat events so much.

We present limit theory for tests of homogeneity for finite mixture models. More specifically, we derive the asymptotic distribution of certain random quantities used for testing that a mixture of two distributions is in fact just a single distribution. Our methods apply to cases where the mixture component distributions come from one of a wide class of one-parameter exponential families, both continous and discrete. We consider two random quantities, one related to testing simple hypotheses, the other composite hypotheses. For simple hypotheses we consider the maximum of the standardised score process, which is itself a test statistic. For composite hypotheses we consider the maximum of the efficient score process, which is itself not a statistic (it depends on the unknown true distribution) but is asymptotically equivalent to certain common test statistics in a certain sense. We show that we can approximate both quantities with the maximum of a certain Gaussian process depending on the sample size and the true distribution of the observations, which when suitably normalised has a limiting distribution of the Gumbel extreme value type. Although the limit theory is not practically useful for computing approximate p-values, we use Monte-Carlo simulations to show that another method suggested by the theory, involving using a Studentised version of the maximum-score statistic and simulating a Gaussian process to compute approximate p-values, is remarkably accurate and uses a fraction of the computing resources that a straight Monte-Carlo approximation would.

Les travaux présentés s'inscrivent dans le cadre de l'inférence statistique. Ils s'articulent autour des quatre thèmes suivants : estimation de quantiles extrêmes, estimation de frontière, réduction de dimension en analyse d'images et estimation de courbes de référence. Le plupart de ces travaux sont issus de collaborations avec des industriels et s'étendent de l'étude théorique d'une méthode statistique au développement d'outils logiciels l'implémentant.

Water resources, in terms of quantity and quality, are significantly influenced by environmental changes, especially by climate and land use changes. The main objective of the present study is to project climate change impacts on the seasonal dynamics of water fluxes, spatial changes in water balance components as well as the future flood and low flow conditions in Germany. This study is based on the modeling results of the process-based eco-hydrological model SWIM (Soil and Water Integrated Model) driven by various regional climate scenarios on one hand. On the other hand, it is supported by statistical analysis on long-term trends of observed and simulated time series. In addition, this study evaluates the impacts of potential land use changes on water quality in terms of NO3-N load in selected sub-regions of the Elbe basin. In the context of climate change, the actual evapotransipration is likely to increase in most parts of Germany, while total runoff generation may decrease in south and east regions in the scenario period 2051-2060. Water discharge in all six studied large rivers (Ems, Weser, Saale, Danube, Main and Neckar) would be 8 – 30% lower in summer and autumn compared to the reference period (1961 – 1990), and the strongest decline is expected for the Saale, Danube and Neckar. The 50-year low flow is likely to occur more frequently in western, southern and central Germany after 2061 as suggested by more than 80% of the model runs. The current low flow period (from August to September) may be extended until the late autumn at the end of this century. Higher winter flow is expected in all of these rivers, and the increase is most significant for the Ems (about 18%). No general pattern of changes in flood directions can be concluded according to the results driven by different RCMs, emission scenarios and multi-realizations. An optimal agricultural land use and management are essential for the reduction in nutrient loads and improvement of water quality. In the Weiße Elster and Unstrut sub-basins (Elbe), an increase of 10% in the winter rape area can result in 12-19% more NO3-N load in rivers. In contrast, another energy plant, maize, has a moderate effect on the water environment. Mineral fertilizers have a much stronger effect on the NO3-N load than organic fertilizers. Cover crops, which play an important role in the reduction of nitrate losses from fields, should be maintained on cropland. The uncertainty in estimating future high flows and, in particular, extreme floods remain high due to different RCM structures, emission scenarios and multi-realizations. In contrast, the projection of low flows under warmer climate conditions appears to be more pronounced and consistent. The largest source of uncertainty related to NO3-N modelling originates from the input data on the agricultural management. / Wasserressourcen werden in Quantität und Qualität von Veränderungen in der Umwelt, insbesondere von Änderungen des Klimas und der Landnutzung, in signifikantem Maße beeinflusst. In dieser Arbeit wurden die Auswirkungen von Klimavariabilität und Klimawandel auf die Wasserressourcen und Extremereignisse wie Hoch- und Niedrigwasser in Deutschland untersucht. Die Analyse erfolgte auf der einen Seite modellgestützt, wobei die Ergebnisse aus verschiedenen regionalen Klimamodellen durch ein ökohydrologisches Modell in Änderungen in den hydrologischen Prozessen transformiert wurden, zum anderen aber auch datengestützt, z.B. durch die statistische Interpretation von beobachteten und simulierten Zeitreihen. Zusätzlich wurden die Auswirkungen von Landnutzungsänderungen auf Umsatz von Stickstoff in der Landschaft und im Wasser untersucht, wobei dasselbe ökohydrologische Modell zum Einsatz kam. Im Rahmen des Klimawandels wird zur Mitte dieses Jahrhunderts die aktuelle Evapotranspiration in den meisten Teilen Deutschlands mit großer Wahrscheinlichkeit zunehmen. Die täglichen Abflussmengen der fünf größten Flussgebiete in Deutschland (Ems, Weser, Elbe, Obere Donau und Rhein) werden dieser Untersuchung zur Folge im Sommer und Herbst um 8%-30% geringer sein als in der Referenzperiode (1961-1990). 80% der Szenariensimulationen stimmen darin überein, dass die 50-jährigen Niedrigwasserereignisse zum Ende dieses Jahrhunderts mit großer Wahrscheinlichkeit häufiger in den westlichen, den südlichen und den zentralen Teilen Deutschlands auftreten werden. Die gegenwärtige Niedrigwasserperiode (August-September) könnte sich zudem dann bis in den späten Herbst ausweiten. Für alle Flüsse werden höhere Winterabflüsse erwartet, wobei diese Zunahme für die Ems am stärksten ausfällt (ca. 18%). Mit größerer Unsicherheit sind dagegen die Aussagen zur Entwicklung der Hochwasser behaftet. Aus den Ergebnissen, die durch unterschiedliche regionale Klimamodelle und Szenarien getrieben wurden, kann jedoch kein allgemeingültiges Muster für die Änderungen der 50-jährigen Hochwässer ausgemacht werden. Eine optimierte Landnutzung und ein optimiertes Landmanagement sind für die Reduzierung der NO3-Einträge in die Oberflächengewässer essentiell. In den Einzusgebieten der Weißen Elster und der Unstrut (Elbe) kann eine Zunahme von 10% in der Anbaufläche von Winterraps zu einer 12-19% höheren NO3 Fracht führen. Mais, eine weitere Energiepflanze, hat hingegen einen mäßigeren Effekt auf die Oberflächengewässer. Die Höhe der Gabe von mineralischen Düngern beeinflußt zudem in starkem Maße die Nitratbelastung von Flüssen. Zwischenfrüchte können den NO3-Austrag im Sommer zusätzlich erheblich verringern. Insgesamt bleibt die Unsicherheit in der Vorhersage von Spitzenabflüssen und im Besonderen von Extrem-Hochwässern als Folge unterschiedlicher regionaler Klimamodelle, Emissionsszenarien und Realisationen sehr hoch. Im Gegensatz dazu erscheinen die Projektionen zu den Niedrigwasserereignissen unter wärmeren Bedingungen sehr viel deutlicher und einheitlicher. Die größte Unsicherheit in der Modellierung von NO3 dagegen sind die Eingangsdaten z.B. für das lokale landwirtschaftliche Management.

A wide range of ecological communities ranging from polar terrestrial to tropical marine environments are affectedby global climate change. Over the last century, atmospheric temperature has increased by an average of 0. 60 C andis expected to rise by 1.1- 6.40C over the next 100 years. This rising temperature has increased the intensity andfrequency of weather extremes due to which a large number of species are facing risk of extinction. Studies haveshown that species existing on lower latitude are more sensitive to temperature variability compared to speciesexisting on higher latitude but temperature is increasing rapidly in higher latitude compare to lower latitude. Thisuneven distribution of temperature sensitive species and warming rate has highlighted the need for combined studiesof temperature variability and sensitiveness of species to predict how the ecosystems will respond to increasinglyvariable climate. Using a generalized Rosenzweig-MacArthur model, I explored how temperature variability andsensitivity of species will affect the extinction risks of species and how the connectance and species-richness ofecological communities will govern this response. This study showed that the risk of extinction of species mostlydepends on their sensitivity to temperature deviation from the optimum value and level of temperature variability.Among these two, sensitivity of species to temperature deviation was most prominent factor affecting extinction risk.In this study, connectance did not show any effect on mean extinction risk and time taken by a certain proportion ofspecies to reach pre-defined extinction thresholds. But, species-richness showed some effect on mean extinction riskof species. It was found that risk of extinction of species in species-rich communities was higher compared tospecies-poor communities. Species-rich communities also took shorter time before they lost 1/6 of the species. Thepresent study also suggests a possible tipping point due to increasing temperature variability in near future. In furtherstudies, different sensitivity of species at different trophic levels and the possible evolution of sensitivity of speciesshould also be consider while predicting how ecological communities will respond to changing climate in the longrun.

Gaussian distribution is the most applied in practice and because of that reason there is a great amount of studies done in this area. In this report we look at Gaussian distribution from a point of view of extreme value theory. More concretely, moments of maximum of normally distributed values are discussed. There are methods to calculate moments of extremes of independent identically distributed normal values, values with different variances and asymptotical results. In this work a case of dependant variables is analyzed and aim is to look for results in similar cases that is done for independent variables. Continuing Bachelor’s work formula for moment calculation of maximum of two dependent normal variables with all different parameters is presented. Also there is a proof of formula for calculation of odd order moments of three dependent variable maximum. This result is generalized for random variable vectors of any length. There is a theorem stated, according to which moments of length n vector maximum could be expressed by same order moments of shorter vectors. Unfortunately, because of requirements for numbers n and m, no recursion method could be applied. Using computer, maximum of various length random vectors with dependent components is simulated and average is analyzed. In experiments relation between mean values of dependent and independent variable maximums is observed. This relation is stated in a form of a formula and proved for vectors of any length. In this... [to full text]

We present limit theory for tests of homogeneity for finite mixture models. More specifically, we derive the asymptotic distribution of certain random quantities used for testing that a mixture of two distributions is in fact just a single distribution. Our methods apply to cases where the mixture component distributions come from one of a wide class of one-parameter exponential families, both continous and discrete. We consider two random quantities, one related to testing simple hypotheses, the other composite hypotheses. For simple hypotheses we consider the maximum of the standardised score process, which is itself a test statistic. For composite hypotheses we consider the maximum of the efficient score process, which is itself not a statistic (it depends on the unknown true distribution) but is asymptotically equivalent to certain common test statistics in a certain sense. We show that we can approximate both quantities with the maximum of a certain Gaussian process depending on the sample size and the true distribution of the observations, which when suitably normalised has a limiting distribution of the Gumbel extreme value type. Although the limit theory is not practically useful for computing approximate p-values, we use Monte-Carlo simulations to show that another method suggested by the theory, involving using a Studentised version of the maximum-score statistic and simulating a Gaussian process to compute approximate p-values, is remarkably accurate and uses a fraction of the computing resources that a straight Monte-Carlo approximation would.