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Natural disasters like flooding have always been a big problem for countries around the world, but as the global climate changes and the number of people living in cities keeps growing, the threat of flooding has become a lot worse. Even though many studies have been conducted on flood mapping and vulnerability assessment in urban areas, this research addresses a significant knowledge gap in this domain. First, we used a flood depth estimation approach has been used to address the overestimation of urban flood mapping areas using Sentinel-1 images. Ten different combinations of the two initial VH and VV polarizations were used to rapidly and accurately map urban floods within open-source Google Earth Engine platforms using four different methods. The inclusion of flood depth has improved the accuracy of these methods by 7% on average. Next, we focused our research to find out who is most at risk in the floodplain areas. Minority communities, such as African Americans, as a result of socioeconomic constraints, face more difficulties. So, next we conducted an analysis of spatial and temporal changes of demographic patterns (Race) in five southern cities in US. From our analysis we have found that in majority of cities, the minority population within the floodplain has increased over the past two decades, with the exception of Charleston, South Carolina, where the white population has increased while the minority population has decreased. Building upon these insights, we have included more socio-economic and demographic variables in our analysis to find out the more holistic view of the vulnerable people in two of these cities (Jackson and Birmingham). Due to high autocorrelation between explanatory variables, we used Principal Component Analysis (PCA) along with global and local regression techniques to find out how much these variables can explain the vulnerability. According to our findings, the spatial components play a significant role in explaining vulnerabilities in greater detail. The findings of this research can serve as an important resource for policymakers, urban planners, and emergency response agencies to make informed decisions in future events and enhancing overall resilience.

Title: Modelling dependence between hydrological and meteorological variables measured on several stations Author: Bc. Marie Turčičová Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Daniela Jarušková CSc., Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mathematics Abstract: The aim of the thesis is to explore the dependence of daily discharge averages of the Opava river on high daily precipitation values in its basin. Three methods are presented that can be used for analyzing the dependence between high values of random variables. Their application on the studied data is also given. First it is the tail-dependence coefficient that measures the dependence between high values of two continuous random variables. The model for the high quantiles of the discharge at a given precipitation value was first determined non-parametrically by quantile regression and then parametrically through the peaks-over-threshold (POT) method. Keywords: extremal dependence, tail-dependence coefficient, quantile regression, peaks over threshold method

Cette thèse a pour but le développement de certains aspects de la modélisation de la dépendance dans la gestion des risques en dimension plus grande que un. Le premier chapitre est constitué d'une introduction générale. Le deuxième chapitre est constitué d'un article s'intitulant « Estimating Bivariate Tail : a copula based approach », soumis pour publication. Il concerne la construction d'un estimateur de la queue d'une distribution bivariée. La construction de cet estimateur se fonde sur une méthode de dépassement de seuil (Peaks Over Threshold method) et donc sur une version bivariée du Théorème de Pickands-Balkema-de Haan. La modélisation de la dépendance est obtenue via la Upper Tail Dependence Copula. Nous démontrons des propriétés de convergence pour l'estimateur ainsi construit. Le troisième chapitre repose sur un article: « A multivariate extension of Value-at-Risk and Conditional-Tail-Expectation», soumis pour publication. Nous abordons le problème de l'extension de mesures de risque classiques, comme la Value-at-Risk et la Conditional-Tail-Expectation, dans un cadre multidimensionnel en utilisant la fonction de Kendall multivariée. Enfin, dans le quatrième chapitre de la thèse, nous proposons un estimateur des courbes de niveau d'une fonction de répartition bivariée avec une méthode plug-in. Nous démontrons des propriétés de convergence pour les estimateurs ainsi construits. Ce chapitre de la thèse est lui aussi constitué d'un article, s'intitulant « Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory», accepté pour publication dans la revue ESAIM:Probability and Statistics. / In this PhD thesis we consider different aspects of dependence modeling with applications in multivariate risk theory. The first chapter is constituted by a general introduction. The second chapter is essentially constituted by the article “Estimating Bivariate Tail: a copula based approach”, actually submitted for publication. It deals with the problem of estimating the tail of a bivariate distribution function. We develop a general extension of the POT (Peaks-Over-Threshold) method, mainly based on a two-dimensional version of the Pickands-Balkema-de Haan Theorem. The dependence structure between the marginals in the upper tails is described by the Upper Tail Dependence Copula. Then we construct a two-dimensional tail estimator and study its asymptotic properties. The third chapter of this thesis is based on the article “A multivariate extension of Value-at-Risk and Conditional-Tail-Expectation” and submitted for publication. We propose a multivariate generalization of risk measures as Value-at-Risk and Conditional-Tail-Expectation and we analyze the behavior of these measures in terms of classical properties of risk measures. We study the behavior of these measures with respect to different risk scenarios and stochastic ordering of marginals risks. Finally in the fourth chapter we introduce a consistent procedure to estimate level sets of an unknown bivariate distribution function, using a plug-in approach in a non-compact setting. Also this chapter is constituted by the article “Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory”, accepted for publication in ESAIM: Probability and Statistics journal.

<p>Хидролошке&nbsp; суше&nbsp; су&nbsp; сложена&nbsp; појава&nbsp; како&nbsp; у погледу&nbsp; фактора&nbsp; који&nbsp; је&nbsp;&nbsp; изазивају,&nbsp; тако&nbsp; и&nbsp; у погледу&nbsp; њеног&nbsp; утицаја&nbsp; на&nbsp; екосистем&nbsp; и друштво.&nbsp; У&nbsp; дисертацији&nbsp; је&nbsp; приказана предност&nbsp; анализе&nbsp; малих вода,&nbsp; односно хидролошких&nbsp; суша&nbsp; са&nbsp; две&nbsp; променљиве (дефицит&nbsp; и&nbsp; трајање),&nbsp; у&nbsp; односу&nbsp; на&nbsp; уобичајену анализу&nbsp; са&nbsp; једном&nbsp; вредношћу(најчешће минимални&nbsp; годишњи&nbsp; протицај).&nbsp; Резултати добијени&nbsp; статистичком&nbsp; анализом&nbsp; суша,&nbsp; које су&nbsp; издвојене&nbsp; методом&nbsp; прага&nbsp; недвосмислено су&nbsp; показали&nbsp; да&nbsp; имају већу&nbsp; применљивост&nbsp; у водопривреди&nbsp; него&nbsp; методе&nbsp; које&nbsp; користе стандардизоване&nbsp; индексе,&nbsp; јер&nbsp; дају&nbsp; конкретне вредности&nbsp; недостајућих&nbsp; количина воде (запремине&nbsp; дефицита&nbsp; суша)&nbsp; у&nbsp; односу&nbsp; на релативне&nbsp; вредности&nbsp; стандардизованих индекса.&nbsp; Метода&nbsp; прага&nbsp; је&nbsp; примењена&nbsp; на39 станица&nbsp; у&nbsp; сливу&nbsp; Велике&nbsp; Мораве&nbsp; за&nbsp; период 1960-2014,&nbsp; што&nbsp; до&nbsp; сад&nbsp; представља&nbsp; највећи узорак&nbsp; на&nbsp; којем&nbsp; је&nbsp; примењивана&nbsp; у&nbsp; Србији, било&nbsp; да&nbsp; се&nbsp; ради&nbsp; о&nbsp; анализи&nbsp; малих&nbsp; или еликих&nbsp; вода.&nbsp; Као&nbsp; праг&nbsp; за&nbsp; издвајање&nbsp; суша узета&nbsp; је вредност Q₉₀ ,&nbsp; јер&nbsp; је&nbsp; циљ&nbsp; био&nbsp; анализа просторних&nbsp; и временских&nbsp; карактеристика екстремних(великих)&nbsp; суша&nbsp; у&nbsp; сливу&nbsp; Велике Мораве.&nbsp; Избор&nbsp; прага&nbsp; утицао&nbsp; је&nbsp; и&nbsp; на&nbsp; избор методе&nbsp; парцијалних&nbsp; серија&nbsp; за&nbsp; статистичку анализу карактеристика суша. За одређивање параметра&nbsp; теоријских&nbsp; расподела&nbsp; коришћени су L-моменти&nbsp; који&nbsp; дају&nbsp; поузданије&nbsp; оцене параметара&nbsp; од&nbsp; обичних&nbsp; момената.&nbsp; У досадашњим&nbsp; радовима,&nbsp; који&nbsp; су&nbsp; анализирали хидролошке&nbsp; суше&nbsp; методом&nbsp; парцијалних серија,&nbsp; функција&nbsp; расподеле&nbsp; се&nbsp; унапред одабирала,&nbsp; а&nbsp; не&nbsp; на&nbsp; основу&nbsp; тестова сагласности&nbsp; и&nbsp; провере&nbsp; графика&nbsp; вероватноће,као&nbsp; што&nbsp; је&nbsp; урађено&nbsp; у&nbsp; овој&nbsp; дисертацији.&nbsp; За проверу&nbsp; сагласности&nbsp; годишњег&nbsp; максимума дефицита&nbsp; и&nbsp; трајања&nbsp; коришћени&nbsp; су&nbsp; тестови Колмогоров-Смирнов&nbsp; и&nbsp; Крамер&ndash;Мизес,&nbsp; на основу&nbsp; којих&nbsp; су&nbsp; изабране&nbsp; меродавне расподеле&nbsp; за&nbsp; прорачун&nbsp; суша&nbsp; различитих повратних&nbsp; периода&nbsp; на&nbsp; станицама,&nbsp; и&nbsp; обрнуто.С&nbsp; помоћу L-момент&nbsp; дијаграма(LC _s/LC_k )утврђена&nbsp; је&nbsp; хомогеност&nbsp; региона,&nbsp; у&nbsp; овом случају&nbsp; целог&nbsp; слива&nbsp; Велике&nbsp; Мораве,&nbsp; као&nbsp; и изабрана&nbsp; регионална&nbsp; расподела(P+W)&nbsp; за дефиците&nbsp; и&nbsp; трајање&nbsp; суше,&nbsp; на&nbsp; основу&nbsp; које&nbsp; су израчунати&nbsp; безразмерни&nbsp; квантили,&nbsp; који&nbsp; се могу&nbsp; користити&nbsp; за&nbsp; оцену&nbsp; суша великих повратних&nbsp; периода&nbsp; на&nbsp; хидролошки неизученим сливовима.</p> / <p>Hidrološke&nbsp; suše&nbsp; su&nbsp; složena&nbsp; pojava&nbsp; kako&nbsp; u pogledu&nbsp; faktora&nbsp; koji&nbsp; je&nbsp;&nbsp; izazivaju,&nbsp; tako&nbsp; i&nbsp; u pogledu&nbsp; njenog&nbsp; uticaja&nbsp; na&nbsp; ekosistem&nbsp; i društvo.&nbsp; U&nbsp; disertaciji&nbsp; je&nbsp; prikazana prednost&nbsp; analize&nbsp; malih voda,&nbsp; odnosno hidroloških&nbsp; suša&nbsp; sa&nbsp; dve&nbsp; promenljive (deficit&nbsp; i&nbsp; trajanje),&nbsp; u&nbsp; odnosu&nbsp; na&nbsp; uobičajenu analizu&nbsp; sa&nbsp; jednom&nbsp; vrednošću(najčešće minimalni&nbsp; godišnji&nbsp; proticaj).&nbsp; Rezultati dobijeni&nbsp; statističkom&nbsp; analizom&nbsp; suša,&nbsp; koje su&nbsp; izdvojene&nbsp; metodom&nbsp; praga&nbsp; nedvosmisleno su&nbsp; pokazali&nbsp; da&nbsp; imaju veću&nbsp; primenljivost&nbsp; u vodoprivredi&nbsp; nego&nbsp; metode&nbsp; koje&nbsp; koriste standardizovane&nbsp; indekse,&nbsp; jer&nbsp; daju&nbsp; konkretne vrednosti&nbsp; nedostajućih&nbsp; količina vode (zapremine&nbsp; deficita&nbsp; suša)&nbsp; u&nbsp; odnosu&nbsp; na relativne&nbsp; vrednosti&nbsp; standardizovanih indeksa.&nbsp; Metoda&nbsp; praga&nbsp; je&nbsp; primenjena&nbsp; na39 stanica&nbsp; u&nbsp; slivu&nbsp; Velike&nbsp; Morave&nbsp; za&nbsp; period 1960-2014,&nbsp; što&nbsp; do&nbsp; sad&nbsp; predstavlja&nbsp; najveći uzorak&nbsp; na&nbsp; kojem&nbsp; je&nbsp; primenjivana&nbsp; u&nbsp; Srbiji, bilo&nbsp; da&nbsp; se&nbsp; radi&nbsp; o&nbsp; analizi&nbsp; malih&nbsp; ili elikih&nbsp; voda.&nbsp; Kao&nbsp; prag&nbsp; za&nbsp; izdvajanje&nbsp; suša uzeta&nbsp; je vrednost Q₉₀ ,&nbsp; jer&nbsp; je&nbsp; cilj&nbsp; bio&nbsp; analiza prostornih&nbsp; i vremenskih&nbsp; karakteristika ekstremnih(velikih)&nbsp; suša&nbsp; u&nbsp; slivu&nbsp; Velike Morave.&nbsp; Izbor&nbsp; praga&nbsp; uticao&nbsp; je&nbsp; i&nbsp; na&nbsp; izbor metode&nbsp; parcijalnih&nbsp; serija&nbsp; za&nbsp; statističku analizu karakteristika suša. Za određivanje parametra&nbsp; teorijskih&nbsp; raspodela&nbsp; korišćeni su L-momenti&nbsp; koji&nbsp; daju&nbsp; pouzdanije&nbsp; ocene parametara&nbsp; od&nbsp; običnih&nbsp; momenata.&nbsp; U dosadašnjim&nbsp; radovima,&nbsp; koji&nbsp; su&nbsp; analizirali hidrološke&nbsp; suše&nbsp; metodom&nbsp; parcijalnih serija,&nbsp; funkcija&nbsp; raspodele&nbsp; se&nbsp; unapred odabirala,&nbsp; a&nbsp; ne&nbsp; na&nbsp; osnovu&nbsp; testova saglasnosti&nbsp; i&nbsp; provere&nbsp; grafika&nbsp; verovatnoće,kao&nbsp; što&nbsp; je&nbsp; urađeno&nbsp; u&nbsp; ovoj&nbsp; disertaciji.&nbsp; Za proveru&nbsp; saglasnosti&nbsp; godišnjeg&nbsp; maksimuma deficita&nbsp; i&nbsp; trajanja&nbsp; korišćeni&nbsp; su&nbsp; testovi Kolmogorov-Smirnov&nbsp; i&nbsp; Kramer&ndash;Mizes,&nbsp; na osnovu&nbsp; kojih&nbsp; su&nbsp; izabrane&nbsp; merodavne raspodele&nbsp; za&nbsp; proračun&nbsp; suša&nbsp; različitih povratnih&nbsp; perioda&nbsp; na&nbsp; stanicama,&nbsp; i&nbsp; obrnuto.S&nbsp; pomoću L-moment&nbsp; dijagrama(LC _s/LC_k )utvrđena&nbsp; je&nbsp; homogenost&nbsp; regiona,&nbsp; u&nbsp; ovom slučaju&nbsp; celog&nbsp; sliva&nbsp; Velike&nbsp; Morave,&nbsp; kao&nbsp; i izabrana&nbsp; regionalna&nbsp; raspodela(P+W)&nbsp; za deficite&nbsp; i&nbsp; trajanje&nbsp; suše,&nbsp; na&nbsp; osnovu&nbsp; koje&nbsp; su izračunati&nbsp; bezrazmerni&nbsp; kvantili,&nbsp; koji&nbsp; se mogu&nbsp; koristiti&nbsp; za&nbsp; ocenu&nbsp; suša velikih povratnih&nbsp; perioda&nbsp; na&nbsp; hidrološki neizučenim slivovima.</p> / <p>Hydrological droughts are a complex phenomenon both in terms of the factors that cause it, and in terms of its impact on ecosystems and society. The dissertation shows the advantage of low water analysis, i.e. hydrological drought with two variables (deficit and duration), compared to the usual analysis of a single value (a minimum annual flow). The results obtained by statistical analysis of drought, which are separated by the threshold method clearly demonstrated to have greater applicability in water management than methods that used standardized indices, because they give concrete value of missing quantities of water (drought deficit volume) with respect to relative values of standardized index. Threshold method was&nbsp; applied to 39 stations in the Morava River Basin for the period 1960-2014, which so far represents the largest sample on which it was applied in Serbia, whether it is on the analysis of low or high water. The value of Q₉₀ was selected as a threshold for separating the drought, because the goal was to analyze the spatial and temporal characteristics of extreme (large) droughts in the basin of Velika Morava. Selected threshold affected the choice of partial duration series method for statistical analysis of the drought characteristics. L-moments were used to determine the parameters of&nbsp; theoretical distributions because they give more reliable estimates of the parameters&nbsp; than ordinarymoments. In previous papers, which analyzed the hydrological drought&nbsp; by partial duration series, distribution function was chosen in advance, and not on the results of goodness-of-fit tests and visual validation of frequency curve on probability paper, as it was done in this thesis. To check the goodness-of-fit tests of annual maximum deficit and duration tests of Kolmogorov-Smirnov and Cramer &ndash;Mises were used, and based on their results representative distribution was chosen for&nbsp;&nbsp; calculation of different return periods of droughts on the stations, and vice versa. The homogeneity of the region was determined by L-moment diagrams (LC s/LC k ), and in this case it was the whole basin of the Velika Morava. L-moments were used for selection of regional distribution (P+W) for the drought duration and deficits, based on which dimensionless quantiles were calculated, which can be used for&nbsp;&nbsp; аеssessment of droughts of great return periods in the hydrological ungauged catchments.</p>