acase@tulane.edu / I review my three papers on ray stretching statistics, hot spot formation, and universality in motion through weak random media. In the first paper, we study the connection between stretching exponents and ray densities in weak ray scattering through a random medium. The stretching exponent is a quantitative measure that describes the degree of exponential convergence or divergence among nearby ray trajectories. In the context of non-relativistic particle motion through a correlated random potential, we show how particle densities are strongly related to the stretching exponents, where the `hot spots' in the intensity profile correspond to minima in the stretching exponents. This strong connection is expected to be valid for different random potential distributions, and is also expected to apply to other physical contexts, such as deep ocean waves. The surprising minimum in the average stretching exponent is of great interest due to the associated appearance of the first generation of hot spots, and a detailed discussion will be found in the third paper. In the second paper, we study the stretching statistics of weak ray scattering in various physical contexts and for different types of correlated disorder. The stretching exponent is mathematically linked to the monodromy matrix that evolves the phase space vector over time. From this point of view, we demonstrate analytically and numerically that the stretching statistics along the forward direction follow universal scaling relationships for different dispersion relations and in disorders of differing correlation structures. Predictions about the location of first caustics can be made using the universal evolution pattern of stretching exponents. Furthermore, we observe that the distribution of stretching exponents in 2D ray dynamics with small angular spread is equivalent to the same distribution in a simple 1D kicked model, which allows us to further explore the relation between stretching statistics and the form of the disorder. Finally, the third paper focuses on the 1D kicked model with stretching statistics that resemble 2D small-angle ray scattering. While the long time behavior of the stretching exponent displays a simple linear growth, the behavior on the scale of the Lyapunov time is mathematically nontrivial. From an analysis of the evolving monodromy matrices, we demonstrate how the stretching exponent depends on the statistics of the second derivative of the random disorder, especially the mean and standard deviation. Furthermore, the maximal Lyapunov exponent or the Lyapunov length can be expressed as nontrivial functions of the mean and standard deviation of the kicks. Lastly, we show that the higher moments of the second derivative of the disorder have small or negligible effect on the evolution of the stretching exponents or the maximal Lyapunov exponents. / 1 / SicongChen

abstract: The increasingly recurrent extraordinary flood events in the metropolitan area of Monterrey, Mexico have led to significant stakeholder interest in understanding the hydrologic response of the Santa Catarina watershed to extreme events. This study analyzes a flood mitigation strategy proposed by stakeholders through a participatory workshop and are assessed using two hydrological models: The Hydrological Modeling System (HEC-HMS) and the Triangulated Irregular Network (TIN)-based Real-time Integrated Basin Simulator (tRIBS). The stakeholder-derived flood mitigation strategy consists of placing new hydraulic infrastructure in addition to the current flood controls in the basin. This is done by simulating three scenarios: (1) evaluate the impact of the current structure, (2) implementing a large dam similar to the Rompepicos dam and (3) the inclusion of three small detention dams. These mitigation strategies are assessed in the context of a major flood event caused by the landfall of Hurricane Alex in July 2010 through a consistent application of the two modeling tools. To do so, spatial information on topography, soil, land cover and meteorological forcing were assembled, quality-controlled and input into each model. Calibration was performed for each model based on streamflow observations and maximum observed reservoir levels from the National Water Commission in Mexico. Simulation analyses focuses on the differential capability of the two models in capturing the spatial variability in rainfall, topographic conditions, soil hydraulic properties and its effect on the flood response in the presence of the different flood mitigation structures. The implementation of new hydraulic infrastructure is shown to have a positive impact on mitigating the flood peak with a more favorable reduction in the peak at the outlet from the larger dam (16.5% in tRIBS and 23% in HEC-HMS) than the collective effect from the small structures (12% in tRIBS and 10% in HEC-HMS). Furthermore, flood peak mitigation depends strongly on the number and locations of the new dam sites in relation to the spatial distribution of rainfall and flood generation. Comparison of the two modeling approaches complements the analysis of available observations for the flood event and provides a framework within which to derive a multi-model approach for stakeholder-driven solutions. / Dissertation/Thesis / Masters Thesis Civil and Environmental Engineering 2016

The development of flexible and interpretable statistical methods is necessary in order to provide appropriate risk assessment measures for extreme events and natural disasters. In this thesis, we address this challenge by contributing to the developing research field of Extreme-Value Theory. We initially study the performance of existing parametric and non-parametric estimators of extremal dependence for multivariate maxima. As the dimensionality increases, non-parametric estimators are more flexible than parametric methods but present some loss in efficiency that we quantify under various scenarios. We introduce a statistical tool which imposes the required shape constraints on non-parametric estimators in high dimensions, significantly improving their performance. Furthermore, by embedding the tree-based max-stable nested logistic distribution in the Bayesian framework, we develop a statistical algorithm that identifies the most likely tree structures representing the data's extremal dependence using the reversible jump Monte Carlo Markov Chain method. A mixture of these trees is then used for uncertainty assessment in prediction through Bayesian model averaging. The computational complexity of full likelihood inference is significantly decreased by deriving a recursive formula for the nested logistic model likelihood. The algorithm performance is verified through simulation experiments which also compare different likelihood procedures. Finally, we extend the nested logistic representation to the spatial framework in order to jointly model multivariate variables collected across a spatial region. This situation emerges often in environmental applications but is not often considered in the current literature. Simulation experiments show that the new class of multivariate max-stable processes is able to detect both the cross and inner spatial dependence of a number of extreme variables at a relatively low computational cost, thanks to its Bayesian hierarchical representation. These innovative methods and models are implemented to study the concentration maxima of various air pollutants and how these are related to extreme weather conditions for a number of sites in California, one of the most populated and polluted states of the US. As a result, we provide comprehensive measures of air quality that can be used by communities and policymakers worldwide to better assess and manage the health, environmental and financial impacts of air pollution extremes.

In 2015-2016 Kwa-Zulu Natal (KZN) and other provinces in South Africa suffered from drought conditions. Drought can have negative impacts on the environment, society and the economy. Climate change is predicted to exacerbate extreme events such as droughts that would adversely affect already vulnerable regions such as KZN. The main aim of this study is to implement the attribution procedure, to determine if climate change has contributed to the 2015-2016 hydrological drought in selected KZN catchments. Methodology of the study followed a general framework of implementation of hydrological attribution experiments with climate data obtained from attribution simulations with HadAM3p global climate model. Prior to simulations in attribution mode, QSWAT model was set up for the study area and calibrated using SWAT-CUP and SUFI-2. Calibration results were poor but the model could be applied in the context of this study, under certain constraints. Results of attribution experiments revealed that for all 3 subbasins studied no increase of risk was observed and hence no influence of climate change on the 2015-2016 magnitude of drought for selected catchments was concluded by this study. These results are limited, as they are based on climate attribution experiments with only one climate model, rather than with a multi-model ensemble. Also, QSWAT model, in its implementation with generic climate data is of limited use in attribution (or hydrological) simulations as even after calibration the model performs poorly.

The 2015 flood event in the Shire River basin was characterised by Malawi Government’s Department of Disaster Management (DoDMA) as the worst on record. It led to the damage in property worth millions of dollars with recovery still ongoing 3 years later. Over 150 fatalities were confirmed at the time with hundreds of others missing. The extent of the damage of the disaster was perhaps underlined by the swift adoption of the disaster management policy which was still in draft format then and the adoption of the climate change management policy a year later. In the aftermath of the disaster, as with most extreme weather events elsewhere around the world, questions were asked as to whether climate change might have had a hand in the occurrence of such an event and whether, going into a warmer climate, events of that nature of extremity will be the new normal. By using the risk-based event attribution methodology based on dedicated attribution experiments with a global climate model, and focusing on one of the sub-catchments of the Shire River basin, this study explored whether climate change from anthropogenic sources might have influenced the likelihood of such an event occurring. However, given the nature of hydrological events and the land use history of the basin, land use and cover change is another potential flood risk factor which, if overlooked, might affect conclusions with regards to the contribution of external factors to the risk of flooding. To account for both climate change and land use and land change, four sets of rainfallrunoff simulations were run using the Hydrologiska Byrans Vattenbalans-avdelning (HBV) hydrological model which has the ability to simulate the impact of land use and climate change on rainfall-runoff relationships. Each set was a combination of a climate scenario-either “factual” or “counter-factual”- and land use and cover change scenario-either factual (historical) or counterfactual (current). The climate scenarios were based on simulated rainfall and temperature from the HadAM3p model run in two modes-the “factual” and “counter-factual”- simulating the climate with atmospheric conditions closely resembling the atmosphere at the time of occurrence of the event and the climate as it would have been without human emissions of greenhouse gases. The proportion of the risk was calculated to determine how the risk of experiencing a flood of the January-April 2015 magnitude (for 1-day, 10- day, and 30-day maximum flows) changes with climate change only, land use and cover change only, as well as both climate change and land use and cover change. The results demonstrated that the probability of exceeding the 1-day maximum flow of the 2015 magnitude was lower in the factual (current) climate than in the counter-factual. However, changes in land use modify the flood risk such that, when land use change was accounted for, the extent of the reduction in the risk was lower. On the other hand, exceedance probabilities for 10-day and 30-day maximum flows were higher in the factual (current) climate. This was further heightened by changes in land use and cover. The study also established that observational uncertainties typical of the region may influence event attribution results to some extent. The results, which are based on a single attribution method and a single global climate model, do not span the method-model uncertainty range. As a consequence, the results are limited and do not constitute a fully defensible attribution statement.

This project summarizes the findings of research organized in two parts. The first involved the characterization of changes in the variability of climate that lead to extreme events. The second focused on the predictability of extreme climate on time-scales ranging from short forecast lead-times to long-lead climate predictions exceeding a year. Initial studies focused on three interrelated, yet regionally unique extreme climate phenomena. First, the relationship between increasing greenhouse gas (GHG) emissions and particulate matter (PM) concentration in basin terrain was investigated. Next, we evaluated changes in large-scale atmospheric circulation associated with two climate phenomena at either extreme side of the water cycle--droughts and floods. In the final analysis, an attempt was made to understand the mechanisms that link two North Pacific ENSO precursor patterns to the ENSO cycle.

The Bulk Electric System (BES) in the United States includes transmission lines of 100kV and above, transformers of 100kV and above on Low Voltage (LV) side and generating units that step up to 100 kV and above. The BES is a power network that connects different states and utility companies via tie lines for exchange of Power. To maintain the integrity of power systems, it is very important to keep the BES intact and for that the regulatory authority, North American Electric Reliability Corporation (NERC), has developed over 100s of reliability standards and is responsible to enforce them. During the past several years, the U.S has experienced power system instability events in which a fault occurred on one part of a system and travelled through the entire interconnection. Some of the extreme events are a major concern for power systems in the U.S that consists of Cascading, Uncontrolled Separation and natural disasters damaging the transmission circuits. Protection System plays important role towards the stability of power systems, but most important aspect of protection system is the Critical Fault Clearing Time. This case study focused on the Critical Fault Clearing Time enhancement by making a comparison between a Gang Operated (GO) and Independent Pole Operated (IPO) Breaker. An extreme event was considered as a fault scenario for the case study that consisted of three phase fault followed by breaker failure scenario. PSS®E 33.9 software was used to perform dynamic study on three different power plants to show the comparison between GO breaker and IPO breaker. A tremendous improvement was achieved using IPO breaker with more than 100% increase in Critical Fault Clearing Time.

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.

Increases in temperature, altered precipitation patterns, and the occurrence and severity of extreme climatic events have been important characteristics of the climate change observed to date. This has had many and diverse impacts upon the living world, with one recent observation being a global reduction in the net primary production of all terrestrial vegetation. Increases in temperature and the frequency of extreme events are predicted to continue throughout the 21st century, and can be expected to have far reaching effects on global terrestrial ecosystems. Increases in temperature and drought occurrence could fundamentally impact upon the growth rates, species composition and biogeography of forests in many regions of the world, with many studies indicating that this process is already underway. European beech, Fagus sylvatica, is one of Europe’s most widespread and significant broadleaved tree species, forming an important and frequently dominant component of around 17 million hectares of forest. However, the species is also considered to be drought sensitive. Thus, much research interest has focused on eliciting the details of its physiological response to increased water stress, whilst dendroecological studies have attempted to identify sites and regions where reductions in growth might be found. A significant knowledge gap exists regarding a multi-regional, range-wide view of growth trends, growth variability, climate sensitivity, and drought response for the species. Predicting the potential effects of climate change on competition and species composition in mixed species forests remains an important challenge. In order to address this knowledge gap, a multi-regional tree-ring network was constructed comprising of 46 sites in a latitudinal transect across the species’ Western European range. This consisted of 2719 tree cores taken from 1398 individual trees, which were used to construct tree-ring chronologies for each site in the network. As a first step in a multi-regional assessment for F. sylvatica, a combination of the tree-ring chronologies and environmental data derived from a large scale gridded climate dataset were used in a multivariate analysis. Sites in the latitudinal transect were partitioned into geographically meaningful regions for further analysis. The resulting regions were then studied using climate-growth analysis, pointer year analysis of drought years, analysis of growth trends and growth variability, in order to examine regional variation in the response of the species to climate. Furthermore, a combination of long-term monitoring data from one specific site was combined with tree-ring sampling of multiple cohorts of F. sylvatica and one co-dominant competitor, Quercus petraea, to study the effects of an extreme drought event in 1976 on mortality and subsequent recovery. Key results of the multi-regional analysis are that large scale growth reductions are not evident in even the most southerly and driest portions of the species’ range. Radial growth is increasing, both in the north and in the core of the species’ range, with southern range edge forests maintaining stable growth. However, the variability of growth from year to year is increasing for all regions, indicative of growing stress. Crucially, the southern range edge, which previous studies had identified as an ‘at risk’ region, was shown to be more robust than expected. Climate sensitivity and drought impacts were low for this region. Instead, forests in the core of the species range, both in continental Europe and in the south of the UK, were identified as having the highest climate sensitivity, highest drought impacts, and experiencing periodic reductions in growth as a result. Northern range edge forests showed little sign of being affected by drought, instead having low climate sensitivity and strongly increasing growth trends. Extreme drought was found to affect species differently: the dominant species (F. sylvatica) failed to recover pre-drought levels of growth, whilst a transient effect of competitive release occurred for the co-dominant species (Q. petraea). There was also a long term effect on the relative abundance of the two species within the woodland, due to differences in the levels of drought induced mortality experienced by the species. This shows that in the case of extreme climatic events where thresholds in the ability of species to tolerate water stress are breached, the effects of drought can be rapid and long lasting. Drought impacts can cascade beyond that experienced by the most drought sensitive species, due to changes in competitive interactions between species in mixed species forests. The implications of this work suggest opportunities, risks and strengths for F. sylvatica. In the northern portion of the species’ range, predicted increases in productivity are confirmed by recent growth trends, indicating a good outlook for the species. At the southern range edge, F. sylvatica forests exist either in locations where precipitation is high or locations where local environmental conditions buffer them from an inhospitable regional climate. These factors result in southern range edge forests which are highly resilient to the effects of increasing climate stress. It is instead in the core of the species’ range where the most sensitive forests are found. The effects of extreme drought on a range core forest demonstrated here provide a cautionary note: where drought stress tolerance thresholds are breached, rapid and long lasting effects on growth and mortality can occur, even in regions where drought has not previously been considered to pose a strong risk to the species.

Submitted by Lucienne Costa (lucienneferreira@ufcg.edu.br) on 2018-08-27T14:18:56Z No. of bitstreams: 1 ROBERTA EVERLLYN PEREIRA RIBEIRO – DISSERTAÇÃO (PPGMET) 2017.pdf: 3094549 bytes, checksum: 6c430507e5f1b39f79836521e1326409 (MD5) / Made available in DSpace on 2018-08-27T14:18:56Z (GMT). No. of bitstreams: 1 ROBERTA EVERLLYN PEREIRA RIBEIRO – DISSERTAÇÃO (PPGMET) 2017.pdf: 3094549 bytes, checksum: 6c430507e5f1b39f79836521e1326409 (MD5) Previous issue date: 2015-02-26 / CNPq / As condições atmosféricas no Estado do Rio Grande do Norte em julho de 2011 foram investigadas através da Análise em Componentes Principais (ACP) e da Análise de Agrupamentos (AA) aplicadas a dados observacionais de ar superior. Totais diários de precipitação, imagens realçadas do satélite meteorológico GOES-12, e dados de reanálise também foram utilizados. Quatro eventos de chuva foram observados na primeira quinzena do mês. Um evento de precipitação intensa registrado no dia 16 em Natal totalizou 60,4 mm na cidade. No ambiente sinótico foi diagnosticado nos baixos níveis um cavado no leste do estado e área costeira próxima, associado a confluência nos baixos níveis e difluência nos altos níveis, e movimento ascendente em toda a troposfera, na véspera do evento. A ACP aplicada separadamente aos dados dos níveis de 1000, 850, 500 e 300 hPa resultou em um modelo com três componentes. O primeiro fator às 00 UTC está relacionado com a umidade, na baixa e média troposfera, e com a temperatura, na alta troposfera. Às 12 UTC, o primeiro fator tem relação com a temperatura em 1000 e 300 hPa, e com a umidade em 850 e 500 hPa. As séries temporais dos fatores das 12 UTC mostram aumento significativo da umidade na baixa troposfera, na véspera do evento. Na aplicação da AA aos fatores obtidos na ACP, os dias foram agrupados com base em características meteorológicas similares, para cada nível isobárico e horário sinótico. A aplicação da ACP e da AA a índices de estabilidade atmosférica agrupou os dias de acordo com a probabilidade de ocorrência de tempestades. Foram identificados sete grupos para cada horário sinótico: um grupo de difícil interpretação, quatro que agruparam dias com baixa probabilidade e sem registro de precipitação, na maioria dos dias, e dois que agruparam dias com probabilidade e registro de precipitação, na maioria dos dias. / The atmospheric conditions in the Rio Grande do Norte State on July 2011 were investigated by applying Principal Component Analysis (PCA) and Cluster Analysis (CA) to observational upper air data. Daily precipitation totals, enhanced GOES-12 satellite imagery and reanalysis data were also used. Four precipitation events were observed in the first half of the month. An intense rainfall event registered on day 16 in Natal accounted for a 60.4 mm daily total in the city. The synoptic ambient was characterized by a low level trough on coastal eastern Rio Grande do Norte and the nearby oceanic area, associated with low level convergence and upper level divergence, and upward motion throughout the troposphere, on the day before the event. The PCA applied separately to data of the 1000, 850, 500 and 300 hPa levels resulted in a three component model for the isobaric levels and synoptic times analyzed. The first factor at 00 UTC is related to moisture, in the low and middle troposphere, and temperature, in the upper troposphere. At 12 UTC the first factor is related to temperature at 1000 and 300 hPa, and moisture at 850 and 500 hPa. The 12 UTC factors time series show a significant increase in moisture in the low troposphere, on the day before the event. The CA applied to the factors obtained by means of PCA resulted in days grouped on the basis of similar meteorological characteristics, for each isobaric level and synoptic time. The application of PCA and CA to atmospheric stability indices grouped the days in accordance with the probability of storm occurrence: one group of difficult interpretation, four groups with low probability and no rainfall in the majority of the days, and two groups with probability and rainfall in the majority of the days.