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.

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.

Intensity-Duration-Frequency (IDF) curves are among the standard design tools for various engineering applications, such as storm water management systems. The current practice is to use IDF curves based on historical extreme precipitation quantiles. A warming climate, however, might change the extreme precipitation quantiles represented by the IDF curves, emphasizing the need for updating the IDF curves used for the design of urban storm water management systems in different parts of the world, including Canada. This study attempts to construct the future IDF curves for Saskatoon, Canada, under possible climate change scenarios. For this purpose, LARS-WG, a stochastic weather generator, is used to spatially downscale the daily precipitation projected by Global Climate Models (GCMs) from coarse grid resolution to the local point scale. The stochastically downscaled daily precipitation realizations were further disaggregated into ensemble hourly and sub-hourly (as fine as 5-minute) precipitation series, using a disaggregation scheme developed using the K-nearest neighbor (K-NN) technique. This two-stage modeling framework (downscaling to daily, then disaggregating to finer resolutions) is applied to construct the future IDF curves in the city of Saskatoon. The sensitivity of the K-NN disaggregation model to the number of nearest neighbors (i.e. window size) is evaluated during the baseline period (1961-1990). The optimal window size is assigned based on the performance in reproducing the historical IDF curves by the K-NN disaggregation models. Two optimal window sizes are selected for the K-NN hourly and sub-hourly disaggregation models that would be appropriate for the hydrological system of Saskatoon. By using the simulated hourly and sub-hourly precipitation series and the Generalized Extreme Value (GEV) distribution, future changes in the IDF curves and associated uncertainties are quantified using a large ensemble of projections obtained for the Canadian and British GCMs (CanESM2 and HadGEM2-ES) based on three Representative Concentration Pathways; RCP2.6, RCP4.5, and RCP8.5 available from CMIP5 – the most recent product of the Intergovernmental Panel on Climate Change (IPCC). The constructed IDF curves are then compared with the ones constructed using another method based on a genetic programming technique. The results show that the sign and the magnitude of future variations in extreme precipitation quantiles are sensitive to the selection of GCMs and/or RCPs, and the variations seem to become intensified towards the end of the 21st century. Generally, the relative change in precipitation intensities with respect to the historical intensities for CMIP5 climate models (e.g., CanESM2: RCP4.5) is less than those for CMIP3 climate models (e.g., CGCM3.1: B1), which may be due to the inclusion of climate policies (i.e., adaptation and mitigation) in CMIP5 climate models. The two-stage downscaling-disaggregation method enables quantification of uncertainty due to natural internal variability of precipitation, various GCMs and RCPs, and downscaling methods. In general, uncertainty in the projections of future extreme precipitation quantiles increases for short durations and for long return periods. The two-stage method adopted in this study and the GP method reconstruct the historical IDF curves quite successfully during the baseline period (1961-1990); this suggests that these methods can be applied to efficiently construct IDF curves at the local scale under future climate scenarios. The most notable precipitation intensification in Saskatoon is projected to occur with shorter storm duration, up to one hour, and longer return periods of more than 25 years.

Les inondations constituent le risque naturel prédominant dans le monde et les dégâts qu'elles causent sont les plus importants parmi les catastrophes naturelles. Un des principaux facteurs expliquant les inondations sont les précipitations extrêmes. En raison des changements climatiques, l'occurrence et l'intensité de ces dernières risquent fort probablement de s'accroître. Par conséquent, le risque d'inondation pourrait vraisemblablement s'intensifier. Les impacts de l'évolution des précipitations extrêmes sont désormais un enjeu important pour la sécurité du public et pour la pérennité des infrastructures. Les stratégies de gestion du risque d'inondation dans le climat futur sont essentiellement basées sur les simulations provenant des modèles numériques de climat. Un modèle numérique de climat procure notamment une série chronologique des précipitations pour chacun des points de grille composant son domaine spatial de simulation. Les séries chronologiques simulées peuvent être journalières ou infra-journalières et elles s'étendent sur toute la période de simulation, typiquement entre 1961 et 2100. La continuité spatiale des processus physiques simulés induit une cohérence spatiale parmi les séries chronologiques. Autrement dit, les séries chronologiques provenant de points de grille avoisinants partagent souvent des caractéristiques semblables. De façon générale, la théorie des valeurs extrêmes est appliquée à ces séries chronologiques simulées pour estimer les quantiles correspondants à un certain niveau de risque. La plupart du temps, la variance d'estimation est considérable en raison du nombre limité de précipitations extrêmes disponibles et celle-ci peut jouer un rôle déterminant dans l'élaboration des stratégies de gestion du risque. Par conséquent, un modèle statistique permettant d'estimer de façon précise les quantiles de précipitations extrêmes simulées par un modèle numérique de climat a été développé dans cette thèse. Le modèle développé est spécialement adapté aux données générées par un modèle de climat. En particulier, il exploite l'information contenue dans les séries journalières continues pour améliorer l'estimation des quantiles non stationnaires et ce, sans effectuer d'hypothèse contraignante sur la nature de la non-stationnarité. Le modèle exploite également l'information contenue dans la cohérence spatiale des précipitations extrêmes. Celle-ci est modélisée par un modèle hiérarchique bayésien où les lois a priori des paramètres sont des processus spatiaux, en l'occurrence des champs de Markov gaussiens. L'application du modèle développé à une simulation générée par le Modèle régional canadien du climat a permis de réduire considérablement la variance d'estimation des quantiles en Amérique du Nord. / Precipitation extremes plays a major role in flooding events and their occurrence as well as their intensity are expected to increase. It is therefore important to anticipate the impacts of such an increase to ensure the public safety and the infrastructure sustainability. Since climate models are the only tools for providing quantitative projections of precipitation, flood risk management for the future climate may be based on their simulations. Most of the time, the Extreme value theory is used to estimate the extreme precipitations from a climate simulation, such as the T-year return levels. The variance of the estimations are generally large notably because the sample size of the maxima series are short. Such variance could have a significant impact for flood risk management. It is therefore relevant to reduce the estimation variance of simulated return levels. For this purpose, the aim of this paper is to develop a non-stationary and regional statistical model especially suited for climate models that estimates precipitation extremes. At first, the non-stationarity is removed by a preprocessing approach. Thereafter, the spatial correlation is modeled by a Bayesian hierarchical model including an intrinsic Gaussian Markov random field. The model has been used to estimate the 100-year return levels over North America from a simulation by the Canadian Regional Climate Model. The results show a large estimation variance reduction when using the regional model.