Quantitative precipitation estimation (QPE) remains a key area of uncertainty in hydrological modeling, particularly in small, urban watersheds which respond rapidly to precipitation and can experience significant spatial variability in rainfall fields. Few studies have compared QPE methods in small, urban watersheds, and studies which have examined this topic only compared model results on an event basis using a small number of storms. This study sought to compare the efficacy of multiple QPE methods when simulating discharge in a small, urban watershed on a continuous basis using an operational hydrologic model and QPE forcings. The Research Distributed Hydrologic Model (RDHM) was used to model a basin in Roanoke, Virginia, USA forced with QPEs from four methods: mean field bias (MFB) correction of radar data, kriging of rain gauge data, uncorrected radar data, and a basin-uniform estimate from a single gauge inside the watershed. Based on comparisons between simulated and observed discharge at the basin outlet for a 6-month period in 2018, simulations forced with the uncorrected radar QPE had the highest accuracy, as measured by root mean square error (RMSE) and peak flow relative error, despite systematic underprediction of the mean areal precipitation (MAP). Simulations forced with MFB corrected radar data consistently and significantly overpredicted discharge but had the highest accuracy in predicting the timing of peak flows. / Master of Science / Estimating the amount of rain that fell during a precipitation event remains a key source of error when predicting how much stormwater runoff will be produced, particularly in small, urban watersheds which respond rapidly to precipitation and can experience significant spatial variability in rainfall distribution. Rainfall estimation in small, urban watersheds has received relatively little attention, and studies which have examined this topic have generally only examined a small number of discrete storm events. This study sought to compare the efficacy of multiple precipitation estimation methods when simulating discharge in a small, urban watershed on a continuous basis using an operational hydrologic model and precipitation inputs. The Research Distributed Hydrologic Model (RDHM), commonly used by the National Weather Service, was used to model a basin in Roanoke, Virginia, USA forced with rainfall estimates from four methods: mean field bias (MFB) correction of radar data, kriging of rain gauge data, uncorrected radar data, and a basin-uniform estimate from a single gauge inside the watershed. Based on comparisons between simulated and observed discharge at the basin outlet for a 6-month period in 2018, simulations forced with the uncorrected radar QPE had the highest accuracy, as measured by several performance statistics, despite systematic underprediction of actual precipitation. Simulations forced with MFB corrected radar data consistently and significantly overpredicted discharge but had the highest accuracy in predicting the timing of peak flows.

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Ces dernières années, de nombreux efforts ont été entrepris pour mieux comprendre les phénomènes précipitants parfois à l’origine de crues de cours d’eau et d’inondations ravageuses. Courant 2009, un consortium auvergnat a été mis en place pour notamment surveiller et prévoir ces événements. Les travaux menés dans cette thèse visent d’une part à améliorer les estimations quantitatives des précipitations (QPE) et d’autre part à vérifier les prévisions issues de modèles numériques sur de petites zones d’étude telles qu’une agglomération. L’observation des précipitations peut être réalisée à l’aide soit d’un pluviomètre qui fournit une mesure directe et précise de la quantité de pluie tombée au sol mais ne renseigne pas sur la variabilité spatiale des pluies soit d'un RADAR météorologique qui donne une représentation détaillée de la structure spatiale des précipitations mais dont les estimations sont sujettes à diverses erreurs d’autant plus prononcées en régions montagneuses. Le premier défit de cette thèse a été de trouver la meilleure façon de combiner ces deux informations complémentaires. Deux techniques géostatistiques ont été sélectionnées pour obtenir la meilleur QPE : le krigeage avec dérive externe (KED) et la fusion conditionnée (MERG). Les performances de ces deux méthodes ont été comparées au travers de deux domaines d’étude qui présentent des résolutions spatio-temporelles différentes. La seconde partie de cette thèse est consacrée à la mise en place d’une méthodologie fiable permettant de comparer spatialement les champs de QPE alors reconstruits et les prévisions quantitatives des précipitations (QPF). L’effort fut porté sur le modèle « Weather Research et Forcasting » (WRF). Une étude préliminaire a été réalisée pour tester les capacités du modèle et plus particulièrement des schémas de microphysique à reproduire la pluie. Cette étude assure ainsi l’obtention de prévisions réalistes pour une application sur des cas réels. L’appréciation de la qualité des QPF s’est focalisée sur la quantification spatiale des erreurs de prévision en termes de structure, d’intensité et de localisation des systèmes précipitants (SAL : Wernli et al. 2008, 2009). / In the last decades, many efforts were made to better understand the origins of rain that sometimes lead to rivers runoff or devastating floods. In 2009, a consortium took place in Auvergne in order to observe and predict these events. These works were focused on the improvement of quantitative precipitation estimations (QPE) and the verification of numerical weather models over small areas such as urban environment. Rainfall measurement could be operated either by rain gauges which provides direct and precise rainfall estimations but unfortunately cannot capture the spatial variability or by using weather RADAR which provides a detailed spatial representation of precipitation but estimates are derived indirectly and are subject to a combination of errors which are most pronounced over complex terrain. The main issue of these works was to find the best way to combine both observational systems which are complementary as well. In order to obtain the more truthful fields of QPE, two geostatistical techniques were selected: the kriging with external drift (KED) and the conditional merging (MERG). The performances of these two methods have been experienced on two catchments with different spatial and temporal resolutions. The second part of these works is focused on a reliable method for QPE comparison and quantitative precipitation forecast (QPF). The main effort was focused on the “Weather Research and Forecasting” (WRF) model. A preliminary study was made to check the performances of the microphysics schemes of the model to ensure realistic forecasts for an application on real cases. The spatial verification of the model set up contains three distinct components that consider aspects of the structure, amplitude and location of the precipitation field (SAL : Wernli et al. 2008, 2009).

The goal of this study is the recovery of functions and finite parametric distributions from their spherical means over spheres and designing a general formula or algorithm for the reconstruction of a function f via its spherical mean transform. The theoretical study is and supported with a numerical implementation based on radar data. In this study, we approach the reconstruction problem in two different way. The first one is to show how the reconstruction problem could be converted to a Prony-type system of equations. After solving this Prony-type system of equations, one can extract the parameters that describe the corresponding functions or distributions efficiently. The second way is to solve this problem via a backprojection procedure.

This cumulative dissertation includes four peer-reviewed and published articles. It evaluates three open-access radar quantitative precipitation estimate (QPE) products from the German Weather Service (DWD) with different temporal resolutions. The improved length and quality of the DWD’s radar QPE products allows a detailed assessment of existing statistical precipitation characteristics and scaling laws, which are established on the basis of traditional point measurements only. The focus of the thesis is on heavy to extreme rainfall and scaling characteristics in time and space. The first publication is a comprehensive assessment of spatio-temporal heavy rainfall pattern in context of urban rainfall modification. The analysis identifies storm alteration by the city of Berlin using the RADOLAN-RW product, suitable for event analysis. Six storm categories were identified and newly introduced tools, such as the amplification factor helped to quantify the changes. The second and third publications focus on the re-evaluation of point-based findings from literature. The first compares depth-duration relationships based on 400,000+ grid cells within Germany for durations of 10 min to 3 days based on 16 years of RADKLIM-YW (5 min and 1 km spatio-temporal resolution) with a well-established global rainfall maxima curve. The German regional curve showed a 'three-phase-regime', governed by the temporal structure of very few extreme rainfall events. Three groups of curve characteristics for single grid cells were identified, based on the rainstorms that had occurred at the individual location. The third article shows the significance of using moving time interval maxima (M-Maxima) over fixed maxima (F-Maxima) and also helps to describe the probabilistic nature of the distribution of potential correction factors, in this case the Sampling Adjustment Factor (SAF), more accurately. It uses both RADKLIM products in order to compare different base resolutions and its effects on the results. Findings add new insights into the importance of identifying good correction factors and also consider the distribution of them instead of using average factors as usually done in practice. The fourth publication studies a new method to extrapolate extreme rainfall to sub-pixel scale via a simple scaling approach, based on 19 years of RADKLIM-RW (hourly and 1 km spatio-temporal resolution) and four regions within Germany of each 256 km x 256 km. Almost smooth power laws were observed when looking at the depth-area-relationships, depending on the considered data length and regions. Closer to the resolution of the radar data (1x1 km²), other influencing factors lead to a shift in rainfall characteristics and thus a bend of the relationship. The two rainfall classes of more convective and more advective characteristics generally had a strong influence on all results of the thesis and are highly dependent on the temporal resolution of the data. The gridded radar QPE data helped to reveal characteristics such as the correlation of small areas with high rain rates (connected to convective pattern) and larger areas with lower rain rates (connected to advective pattern). The analysed radar QPE products are suitable for analysing spatial and temporal rainfall pattern. However, for extreme values, uncertainty remains, since it is not clear if very extreme values are outliers or 'true' observations. / Diese kumulative Dissertation umfasst vier begutachtete und veröffentlichte Artikel. Sie wertet drei frei zugängliche Radarkomposite (QPE) des Deutschen Wetterdienstes (DWD) mit unterschiedlichen zeitlichen Auflösungen aus. Die verbesserte Länge und Qualität dieser Produkte ermöglicht eine detaillierte Bewertung vorhandener Niederschlagscharakteristika, die auf Punktmessungen beruhen. Der Schwerpunkt der Arbeit liegt dabei auf Stark- bis Extremniederschlägen und deren Skalierungseigenschaften. Die erste Veröffentlichung ist eine umfassende Bewertung der raum-zeitlichen Starkregenmuster im Kontext der städtischen Niederschlagsmodifikation. Die Analyse identifiziert den Einfluss der Stadt Berlins auf Starkregenereignisse unter Verwendung des RADOLAN-RW-Produkts. Sechs Kategorien von Niederschlagsmodifikationen wurden identifiziert und neu eingeführte Werkzeuge, wie der Verstärkungsfaktor, halfen bei der Quantifizierung der Veränderungen. Die zweite und dritte Publikationen konzentrieren sich auf die Neubewertung von punktbasierten Erkenntnissen aus der Literatur. Erstere vergleicht Niederschlags-Dauer-Beziehungen auf der Basis von mehr als 400.000 Rasterzellen innerhalb Deutschlands für Dauern von 10 min bis 3 Tagen auf der Grundlage von 16 Jahren RADKLIM-YW (5 min und 1 km räumlich-zeitliche Auflösung) mit einer bekannten globalen Niederschlagsmaximumkurve. Die regionale Kurve in Deutschland zeigte ein 'Drei-Phasen-Regime', das durch die zeitliche Struktur von sehr wenigen extremen Niederschlagsereignissen bestimmt wird. Es wurden drei Gruppen von Kurvencharakteristika für einzelne Gitterzellen identifiziert, die auf den am jeweiligen Standort aufgetretenen Regenfällen basieren. Zweitere zeigt die Bedeutung der Verwendung von gleitenden (M-Maxima) gegenüber festen Niederschlagsmaxima (F-Maxima) und hilft dabei, die probabilistische Natur der Verteilung potenzieller Korrekturfaktoren, in unserem Fall des 'Sampling Adjustment Factor' (SAF), genauer zu beschreiben. Es wurden beide RADKLIM-Produkte verwendet, um verschiedene Basisauflösungen und ihre Auswirkungen auf die Ergebnisse zu vergleichen. Die Ergebnisse liefern neue Erkenntnisse darüber, wie wichtig es ist, gute Korrekturfaktoren zu ermitteln und auch deren Verteilung zu berücksichtigen, anstatt wie in der Praxis üblich Durchschnittsfaktoren zu verwenden. Die vierte Veröffentlichung untersucht eine neue Methode zur Extrapolation extremer Niederschläge mittels eines einfachen Skalierungsansatzes, basierend auf 19 Jahren RADKLIM-RW (stündliche und 1 km räumlich-zeitliche Auflösung) und vier Regionen in Deutschland mit jeweils 256 km x 256 km. Es wurden nahezu perfekte Potenzgesetze in der Beziehung von Niederschlag und Fläche beobachtet, abhängig von der betrachteten Datenlänge und den Regionen. Nahe an der Auflösung des Radars (1x1 km²) knicken die Beziehungen ab, was auf eine Veränderung der Niederschlagscharakteristika hinweist. Die beiden Niederschlagsklassen mit eher konvektiven und eher advektiven Eigenschaften hatten generell einen starken Einfluss auf alle Ergebnisse der Arbeit und sind stark von der zeitlichen Auflösung der Daten abhängig. Die Radarkomposite halfen dabei, Merkmale wie die Korrelation von kleinen Gebieten mit hohen Niederschlagsmengen (verbunden mit konvektiven Mustern) und größeren Gebieten mit niedrigeren Niederschlagsmengen (verbunden mit advektiven Mustern) aufzuzeigen. Die analysierten Radarkomposite sind für die Analyse räumlicher und zeitlicher Niederschlagsmuster geeignet. Bei Extremwerten bleibt jedoch eine gewisse Unsicherheit, da nicht klar ist, ob es sich bei sehr extremen Werten um Ausreißer oder 'echte' Beobachtungen handelt.

abstract: This doctoral thesis investigates the predictability characteristics of floods and flash floods by coupling high resolution precipitation products to a distributed hydrologic model. The research hypotheses are tested at multiple watersheds in the Colorado Front Range (CFR) undergoing warm-season precipitation. Rainfall error structures are expected to propagate into hydrologic simulations with added uncertainties by model parameters and initial conditions. Specifically, the following science questions are addressed: (1) What is the utility of Quantitative Precipitation Estimates (QPE) for high resolution hydrologic forecasts in mountain watersheds of the CFR?, (2) How does the rainfall-reflectivity relation determine the magnitude of errors when radar observations are used for flood forecasts?, and (3) What are the spatiotemporal limits of flood forecasting in mountain basins when radar nowcasts are used into a distributed hydrological model?. The methodology consists of QPE evaluations at the site (i.e., rain gauge location), basin-average and regional scales, and Quantitative Precipitation Forecasts (QPF) assessment through regional grid-to-grid verification techniques and ensemble basin-averaged time series. The corresponding hydrologic responses that include outlet discharges, distributed runoff maps, and streamflow time series at internal channel locations, are used in light of observed and/or reference data to diagnose the suitability of fusing precipitation forecasts into a distributed model operating at multiple catchments. Results reveal that radar and multisensor QPEs lead to an improved hydrologic performance compared to simulations driven with rain gauge data only. In addition, hydrologic performances attained by satellite products preserve the fundamental properties of basin responses, including a simple scaling relation between the relative spatial variability of runoff and its magnitude. Overall, the spatial variations contained in gridded QPEs add value for warm-season flood forecasting in mountain basins, with sparse data even if those products contain some biases. These results are encouraging and open new avenues for forecasting in regions with limited access and sparse observations. Regional comparisons of different reflectivity -rainfall (Z-R) relations during three summer seasons, illustrated significant rainfall variability across the region. Consistently, hydrologic errors introduced by the distinct Z-R relations, are significant and proportional (in the log-log space) to errors in precipitation estimations and stream flow magnitude. The use of operational Z-R relations without prior calibration may lead to wrong estimation of precipitation, runoff magnitude and increased flood forecasting errors. This suggests that site-specific Z-R relations, prior to forecasting procedures, are desirable in complex terrain regions. Nowcasting experiments show the limits of flood forecasting and its dependence functions of lead time and basin scale. Across the majority of the basins, flood forecasting skill decays with lead time, but the functional relation depends on the interactions between watershed properties and rainfall characteristics. Both precipitation and flood forecasting skills are noticeably reduced for lead times greater than 30 minutes. Scale dependence of hydrologic forecasting errors demonstrates reduced predictability at intermediate-size basins, the typical scale of convective storm systems. Overall, the fusion of high resolution radar nowcasts and the convenient parallel capabilities of the distributed hydrologic model provide an efficient framework for generating accurate real-time flood forecasts suitable for operational environments. / Dissertation/Thesis / Ph.D. Civil and Environmental Engineering 2012

Ces dernières années, de nombreux efforts ont été entrepris pour mieux comprendre les phénomènes précipitants parfois à l'origine de crues de cours d'eau et d'inondations ravageuses. Courant 2009, un consortium auvergnat a été mis en place pour notamment surveiller et prévoir ces événements. Les travaux menés dans cette thèse visent d'une part à améliorer les estimations quantitatives des précipitations (QPE) et d'autre part à vérifier les prévisions issues de modèles numériques sur de petites zones d'étude telles qu'une agglomération. L'observation des précipitations peut être réalisée à l'aide soit d'un pluviomètre qui fournit une mesure directe et précise de la quantité de pluie tombée au sol mais ne renseigne pas sur la variabilité spatiale des pluies soit d'un RADAR météorologique qui donne une représentation détaillée de la structure spatiale des précipitations mais dont les estimations sont sujettes à diverses erreurs d'autant plus prononcées en régions montagneuses. Le premier défit de cette thèse a été de trouver la meilleure façon de combiner ces deux informations complémentaires. Deux techniques géostatistiques ont été sélectionnées pour obtenir la meilleur QPE : le krigeage avec dérive externe (KED) et la fusion conditionnée (MERG). Les performances de ces deux méthodes ont été comparées au travers de deux domaines d'étude qui présentent des résolutions spatio-temporelles différentes. La seconde partie de cette thèse est consacrée à la mise en place d'une méthodologie fiable permettant de comparer spatialement les champs de QPE alors reconstruits et les prévisions quantitatives des précipitations (QPF). L'effort fut porté sur le modèle " Weather Research et Forcasting " (WRF). Une étude préliminaire a été réalisée pour tester les capacités du modèle et plus particulièrement des schémas de microphysique à reproduire la pluie. Cette étude assure ainsi l'obtention de prévisions réalistes pour une application sur des cas réels. L'appréciation de la qualité des QPF s'est focalisée sur la quantification spatiale des erreurs de prévision en termes de structure, d'intensité et de localisation des systèmes précipitants (SAL : Wernli et al. 2008, 2009).

Main extrinsic and intrinsic modifiers factors of crack growth rate in AA7050-T7451 were assessed in order to provide tools for aeronautical structures designers. These tools cover most necessary information to project aircraft\'s structures using the studied alloy, under damage tolerance philosophy. The experimental methodology consisted of use CT specimens, on TL and LT rolling direction to test its behavior under different conditions of stress ratio, force waveform, and the environment. The stress ratio values were 0.1 and 0.5, the force waveform used were sine and trapezoidal or Dwell under normal air laboratory conditions and salt fog 3.5%NaCl weight in order to simulate the marine environment. In Dwell tests, results were checked with the electrical potential drop technique (DCPD) in addition to the crack opening displacement (COD) method. Using the Walker coefficients, calculated on the present research, could be projected accurately the crack propagation behavior on Paris region and do fatigue life predictions using da/dN and S-N diagrams for different stress ratio values. The corrosion environment increases both crack growth rate and ΔKth due to oxides formation on the crack path that generates a crack closure effect. Dwell carrying makes decrease the crack growth rate by decreasing the slope of the Paris line on log (da/dN) versus log (ΔK) curve, instead of shifting down the line as occurs on titanium alloys. Rolling direction change from LT to TL increase the FCG rate in both threshold and Paris region, where the rate change use to be small. / Os principais fatores modificadores extrínsecos e intrínsecos da taxa de propagação de trincas na liga AA7050-T7451 foram avaliados para fornecer subsídios para projetistas de estruturas aeronáuticas, com base na filosofía de tolerância ao dano. A metodologia experimental consistiu em ensaiar corpos de prova do tipo compact tension (CT) da liga nas direções de laminação TL e LT, para verificar seu comportamento sob diferentes razões de tensões, forma de onda e condição ambiente. Os valores de razão de tensão estudados foram 0,1 e 0,5, as formas de onda foram senoidal e trapezoidal ou de Dwell, em condições normais de laboratório, ao ar, e névoa salina 3,5% NaCl, em massa, para simular um ambiente marinho. No caso dos ensaios Dwell, os resultados foram conferidos pelo método de queda de potencial eléctrico (QPE), além do método de flexibilidade elástica. Usando os coeficientes de Walker calculados a partir dos resultados obtidos, pôde-se projetar com precisão o comportamento da propagação de trinca na região de Paris e prever a vida em fadiga usando os diagramas da/dN e S-N para diferentes valores da razão de tensões. O ambiente corrosivo aumenta tanto a taxa de propagação de trinca, quanto o valor de ΔKth por causa da formação de óxidos na trajetória da trinca, que geram um efeito de fechamento sobre a mesma. Quanto à forma de onda, verificou-se que o carregamento Dwell diminui a taxa de propagação de trinca, diminuindo a inclinação das curvas log (da/dN) versus log (ΔK) na região de Paris, ao invés de deslocá-la paralelamente como ocorre com ligas de titânio. A mudança da direção de laminação de LT para TL aumenta a taxa de propagação de trinca por fadiga (PTF) tanto na região de threshold, quanto na região de Paris, onde a mudança de taxa é pequena.

Main extrinsic and intrinsic modifiers factors of crack growth rate in AA7050-T7451 were assessed in order to provide tools for aeronautical structures designers. These tools cover most necessary information to project aircraft\'s structures using the studied alloy, under damage tolerance philosophy. The experimental methodology consisted of use CT specimens, on TL and LT rolling direction to test its behavior under different conditions of stress ratio, force waveform, and the environment. The stress ratio values were 0.1 and 0.5, the force waveform used were sine and trapezoidal or Dwell under normal air laboratory conditions and salt fog 3.5%NaCl weight in order to simulate the marine environment. In Dwell tests, results were checked with the electrical potential drop technique (DCPD) in addition to the crack opening displacement (COD) method. Using the Walker coefficients, calculated on the present research, could be projected accurately the crack propagation behavior on Paris region and do fatigue life predictions using da/dN and S-N diagrams for different stress ratio values. The corrosion environment increases both crack growth rate and ΔKth due to oxides formation on the crack path that generates a crack closure effect. Dwell carrying makes decrease the crack growth rate by decreasing the slope of the Paris line on log (da/dN) versus log (ΔK) curve, instead of shifting down the line as occurs on titanium alloys. Rolling direction change from LT to TL increase the FCG rate in both threshold and Paris region, where the rate change use to be small. / Os principais fatores modificadores extrínsecos e intrínsecos da taxa de propagação de trincas na liga AA7050-T7451 foram avaliados para fornecer subsídios para projetistas de estruturas aeronáuticas, com base na filosofía de tolerância ao dano. A metodologia experimental consistiu em ensaiar corpos de prova do tipo compact tension (CT) da liga nas direções de laminação TL e LT, para verificar seu comportamento sob diferentes razões de tensões, forma de onda e condição ambiente. Os valores de razão de tensão estudados foram 0,1 e 0,5, as formas de onda foram senoidal e trapezoidal ou de Dwell, em condições normais de laboratório, ao ar, e névoa salina 3,5% NaCl, em massa, para simular um ambiente marinho. No caso dos ensaios Dwell, os resultados foram conferidos pelo método de queda de potencial eléctrico (QPE), além do método de flexibilidade elástica. Usando os coeficientes de Walker calculados a partir dos resultados obtidos, pôde-se projetar com precisão o comportamento da propagação de trinca na região de Paris e prever a vida em fadiga usando os diagramas da/dN e S-N para diferentes valores da razão de tensões. O ambiente corrosivo aumenta tanto a taxa de propagação de trinca, quanto o valor de ΔKth por causa da formação de óxidos na trajetória da trinca, que geram um efeito de fechamento sobre a mesma. Quanto à forma de onda, verificou-se que o carregamento Dwell diminui a taxa de propagação de trinca, diminuindo a inclinação das curvas log (da/dN) versus log (ΔK) na região de Paris, ao invés de deslocá-la paralelamente como ocorre com ligas de titânio. A mudança da direção de laminação de LT para TL aumenta a taxa de propagação de trinca por fadiga (PTF) tanto na região de threshold, quanto na região de Paris, onde a mudança de taxa é pequena.