This dissertation describes research designed to enhance hydrometeorological forecasts. The objective of the research is to deliver an optimal methodology to produce reliable, skillful and economically valuable probabilistic temperature and precipitation forecasts. Weather plays a dominant role for energy companies relying on forecasts of watershed precipitation and temperature to drive reservoir models, and forecasts of temperatures to meet energy demand requirements. Extraordinary precipitation events and temperature extremes involve consequential water- and power-management decisions. This research compared weighted-average, recursive, and model output statistics bias-correction methods and determined optimal window-length to calibrate temperature and precipitation forecasts. The research evaluated seven different methods for daily maximum and minimum temperature forecasts, and three different methods for daily quantitative precipitation forecasts, within a region of complex terrain in southwestern British Columbia, Canada. This research then examined ensemble prediction system design by assessing a three-model suite of multi-resolution limited area mesoscale models. The research employed two different economic models to investigate the ensemble design that produced the highest-quality, most valuable forecasts. The best post-processing methods for temperature forecasts included moving-weighted average methods and a Kalman filter method. The optimal window-length proved to be 14 days. The best post-processing methods for achieving mass balance in quantitative precipitation forecasts were a moving-average method and the best easy systematic estimator method. The optimal window-length for moving-average quantitative precipitation forecasts was 40 days. The best ensemble configuration incorporated all resolution members from all three models. A cost/loss model adapted specifically for the hydro-electric energy sector indicated that operators managing rainfall-dominated, high-head reservoirs should lower their reservoir with relatively low probabilities of forecast precipitation. A reservoir-operation model based on decision theory and variable energy pricing showed that applying an ensemble-average or full-ensemble precipitation forecast provided a much greater profit than using only a single deterministic high-resolution forecast. Finally, a bias-corrected super-ensemble prediction system was designed to produce probabilistic temperature forecasts for ten cities in western North America. The system exhibited skill and value nine days into the future when using the ensemble average, and 12 days into the future when employing the full ensemble forecast.

This dissertation describes research designed to enhance hydrometeorological forecasts. The objective of the research is to deliver an optimal methodology to produce reliable, skillful and economically valuable probabilistic temperature and precipitation forecasts. Weather plays a dominant role for energy companies relying on forecasts of watershed precipitation and temperature to drive reservoir models, and forecasts of temperatures to meet energy demand requirements. Extraordinary precipitation events and temperature extremes involve consequential water- and power-management decisions. This research compared weighted-average, recursive, and model output statistics bias-correction methods and determined optimal window-length to calibrate temperature and precipitation forecasts. The research evaluated seven different methods for daily maximum and minimum temperature forecasts, and three different methods for daily quantitative precipitation forecasts, within a region of complex terrain in southwestern British Columbia, Canada. This research then examined ensemble prediction system design by assessing a three-model suite of multi-resolution limited area mesoscale models. The research employed two different economic models to investigate the ensemble design that produced the highest-quality, most valuable forecasts. The best post-processing methods for temperature forecasts included moving-weighted average methods and a Kalman filter method. The optimal window-length proved to be 14 days. The best post-processing methods for achieving mass balance in quantitative precipitation forecasts were a moving-average method and the best easy systematic estimator method. The optimal window-length for moving-average quantitative precipitation forecasts was 40 days. The best ensemble configuration incorporated all resolution members from all three models. A cost/loss model adapted specifically for the hydro-electric energy sector indicated that operators managing rainfall-dominated, high-head reservoirs should lower their reservoir with relatively low probabilities of forecast precipitation. A reservoir-operation model based on decision theory and variable energy pricing showed that applying an ensemble-average or full-ensemble precipitation forecast provided a much greater profit than using only a single deterministic high-resolution forecast. Finally, a bias-corrected super-ensemble prediction system was designed to produce probabilistic temperature forecasts for ten cities in western North America. The system exhibited skill and value nine days into the future when using the ensemble average, and 12 days into the future when employing the full ensemble forecast.

This dissertation describes research designed to enhance hydrometeorological forecasts. The objective of the research is to deliver an optimal methodology to produce reliable, skillful and economically valuable probabilistic temperature and precipitation forecasts. Weather plays a dominant role for energy companies relying on forecasts of watershed precipitation and temperature to drive reservoir models, and forecasts of temperatures to meet energy demand requirements. Extraordinary precipitation events and temperature extremes involve consequential water- and power-management decisions. This research compared weighted-average, recursive, and model output statistics bias-correction methods and determined optimal window-length to calibrate temperature and precipitation forecasts. The research evaluated seven different methods for daily maximum and minimum temperature forecasts, and three different methods for daily quantitative precipitation forecasts, within a region of complex terrain in southwestern British Columbia, Canada. This research then examined ensemble prediction system design by assessing a three-model suite of multi-resolution limited area mesoscale models. The research employed two different economic models to investigate the ensemble design that produced the highest-quality, most valuable forecasts. The best post-processing methods for temperature forecasts included moving-weighted average methods and a Kalman filter method. The optimal window-length proved to be 14 days. The best post-processing methods for achieving mass balance in quantitative precipitation forecasts were a moving-average method and the best easy systematic estimator method. The optimal window-length for moving-average quantitative precipitation forecasts was 40 days. The best ensemble configuration incorporated all resolution members from all three models. A cost/loss model adapted specifically for the hydro-electric energy sector indicated that operators managing rainfall-dominated, high-head reservoirs should lower their reservoir with relatively low probabilities of forecast precipitation. A reservoir-operation model based on decision theory and variable energy pricing showed that applying an ensemble-average or full-ensemble precipitation forecast provided a much greater profit than using only a single deterministic high-resolution forecast. Finally, a bias-corrected super-ensemble prediction system was designed to produce probabilistic temperature forecasts for ten cities in western North America. The system exhibited skill and value nine days into the future when using the ensemble average, and 12 days into the future when employing the full ensemble forecast. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

La prévision d'ensemble à l'échelle saisonnière avec des modèles de circulation générale a connu un essor certain au cours des vingt dernières années avec la croissance exponentielle des capacités de calcul, l'amélioration de la résolution des modèles, et l'introduction progressive dans ceux-ci des différentes composantes (océan, atmosphère, surfaces continentales et glace de mer) régissant l'évolution du climat à cette échelle. Malgré ces efforts, prévoir la température et les précipitations de la saison à venir reste délicat, non seulement sur les latitudes tempérées mais aussi sur des régions sujettes à des aléas climatiques forts comme l'Afrique de l'ouest pendant la saison de mousson. L'une des clés d'une bonne prévision est la prise en compte des incertitudes liées à la formulation des modèles (résolution, paramétrisations, approximations et erreurs). Une méthode éprouvée est l'approche multi-modèle consistant à regrouper les membres de plusieurs modèles couplés en un seul ensemble de grande taille. Cette approche a été mise en œuvre notamment dans le cadre du projet européen ENSEMBLES, et nous montrons qu'elle permet généralement d'améliorer les rétro-prévisions saisonnières des précipitations sur plusieurs régions d'Afrique par rapport aux modèles pris individuellement. On se propose dans le cadre de cette thèse d'étudier une autre piste de prise en compte des incertitudes du modèle couplé CNRM-CM5, consistant à ajouter des perturbations stochastiques de la dynamique du modèle d'atmosphère ARPEGE-Climat. Cette méthode, baptisée “dynamique stochastique”, consiste à introduire des perturbations additives de température, humidité spécifique et vorticité corrigeant des estimations d'erreur de tendance initiale du modèle. Dans cette thèse, deux méthodes d'estimation des erreurs de tendance initiale ont été étudiées, basées sur la méthode de nudging (guidage) du modèle vers des données de référence. Elles donnent des résultats contrastés en termes de scores des rétro-prévisions selon les régions étudiées. Si on estime les corrections d'erreur de tendance initiale par une méthode de nudging itéré du modèle couplé vers les réanalyses ERA-Interim, on améliore significativement les scores sur l'hémisphère Nord en hiver en perturbant les prévisions saisonnières en tirant aléatoirement parmi ces corrections. Cette amélioration est accompagnée d'une nette réduction des biais de la hauteur de géopotentiel à 500 hPa. Une rétro-prévision en utilisant des perturbations dites“optimales” correspondant aux corrections d'erreurs de tendance initiale du mois en cours de prévision montre l'existence d'une information à l'échelle mensuelle qui pourrait permettre de considérablement améliorer les prévisions. La dernière partie de cette thèse explore l'idée d'un conditionnement des perturbations en fonction de l'état du modèle en cours de prévision, afin de se rapprocher si possible des améliorations obtenues avec ces perturbations optimales / Over the last twenty years, research in ensemble predictions at a seasonal timescale using general circulation models has undergone a considerable development due to the exponential growth rate of computing capacities, the improved model resolution and the introduction of more and more components (ocean, atmosphere, land surface and sea-ice) that have an impact on climate at this time scale. Regardless of these efforts, predicting temperature and precipitation for the upcoming season is a difficult task, not only over mid-latitudes but also over regions subject to high climate risk, like West Africa during the monsoon season. One key to improving predictions is to represent model uncertainties (due to resolution, parametrizations, approximations and model error). The multimodel approach is a well-tried method which consists in pooling members from different individual coupled models into a single superensemble. This approach was undertaken as part of the European Commission funded ENSEMBLES project, and we find that it usually improves seasonal precipitation re-forecasts over several regions of Africa with respect to individual model predictions. The main goal of this thesis is to study another approach to addressing model uncertainty in the global coupled model CNRM-CM5, by adding stochastic perturbations to the dynamics of the atmospheric model ARPEGE-Climat. Our method, called “stochastic dynamics”, consists in adding additive perturbations to the temperature, specific humidity and vorticity fields, thus correcting estimations of model initial tendency errors. In this thesis, two initial tendency error estimation techniques were studied, based on nudging the model towards reference data. They yield different results in terms of re-forecast scores, depending on the regions studied. If the initial tendency error corrections are estimated using an iterative nudging method towards the ERA-Interim reanalysis, seasonal prediction scores over the Northern Hemisphere in winter are significantly improved by drawing random corrections. The 500 hPa geopotential height is also clearly reduced. A re-forecast using “optimal” perturbations drawn within the initial tendency error corrections from the current forecast month shows that useful information at a monthly timescale exists, and could allow significant forecast improvement. The last part of this thesis focuses on the idea of classifying the model perturbations according to its current state during the forecast, in order to take a step closer (if possible) to the improvements noted with these optimal perturbations

The number of flood events and the estimated costs of floods have increased dramatically over the past few decades. To reduce the negative impacts of flooding, reliable flood forecasting is essential for early warning and decision making. Although various flood forecasting models and techniques have been developed, the assessment and reduction of uncertainties associated with the forecast remain a challenging task. Therefore, this thesis focuses on the investigation of Bayesian methods for producing probabilistic flood forecasts to accurately quantify predictive uncertainty and enhance the forecast performance and reliability. In the thesis, hydrologic uncertainty was quantified by a Bayesian post-processor - Hydrologic Uncertainty Processor (HUP), and the predictability of HUP with different hydrologic models under different flow conditions were investigated. Followed by an extension of HUP into an ensemble prediction framework, which constitutes the Bayesian Ensemble Uncertainty Processor (BEUP). Then the BEUP with bias-corrected ensemble weather inputs was tested to improve predictive performance. In addition, the effects of input and model type on BEUP were investigated through different combinations of BEUP with deterministic/ensemble weather predictions and lumped/semi-distributed hydrologic models. Results indicate that Bayesian method is robust for probabilistic flood forecasting with uncertainty assessment. HUP is able to improve the deterministic forecast from the hydrologic model and produces more accurate probabilistic forecast. Under high flow condition, a better performing hydrologic model yields better probabilistic forecast after applying HUP. BEUP can significantly improve the accuracy and reliability of short-range flood forecasts, but the improvement becomes less obvious as lead time increases. The best results for short-range forecasts are obtained by applying both bias correction and BEUP. Results also show that bias correcting each ensemble member of weather inputs generates better flood forecast than only bias correcting the ensemble mean. The improvement on BEUP brought by the hydrologic model type is more significant than the input data type. BEUP with semi-distributed model is recommended for short-range flood forecasts. / Dissertation / Doctor of Philosophy (PhD) / Flood is one of the top weather related hazards and causes serious property damage and loss of lives every year worldwide. If the timing and magnitude of the flood event could be accurately predicted in advance, it will allow time to get well prepared, and thus reduce its negative impacts. This research focuses on improving flood forecasts through advanced Bayesian techniques. The main objectives are: (1) enhancing reliability and accuracy of flood forecasting system; and (2) improving the assessment of predictive uncertainty associated with the flood forecasts. The key contributions include: (1) application of Bayesian forecasting methods in a semi-urban watershed to advance the predictive uncertainty quantification; and (2) investigation of the Bayesian forecasting methods with different inputs and models and combining bias correction technique to further improve the forecast performance. It is expected that the findings from this research will benefit flood impact mitigation, watershed management and water resources planning.

La prévision des crues est un exercice hydrologique complexe : les incertitudes y sont nombreuses, aussi bien dans le processus de modélisation hydrologique, dans la détermination de l'état initial du bassin versant avant le lancement de la prévision, que dans l'évolution des conditions météorologiques futures. Dans le cas des bassins versants non jaugés, où les observations de débits sont lacunaires voire absentes, ces incertitudes sont encore plus importantes, et le besoin de les réduire devient incontournable. Cette thèse s'intéresse à des méthodes simples et robustes qui peuvent apporter de l'information pertinente pour quantifier les incertitudes de prévision dans les bassins versants non jaugés. Le but est d'étudier la meilleure stratégie pour chercher l'information dans les bassins jaugés "donneurs", et pour la transférer vers le site non jaugé. Nous étudions les besoins pour mettre en place un modèle de simulation pluie-débit et pour effectuer une mise à jour du modèle de prévision en temps réel. Ces deux composantes de la prévision sont ainsi découplées dans notre approche. Cette thèse s'appuie sur une large base de données constituée d'environ 1000 bassins versants français, dont un jeu clé de 211 bassins versants qui permet la validation des approches développées. Elle s'appuie également sur une archive d'environ 4,5 années de prévisions d'ensemble de pluies, utilisées en forçage à la modélisation hydrologique journalière. La démarche adoptée consiste à intégrer les scenarios de transfert de l'information régionale disponible et les scenarios de la prévision météorologique d'ensemble dans un système de prévision orienté vers les bassins versants non jaugés. L'approche de prévision d'ensemble est ainsi généralisée à ce cas particulier de la prévision hydrologique. A travers plusieurs scénarios de débits futurs, nous cherchons à quantifier les incertitudes de prévisions dans les sites cibles non jaugés. Pour évaluer les différents scénarios des prévisions hydrologiques émis, un cadre de diagnostic d'évaluation des principales qualités d'un système de prévision d'ensemble, comprenant plusieurs critères numériques et graphiques, a été mis en place. Dans cette thèse, une attention particulière est prêtée aux attributs "fiabilité" et "précision" des prévisions. Nous proposons ainsi un nouveau critère graphique, nommé diagramme de précision d'ensemble. Ce critère permet notamment de mettre en valeur la qualité des prévisions qui ne sont pas forcément fiables, mais qui sont précises. Les résultats obtenus ont mis en évidence que la fiabilité des prévisions peut être améliorée sur un bassin versant non jaugé par l'utilisation de plusieurs jeux de paramètres issus des bassins versants voisins. Si la variabilité apportée par le voisinage géographique influe sur la dispersion des membres, et augmente ainsi la fiabilité des prévisions, la prise en compte des caractéristiques physiques, principalement de la surface des bassins versants, est apparue comme une alternative intéressante, influençant positivement aussi l'attribut précision des prévisions sur le site cible. De plus, il a été montré que la précision des prévisions d'ensemble sur le site non jaugé est améliorée par l'intermédiaire du transfert des bassins versants jaugés vers le site cible des corrections faites lors de la mise à jour sur les bassins voisins (mise à jour caractérisée ici par l'assimilation de la dernière observation de débit dans le modèle hydrologique, avant l'instant de prévision). Les différentes mesures de performance ont montré que la meilleure option pour améliorer la précision des prévisions serait de considérer les corrections effectuées sur le bassin le plus proche à chaque pas de temps de prévision. Le krigeage a également donné des résultats satisfaisants, marqués en plus par l'influence positive sur l'attribut fiabilité des prévisions. / Flood forecasting is a complex hydrological task: there are numerous uncertainties in the hydrological modelling process, in the determination of the initial catchment conditions before launching the forecast, and in the evolution of future weather conditions. In ungauged catchments, where streamflow observations are incomplete or absent, these uncertainties are even greater, and the need to reduce them becomes essential.This thesis focuses on simple and robust methods that can provide relevant information to quantify the uncertainty in ungauged catchments. The aim is to study the best strategy to search for information in gauged "donors" basins and to transfer it to the ungauged site. We investigate what information is needed to set up a rainfall-runoff model and to perform forecast updating in real time. These two components of a flood forecasting system are thus decoupled in our approach.This thesis is based on a large database of about 1000 French catchments, which includes a key set of 211 catchments that are used to validate the developed approaches. It also relies on an archive of about 4.5 years of ensemble forecasts of rainfall, which are used for hydrological modelling on a daily time step. The methodology adopted here integrates the scenarios of regional transfer of information and the scenarios of weather forecasting together in a forecasting system for ungauged basins. The approach of ensemble forecasting is thus generalised to this particular case of hydrological forecasting. Using several scenarios of future flows, we seek to quantify the predictive uncertainty in ungauged sites.To evaluate the flow forecast scenarios of the hydrological ensemble prediction system, a diagnostic framework with several numerical and graphical criteria is developed. Special attention is paid to the attributes of "reliability" and "accuracy" of the forecasts. We propose a new graphic criterion, named "diagram of ensemble accuracy". This criterion allows to highlight the quality of forecasts that are not necessarily reliable, but are accurate.The results show that forecast reliability in ungauged sites can be improved by using several sets of parameters from neighbour catchments. If on the one hand the variability brought by the information from the geographical proximity influences the spread of the ensemble forecasts, and thus improves forecast reliability, on the other hand taking into account the physical characteristics of the catchments, especially the surface, emerged as an interesting alternative, as it positively influences also the accuracy of the forecasts at the ungauged site.It is also shown that the accuracy of ensemble forecasts at ungauged sites can be improved with the transfer of updating information from gauged neighbour catchments (forecasting updating is here characterized by the assimilation of the last discharge observation in the hydrological model before the time of forecast). The updating information transferred to the ungauged site is the correction applied to the routing reservoir of the hydrological model. Different measures of forecast performance showed that the best option to improve forecast accuracy is to consider the corrections made at the closest gauged site. Kriging also gave satisfactory results, with additionally a positive impact also on the reliability of the ensemble flow forecasts.

Submitted by Maria Cristina (library@lncc.br) on 2015-09-25T19:05:07Z No. of bitstreams: 1 thesis.pdf: 3598969 bytes, checksum: 03cf8e5a078613d707c68e89e449d6d3 (MD5) / Approved for entry into archive by Maria Cristina (library@lncc.br) on 2015-09-25T19:05:20Z (GMT) No. of bitstreams: 1 thesis.pdf: 3598969 bytes, checksum: 03cf8e5a078613d707c68e89e449d6d3 (MD5) / Made available in DSpace on 2015-09-25T19:05:31Z (GMT). No. of bitstreams: 1 thesis.pdf: 3598969 bytes, checksum: 03cf8e5a078613d707c68e89e449d6d3 (MD5) Previous issue date: 2015-05-27 / Conselho Nacional de Desenvolvimento Cientifico e Tecnológico / In this thesis, the evolutionary computation algorithm known as Genetic Programming has been explored as an alternative tool for improving the ensemble forecast of rainfall amount. The efficiency of Genetic Programming to deal with the problem of ensemble forecast of rainfall amount was confirmed on three artificial experiments. The work continued with the application of the evolutionary algorithms on some real-world data sets over south, southeast and central parts of Brazil during the period from October to February of 2008 to 2013. According to the results, Genetic Programming obtained a higher performance relative to two traditional statistical methods, reaching mean errors 27-49% lower than simple mean and the MASTER Super Model Ensemble System. In addition, the results revealed that the evolutionary algorithms outperformed the best individual forecasts, achieving an improvement of 30%. On the other hand, the evolutionary algorithms had a performance similar to the Bayesian Model Averaging technique, but the former are methods far more versatile. In general, the real and artificial experiments showed the potential of Genetic Programming and suggest that further research on the improvement of the technique is needed. / Na presente tese de doutorado, o algoritmo da computação evolutiva conhecido por Programação Genética foi explorado como ferramenta alternativa para o aperfeiçoamento da previsão quantitativa de chuva por conjunto. A aplicabilidade da Programação Genética no problema de previsão quantitativa de chuva por conjunto foi confirmada em três experimentos controlados. O trabalho seguiu com a aplicação dos algoritmos evolutivos sobre algumas bases de dados reais referentes a localidades situadas no sul, sudeste e parte do centro-oeste do Brasil durante o período de outubro a fevereiro de 2008-2013. Os resultados evidenciaram a superioridade da Programação Genética frente aos métodos estatísticos tradicionais: média simples e MASTER Super Model Ensemble System, com erros médios da ordem de 27-49% menores. Ademais, a previsão por conjunto via algoritmos evolutivos ofereceu previsões consideravelmente mais acuradas que as melhores previsões obtidas individualmente, chegando a uma melhora de 30%. Por outro lado, os algoritmos evolutivos apresentaram desempenho equivalente à técnica Bayesian Model Averaging, mas os primeiros são métodos bem mais versáteis. De maneira geral, os experimentos baseados em dados reais e artificiais revelaram a potencialidade da Programação Genética, e encorajam o seu aprimoramento para o problema de previsão quantitativa de chuva por conjunto.

La Mer d’Iroise est observée depuis 2006, par des radars à haute fréquence (HF) qui estiment les courants de surface. Ces mesures ont une finesse temporelle et spatiale pour permettre de capturer la dynamique fine du domaine côtier. Ce travail de thèse vise à la conception et l’application d’une méthode d’assimilation de ces données dans un modèle numérique réaliste pour optimiser le frottement sur le fond et corriger l’état du modèle afin de mieux représenter la circulation résiduelle de marée et les positions des fronts d’Ouessant en mer d’Iroise. La méthode d’assimilation de données utilisée est le Filtre de Kalman d’Ensemble dont l’originalité est l’utilisation d’une modélisation stochastique pour estimer l’erreur du modèle. Premièrement, des simulations d’ensemble ont été réalisées à partir de la perturbation de différents paramètres du modèle considérés comme sources d’erreur : le forçage météo, la rugosité de fond, la fermeture turbulente horizontale et la rugosité de surface. Ces ensembles ont été explorés en termes de dispersion et de corrélation d’ensemble. Un Lisseur de Kalman d’Ensemble a ensuite été utilisé pour optimiser la rugosité de fond (z0) à partir des données de courant de surface et d’un ensemble modèle réalisé à partir d’un z0 perturbé et spatialisé. La méthode a d’abord été testée en expérience jumelle puis avec des observations réelles. Les cartes du paramètre z0, optimisés, réalisées avec des observations réelles, ont ensuite été utilisées dans le modèle sur une autre période et les résultats ont été comparés avec des observations sur la zone. Enfin, des expériences jumelles ont été mises en place pour corriger l’état modèle. Deux méthodes ont été comparées, une prenant en compte la basse fréquence en filtrant la marée des données et du modèle pour réaliser l’analyse ; l’autre prenant en compte tout le signal. Avec ces expériences, on a tenté d’évaluer la capacité du filtre à contrôler à la fois la partie observée du vecteur d’état (courant de surface) et la partie non-observée du système (température de surface). / The Iroise Sea has been observed since 2006 by High Frequency (HF) radars, which estimate surface currents. These measurements offer high resolution and high frequency to capture the dynamics of the coastal domain. This thesis aims at designing and applying a method of assimilation of these data in a realistic numerical model to optimize the bottom friction and to correct the model state in order to improve the representation of the residual tidal circulation and the positions of the Ushant fronts in the Iroise Sea. The method of data assimilation used is the Ensemble Kalman Filter. The originality of this method is the use of a stochastic modeling to estimate the model error. First, ensemble simulations were carried out from the perturbation of various model parameters which are the model error sources: meteorological forcing, bottom friction, horizontal turbulent closure and surface roughness. These ensembles have been explored in terms of dispersion and correlation. An Ensemble Kalman smoother was used to optimize the bottom friction (z0) from the surface current data and from an ensemble produced from a perturbed and spatialized z0. The method is tested with a twin experiment and then with real observations. The optimized maps of parameter z0, produced with the real currents, were used in the model over another period and the results were compared with independent observations. Finally, twin experiments were conducted to test the model state correction. Two approaches were compared; first, only the low frequency, by filtering the tide in the data and in the model, is used to perform the analysis. The other approach takes the whole signal into account. With these experiments, we assess the filter's ability to control both the observed part of the state vector (currents) and the unobserved part of the system (Sea surface Temperature).

Cette thèse concerne le développement, l'extension et l'application d'une formulation stochastique des équations de la mécanique des fluides introduite par Mémin (2014). La vitesse petite échelle, non-résolue, est modélisée au moyen d'un champ aléatoire décorrélé en temps. Cela modifie l'expression de la dérivée particulaire et donc les équations de la mécanique des fluides. Les modèles qui en découlent sont dénommés modèles sous incertitude de position. La thèse s'articulent autour de l'étude successive de modèles réduits, de versions stochastiques du transport et de l'advection à temps long d'un champ de traceur par une vitesse mal résolue. La POD est une méthode de réduction de dimension, pour EDP, rendue possible par l'utilisation d'observations. L'EDP régissant l'évolution de la vitesse du fluide est remplacée par un nombre fini d'EDOs couplées. Grâce à la modélisation sous incertitude de position et à de nouveaux estimateurs statistiques, nous avons dérivé et simulé des versions réduites, déterministe et aléatoire, de l'équation de Navier-Stokes. Après avoir obtenu des versions aléatoires de plusieurs modèles océaniques, nous avons montré numériquement que ces modèles permettaient de mieux prendre en compte les petites échelles des écoulements, tout en donnant accès à des estimés de bonne qualité des erreurs du modèle. Ils permettent par ailleurs de mieux rendre compte des évènements extrêmes, des bifurcations ainsi que des phénomènes physiques réalistes absents de certains modèles déterministes équivalents. Nous avons expliqué, démontré et quantifié mathématiquement l'apparition de petites échelles de traceur, lors de l'advection par une vitesse mal résolu. Cette quantification permet de fixer proprement des paramètres de la méthode d'advection Lagrangienne, de mieux le comprendre le phénomène de mélange et d'aider au paramétrage des simulations grande échelle en mécanique des fluides. / This thesis develops, analyzes and demonstrates several valuable applications of randomized fluid dynamics models referred to as under location uncertainty. The velocity is decomposed between large-scale components and random time-uncorrelated small-scale components. This assumption leads to a modification of the material derivative and hence of every fluid dynamics models. Through the thesis, the mixing induced by deterministic low-resolution flows is also investigated. We first applied that decomposition to reduced order models (ROM). The fluid velocity is expressed on a finite-dimensional basis and its evolution law is projected onto each of these modes. We derive two types of ROMs of Navier-Stokes equations. A deterministic LES-like model is able to stabilize ROMs and to better analyze the influence of the residual velocity on the resolved component. The random one additionally maintains the variability of stable modes and quantifies the model errors. We derive random versions of several geophysical models. We numerically study the transport under location uncertainty through a simplified one. A single realization of our model better retrieves the small-scale tracer structures than a deterministic simulation. Furthermore, a small ensemble of simulations accurately predicts and describes the extreme events, the bifurcations as well as the amplitude and the position of the ensemble errors. Another of our derived simplified model quantifies the frontolysis and the frontogenesis in the upper ocean. This thesis also studied the mixing of tracers generated by smooth fluid flows, after a finite time. We propose a simple model to describe the stretching as well as the spatial and spectral structures of advected tracers. With a toy flow but also with satellite images, we apply our model to locally and globally describe the mixing, specify the advection time and the filter width of the Lagrangian advection method, as well as the turbulent diffusivity in numerical simulations.