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Modeling and simulations of large-scale systems are used extensively to not only better understand a natural phenomenon, but also to predict future events. Accurate model results are critical for design optimization and policy making. They can be used effectively to reduce the impact of a natural disaster or even prevent it from happening. In reality, model predictions are often affected by uncertainties in input data and model parameters, and by incomplete knowledge of the underlying physics. A deterministic simulation assumes one set of input conditions, and generates one result without considering uncertainties. It is of great interest to include uncertainty information in the simulation. By ``Uncertainty Quantification,'' we denote the ensemble of techniques used to model probabilistically the uncertainty in model inputs, to propagate it through the system, and to represent the resulting uncertainty in the model result. This added information provides a confidence level about the model forecast. For example, in environmental modeling, the model forecast, together with the quantified uncertainty information, can assist the policy makers in interpreting the simulation results and in making decisions accordingly. Another important goal in modeling and simulation is to improve the model accuracy and to increase the model prediction power. By merging real observation data into the dynamic system through the data assimilation (DA) technique, the overall uncertainty in the model is reduced. With the expansion of human knowledge and the development of modeling tools, simulation size and complexity are growing rapidly. This poses great challenges to uncertainty analysis techniques. Many conventional uncertainty quantification algorithms, such as the straightforward Monte Carlo method, become impractical for large-scale simulations. New algorithms need to be developed in order to quantify and reduce uncertainties in large-scale simulations. This research explores novel uncertainty quantification and reduction techniques that are suitable for large-scale simulations. In the uncertainty quantification part, the non-sampling polynomial chaos (PC) method is investigated. An efficient implementation is proposed to reduce the high computational cost for the linear algebra involved in the PC Galerkin approach applied to stiff systems. A collocation least-squares method is proposed to compute the PC coefficients more efficiently. A novel uncertainty apportionment strategy is proposed to attribute the uncertainty in model results to different uncertainty sources. The apportionment results provide guidance for uncertainty reduction efforts. The uncertainty quantification and source apportionment techniques are implemented in the 3-D Sulfur Transport Eulerian Model (STEM-III) predicting pollute concentrations in the northeast region of the United States. Numerical results confirm the efficacy of the proposed techniques for large-scale systems and the potential impact for environmental protection policy making. ``Uncertainty Reduction'' describes the range of systematic techniques used to fuse information from multiple sources in order to increase the confidence one has in model results. Two DA techniques are widely used in current practice: the ensemble Kalman filter (EnKF) and the four-dimensional variational (4D-Var) approach. Each method has its advantages and disadvantages. By exploring the error reduction directions generated in the 4D-Var optimization process, we propose a hybrid approach to construct the error covariance matrix and to improve the static background error covariance matrix used in current 4D-Var practice. The updated covariance matrix between assimilation windows effectively reduces the root mean square error (RMSE) in the solution. The success of the hybrid covariance updates motivates the hybridization of EnKF and 4D-Var to further reduce uncertainties in the simulation results. Numerical tests show that the hybrid method improves the model accuracy and increases the model prediction quality. / Ph. D.

Ensemble and variational techniques have gained wide popularity as the two main approaches for solving data assimilation and inverse problems. The majority of the methods in these two approaches are derived (at least implicitly) under the assumption that the underlying probability distributions are Gaussian. It is well accepted, however, that the Gaussianity assumption is too restrictive when applied to large nonlinear models, nonlinear observation operators, and large levels of uncertainty. This work develops a family of fully non-Gaussian data assimilation algorithms that work by directly sampling the posterior distribution. The sampling strategy is based on a Hybrid/Hamiltonian Monte Carlo (HMC) approach that can handle non-normal probability distributions. The first algorithm proposed in this work is the "HMC sampling filter", an ensemble-based data assimilation algorithm for solving the sequential filtering problem. Unlike traditional ensemble-based filters, such as the ensemble Kalman filter and the maximum likelihood ensemble filter, the proposed sampling filter naturally accommodates non-Gaussian errors and nonlinear model dynamics, as well as nonlinear observations. To test the capabilities of the HMC sampling filter numerical experiments are carried out using the Lorenz-96 model and observation operators with different levels of nonlinearity and differentiability. The filter is also tested with shallow water model on the sphere with linear observation operator. Numerical results show that the sampling filter performs well even in highly nonlinear situations where the traditional filters diverge. Next, the HMC sampling approach is extended to the four-dimensional case, where several observations are assimilated simultaneously, resulting in the second member of the proposed family of algorithms. The new algorithm, named "HMC sampling smoother", is an ensemble-based smoother for four-dimensional data assimilation that works by sampling from the posterior probability density of the solution at the initial time. The sampling smoother naturally accommodates non-Gaussian errors and nonlinear model dynamics and observation operators, and provides a full description of the posterior distribution. Numerical experiments for this algorithm are carried out using a shallow water model on the sphere with observation operators of different levels of nonlinearity. The numerical results demonstrate the advantages of the proposed method compared to the traditional variational and ensemble-based smoothing methods. The HMC sampling smoother, in its original formulation, is computationally expensive due to the innate requirement of running the forward and adjoint models repeatedly. The proposed family of algorithms proceeds by developing computationally efficient versions of the HMC sampling smoother based on reduced-order approximations of the underlying model dynamics. The reduced-order HMC sampling smoothers, developed as extensions to the original HMC smoother, are tested numerically using the shallow-water equations model in Cartesian coordinates. The results reveal that the reduced-order versions of the smoother are capable of accurately capturing the posterior probability density, while being significantly faster than the original full order formulation. In the presence of nonlinear model dynamics, nonlinear observation operator, or non-Gaussian errors, the prior distribution in the sequential data assimilation framework is not analytically tractable. In the original formulation of the HMC sampling filter, the prior distribution is approximated by a Gaussian distribution whose parameters are inferred from the ensemble of forecasts. The Gaussian prior assumption in the original HMC filter is relaxed. Specifically, a clustering step is introduced after the forecast phase of the filter, and the prior density function is estimated by fitting a Gaussian Mixture Model (GMM) to the prior ensemble. The base filter developed following this strategy is named cluster HMC sampling filter (ClHMC ). A multi-chain version of the ClHMC filter, namely MC-ClHMC , is also proposed to guarantee that samples are taken from the vicinities of all probability modes of the formulated posterior. These methodologies are tested using a quasi-geostrophic (QG) model with double-gyre wind forcing and bi-harmonic friction. Numerical results demonstrate the usefulness of using GMMs to relax the Gaussian prior assumption in the HMC filtering paradigm. To provide a unified platform for data assimilation research, a flexible and a highly-extensible testing suite, named DATeS , is developed and described in this work. The core of DATeS is implemented in Python to enable for Object-Oriented capabilities. The main components, such as the models, the data assimilation algorithms, the linear algebra solvers, and the time discretization routines are independent of each other, such as to offer maximum flexibility to configure data assimilation studies. / Ph. D.

Reconstruire des champs géophysiques à partir d'observations bruitées et partielles est un problème classique bien étudié dans la littérature. L'assimilation de données est une méthode populaire pour aborder ce problème, et se fait par l'utilisation de techniques classiques, comme le filtrage de Kalman d’ensemble ou des filtres particulaires qui procèdent à une évaluation online du modèle physique afin de fournir une prévision de l'état. La performance de l'assimilation de données dépend alors fortement de du modèle physique. En revanche, la quantité de données d'observation et de simulation a augmenté rapidement au cours des dernières années. Cette thèse traite l'assimilation de données d'une manière data-driven et ce, sans avoir accès aux équations explicites du modèle. Nous avons développé et évalué l'assimilation des données par analogues (AnDA), qui combine la méthode des analogues et des méthodes de filtrage stochastiques (filtres Kalman, filtres à particules, chaînes de Markov cachées). Des applications aux modèles chaotiques simplifiés et à des études de cas de télédétection réelle (température de surface de lamer, anomalies du niveau de la mer), nous démontrons la pertinence d'AnDA pour l'interpolation de données manquantes des systèmes dynamiques non linéaires et à haute dimension à partir d'observations irrégulières et bruyantes.Motivé par l'essor du machine learning récemment, la dernière partie de cette thèse est consacrée à l'élaboration de modèles deep learning pour la détection et de tourbillons océaniques à partir de données de sources multiples et/ou multi temporelles (ex: SST-SSH), l'objectif général étant de surpasser les approches dites expertes. / Reconstructing geophysical fields from noisy and partial remote sensing observations is a classical problem well studied in the literature. Data assimilation is one class of popular methods to address this issue, and is done through the use of classical stochastic filtering techniques, such as ensemble Kalman or particle filters and smoothers. They proceed by an online evaluation of the physical modelin order to provide a forecast for the state. Therefore, the performanceof data assimilation heavily relies on the definition of the physical model. In contrast, the amount of observation and simulation data has grown very quickly in the last decades. This thesis focuses on performing data assimilation in a data-driven way and this without having access to explicit model equations. The main contribution of this thesis lies in developing and evaluating the Analog Data Assimilation(AnDA), which combines analog methods (nearest neighbors search) and stochastic filtering methods (Kalman filters, particle filters, Hidden Markov Models). Through applications to both simplified chaotic models and real ocean remote sensing case-studies (sea surface temperature, along-track sea level anomalies), we demonstrate the relevance of AnDA for missing data interpolation of nonlinear and high dimensional dynamical systems from irregularly-sampled and noisy observations. Driven by the rise of machine learning in the recent years, the last part of this thesis is dedicated to the development of deep learning models for the detection and tracking of ocean eddies from multi-source and/or multi-temporal data (e.g., SST-SSH), the general objective being to outperform expert-based approaches.

Currently, existing devices for extracting electrical power from ocean waves all suffer from problems with low efficiency due to a lack of information about the incoming waves in advance. The complex dynamic nonlinear characteristics of the ocean make the prediction of these incoming waves a great challenge. This paper aims to investigate a deterministic short-term wave-by-wave prediction system, that can accurately predict the wave height and timing of the incoming waves, based on measurements from a submerged pressure sensor. The complete prediction process contains three steps, namely reconstruction, assimilation, and prediction. A nonlinear Weakly Dispersive Reconstruction method (WDM) is firstly employed to accurately calculate the surface elevation from the measured pressures. Afterwards, a variational assimilation method is used to convert the time series surface elevation to a spatial wavefield, to obtain initial conditions for the prediction. Lastly, a High Order Spectral Method (HOSM) deterministically predicts the evolution of the 2D irregular wavefield based on the acquired initial conditions. To verify the performance of this proposed prediction system, tests were conducted with data from irregular sea states with varying wave parameters, generated by simulations as well as model experiments in the controlled environment of a wave tank. The results show that the surface elevation can be predicted within 5% from the reference, for a future period of about 10 seconds for wavefields commonly experienced by a wave energy converter. Based on the results, a prediction is possible, but the accuracy heavily depends on the current sea state and the chosen prediction distance.The results have been compared against similar tests made using radar data and proven to be a viable alternative for certain sea states. In conclusion, pressure measurements, as a mean to sample an ocean wavefield, is shown to be a good option when combined with nonlinear reconstruction and prediction methods to assist the power harvesting capabilities of a wave energy converter. / Nuvarande enheter för att extrahera elektrisk energi från havsvågor lider av stora problem med låg effektivitet på grund av brist på information om de inkommande vågorna. Det komplexa ickelinjära dynamiska beteendet hos havsvågor gör förutsägelsen av dem till en stor utmaning. Det här arbetet syftar till att undersöka ett deterministiskt kortsiktigt system för att förutspå våg för våg, som noggrant kan förutspå våghöjd och tidpunkt för de inkommande vågorna, baserat på mätdata från en dränkbar trycksensor. Den kompletta förutsägelseprocessen innehåller tre steg, rekonstruktion, assimilering och förutsägelse. En ickelinjär weakly dispersive reconstruction method används först för att med hög noggrannhet beräkna ythöjningen från det uppmätta trycket. Därefter, används en variational assimilation method för att konvertera en tidsserie av ythöjningen till ett rumsligt vågfält, för att erhålla initialvillkor för förutsägelsen. Slutligen används en High Order Spectral Method för att deterministiskt förutspå utvecklingen av det tvådimensionella oregelbundna vågfältet baserat på de förvärvade initialvillkoren. För att verifiera prestandan av det föreslagna förutsägelsesystemet, så genomfördes tester med data från olika oregelbundna havstillstånd med varierande parametrar, genererade av simuleringar, såväl som modellexperiment utförda i en kontrollerad miljö i form av en vågtank. Resultaten från testerna visar att ythöjningen förutspås inom 5% från referensen, för en period på 10 sekunder framåt i tiden, för vågor som ett vågkraftverk vanligtvis utsätts för. Baserat på resultatet, så är det möjligt att förutspå inkommande vågor, men noggrannheten beror kraftigt på det aktuella havstillståndet och det valda avståndet för förutsägelsen. Resultaten har jämförts mot liknande tester gjorda med radardata och visat sig vara ett genomförbart alternativ för vissa havstillstånd. Sammanfattningsvis visas det att tryckmätningar, som ett medel för att mäta ett havsvågfält, är ett bra alternativ när de kombineras med ickelinjära rekonstruktions- och förutsägelsemetoder för att hjälpa till att öka ett vågkraftverks energigenerering.

Data assimilation arises in a vast array of different topics: traditionally in meteorological and oceanographic modelling, wind tunnel or water tunnel experiments and recently from biomedical engineering. Data assimilation is a process for combine measured or observed data with a mathematical model, to obtain estimates of the expected data. The measured data usually contains inaccuracies and is given with low spatial and/or temporal resolution. In this thesis data assimilation for time dependent fluid flow is considered. The flow is assumed to satisfy a given partial differential equation, representing the mathematical model. The problem is to determine the initial state which leads to a flow field which satisfies the flow equation and is close to the given data. In the first part we consider one-dimensional flow governed by Burgers’ equation. We analyze two iterative methods for data assimilation problem for this equation. One of them so called adjoint optimization method, is based on minimization in L2-norm. We show that this minimization problem is ill-posed but the adjoint optimization iterative method is regularizing, and represents the well-known Landweber method in inverse problems. The second method is based on L2-minimization of the gradient. We prove that this problem always has a solution. We present numerical comparisons of these two methods. In the second part three-dimensional inviscid compressible flow represented by the Euler equations is considered. Adjoint technique is used to obtain an explicit formula for the gradient to the optimization problem. The gradient is used in combination with a quasi-Newton method to obtain a solution. The main focus regards the derivation of the adjoint equations with boundary conditions. An existing flow solver EDGE has been modified to solve the adjoint Euler equations and the gradient computations are validated numerically. The proposed iteration method are applied to a test problem where the initial pressure state is reconstructed, for exact data as well as when disturbances in data are present. The numerical convergence and the result are satisfying.

Environmental monitoring of Earth from space has provided invaluable information for understanding the land-atmosphere water and energy exchanges. However, the use of satellite observations in hydrologic applications is often limited by coarse space-time resolutions. This study aims to develop a data assimilation system that integrates remotely-sensed precipitation and soil moisture observations into physically-based models to produce fine-scale precipitation, soil moisture, and other relevant hydrometeorological variables. This is particularly useful with the active Global Precipitation Measurement and Soil Moisture Active Passive missions. The system consists of two major components: (1) a framework for dynamic downscaling of satellite precipitation products using the Weather Research and Forecasting (WRF) model with four-dimensional variational data assimilation (4D-Var) and (2) a variational data assimilation system using spatio-temporally varying background error covariance for directly assimilating satellite soil moisture data into the Noah land surface model coupled with the WRF model. The WRF 4D-Var system can effectively assimilate and downscale six-hour precipitation products of a spatial resolution of about 20 km (i.e., those derived from the National Centers for Environmental Prediction Stage IV data and the Tropical Rainfall Measuring Mission (TRMM) 3B42 dataset) to hourly precipitation with a spatial resolution of less than 10 km. The system is able to assimilate and downscale daily soil moisture products at a gridded 36-km resolution obtained from the Soil Moisture and Ocean Salinity (SMOS) mission to produce hourly 4-by-4 km surface soil moisture forecasts with a reduction of mean absolute error by 35% on average. The results from the system with coupled components show that assimilation of the TRMM 3B42 precipitation improves the quality of both downscaled precipitation and soil moisture analyses, while the effect of SMOS soil moisture data assimilation is largely on the soil moisture analyses. The downscaled WRF precipitation, with and without assimilation of TRMM precipitation, was preliminarily tested with a spatially distributed simulation of streamflow using the TIN (Triangular Irregular Network)-based Real-time Integrated Basin Simulator (tRIBS).

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.

Le sondeur infrarouge hyperspectral IASI (Interféromètre Atmosphérique de Sondage Infrarouge), développé conjointement par le CNES et EUMETSAT à bord du satellite européen Metop, permet, entre autres, le sondage de la température, de l'humidité ainsi que la restitution de paramètres de surface. Bien que l'on tire le meilleur parti de ces données sur la mer, leur utilisation est encore limitée au-dessus des terres dans le contexte de la prévision numérique du temps, à cause de l'incertitude plus grande sur l'émissivité et la température de surface (Ts). Ces erreurs se répercutent sur la qualité des simulations de transfert radiatif et empêche l'utilisation de ces mesures dans les modèles de prévision numérique du temps. Seuls les canaux non sensibles à la surface terrestre sont assimilés de façon opérationnelle, limitant ainsi le potentiel de sondage aux couches atmosphériques les plus élevées. Cette thèse a pour but l'amélioration de la description des paramètres de surface dans le modèle global ARPEGE de Météo-France en vue de l'assimilation des données du sondeur IASI sur les continents. Nous avons d'abord cherché à améliorer la modélisation de la surface (émissivité et Ts) sur les continents dans le modèle ARPEGE. Pour cela, différents atlas d'émissivité ont été intégrés dans ce modèle : l'un a été calculé à partir des données MODIS (Moderate-Resolution Imaging Spectroradiometer) par l'Université du Wisconsin et le second a été construit à partir des produits IASI de niveau 2 (L2) développés par EUMETSAT. La Ts a ensuite été restituée à partir de canaux de surface IASI en profitant d'une meilleure connaissance de l'émissivité de surface donnée par ces atlas. Ces Ts ont été évaluées par comparaison avec les produits MODIS de la NASA et les produits IASI L2 d'EUMETSAT. Ces comparaisons nous ont permis de sélectionner une combinaison de canaux qui fournit les meilleures estimations de Ts. L'utilisation d'une modélisation de surface réaliste a contribué à l'amélioration de la qualité des simulations de transfert radiatif pour les canaux sensibles à la surface. Les radiances IASI sensibles à la surface ont alors pu être assimilées sur les continents dans le modèle ARPEGE en ciel clair et en utilisant la paramétrisation de surface définie précédemment. Les impacts sur la qualité des analyses et des prévisions ont été étudiés. La prise en compte d'une émissivité et d'une Ts précises a permis d'augmenter significativement le nombre d'observations assimilées. Les principales améliorations concernent les prévisions de géopotentiel et de température pour des pressions inférieures à 400~hPa (en dehors des tropiques). Enfin, dans un cadre plus spécifique et climatologique, nous nous sommes intéressés à la validation de l'utilisation des données IASI en Antarctique durant la campagne Concordiasi. Cette étude a permis d'améliorer les profils inversés de température et de vapeur d'eau par comparaison avec les profils provenant du modèle. L'amélioration est particulièrement importante pour la température de surface. Dans ce cadre, les Ts restituées dans cette thèse ont été comparées à Concordia et au Pôle Sud avec des mesures in-situ et se sont révélées particulièrement précises à Concordia. / The Infrared Atmospheric Sounding Interferometer (IASI), on-board the EUMETSAT Polar System Metop satellite, is developed by CNES in the framework of a co-operation agreement with EUMETSAT. IASI enables, amongst other, infrared soundings of temperature, moisture and retrievals of surface parameters. However in the numerical weather prediction context, these observations are not as intensively used over land as they are over sea because of larger uncertainties about land emissivity and land surface temperature (LST). These uncertainties have an impact on the quality of radiative transfer simulation and hinder the use of these measurements in numerical weather prediction models. Only channels that are not sensitive to the surface are currently assimilated in operations, which limits the potential of sounding instruments to the highest atmospheric layers. This PhD aims to improve the description of land surface parameters in the ARPEGE global model of Météo-France to assimilate IASI data over land. First of all, we tried to improve the surface modelling (surface emissivity and LST) over land in the ARPEGE model. To this end, two emissivity atlases were integrated in this model. The first one is the emissivity climatology computed from the IASI Level-2 products from EUMETSAT and the second one is the global high spectral resolution infrared land surface emissivity database (called UWIREMIS) developed by the Space Science and Engineering Center at University of Wisconsin. Hence, the LST was retrieved from IASI surface channels using these atlases as input parameters in the radiative transfer model. These LSTs were compared to land LST products: the MODIS (Moderate-Resolution Imaging Spectroradiometer) products from the NASA and the IASI Level-2 products from EUMETSAT. These comparisons enabled us to choose the IASI channel combination that provided the best LST estimates. The use of a realistic surface modelling contributed to improve the quality of radiative transfer simulations for surface sensitive channels. Then, surface sensitive IASI radiances were assimilated over land in ARPEGE in clear sky conditions using the surface parameters as previously defined. The impact on analysis and forecast quality was studied. The use of good estimates of surface emissivity and LST significantly increased the number of assimilated observations. The main improvements are for geopotential and temperature forecasts for pressure levels lower than 400~hPa (except in the tropics and in the stratosphere). Finally, from a climatological point of view and within the more specific framework of the Concordiasi campaign, we assessed and validated the use of IASI data in Antarctica. The temperature and humidity retrieved in this particular study proved of better quality than the model profiles, as assessed against the sonde measurements. The improvement is particularly striking for surface temperature. In this framework, the LST retrieved in this PhD were compared with in situ measurements at Concordia and at South Pole station. These estimates are of a great accuracy at Concordia.