A deep scientific understanding of complex physical systems, such as the atmosphere, can be achieved neither by direct measurements nor by numerical simulations alone. Data assimilation is a rigorous procedure to fuse information from a priori knowledge of the system state, the physical laws governing the evolution of the system, and real measurements, all with associated error statistics. Data assimilation produces best (a posteriori) estimates of model states and parameter values, and results in considerably improved computer simulations. The acquisition and use of observations in data assimilation raises several important scientific questions related to optimal sensor network design, quantification of data impact, pruning redundant data, and identifying the most beneficial additional observations. These questions originate in operational data assimilation practice, and have started to attract considerable interest in the recent past. This dissertation advances the state of knowledge in four dimensional variational (4D-Var) - data assimilation by developing, implementing, and validating a novel computational framework for estimating observation impact and for optimizing sensor networks. The framework builds on the powerful methodologies of second-order adjoint modeling and the 4D-Var sensitivity equations. Efficient computational approaches for quantifying the observation impact include matrix free linear algebra algorithms and low-rank approximations of the sensitivities to observations. The sensor network configuration problem is formulated as a meta-optimization problem. Best values for parameters such as sensor location are obtained by optimizing a performance criterion, subject to the constraint posed by the 4D-Var optimization. Tractable computational solutions to this "optimization-constrained" optimization problem are provided. The results of this work can be directly applied to the deployment of intelligent sensors and adaptive observations, as well as to reducing the operating costs of measuring networks, while preserving their ability to capture the essential features of the system under consideration. / Ph. D.

The thermally-driven rotating annulus is a laboratory experiment used to study the dynamics of planetary atmospheres under controlled and reproducible conditions. The predictability of this experiment is studied by applying the same principles used to predict the atmosphere. A forecasting system for the annulus is built using the analysis correction method for data assimilation and the breeding method for ensemble generation. The results show that a range of flow regimes with varying complexity can be accurately assimilated, predicted, and studied in this experiment. This framework is also intended to demonstrate a proof-of-concept: that the annulus could be used as a testbed for meteorological techniques under laboratory conditions. First, a regime diagram is created using numerical simulations in order to select points in parameter space to forecast, and a new chaotic flow regime is discovered within it. The two components of the framework are then used as standalone algorithms to measure predictability in the perfect model scenario and to demonstrate data assimilation. With a perfect model, regular flow regimes are found to be predictable until the end of the forecasts, and chaotic regimes are predictable over hundreds of seconds. There is a difference in the way predictability is lost between low-order chaotic regimes and high-order chaos. Analysis correction is shown to be accurate in both regular and chaotic regimes, with residual velocity errors about 3-8 times the observational error. Specific assimilation scenarios studied include information propagation from data-rich to data-poor areas, assimilation of vortex shedding observations, and assimilation over regime and rotation rate transitions. The full framework is used to predict regular and chaotic flow, verifying the forecasts against laboratory data. The steady wave forecasts perform well, and are predictable until the end of the available data. The amplitude and structural vacillation forecasts lose quality and skill by a combination of wave drift and wavenumber transition. Amplitude vacillation is predictable up to several hundred seconds ahead, and structural vacillation is predictable for a few hundred seconds.

Le bassin Amazonien est connu comme le plus grand système hydrologique du monde et pour son rôle important sur le système terre, influençant le cycle du carbone et le climat global. Les pressions anthropiques récentes, telles que la déforestation, les changements climatiques, la construction de barrage hydro-électriques, ainsi que l’augmentation des crues et sécheresse extrêmes qui se produisent dans cette région, motivent l’étude de l’hydrologie du bassin Amazonien. Dans le même temps, des méthodes hydrologiques de modélisation et de surveillance par observation satellitaire ont été développées qui peuvent fournir les bases techniques à cette fin. Ce travail a eu pour objectif la compréhension et la prévision du régime hydrologique du bassin Amazonien. Nous avons développé et évaluer des techniques de modélisation hydrologique-hydrodynamique de grande échelle, d’assimilation de données in situ et spatiales et de prévision hydrologique. L’ensemble de ces techniques nous a permis d’explorer le fonctionnement du bassin Amazonien en terme de processus physiques et de prévisibilité hydrologique. Nous avons utilisé le modèle hydrologique-hydrodynamique de grande échelle MGB-IPH pour simuler le bassin, le forçage précipitation étant fourni par l’observation spatiale. Les résultats de la modélisation sont satisfaisants lorsque validés à partir de données in situ de débit et de hauteurs d’eau mais également de données dérivées de l’observation spatiale incluant les niveaux d’eau déduits de l’altimétrie radar, le contenu en eau total issu de la gravimétrie satellitaire, l’extension des zones inondées. Nous avons montré que les eaux superficielles sont responsables en grande partie de la variation du stock total d’eau, l’influence des grands plans d’eau sur la variabilité spatiale des précipitations et l’influence des plaines d’inondation et des effets de remous sur la propagation des ondes de crues. Nos analyses ont montré le rôle prépondérant des conditions initiales, en particulier des eaux superficielles, pour la prévisibilité des grands fleuves Amazoniens, la connaissance des précipitations futures n’ayant qu’une influence secondaire. Ainsi, pour améliorer l’estimation des variables d’état hydrologiques, nous avons développé, pour la première fois, un schéma d’assimilation de données pour un modèle hydrologique-hydrodynamique de grande échelle, pour l’assimilation de données de jaugeages in situ et dérivées de l’altimétrie radar (débit et hauteur d’eau), dont les résultats se sont montrés satisfaisants. Nous avons également développé un prototype de système de prévision des débits pour le bassin Amazonien, basé sur le modèle initialisé avec les conditions initiales optimales fournies par le schéma d’assimilation de données, et en utilisant la pluie estimée par satellite disponible en temps réel. Les résultats ont été prometteurs, le modèle étant capable de prévoir les débits dans les principaux fleuves Amazoniens avec une antécédence importante (entre 1 et 3 mois), permettant d’anticiper, par exemple, la sècheresse extrême de 2005. Ces résultats démontrent le potentiel de la modélisation hydrologique appuyé par l’observation spatiale pour la prévision des débits avec une grande antécédence dans les grands bassins versant mondiaux. / A bacia Amazônica se destaca como o principal sistema hidrológico do mundo e pelo seu importante papel no sistema terrestre, influenciando o ciclo de carbono e o clima global. Recentes pressões antrópicas, como o desflorestamento, mudanças climáticas e a construção de barragens hidroelétricas, somados às crescentes cheias e secas extremas ocorridas nesta região, motivam o estudo da hidrologia da bacia Amazônica. Ao mesmo tempo, têm se desenvolvido métodos hidrológicos de modelagem e monitoramento via sensoriamento remoto que podem fornecer as bases técnicas para este fim. Este trabalho objetivou a compreensão e previsão da hidrologia da bacia Amazônica. Foram desenvolvidas e avaliadas diversas técnicas, incluindo de modelagem hidrológica-hidrodinâmica de larga escala, de assimilação de dados in situ e de sensoriamento remoto, e de previsão hidrológica. Este conjunto de técnicas foi utilizado para compreender o funcionamento da bacia Amazônica em termos de seus processos hidrológicos e sua previsibilidade hidrológica. O modelo hidrológico-hidrodinâmico de larga escala MGB-IPH foi utilizado para simular a bacia, sendo forçado com dados de chuva estimados por satélite. O modelo mostrou bom desempenho em uma validação detalhada contra observações de vazões e cotas in situ além de dados oriundos de sensoriamento remoto, incluindo níveis d’água de altimetria por radar, armazenamento d’água de gravimetria espacial e extensão de áreas alagadas. Mostrou-se a dominância das águas superficiais nas variações do armazenamento de água, a influência dos grandes corpos d’água sobre a variabilidade espacial da precipitação, além da importância das várzeas da inundação e efeitos de remanso sobre a propagação das ondas de cheia Amazônicas. As condições hidrológicas iniciais, com destaque para as águas superficiais, mostraram dominar a previsibilidade hidrológica nos grandes rios amazônicos, tendo assim a precipitação no futuro um papel secundário. Portanto, afim de melhor estimar os estados hidrológicos, de forma pioneira, foi desenvolvido um esquema de assimilação de dados para um modelo hidrológicohidrodinâmico de larga escala para assimilar informações in situ e de altimetria por radar, cujo desempenho se mostrou satisfatório. Desenvolveu-se também um protótipo de sistema de previsão de vazões para a bacia Amazônica, baseado no modelo inicializado com condições iniciais ótimas do esquema de assimilação de dados e utilizando precipitação estimada por satélite disponível em tempo real. Os resultados foram promissores e o modelo foi capaz de prever vazões nos principais rios amazônicos com grande antecedência (~1 a 3 meses), antecipando, por exemplo, a grande seca de 2005. Estes resultados mostram o potencial da modelagem hidrológica de larga escala apoiada por informação de sensoriamento remoto na previsão de vazões com alta antecedência nas grandes bacias hidrográficas do mundo. / The Amazon basin is known as the world’s main hydrological system and by its important role in the earth system, carbon cycle and global climate. Recent anthropogenic pressure, such as deforestation, climate change and the construction of hydropower dams, together with increasing extreme floods and droughts, encourage the research on the hydrology of the Amazon basin. On the other hand, hydrological methods for modeling and remotely sensed observation are being developed, and can be used for this goal. This work aimed at understanding and forecasting the hydrology of the Amazon River basin. We developed and evaluated techniques for large scale hydrologic-hydrodynamic modeling, data assimilation of both in situ and remote sensing data and hydrological forecasting. By means of these techniques, we explored the functioning of the Amazon River basin, in terms of its physical processes and its hydrological predictability. We used the MGB-IPH large scale hydrologichydrodynamic model forced by satellite-based precipitation. The model had a good performance when extensively validated against in situ discharge and stage measurements and also remotely sensed data, including radar altimetry-based water levels, gravimetric-based terrestrial water storage and flood inundation extent. We showed that surface waters governs most of the terrestrial water storage changes, the influence of large water bodies on precipitation spatial variability and the importance of the floodplains and backwater effects on the routing of the Amazon floodwaves. Analyses showed the dominant role of hydrological initial conditions, mainly surface waters, on hydrological predictability on the main Amazon Rivers, while the knowledge of future precipitation may be secondary. Aiming at the optimal estimation of these hydrological states, we developed, for the first time, a data assimilation scheme for both gauged and satellite altimetry-based discharge and water levels into a large scale hydrologic-hydrodynamic model, and it showed a good performance. We also developed a forecast system prototype, where the model is based on initial conditions gathered by the data assimilation scheme and forced by satellite-based precipitation. Results are promising and the model was able to provide accurate discharge forecasts in the main Amazon rivers even for very large lead times (~1 to 3 months), predicting, for example, the historical 2005 drought. These results point to the potential of large scale hydrological models supported with remote sensing information for providing hydrological forecasts well in advance at world’s large rivers and poorly monitored regions.

Le bassin Amazonien est connu comme le plus grand système hydrologique du monde et pour son rôle important sur le système terre, influençant le cycle du carbone et le climat global. Les pressions anthropiques récentes, telles que la déforestation, les changements climatiques, la construction de barrage hydro-électriques, ainsi que l’augmentation des crues et sécheresse extrêmes qui se produisent dans cette région, motivent l’étude de l’hydrologie du bassin Amazonien. Dans le même temps, des méthodes hydrologiques de modélisation et de surveillance par observation satellitaire ont été développées qui peuvent fournir les bases techniques à cette fin. Ce travail a eu pour objectif la compréhension et la prévision du régime hydrologique du bassin Amazonien. Nous avons développé et évaluer des techniques de modélisation hydrologique-hydrodynamique de grande échelle, d’assimilation de données in situ et spatiales et de prévision hydrologique. L’ensemble de ces techniques nous a permis d’explorer le fonctionnement du bassin Amazonien en terme de processus physiques et de prévisibilité hydrologique. Nous avons utilisé le modèle hydrologique-hydrodynamique de grande échelle MGB-IPH pour simuler le bassin, le forçage précipitation étant fourni par l’observation spatiale. Les résultats de la modélisation sont satisfaisants lorsque validés à partir de données in situ de débit et de hauteurs d’eau mais également de données dérivées de l’observation spatiale incluant les niveaux d’eau déduits de l’altimétrie radar, le contenu en eau total issu de la gravimétrie satellitaire, l’extension des zones inondées. Nous avons montré que les eaux superficielles sont responsables en grande partie de la variation du stock total d’eau, l’influence des grands plans d’eau sur la variabilité spatiale des précipitations et l’influence des plaines d’inondation et des effets de remous sur la propagation des ondes de crues. Nos analyses ont montré le rôle prépondérant des conditions initiales, en particulier des eaux superficielles, pour la prévisibilité des grands fleuves Amazoniens, la connaissance des précipitations futures n’ayant qu’une influence secondaire. Ainsi, pour améliorer l’estimation des variables d’état hydrologiques, nous avons développé, pour la première fois, un schéma d’assimilation de données pour un modèle hydrologique-hydrodynamique de grande échelle, pour l’assimilation de données de jaugeages in situ et dérivées de l’altimétrie radar (débit et hauteur d’eau), dont les résultats se sont montrés satisfaisants. Nous avons également développé un prototype de système de prévision des débits pour le bassin Amazonien, basé sur le modèle initialisé avec les conditions initiales optimales fournies par le schéma d’assimilation de données, et en utilisant la pluie estimée par satellite disponible en temps réel. Les résultats ont été prometteurs, le modèle étant capable de prévoir les débits dans les principaux fleuves Amazoniens avec une antécédence importante (entre 1 et 3 mois), permettant d’anticiper, par exemple, la sècheresse extrême de 2005. Ces résultats démontrent le potentiel de la modélisation hydrologique appuyé par l’observation spatiale pour la prévision des débits avec une grande antécédence dans les grands bassins versant mondiaux. / A bacia Amazônica se destaca como o principal sistema hidrológico do mundo e pelo seu importante papel no sistema terrestre, influenciando o ciclo de carbono e o clima global. Recentes pressões antrópicas, como o desflorestamento, mudanças climáticas e a construção de barragens hidroelétricas, somados às crescentes cheias e secas extremas ocorridas nesta região, motivam o estudo da hidrologia da bacia Amazônica. Ao mesmo tempo, têm se desenvolvido métodos hidrológicos de modelagem e monitoramento via sensoriamento remoto que podem fornecer as bases técnicas para este fim. Este trabalho objetivou a compreensão e previsão da hidrologia da bacia Amazônica. Foram desenvolvidas e avaliadas diversas técnicas, incluindo de modelagem hidrológica-hidrodinâmica de larga escala, de assimilação de dados in situ e de sensoriamento remoto, e de previsão hidrológica. Este conjunto de técnicas foi utilizado para compreender o funcionamento da bacia Amazônica em termos de seus processos hidrológicos e sua previsibilidade hidrológica. O modelo hidrológico-hidrodinâmico de larga escala MGB-IPH foi utilizado para simular a bacia, sendo forçado com dados de chuva estimados por satélite. O modelo mostrou bom desempenho em uma validação detalhada contra observações de vazões e cotas in situ além de dados oriundos de sensoriamento remoto, incluindo níveis d’água de altimetria por radar, armazenamento d’água de gravimetria espacial e extensão de áreas alagadas. Mostrou-se a dominância das águas superficiais nas variações do armazenamento de água, a influência dos grandes corpos d’água sobre a variabilidade espacial da precipitação, além da importância das várzeas da inundação e efeitos de remanso sobre a propagação das ondas de cheia Amazônicas. As condições hidrológicas iniciais, com destaque para as águas superficiais, mostraram dominar a previsibilidade hidrológica nos grandes rios amazônicos, tendo assim a precipitação no futuro um papel secundário. Portanto, afim de melhor estimar os estados hidrológicos, de forma pioneira, foi desenvolvido um esquema de assimilação de dados para um modelo hidrológicohidrodinâmico de larga escala para assimilar informações in situ e de altimetria por radar, cujo desempenho se mostrou satisfatório. Desenvolveu-se também um protótipo de sistema de previsão de vazões para a bacia Amazônica, baseado no modelo inicializado com condições iniciais ótimas do esquema de assimilação de dados e utilizando precipitação estimada por satélite disponível em tempo real. Os resultados foram promissores e o modelo foi capaz de prever vazões nos principais rios amazônicos com grande antecedência (~1 a 3 meses), antecipando, por exemplo, a grande seca de 2005. Estes resultados mostram o potencial da modelagem hidrológica de larga escala apoiada por informação de sensoriamento remoto na previsão de vazões com alta antecedência nas grandes bacias hidrográficas do mundo. / The Amazon basin is known as the world’s main hydrological system and by its important role in the earth system, carbon cycle and global climate. Recent anthropogenic pressure, such as deforestation, climate change and the construction of hydropower dams, together with increasing extreme floods and droughts, encourage the research on the hydrology of the Amazon basin. On the other hand, hydrological methods for modeling and remotely sensed observation are being developed, and can be used for this goal. This work aimed at understanding and forecasting the hydrology of the Amazon River basin. We developed and evaluated techniques for large scale hydrologic-hydrodynamic modeling, data assimilation of both in situ and remote sensing data and hydrological forecasting. By means of these techniques, we explored the functioning of the Amazon River basin, in terms of its physical processes and its hydrological predictability. We used the MGB-IPH large scale hydrologichydrodynamic model forced by satellite-based precipitation. The model had a good performance when extensively validated against in situ discharge and stage measurements and also remotely sensed data, including radar altimetry-based water levels, gravimetric-based terrestrial water storage and flood inundation extent. We showed that surface waters governs most of the terrestrial water storage changes, the influence of large water bodies on precipitation spatial variability and the importance of the floodplains and backwater effects on the routing of the Amazon floodwaves. Analyses showed the dominant role of hydrological initial conditions, mainly surface waters, on hydrological predictability on the main Amazon Rivers, while the knowledge of future precipitation may be secondary. Aiming at the optimal estimation of these hydrological states, we developed, for the first time, a data assimilation scheme for both gauged and satellite altimetry-based discharge and water levels into a large scale hydrologic-hydrodynamic model, and it showed a good performance. We also developed a forecast system prototype, where the model is based on initial conditions gathered by the data assimilation scheme and forced by satellite-based precipitation. Results are promising and the model was able to provide accurate discharge forecasts in the main Amazon rivers even for very large lead times (~1 to 3 months), predicting, for example, the historical 2005 drought. These results point to the potential of large scale hydrological models supported with remote sensing information for providing hydrological forecasts well in advance at world’s large rivers and poorly monitored regions.

Le bassin Amazonien est connu comme le plus grand système hydrologique du monde et pour son rôle important sur le système terre, influençant le cycle du carbone et le climat global. Les pressions anthropiques récentes, telles que la déforestation, les changements climatiques, la construction de barrage hydro-électriques, ainsi que l’augmentation des crues et sécheresse extrêmes qui se produisent dans cette région, motivent l’étude de l’hydrologie du bassin Amazonien. Dans le même temps, des méthodes hydrologiques de modélisation et de surveillance par observation satellitaire ont été développées qui peuvent fournir les bases techniques à cette fin. Ce travail a eu pour objectif la compréhension et la prévision du régime hydrologique du bassin Amazonien. Nous avons développé et évaluer des techniques de modélisation hydrologique-hydrodynamique de grande échelle, d’assimilation de données in situ et spatiales et de prévision hydrologique. L’ensemble de ces techniques nous a permis d’explorer le fonctionnement du bassin Amazonien en terme de processus physiques et de prévisibilité hydrologique. Nous avons utilisé le modèle hydrologique-hydrodynamique de grande échelle MGB-IPH pour simuler le bassin, le forçage précipitation étant fourni par l’observation spatiale. Les résultats de la modélisation sont satisfaisants lorsque validés à partir de données in situ de débit et de hauteurs d’eau mais également de données dérivées de l’observation spatiale incluant les niveaux d’eau déduits de l’altimétrie radar, le contenu en eau total issu de la gravimétrie satellitaire, l’extension des zones inondées. Nous avons montré que les eaux superficielles sont responsables en grande partie de la variation du stock total d’eau, l’influence des grands plans d’eau sur la variabilité spatiale des précipitations et l’influence des plaines d’inondation et des effets de remous sur la propagation des ondes de crues. Nos analyses ont montré le rôle prépondérant des conditions initiales, en particulier des eaux superficielles, pour la prévisibilité des grands fleuves Amazoniens, la connaissance des précipitations futures n’ayant qu’une influence secondaire. Ainsi, pour améliorer l’estimation des variables d’état hydrologiques, nous avons développé, pour la première fois, un schéma d’assimilation de données pour un modèle hydrologique-hydrodynamique de grande échelle, pour l’assimilation de données de jaugeages in situ et dérivées de l’altimétrie radar (débit et hauteur d’eau), dont les résultats se sont montrés satisfaisants. Nous avons également développé un prototype de système de prévision des débits pour le bassin Amazonien, basé sur le modèle initialisé avec les conditions initiales optimales fournies par le schéma d’assimilation de données, et en utilisant la pluie estimée par satellite disponible en temps réel. Les résultats ont été prometteurs, le modèle étant capable de prévoir les débits dans les principaux fleuves Amazoniens avec une antécédence importante (entre 1 et 3 mois), permettant d’anticiper, par exemple, la sècheresse extrême de 2005. Ces résultats démontrent le potentiel de la modélisation hydrologique appuyé par l’observation spatiale pour la prévision des débits avec une grande antécédence dans les grands bassins versant mondiaux. / A bacia Amazônica se destaca como o principal sistema hidrológico do mundo e pelo seu importante papel no sistema terrestre, influenciando o ciclo de carbono e o clima global. Recentes pressões antrópicas, como o desflorestamento, mudanças climáticas e a construção de barragens hidroelétricas, somados às crescentes cheias e secas extremas ocorridas nesta região, motivam o estudo da hidrologia da bacia Amazônica. Ao mesmo tempo, têm se desenvolvido métodos hidrológicos de modelagem e monitoramento via sensoriamento remoto que podem fornecer as bases técnicas para este fim. Este trabalho objetivou a compreensão e previsão da hidrologia da bacia Amazônica. Foram desenvolvidas e avaliadas diversas técnicas, incluindo de modelagem hidrológica-hidrodinâmica de larga escala, de assimilação de dados in situ e de sensoriamento remoto, e de previsão hidrológica. Este conjunto de técnicas foi utilizado para compreender o funcionamento da bacia Amazônica em termos de seus processos hidrológicos e sua previsibilidade hidrológica. O modelo hidrológico-hidrodinâmico de larga escala MGB-IPH foi utilizado para simular a bacia, sendo forçado com dados de chuva estimados por satélite. O modelo mostrou bom desempenho em uma validação detalhada contra observações de vazões e cotas in situ além de dados oriundos de sensoriamento remoto, incluindo níveis d’água de altimetria por radar, armazenamento d’água de gravimetria espacial e extensão de áreas alagadas. Mostrou-se a dominância das águas superficiais nas variações do armazenamento de água, a influência dos grandes corpos d’água sobre a variabilidade espacial da precipitação, além da importância das várzeas da inundação e efeitos de remanso sobre a propagação das ondas de cheia Amazônicas. As condições hidrológicas iniciais, com destaque para as águas superficiais, mostraram dominar a previsibilidade hidrológica nos grandes rios amazônicos, tendo assim a precipitação no futuro um papel secundário. Portanto, afim de melhor estimar os estados hidrológicos, de forma pioneira, foi desenvolvido um esquema de assimilação de dados para um modelo hidrológicohidrodinâmico de larga escala para assimilar informações in situ e de altimetria por radar, cujo desempenho se mostrou satisfatório. Desenvolveu-se também um protótipo de sistema de previsão de vazões para a bacia Amazônica, baseado no modelo inicializado com condições iniciais ótimas do esquema de assimilação de dados e utilizando precipitação estimada por satélite disponível em tempo real. Os resultados foram promissores e o modelo foi capaz de prever vazões nos principais rios amazônicos com grande antecedência (~1 a 3 meses), antecipando, por exemplo, a grande seca de 2005. Estes resultados mostram o potencial da modelagem hidrológica de larga escala apoiada por informação de sensoriamento remoto na previsão de vazões com alta antecedência nas grandes bacias hidrográficas do mundo. / The Amazon basin is known as the world’s main hydrological system and by its important role in the earth system, carbon cycle and global climate. Recent anthropogenic pressure, such as deforestation, climate change and the construction of hydropower dams, together with increasing extreme floods and droughts, encourage the research on the hydrology of the Amazon basin. On the other hand, hydrological methods for modeling and remotely sensed observation are being developed, and can be used for this goal. This work aimed at understanding and forecasting the hydrology of the Amazon River basin. We developed and evaluated techniques for large scale hydrologic-hydrodynamic modeling, data assimilation of both in situ and remote sensing data and hydrological forecasting. By means of these techniques, we explored the functioning of the Amazon River basin, in terms of its physical processes and its hydrological predictability. We used the MGB-IPH large scale hydrologichydrodynamic model forced by satellite-based precipitation. The model had a good performance when extensively validated against in situ discharge and stage measurements and also remotely sensed data, including radar altimetry-based water levels, gravimetric-based terrestrial water storage and flood inundation extent. We showed that surface waters governs most of the terrestrial water storage changes, the influence of large water bodies on precipitation spatial variability and the importance of the floodplains and backwater effects on the routing of the Amazon floodwaves. Analyses showed the dominant role of hydrological initial conditions, mainly surface waters, on hydrological predictability on the main Amazon Rivers, while the knowledge of future precipitation may be secondary. Aiming at the optimal estimation of these hydrological states, we developed, for the first time, a data assimilation scheme for both gauged and satellite altimetry-based discharge and water levels into a large scale hydrologic-hydrodynamic model, and it showed a good performance. We also developed a forecast system prototype, where the model is based on initial conditions gathered by the data assimilation scheme and forced by satellite-based precipitation. Results are promising and the model was able to provide accurate discharge forecasts in the main Amazon rivers even for very large lead times (~1 to 3 months), predicting, for example, the historical 2005 drought. These results point to the potential of large scale hydrological models supported with remote sensing information for providing hydrological forecasts well in advance at world’s large rivers and poorly monitored regions.

<p>The Ensemble Kalman filter (EnKF) has achieved great successes in data assimilation in atmospheric and oceanic sciences, but its failure in convergence to the right filtering distribution precludes its use for uncertainty quantification. Other existing methods, such as particle filter or sequential importance sampler, do not scale well to the dimension of the system and the sample size of the datasets. In this dissertation, we address these difficulties in a coherent way.</p><p><br></p><p> </p><p>In the first part of the dissertation, we reformulate the EnKF under the framework of Langevin dynamics, which leads to a new particle filtering algorithm, the so-called Langevinized EnKF (LEnKF). The LEnKF algorithm inherits the forecast-analysis procedure from the EnKF and the use of mini-batch data from the stochastic gradient Langevin-type algorithms, which make it scalable with respect to both the dimension and sample size. We prove that the LEnKF converges to the right filtering distribution in Wasserstein distance under the big data scenario that the dynamic system consists of a large number of stages and has a large number of samples observed at each stage, and thus it can be used for uncertainty quantification. We reformulate the Bayesian inverse problem as a dynamic state estimation problem based on the techniques of subsampling and Langevin diffusion process. We illustrate the performance of the LEnKF using a variety of examples, including the Lorenz-96 model, high-dimensional variable selection, Bayesian deep learning, and Long Short-Term Memory (LSTM) network learning with dynamic data.</p><p><br></p><p> </p><p>In the second part of the dissertation, we focus on two extensions of the LEnKF algorithm. Like the EnKF, the LEnKF algorithm was developed for Gaussian dynamic systems containing no unknown parameters. We propose the so-called stochastic approximation- LEnKF (SA-LEnKF) for simultaneously estimating the states and parameters of dynamic systems, where the parameters are estimated on the fly based on the state variables simulated by the LEnKF under the framework of stochastic approximation. Under mild conditions, we prove the consistency of resulting parameter estimator and the ergodicity of the SA-LEnKF. For non-Gaussian dynamic systems, we extend the LEnKF algorithm (Extended LEnKF) by introducing a latent Gaussian measurement variable to dynamic systems. Those two extensions inherit the scalability of the LEnKF algorithm with respect to the dimension and sample size. The numerical results indicate that they outperform other existing methods in both states/parameters estimation and uncertainty quantification.</p>