This thesis presents our efforts to build an operational ensemble forecasting system for the Red Sea, based on the Data Research Testbed (DART) package for ensemble data assimilation and the Massachusetts Institute of Technology general circulation ocean model (MITgcm) for forecasting. The Red Sea DART-MITgcm system efficiently integrates all the ensemble members in parallel, while accommodating different ensemble assimilation schemes. The promising ensemble adjustment Kalman filter (EAKF), designed to avoid manipulating the gigantic covariance matrices involved in the ensemble assimilation process, possesses relevant features required for an operational setting. The need for more efficient filtering schemes to implement a high resolution assimilation system for the Red Sea and to handle large ensembles for proper description of the assimilation statistics prompted the design and implementation of new filtering approaches. Making the most of our world-class supercomputer, Shaheen, we first pushed the system limits by designing a fault-tolerant scheduler extension that allowed us to test for the first time a fully realistic and high resolution 1000 ensemble members ocean ensemble assimilation system. In an operational setting, however, timely forecasts are of essence, and running large ensembles, albeit preferable and desirable, is not sustainable. New schemes aiming at lowering the computational burden while preserving reliable assimilation results, were developed. The ensemble Optimal Interpolation (EnOI) algorithm requires only a single model integration in the forecast step, using a static ensemble of preselected members for assimilation, and is therefore computationally significantly cheaper than the EAKF. To account for the strong seasonal variability of the Red Sea circulation, an EnOI with seasonally-varying ensembles (SEnOI) was first implemented. To better handle intra-seasonal variabilities and enhance the developed seasonal EnOI system, an automatic procedure to adaptively select the ensemble members through the assimilation cycles was then introduced. Finally, an efficient Hybrid scheme combining the dynamical flow-dependent covariance of the EAKF and a static covariance of the EnOI was proposed and successfully tested in the Red Sea. The developed Hybrid ensemble data assimilation system will form the basis of the first operational Red Sea forecasting system that is currently being implemented to support Saudi Aramco operations in this basin.

Les radars à nuages sont des atouts indéniables pour la Prévision Numérique du Temps (PNT). De par leur petite longueur d’onde, ils possèdent une excellente sensibilité aux particules nuageuses et ils sont facilement déployables à bord de plates-formes mobiles. Cette thèse a permis d’évaluer l’apport des observations de radars à nuages pour la validation et l’initialisation de modèles de PNT à échelle kilométrique. Dans la première partie, un opérateur d’observation pour la réflectivité en bande W a été conçu en cohérence avec le schéma microphysique à un moment d'Arome, le modèle de PNT à échelle kilométrique de Météo-France, mais de façon suffisamment générale pour pouvoir être adapté à un autre modèle de PNT à échelle kilométrique. Il est adaptable pour des radars à visée verticale aéroportés ou au sol. Afin de dissocier les erreurs de positionnement des nuages prévus par Arome, de celles présentes dans l’opérateur d’observation, une nouvelle méthode de validation, appelée "la méthode de la colonne la plus ressemblante (CPR), a été élaborée. Cette méthode a été employée afin de valider et de calibrer l'opérateur d'observation en utilisant les profils de réflectivité collectés par le radar à nuages aéroporté Rasta dans des conditions variées durant la première période d’observations (SOP1) du programme international HyMeX, qui vise à améliorer notre compréhension du cycle de l'eau en méditerranée. La seconde partie s'est intéressée à l'apport respectif de l'assimilation de profils verticaux de réflectivité et de vents horizontaux mesurés par le radar à nuages Rasta dans le système d'assimilation variationnel tridimensionnel (3DVar) d'Arome. Le bénéfice apporté par des conditions thermodynamiques, via l'assimilation de la réflectivité en bande W, et dynamiques, via l'assimilation des profils de vents horizontaux, cohérentes dans l'état initial a également été étudié. Pour assimiler la réflectivité en bande W, la méthode d'assimilation "1D+3DVar", qui est opérationnelle dans Arome pour assimiler les réflectivités des radars de précipitation au sol, a été employée. La méthode de restitution bayésienne 1D de profils d'humidité a été validée avec des mesures d'humidité in situ indépendantes. Puis, les expériences d'assimilation ont été menées sur un événement fortement convectif, ainsi que sur une plus longue période de 45 jours. Les résultats suggèrent notamment que l'assimilation conjointe des profils de réflectivité en bande W et des profils verticaux de vents horizontaux permet d'améliorer les analyses d'humidité, mais suggèrent également une légère amélioration des prévisions des cumuls de précipitation / Cloud radars are an undeniable assets for Numerical Weather Prediction (NWP) models. Because of their very short wavelength, they are extremely sensitive to cloud microphysical properties and are easily deployable aboard moving platforms such as aircraft or spacecraft. This PhD has explored the potential of cloud radar data for the validation and initialisation of kilometre-scale NWP models. In the first part of the PhD, a W-band reflectivity forward operator was designed. It is consistent with the one-moment microphysical scheme used in the Météo-France kilometre-scale NWP model AROME, but in a sufficiently general way that it could be adapted to other kilometrescale NWP models. It was designed in particular for airborne or ground-based vertically pointing cloud radars. To disentangle spatial location errors in the model from errors in the forward operator, a neighbourhood validation method, called the “Most Resembling Method” (MRC), was designed. This validation method was used to validate and calibrate the forward operator using the data collected by the airborne cloud radar RASTA in diverse conditions during the first Special Observation Period (SOP1) of the HyMeX international program, which aims to improve our understanding of the Mediterranean water cycle. The second part focused on the respective roles of the assimilation of reflectivity and horizontal wind profiles, measured by the cloud radar RASTA, in the three dimensional variational (3DVar) assimilation system of AROME. The benefit brought by consistent thermodynamic conditions in the initial state, through the assimilation of the W-band reflectivity, and dynamic ones, through the assimilation of horizontal wind profiles, was also investigated.To assimilate the W-band reflectivity, the two-step assimilation method “1D+3DVar”, operationally employed in AROME to assimilate ground-based precipitation radar data, was used. The efficiency of the 1D Bayesian method in retrieving humidity fields is assessed using independent in-flight humidity measurements. The assimilation experiments were performed for a heavy convective event, as well as over a longer period of 45 days. In particular, the results indicate that the joint assimilation of W-band reflectivity and horizontal wind profiles suggest an improvement of moisture analyses, along with a slight improvement of the rainfall precipitation forecasts.

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第18699号 / 情博第549号 / 新制||情||97(附属図書館) / 31632 / 京都大学大学院情報学研究科知能情報学専攻 / (主査)教授 阿久津 達也, 教授 鹿島 久嗣, 教授 石井 信 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

Indiana University-Purdue University Indianapolis (IUPUI) / Numerical models are important tools for simulating processes within complex natural systems, such as hydrodynamics and water quality processes within a water body. From decision makers’ perspectives, such models also serve as useful tools for predicting the impacts of water quality problems or develop early warning systems. However, accuracy of a numerical model developed for a specific site is dependent on multiple model parameters and variables whose values are attained via calibration processes and/or expert knowledge. Real time variations in the actual aquatic system at a site necessitate continuous monitoring of the system so that model parameters and variables are regularly updated to reflect accurate conditions. Multiple sources of observations can help adjust the model better by providing benefits of individual monitoring technology within the model updating process. For example, remote sensing data provide a spatially dense dataset of model variables at the surface of a water body, while in-situ monitoring technologies can provide data at multiple depths and at more frequent time intervals than remote sensing technologies. This research aims to present an overview of an integrated modeling and data assimilation framework that combines three-dimensional numerical model with multiple sources of observations to simulate water column temperature in a eutrophic reservoir in central Indiana. A variational data assimilation approach is investigated for incorporating spatially continuous remote sensing observations and spatially discrete in-situ observations to change initial conditions of the numerical model. This research addresses the challenge of improving the model performance by combining water temperature from multi-spectral remote sensing analysis and in-situ measurements. Results of the approach on a eutrophic reservoir in Central Indiana show that with four images of multi-spectral remote sensing data assimilated, the model results oscillate more from the in-situ measurements during the data assimilation period. For validation, the data assimilation has negative impacts on the root mean square error. According to quantitative analysis, more significant water temperature stratification leads to larger deviations. Sampling depth differences for remote sensing technology, in-situ measurements and model output are considered as possible error source.

Many problems in applied mathematics involve simulating the evolution of a system using differential equations with known initial conditions. But what if one records observations and seeks to determine the causal factors which produced them? This is known as an inverse problem. Some prominent inverse problems include data assimilation and parameter recovery, which use partial observations of a system of evolutionary, dissipative partial differential equations to estimate the state of the system and relevant physical parameters (respectively). Recently a set of procedures called nudging algorithms have shown promise in performing simultaneous data assimilation and parameter recovery for the Lorentz equations and the Kuramoto-Sivashinsky equation. This work applies these algorithms and extensions of them to the case of Rayleigh-B\'enard convection, one of the most ubiquitous and commonly-studied examples of turbulent flow. The performance of various parameter update formulas is analyzed through direct numerical simulation. Under appropriate conditions and given the correct parameter update formulas, convergence is also established, and in one case, an analytical proof is obtained.

This text provides an overview of problems in the field of data assimilation. We explore the possibility of recreating unknown data by continuously inserting known data into certain dynamical systems, under certain regularity assumptions. Additionally, we discuss an alternative statistical approach to data assimilation and investigate the utilization of the Ensemble Kalman Filter for assimilating data into dynamical models. A key challenge in numerical weather prediction is incorporating convective precipitation into an idealized setting for numerical computations. To answer this question we examine the modified rotating shallow water equations, a nonlinear coupled system of partial differential equations and further assess if this primitive model accurately mimics phenomena observed in operational numerical weather prediction models. Numerical experiments conducted using a Deterministic Ensemble Kalman Filter algorithm support its applicability for convective-scale data assimilation. Furthermore, we analyze the frequency spectrum of numerical forecasts using the Wavelet transform. Our frequency analysis suggests that, under certain experimental settings, there are similarities in the initialization of operational models, which can aid in understanding the problem of intialization of numerical weather prediction models.

Predicting and characterizing the state of the ocean is needed for various scientific, industrial, social, management, and recreational activities. Despite the tremendous progress in ocean modeling and simulation capabilities, the ocean models still suffer from different sources of uncertainties. To obtain accurate ocean state predictions, data assimilation (DA) is widely used to constrain the ocean model outputs with available observations. Ensemble Kalman filtering (EnKF) is a sequential DA approach that represents the distribution of the system state through an ensemble of ocean state samples. Different factors may limit the performance of an EnKF in realistic ocean applications, particularly the use of small ensembles and poorly known model error statistics, and also to a lesser extent the strongly nonlinear variations and abrupt regime changes, and unsatisfied underlying assumptions such as the commonly used white observation noise assumption. The objective of this PhD thesis is to develop, implement and test efficient ensemble filtering schemes to enhance the performances of EnKFs in such challenging settings. We resort to the one-step-ahead (OSA) smoothing formulation of the Bayesian filtering problem to introduce EnKFs involving a new update step with future observations (smoothing) between two successive analyses, thereby conditioning the ensemble sampling with more information. We show that this approach enhances the EnKFs performances by providing improved ensemble background statistics, and showcase its performance with realistic ocean DA and forecasting applications, namely a storm surge EnKF forecasting system and the Red Sea ensemble DA and forecasting system. We then derive new EnKF-based schemes accounting for time-correlated observation errors for efficient DA into the class of large dimensional DA problems where observation errors statistics are correlated in time, and further propose a new approach for online estimation of the parameters of the observation error time-correlations model concurrently with the state. We also exploit the OSA-smoothing formulation to propose a new joint EnKF with OSA-smoothing which mitigates for the reported inconsistencies in the joint EnKF update for efficient DA into one-way-coupled systems.

For accurate prediction of tsunami wave propagation, information on the system of PDEs modelling its evolution and full initial and/or boundary data is required. However the latter is not generally fully available, and so the primary objective becomes to find an optimal estimate of these conditions, using available information. Data Assimilation is a methodology used to optimally integrate observed measurements into a mathematical model, to generate a better estimate of some control parameter, such as the initial condition of the wave, or the sea floor bathymetry. In this study, we considered the shallow water equations in both linear and non-linear form as an approximation for ocean wave propagation, and derived a data assimilation scheme based on the calculus of variations, the purpose of which is to optimise some distorted form of the initial condition to give a prediction closer to the exact initial data. We considered two possible forms of distortion, by adding noise to our initial wave, and by rescaling the wave amplitude. Multiple cases were analysed, with observations measured at different points in our spatial domain, as well as variations in the number of observation points. We found that the error between measurements and observation data was sufficiently minimised across all cases. A relationship was found between the number of measurement points and the error, dependent on the choice of where measurements were taken. In the linear case, since the wave form simply translates a fixed form, multiple measurement points did not necessarily provide more information. In the nonlinear case, because the waveform changes shape as it translates, adding more measurement points provides more information about the dynamics and the wave shape. This is reflected in the fact that in the nonlinear case adding more points gave a bigger decrease in error, and much closer convergence of the optimised guess for our initial condition to the exact initial wave profile. / Thesis / Master of Science (MSc) / In ocean wave modelling, information on the system dynamics and full initial and/or boundary data is required. When the latter is not fully available the primary objective is to find an optimal estimate of these conditions, using available information. Data Assimilation is a methodology used to optimally integrate observed measurements into a mathematical model, to generate a better estimate of some control parameter, such as the initial condition of the wave, or the sea floor bathymetry. In this study, we considered the shallow water equations in both linear and non-linear form as an approximation for ocean wave propagation, and derived a data assimilation scheme to optimise some distorted form of the initial condition to generate predictions converging to the exact initial data. The error between measurements and observation data was sufficiently minimised across all cases. A relationship was found between the number of measurement points and the error, dependent on the choice of where measurements were taken.

京都大学 / 新制・課程博士 / 博士(工学) / 甲第24613号 / 工博第5119号 / 新制||工||1979(附属図書館) / 京都大学大学院工学研究科原子核工学専攻 / (主査)教授 村上 定義, 教授 横峯 健彦, 教授 宮寺 隆之 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

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