Les flux turbulents à l’interface air-mer représentent le lien entre l’océan et l’atmosphère et jouent donc un rôle majeur dans le système climatique. Dans les modèles de climat, les processus turbulents sont des processus sous-maille, non résolus explicitement, et doivent donc être paramétrés. Ils sont estimés à partir des variables d’états atmosphériques et océaniques au moyen de modèles mathématiques qu’on nomme « paramétrisations bulk ». Ce travail de thèse a pour objectif de caractériser et comprendre les liens entre la représentation des flux turbulents à l’interface air-mer et le fonctionnement d’un modèle de climat à différentes échelles de temps dans les régions tropicales. Pour étudier ces liens, j’ai développé une stratégie de modélisation utilisant un modèle 1D atmosphérique (SCM), un modèle de circulation générale océanique (OGCM) où atmosphérique (AGCM) et un modèle couplé (GCM). L’analyse des simulations SCM permet d’étudier la réponse directe d’un modèle à la modification de la paramétrisation des flux turbulents. On montre que cette dernière régule la quantité d’eau, d’énergie et de quantité de mouvement disponible pour le système et donc son fonctionnement. Elle représente plus de 60% des différences de flux de chaleur latente simulées entre deux modèles de climat dans les périodes convectives. L’impact spatial de la paramétrisation des flux turbulents est étudié au travers des simulations AGCM. Elles mettent en évidence le lien entre la paramétrisation, son effet sur les gradients d’humidité et de température à grande échelle, et donc son influence sur la circulation atmosphérique. L’étude des simulations OGCM souligne quant à elle le rôle principal du vent pour le fonctionnement des océans tropicaux. Si le vent pilote les variations de SST dues à son impact sur la dynamique océanique et principalement sur le sous-courant équatorial, l’humidité, la température et les flux radiatifs n’influencent quant à eux que la surface océanique et sont donc d’une moindre importance. Enfin, l’analyse des simulations GCM met en évidence les rétroactions et l’ajustement engendrés par la modification des flux turbulents. Lors du couplage des deux composantes l’océan agi comme un tampon et absorbe la modification des flux turbulents ce qui entraine une modification de la SST. L’ajustement qui se produit entraine une modification des variables atmosphériques qui amène à un nouvel état d’équilibre du système. La paramétrisation des flux turbulents de surface agit au premier ordre sur l'équilibre énergétique d'un modèle couplé et peut donc amener à des climats simulés différents. Cette étude étant centrée sur les tropiques, une perspective intéressante serait d’étendre l’étude de la représentation des flux turbulents à d’autres échelles spatio-temporelles (i.e. zones extratropicales/fréquence journalière). Cela permettrait de valider le fonctionnement systématique des paramétrisations définies dans cette thèse à l’échelle globale. / The turbulent fluxes at the air-sea interface represent the link between the ocean and the atmosphere and therefore play a major role in the climate system. In climate models, turbulent processes are subgrid scale processes, not explicitly resolved, and must therefore be parameterized. They are estimated from atmospheric and oceanic state variables using mathematical models called “bulk parameterizations”. This thesis aims to characterize and understand the links between the representation of turbulent fluxes at the air-sea interface and the behavior of a climate model at different time scales in tropical regions. To study these links, I developed a modeling strategy using an atmospheric 1D model (SCM), an oceanic (OGCM) or atmospheric (AGCM) general circulation model and a coupled model (GCM). The analysis of SCM simulations allows us to study the direct response of a model to modifications of the turbulent fluxes parameterization. It is shown that it regulates the amount of water, energy and momentum available to the system and therefore its behavior. It can thus represent more than 60% of simulated latent heat flux differences between two climate models in convective periods. The spatial impact of the parameterization of turbulent fluxes is studied through AGCM simulations. They highlight the link between parameterization, its effect on large-scale moisture and temperature gradients, and thus its influence on atmospheric circulation. The study of OGCM simulations underlines the main role of the wind for the behavior of the tropical oceans. If the wind drives changes in SST due to its impact on ocean dynamics and mainly on the equatorial undercurrent, humidity, temperature and radiative flux only influence the ocean surface and are therefore of lesser importance. Finally, the analysis of GCM simulations highlights the feedbacks and the adjustment generated by the modification of turbulent fluxes. When coupling the two components, the ocean acts as a buffer and absorbs the modification of the turbulent fluxes, which leads to a modification of the SST. The adjustment that occurs causes a modification of the atmospheric variables which leads to a new state of equilibrium of the system. The parameterization of surface turbulent fluxes acts at first order on the energy equilibrium of a coupled model and can therefore lead to different simulated climate state. Since this study is focused on the tropics, an interesting perspective would be to extend the study of the turbulent fluxes representation to other spatio-temporal scales (i.e. extra-tropical areas / daily frequency). This would make it possible to validate the systematic behavior of the parameterizations defined in this thesis on a global scale.

The use of numerical weather prediction (NWP) has brought significant improvements to severe weather outbreak forecasting; however, determination of the primary mode of severe weather (in particular tornadic and nontornadic outbreaks) continues to be a challenge. Uncertainty in model runs contributes to forecasting difficulty; therefore it is beneficial to a forecaster to understand the sources and magnitude of uncertainty in a severe weather forecast. This research examines the impact of data assimilation, microphysics parameterizations, and planetary boundary layer (PBL) physics parameterizations on severe weather forecast accuracy and model variability, both at a mesoscale and synoptic-scale level. NWP model simulations of twenty United States tornadic and twenty nontornadic outbreaks are generated. In the first research phase, each case is modeled with three different modes of data assimilation and a control. In the second phase, each event is modeled with 15 combinations of physics parameterizations: five microphysics and three PBL, all of which were designed to perform well in convective weather situations. A learning machine technique known as a support vector machine (SVM) is used to predict outbreak mode for each run for both the data assimilated model simulations and the different parameterization simulations. Parameters determined to be significant for outbreak discrimination are extracted from the model simulations and input to the SVM, which issues a diagnosis of outbreak type (tornadic or nontornadic) for each model run. In the third phase, standard synoptic parameters are extracted from the model simulations and a k-means cluster analysis is performed on tornadic and nontornadic outbreak data sets to generate synoptically distinct clusters representing atmospheric conditions found in each type of outbreak. Variations among the synoptic features in each cluster are examined across the varied physics parameterization and data assimilation runs. Phase I found that conventional and HIRS-4 radiance assimilation performs best of all examined assimilation variations by lowering false alarm ratios relative to other runs. Phase II found that the selection of PBL physics produces greater spread in the SVM classification ability. Phase III found that data assimilation generates greater model changes in the strength of synoptic-scale features than either microphysics or PBL physics parameterization.

<p>Statistical modeling aims at constructing a mathematical model for an existing data set. As a comprehensive concept, statistical modeling leads to a wide range of interesting problems. Modern parametric models, such as deepnets, have achieved remarkable success in quite a few application areas with massive data. Although being powerful in practice, many fitted over-parameterized models potentially suffer from losing good statistical properties. For this reason, a new framework named the Auto-modeling (AM) framework is proposed. Philosophically, the mindset is to fit models to future observations rather than the observed sample. Technically, choosing an imputation model for generating future observations, we fit models to future observations via optimizing an approximation to the desired expected loss function based on its sample counterpart and what we call an adaptive {\it duality function}.</p> <p><br></p> <p>The first part of the dissertation (Chapter 2 to 7) focuses on the new philosophical perspective of the method, as well as the details of the main framework. Technical details, including essential theoretical properties of the method are also investigated. We also demonstrate the superior performance of the proposed method via three applications: Many-normal-means problem, $n < p$ linear regression and image classification.</p> <p><br></p> <p>The second part of the dissertation (Chapter 8) focuses on the application of the AM framework to the construction of linear regression models. Our primary objective is to shed light on the stability issue associated with the commonly used data-driven model selection methods such as cross-validation (CV). Furthermore, we highlight the philosophical distinctions between CV and AM. Theoretical properties and numerical examples presented in the study demonstrate the potential and promise of AM-based linear model selection. Additionally, we have devised a conformal prediction method specifically tailored for quantifying the uncertainty of AM predictions in the context of linear regression.</p>

The vocal folds are an essential component of human speech production and communication. Advancements in voice research allow for improved voice disorder treatments. Since in vivo analysis of vocal fold function is limited, models have been developed to simulate vocal fold motion. In this research, synthetic and computational vocal fold models were used to investigate various aspects of vocal fold vibratory characteristics. A series of tests were performed to quantify the effect of varying material and geometric parameters on the models' flow-induced responses. First, the influence of asymmetric vocal fold stiffness on voice production was evaluated using life-sized, self-oscillating vocal fold models with idealized vocal fold geometry. Asymmetry significantly influenced glottal jet flow, glottal area, and vibration frequency. Second, flow-induced responses of simplified and MRI-based synthetic models were compared. The MRI-based models showed remarkable improvements, including less vertical motion, alternating convergent-divergent glottal profile patterns, and mucosal wave-like movement. Third, a simplified model was parametrically investigated via computational modeling techniques to determine which geometric features influenced model motion. This parametric study led to identification and ranking of key geometric parameters based on their effects on various measures of vocal fold motion (e.g., mucosal wavelike movement). Incorporation of the results of these studies into the definition of future models could lead to models with more life-like motion.

Implementing a nonlinear gravity wave (GW) parameterization into a mechanistic middle and upper atmosphere model, which extends to the lower thermosphere (160 km), we study the response of the atmosphere in terms of the circulation patterns, temperature distribution, and migrating terdiurnal solar tide activity to the upward propagating smallscale internal GWs originating in the lower atmosphere. We perform three test simulations for the Northern Hemisphere winter conditions in order to assess the effects of variations in the initial GWspectrum on the climatology and tidal patterns of the mesosphere and lower thermosphere. We find that the overall strength of the source level momentum flux has a relatively small impact on the zonal mean climatology. The tails of the GW source level spectrum, however, are crucial for the lower thermosphere climatology. With respect to the terdiurnal tide, we find a strong dependence of tidal amplitude on the induced GW drag, generally being larger when GW drag is increased.

Implementing a nonlinear gravity wave (GW) parameterization into a mechanistic middle and upper atmosphere model, which extends to the lower thermosphere (160 km), we study the response of the atmosphere in terms of the circulation patterns, temperature distribution, and migrating terdiurnal solar tide activity to the upward propagating small scale internal GWs originating in the lower atmosphere. We perform three test simulations for the Northern Hemisphere winter conditions in order to assess the effects of variations in the initial GW spectrum on the climatology and tidal patterns of the mesosphere and lower thermosphere. We find that the overall strength of the source level momentum flux has a relatively small impact on the zonal mean climatology. The tails of the GW source level spectrum, however, are crucial for the lower thermosphere climatology. With respect to the terdiurnal tide, we find a strong dependence of tidal amplitude on the induced GW drag, generally being larger when GW drag is increased.

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Dirichlet process mixture (DPM) has been widely used as exible prior in nonparametric Bayesian literature, and Weighted Dirichlet process mixture (WDPM) can be viewed as extension of DPM which relaxes model distribution assumptions. Meanwhile, WDPM requires to set weight functions and can cause extra computation burden. In this dissertation, we develop more efficient and exible WDPM approaches under three research topics. The first one is semiparametric cubic spline regression where we adopt a nonparametric prior for error terms in order to automatically handle heterogeneity of measurement errors or unknown mixture distribution, the second one is to provide an innovative way to construct weight function and illustrate some decent properties and computation efficiency of this weight under semiparametric stochastic volatility (SV) model, and the last one is to develop WDPM approach for Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model (as an alternative approach for SV model) and propose a new model evaluation approach for GARCH which produces easier-to-interpret result compared to the canonical marginal likelihood approach. In the first topic, the response variable is modeled as the sum of three parts. One part is a linear function of covariates that enter the model parametrically. The second part is an additive nonparametric model. The covariates whose relationships to response variable are unclear will be included in the model nonparametrically using Lancaster and Šalkauskas bases. The third part is error terms whose means and variance are assumed to follow non-parametric priors. Therefore we denote our model as dual-semiparametric regression because we include nonparametric idea for both modeling mean part and error terms. Instead of assuming all of the error terms follow the same prior in DPM, our WDPM provides multiple candidate priors for each observation to select with certain probability. Such probability (or weight) is modeled by relevant predictive covariates using Gaussian kernel. We propose several different WDPMs using different weights which depend on distance in covariates. We provide the efficient Markov chain Monte Carlo (MCMC) algorithms and also compare our WDPMs to parametric model and DPM model in terms of Bayes factor using simulation and empirical study. In the second topic, we propose an innovative way to construct weight function for WDPM and apply it to SV model. SV model is adopted in time series data where the constant variance assumption is violated. One essential issue is to specify distribution of conditional return. We assume WDPM prior for conditional return and propose a new way to model the weights. Our approach has several advantages including computational efficiency compared to the weight constructed using Gaussian kernel. We list six properties of this proposed weight function and also provide the proof of them. Because of the additional Metropolis-Hastings steps introduced by WDPM prior, we find the conditions which can ensure the uniform geometric ergodicity of transition kernel in our MCMC. Due to the existence of zero values in asset price data, our SV model is semiparametric since we employ WDPM prior for non-zero values and parametric prior for zero values. On the third project, we develop WDPM approach for GARCH type model and compare different types of weight functions including the innovative method proposed in the second topic. GARCH model can be viewed as an alternative way of SV for analyzing daily stock prices data where constant variance assumption does not hold. While the response variable of our SV models is transformed log return (based on log-square transformation), GARCH directly models the log return itself. This means that, theoretically speaking, we are able to predict stock returns using GARCH models while this is not feasible if we use SV model. Because SV models ignore the sign of log returns and provides predictive densities for squared log return only. Motivated by this property, we propose a new model evaluation approach called back testing return (BTR) particularly for GARCH. This BTR approach produces model evaluation results which are easier to interpret than marginal likelihood and it is straightforward to draw conclusion about model profitability by applying this approach. Since BTR approach is only applicable to GARCH, we also illustrate how to properly cal- culate marginal likelihood to make comparison between GARCH and SV. Based on our MCMC algorithms and model evaluation approaches, we have conducted large number of model fittings to compare models in both simulation and empirical study. / Ph. D.

This work is motivated by the question: how much complexity is appropriate for a cloud parameterization used in general circulation models (GCM). To approach this question, cloud parameterizations across the complexity range are explored using general circulation models and theoretical Monte-Carlo simulations. Their results are compared with high-resolution satellite observations and simulations that resolve the GCM subgrid-scale variability explicitly. A process-orientated evaluation is facilitated by GCM forecast simulations which reproduce the synoptic state. For this purpose novel methods were develop to a) conceptually relate the underlying saturation deficit probability density function (PDF) with its saturated cloudy part, b) analytically compute the vertical integrated liquid water path (LWP) variability, c) diagnose the relevant PDF-moments from cloud parameterizations, d) derive high-resolution LWP from satellite observations and e) deduce the LWP statistics by aggregating the LWP onto boxes equivalent to the GCM grid size. On this basis, this work shows that it is possible to evaluate the sub-grid scale variability of cloud parameterizations in terms of cloud variables. Differences among the PDF types increase with complexity, in particular the more advanced cloud parameterizations can make use of their double Gaussian PDF in conditions, where cumulus convection forms a separate mode with respect to the remainder of the grid-box. Therefore, it is concluded that the difference between unimodal and bimodal PDFs is more important, than the shape within each mode. However, the simulations and their evaluation reveals that the advanced parameterizations do not take full advantage of their abilities and their statistical relationships are broadly similar to less complex PDF shapes, while the results from observations and cloud resolving simulations indicate even more complex distributions. Therefore, this work suggests that the use of less complex PDF shapes might yield a better trade-off. With increasing model resolution initial weaknesses of simpler, e.g. unimodal PDFs, will be diminished. While cloud schemes for coarse-resolved models need to parameterize multiple cloud regimes per grid-box, higher spatial resolution of future GCMs will separate them better, so that the unimodal approximation improves.

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