Currently, the effect of the vertical resolution on the brightness temperature (BT) has not been examined in depth. The uncertainty of the freezing level (FL) retrieved using two different satellites' data is large. Various radiative transfer (RT) codes yield different BTs in strong scattering conditions. The purposes of this research were: 1) to understand the uncertainty of the BT contributed by the vertical resolution numerically and analytically; 2) to reduce the uncertainty of the FL retrieval using new thermodynamic observations; and 3) to investigate the characteristics of four different RT codes. Firstly, a plane-parallel RT Model (RTM) of n layers in light rainfall was used for the analytical and computational derivation of the vertical resolution effect on the BT. Secondly, a new temperature profile based on observations was absorbed in the Texas A&M University (TAMU) algorithm. The Precipitation Radar (PR) and Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) data were utilized for the improved FL retrieval. Thirdly, the TAMU, Eddington approximation (EDD), Discrete Ordinate, and backward Monte Carlo codes were compared under various view angles, rain rates, FLs, frequencies, and surface properties. The uncertainty of the BT decreased as the number of layers increased. The uncertainty was due to the optical thickness rather than due to relative humidity, pressure distribution, water vapor, and temperature profile. The mean TMI FL showed a good agreement with mean bright band height. A new temperature profile reduced the uncertainty of the TMI FL by about 10%. The differences of the BTs among the four different RT codes were within 1 K at the current sensor view angle over the entire dynamic rain rate range of 10-37 GHz. The differences between the TAMU and EDD solutions were less than 0.5 K for the specular surface. In conclusion, this research suggested the vertical resolution should be considered as a parameter in the forward model. A new temperature profile improved the TMI FL in the tropics, but the uncertainty still exists with low FL. Generally, the four RT codes agreed with each other, except at nadir, near limb or in heavy rainfall. The TAMU and the EDD codes had better agreement than other RT codes.

The vertical structure of the tangential wind field in tropical cyclones is investigated through observations, theory, and numerical simulations. First, a dataset of Doppler radar wind swaths obtained from NOAA/AOML/HRD is used to create azimuthal mean tangential wind fields for 7 storms on 17 different days. Three conventional wisdoms of vertical structure are reexamined: the outward slope of the Radius of Maximum Winds (RMW) decreases with increasing intensity, the slope increases with the size of the RMW, and the RMW is a surface of constant absolute angular momentum (M). The slopes of the RMW and of M surfaces are objectively determined. The slopes are found to increase linearly with the size of the low-level RMW, and to be independent of the intensity of the storm. While the RMW is approximately an M surface, M systematically decreases with height along the RMW. The steady-state analytical theory of Emanuel (1986) is shown to make specific predictions regarding the vertical structure of tropical cyclones. It is found that in this model, the slope of the RMW is a linear function of its size and is independent of intensity, and that the RMW is almost exactly an M surface. A simple time-dependent model which is governed by the same assumptions as the analytical theory yields the same results. Idealized hurricane simulations are conducted using the Weather Research and Forecasting (WRF) model. The assumptions of Emanuel's theory, slantwise moist neutrality and thermal wind balance, are both found to be violated. Nevertheless, the vertical structure of the wind field itself is generally well predicted by the theory. The percentage rate at which the winds decay with height is found to be nearly independent of both size and intensity, in agreement with observations and theory. Deviations from this decay profile are shown to be due to gradient wind imbalance. The slope of the RMW increases linearly with its size, but is systematically too large compared to observations. Also in contrast to observations, M generally increases with height along the RMW.

La thèse est principalement centrée sur l'étude de la résolution verticale des diagraphies. On outre, l'arithmétique floue est appliquée aux modèles expérimentaux pétrophysiques en vue de transmettre l'incertitude des données d'entrée aux données de sortie, ici la saturation irréductible en eau et la perméabilité. Les diagraphies sont des signaux digitaux dont les données sont des mesures volumétriques. Le mécanisme d'enregistrement de ces données est modélisé par des fonctions d'appartenance floues. On a montré que la Résolution Verticale de la Fonction d'Appartenance (VRmf) est supérieur d'espacement. Dans l'étape suivante, la fréquence de Nyquist est revue en fonction du mécanisme volumétrique de diagraphie ; de ce fait, la fréquence volumétrique de Nyquist est proposée afin d'analyser la précision des diagraphies. Basé sur le modèle de résolution verticale développée, un simulateur géométrique est conçu pour générer les registres synthétiques d'une seule couche mince. Le simulateur nous permet d'analyser la sensibilité des diagraphies en présence d'une couche mince. Les relations de régression entre les registres idéaux (données d'entrée de ce simulateur) et les registres synthétiques (données de sortie de ce simulateur) sont utilisées comme relations de déconvolution en vue d'enlever l'effet des épaules de couche d'une couche mince sur les diagraphies GR, RHOB et NPHI. Les relations de déconvolution ont bien été appliquées aux diagraphies pour caractériser les couches minces. Par exemple, pour caractériser une couche mince poreuse, on a eu recours aux données de carottage qui étaient disponibles pour la vérification : NPHI mesuré (3.8%) a été remplacé (corrigé) par 11.7%. NPHI corrigé semble être plus précis que NPHI mesuré, car la diagraphie a une valeur plus grande que la porosité de carottage (8.4%). Il convient de rappeler que la porosité totale (NPHI) ne doit pas être inférieure à la porosité effective (carottage). En plus, l'épaisseur de la couche mince a été estimée à 13±7.5 cm, compatible avec l'épaisseur de la couche mince dans la boite de carottage (<25 cm). Normalement, l'épaisseur in situ est inférieure à l'épaisseur de la boite de carottage, parce que les carottes obtenues ne sont plus soumises à la pression lithostatique, et s'érodent à la surface du sol. La DST est appliquée aux diagraphies, et l'intervalle d'incertitude de DST est construit. Tandis que la VRmf des diagraphies GR, RHOB, NPHI et DT est ~60 cm, la VRmf de l'intervalle d'incertitude est ~15 cm. Or, on a perdu l'incertitude de la valeur de diagraphie, alors que la VRmf est devenue plus précise. Les diagraphies ont été ensuite corrigées entre l'intervalle d'incertitude de DST avec quatre simulateurs. Les hautes fréquences sont amplifiées dans les diagraphies corrigées, et l'effet des épaules de couche est réduit. La méthode proposée est vérifiée dans les cas synthétiques, la boite de carottage et la porosité de carotte. L'analyse de partitionnement est appliquée aux diagraphies NPHI, RHOB et DT en vue de trouver l'intervalle d'incertitude, basé sur les grappes. Puis, le NPHI est calibré par la porosité de carottes dans chaque grappe. Le √MSE de NPHI calibré est plus bas par rapport aux cinq modèles conventionnels d'estimation de la porosité (au minimum 33% d'amélioration du √MSE). Le √MSE de généralisation de la méthode proposée entre les puits voisins est augmenté de 42%. L'intervalle d'incertitude de la porosité est exprimé par les nombres flous. L'arithmétique floue est ensuite appliquée dans le but de calculer les nombres flous de la saturation irréductible en eau et de la perméabilité. Le nombre flou de la saturation irréductible en eau apporte de meilleurs résultats en termes de moindre sous-estimation par rapport à l'estimation nette. Il est constaté que lorsque les intervalles de grappes de porosité ne sont pas compatibles avec la porosité de carotte, les nombres flous de la perméabilité ne sont pas valables. / In the subsurface geology, characterization of geological beds by well-logs is an uncertain task. The thesis mainly concerns studying vertical resolution of well-logs (question 1). In the second stage, fuzzy arithmetic is applied to experimental petrophysical relations to project the uncertainty range of the inputs to the outputs, here irreducible water saturation and permeability (question 2). Regarding the first question, the logging mechanism is modelled by fuzzy membership functions. Vertical resolution of membership function (VRmf) is larger than spacing and sampling rate. Due to volumetric mechanism of logging, volumetric Nyquist frequency is proposed. Developing a geometric simulator for generating synthetic-logs of a single thin-bed enabled us analysing sensitivity of the well-logs to the presence of a thin-bed. Regression-based relations between ideal-logs (simulator inputs) and synthetic-logs (simulator outputs) are used as deconvolution relations for removing shoulder-bed effect of thin-beds from GR, RHOB and NPHI well-logs. NPHI deconvolution relation is applied to a real case where the core porosity of a thin-bed is 8.4%. The NPHI well-log is 3.8%, and the deconvolved NPHI is 11.7%. Since it is not reasonable that the core porosity (effective porosity) be higher than the NPHI (total porosity), the deconvolved NPHI is more accurate than the NPHI well-log. It reveals that the shoulder-bed effect is reduced in this case. The thickness of the same thin-bed was also estimated to be 13±7.5 cm, which is compatible with the thickness of the thin-bed in the core box (<25 cm). Usually, in situ thickness is less than the thickness of the core boxes, since at the earth surface, there is no overburden pressure, also the cores are weathered. Dempster-Shafer Theory (DST) was used to create well-log uncertainty range. While the VRmf of the well-logs is more than 60 cm, the VRmf of the belief and plausibility functions (boundaries of the uncertainty range) would be about 15 cm. So, the VRmf is improved, while the certainty of the well-log value is lost. In comparison with geometric method, DST-based algorithm resulted in a smaller uncertainty range of GR, RHOB and NPHI logs by 100%, 71% and 66%, respectively. In the next step, cluster analysis is applied to NPHI, RHOB and DT for the purpose of providing cluster-based uncertainty range. Then, NPHI is calibrated by core porosity value in each cluster, showing low √MSE compared to the five conventional porosity estimation models (at least 33% of improvement in √MSE). Then, fuzzy arithmetic is applied to calculate fuzzy numbers of irreducible water saturation and permeability. Fuzzy number of irreducible water saturation provides better (less overestimation) results than the crisp estimation. It is found that when the cluster interval of porosity is not compatible with the core porosity, the permeability fuzzy numbers are not valid, e.g. in well#4. Finally, in the possibilistic approach (the fuzzy theory), by calibrating α-cut, the right uncertainty interval could be achieved, concerning the scale of the study.