We adapt the theory of Empirical Normal Modes (ENMs) to diagnose gravity waves generated by a relatively high resolution numerical model solving the primitive equations. The ENM approach is based on the Principal Component Analysis (which consists of finding the most efficient basis explaining the variance of a time series), except that it takes advantage of wave-activity conservation laws. In the present work, the small-amplitude version of the pseudoenergy is used to extract from data quasi-monochromatic three-dimensional empirical modes that describe atmospheric wave activity. The spatial distributions of these quasi-monochromatic modes are identical to the normal modes of the linearized primitive equations when the underlying dynamics can be described with a stochastic linear and forced model, thus establishing a bridge between statistics and dynamics. We use this diagnostic method to study inertia-gravity wave generation, propagation, transience, and breaking over the Rockies, the North Pacific, and Central America in the troposphere-stratosphere-mesosphere GFDL SKYHI general circulation model at a resolution of 18° of latitude by 1.2° of longitude. Besides the action of mountains in exciting orographic waves, inertia-gravity wave activity has been found to be generated at the jet stream level as a possible consequence of a sustained nonlinear and ageostrophic flow. In the Tropical region of the model, the "obstacle effect" has been found to be the major source of inertia-gravity waves. A significant proportion of these inertia-gravity waves was able to reach the model mesosphere without much dissipation and absorption.

The goal of this study is to improve knowledge about how cloud inhomogeneities affect the reflection of solar radiation. In particular, it addresses two main questions: what the processes through which inhomogeneities influence solar reflection are, and how this influence can be taken into account in albedo retrievals based on future satellite measurements. / The first question is important, since present methods give numerical results only about the overall radiative effect of cloud inhomogeneities, but cannot determine the degree to which various mechanisms are responsible for this overall effect. This study establishes a theoretical framework which defines and evaluates the various processes through which cloud inhomogeneities influence solar radiation. This framework is then used to examine quantitatively the inhomogeneity effects that occur in irregular cloud fields. Among other insights, it is shown and explained that identical variations in cloud optical thickness can cause much stronger inhomogeneity effects if they are due to variations in geometrical cloud thickness, and not in volume extinction coefficient (as assumed in previous studies of irregular cloud fields). The differences in albedo can exceed 0.05, and the relative differences in reflectance toward the zenith can be greater than 25% for overhead sun, and 50% for oblique sun. Also, a possible explanation is given for a phenomenon observed in previous studies: that cloud reflectivity toward the zenith increases with decreasing solar elevation. / This study also develops an albedo retrieval algorithm that considers radiative inhomogeneity effects. The algorithm takes advantage of the unique multi-view capability of the Multi-angle Imaging SpectroRadiometer (MISR) placed on the Earth Observing System-AM satellite (to be launched in 1998). This instrument will offer new possibilities for albedo retrievals since, unlike present instruments, it will measure the radiation reflected in not only one, but nine directions. The potential accuracy of the algorithm is analyzed for a dataset obtained by using a Monte Carlo model to simulate radiative transfer through a large number of irregular cloud fields. The results indicate that using multi-view measurements can improve the accuracy of satellite-based albedo retrievals by a factor of three or more.

A study of Kalman filtering in atmospheric data assimilation is presented. Our research aims at an understanding of the physical and statistical mechanisms as well as the principles underlying its application to atmospheric data assimilation. Both the continuous and the discrete formulations of the filter were considered. Using nonlinear advection diffusion dynamics, a number of aspects in data assimilation were addressed, often by exploring the parameter space or by performing Monte Carlo simulations. The filtering properties, the spatial regularity and indirect inference about the model error covariance were examined with a discrete linear Kalman filter. The dynamics of the mean, variance, and correlation of forecast errors for Burgers' equation were studied. The validity of the tangent linear approximation for Burgers' equation was examined. An ensemble of realizations of the extended Kalman filter has permitted a statistical investigation of its performance, errors and limit of validity.

This study examines the large-scale fields of eight stronger and eight weaker cyclones prior to rapid cyclogenesis to help explain their subsequent deepening rate. The cyclones all commenced their rapid development within the same small geographical region over the Kuroshio and are compared using composites, ensembles and individual case studies. / Colder air and stronger anticyclogenesis over East Asia track the stronger cases along the Kuroshio, while the weaker cases tend to track across Japan. Anticylogenesis is also present to the east of the stronger cases which hence have warm advection ahead of them. The weaker cases generally form as transitory features in the northerly flow to the west of large cyclones and so have cold advection ahead of them. This affects a deep layer, producing a ridge-trough couplet at 500 mb for the stronger cases and a more zonal flow above the weaker cases.

An X-band transmitter ($ lambda$ = 3,2 cm) should perform better than an S-band transmitter ($ lambda$ = 10,4 cm) in the remote measurement of snowfall by radar. Comparisons between groundtruth measurements and their radar measured counterparts are done for two similar snowstorms (November 20th and 21st 1986, January 30th and 31st 1987), scanned respectively with an S-band and an X-band transmitter, mounted on the 10 m wide antenna of the Weather Radar Observatory of McGill University; these observations confirmed the hypothesis. A mixed rain-snow precipitation event was also observed on February 21st 1989, using alternatively the X-band and the S-band transmitter on the same antenna during the course of the event; this allowed an almost simultaneous comparison of the transmitters. Modifications to the regular sequence of observation of the weather radar during winter are proposed to take advantage of the potential of the X-band transmitter in the measurement of snowfall.

A two-dimensional anelastic model is used to study slantwise convection. The initial atmosphere is specified to be statically, inertially and symmetrically stable for dry convection. By varying the distribution of environmental relative humidity, a moist basic state potentially stable for upright convection but unstable for slantwise convection was obtained. The conditional symmetric instability (CSI) is released by specifying an initial streamfunction impulse. / The results show a typical slantwise convective circulation. A cloudband extends along the updraft of the CSI circulation. An energy budget analysis shows that the main source of perturbation kinetic energy comes from the vertical shear of the basic state flow, although the buoyancy term is important during the initial onset stage. It is also found that the CSI circulation induces both upright convective unstable layers and horizontal inertial unstable layers. / Although the decay stage has already been reached at the end of simulation, a neutral state with zero moist potential vorticity was not achieved. Our results also show that a high vertical resolution is necessary for the simulation of moist symmetric instability.

A theoretical analysis of the space-time correlation function for rainfall and its relationship to Taylor's hypothesis is presented. The analysis assumes a homogeneous and stationary random field being advected past a fixed coordinate system with a constant velocity. Within the moving reference frame, the random field is assumed to possess quadrant symmetry. The concept of space-time isotropy is defined relative to a velocity. This is called the intrinsic velocity and represents a kinematic characteristic of the storm system apart from the advection velocity. A radial space-time correlation function is defined over a range of scales where the intrinsic velocity remains constant. The effect of the intrinsic velocity on Taylor's hypothesis is examined and an alternative is proposed. The effect of spatial resolution is evaluated theoretically on a model space-time correlation. The results from the theoretical calculation are compared with those obtained from two rain events. The radial space-time correlation functions of the rain events vary as expected with spatial resolution, but the intrinsic and advection velocities are inconclusive. The uncertainty for the intrinsic and advection velocities does not allow for a clear relationship with spatial resolution. Nor does it allow a clear determination of the effect of spatial resolution on the validity of Taylor's hypothesis. The intrinsic velocity may be approximated as constant over a certain range of time scales (15 to 70 min). Of the cases considered, the effect of the internal storm development on Taylor's hypothesis is slight. Therefore, a 'frozen turbulence' model for Taylor's hypothesis is still a good approximation.

The transfer of radiant energy in highly inhomogeneous media is a difficult problem that is encountered in many geophysical applications. It is the purpose of this thesis to study some problems connected with the scattering of solar radiation in natural clouds. Extreme variability in the optical density of these clouds is often believed to occur regularly. / In order to facilitate study of very inhomogeneous optical media such as clouds, the difficult angular part of radiative transfer calculations is simplified by considering a series of models in which conservative scattering only occurs in discrete directions. Analytic and numerical results for the radiative properties of these Discrete Angle Radiative Transfer (DART) systems are obtained in the limits of both optically thin and thick media. Specific results include: (a) In thick homogeneous media, the albedo (reflection coefficient), unlike the transmission, cannot be obtained by a diffusion equation. (b) With the aid of an exact analogy with an early model of conductor/superconductor mixtures, it is argued that inhomogeneous media with embedded holes, neither the transmission, nor the albedo can be described by diffusive random walks. (c) Using renormalization methods, it is shown that thin cloud behaviour is sensitive to the scattering phase functions since it is associated with a repelling fixed point, whereas, the thick cloud limit is universal in that it is phase function independent, and associated with an attracting fixed point. (d) In fractal media, the optical thickness required for a given albedo or transmission can differ by large factors from that required in the corresponding plane parallel geometry. The relevant scaling exponents have been calculated in a very simple example. (e) Important global meteorological and climatological implications of the above are discussed when applied to the scattering of visible light in clouds. / In the remote sensing context, an analysis of satellite data reveals that augmenting a satellite's resolution reveals increasingly detailed structures that are found to occupy a decreasing fraction of the image, while simultaneously brightening to compensate. By systematically degrading the resolution of visible and infra red satellite cloud and surface data as well as radar rain data, resolution-independent co-dimension functions were defined which were useful in describing the spatial distribution of image features as well as the resolution dependence of the intensities themselves. The scale invariant functions so obtained fit into theoretically predicted functional forms. These multifractal techniques have implications for our ability to meaningfully estimate cloud brightness fraction, total cloud amount, as well as other remotely sensed quantities.

A numerical modelling of the 4--5 July 1999 derecho was performed. The storm caused over 40 million dollars of damages, several deaths and injuries across the United States and Canada. The unseasonal synoptic settings resulted in the formation of low-level moisture pooling and the buildup of convective available potential energy. The upper-level jet streak eventually furnished the trigger for the outbreak of precursor deep convection leading to the development of this derecho. / The results illustrated the feasibility of simulating the derecho using a mesoscale model with the NCEP (National Centers for Environmental Prediction) reanalysis. Convection was not initiated properly using as initial conditions the CMC (Canadian Meteorological Centre) analysis which displays less low-level moisture and potential instability, as well as downward motion over the area of convective outbreak. Similarities between the modelled profile and the environment conducive to wet microburst are discussed. Sensitivity experiments were performed to explore the effects of shallow convection, deep convective parameterization, and a different surface scheme on the simulation of the derecho.

Damage from large hail is a costly problem in Canada and other parts of the world. With continuous increase in computer power, numerical weather prediction (NWP) models are getting closer to resolving the convective scale, where it is appropriate to employ explicit microphysics schemes. / This dissertation examines the potential to predict hail using an explicit microphysics scheme in an NWP model. To this end, the requirements of a bulk scheme to model the hydrometeor size distribution are investigated. A number of schemes in the literature use the double-moment method with a three-parameter gamma distribution function to represent the size spectrum. In general, two of the parameters vary with the predicted moments while the third, normally the shape parameter, is held constant. In a simple 1D context, the role of the shape parameter is analyzed by comparing results from bulk schemes using different numbers of predicted moments and an analytic bin model. It is shown that this parameter is important in the overall prediction of the size distribution by affecting both the instantaneous growth rates and the sedimentation. In view of this, two alternatives to the fixed-value approach are presented. One is a double-moment method, where the shape parameter is diagnosed from the predicted moments; the other is a triple-moment approach, where all distribution parameters are fully prognosed. / A new microphysics scheme using the proposed approaches has been designed and interfaced with the Mesoscale Compressible Community model (MC2). High-resolution (1 km) simulations of a severe hailstorm are conducted. The control simulation using the full triple-moment version of the scheme is compared to radar observations and is shown to realistically simulate the observed storm, including the spatial distribution and sizes of hail at the ground. Experiments are performed to determine the sensitivity of the different approaches on the simulation of hail. The results indicated that the triple-moment scheme gives the best results. For a double-moment scheme, the diagnostic approach for the shape parameter exhibits distinct improvement over the fixed-value approach. It is also shown that double-moment schemes are dramatically better in reproducing the control simulation than single-moment schemes, owing largely to the ability of multi-moment schemes to account for the effects of size-sorting.