published_or_final_version / Mathematics / Master / Master of Philosophy

"The most widely used spectral models with the transform method are the de-aliased spectral model in which the de-aliased technique is used in the discrete Fourier transform according to the 3/2-rule. From the viewpoint of the Walsh-Hadamard transform, the multiplications of the values of the variables on the gridpoints do not yield the aliasing terms. In the shallow water equations, we compare the aliased spectral model with the de-aliased spectral model using the initial conditions of the Rossby-Haurwitz wave and the FGGE data. The aliased spectral models are more accurate and more efficient than the de-aliased spectral models. For the same wavenumber truncation, the computational amount of the aliased spectral model is only 60 percent of the de-aliased spectral model. We have not yet discovered the phenomenon of the nonlinear computational instability induced by the aliasing terms in the long time integration of the aliased spectral models. Thus, in the spectral models with the transform method the necessity of using the 3/2-rule in the discrete Fourier transform may be viewed with suspicion"--Abstract. / Typescript. / "Spring Semester, 1991." / "Submitted to the Department of Meteorology in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: Richard L. Pfeffer, Professor Directing Thesis. / Includes bibliographical references (leaves 92-95).

Data assimilation plays an important role in weather forecasting. The purpose of data assimilation is try to provide a more accurate atmospheric state for future forecast. Several existed methods currently used in this field fall into two categories: statistical data assimilation and variational data assimilation. This thesis focuses mainly on variational data assimilation. The original objective function of three dimensional data assimilation (3D-VAR) consists of two terms: the difference between the pervious forecast and analysis and the difference between the observations and analysis in observation space. Considering the inaccuracy of previous forecasting results, we replace the first term by the difference between the previous forecast gradients and analysis gradients. The associated data fitting term can be interpreted using the second-order finite difference matrix as the inverse of the background error covariance matrix in the 3D-VAR setting. In our approach, it is not necessary to estimate the background error covariance matrix and to deal with its inverse in the 3D-VAR algorithm. Indeed, the existence and uniqueness of the analysis solution of the proposed objective function are already established. Instead, the solution can be calculated using the conjugate gradient method iteratively. We present the experimental results based on WRF simulations. We show that the performance of this forecast gradient based DA model is better than that of 3D-VAR. Next, we propose another optimization method of variational data assimilation. Using the tensor completion in the cost function for the analysis, we replace the second term in the 3D-VAR cost function. This model is motivated by a small number of observations compared with the large portion of the grids. Applying the alternating direction method of multipliers to solve this optimization problem, we conduct numerical experiments on real data. The results show that this tensor completion based DA model is competitive in terms of prediction accuracy with 3D-VAR and the forecast gradient based DA model. Then, 3D-VAR and the two model proposed above lack temporal information, we construct a third model in four-dimensional space. To include temporal information, this model is based on the second proposed model, in which introduce the total variation to describe the change of atmospheric state. To this end, we use the alternating direction method of multipliers. One set of experimental results generates a positive performance. In fact, the prediction accuracy of our third model is better than that of 3D-VAR, the forecast gradient based DA model, and the tensor completion based DA model. Nevertheless, although the other sets of experimental results show that this model has a better performance than 3D-VAR and the forecast gradient based DA model, its prediction accuracy is slightly lower than the tensor completion based model.

The Madden-Julian oscillation (MJO) and the quasi-biennial oscillation (QBO) are two key modes of variability in the tropical atmosphere. The MJO, characterized by propagating, planetary-scale signals in convection and winds, is the main source of subseasonal variability and predictability in the tropics. The QBO is a ~28-month cycle in which the tropical stratospheric zonal winds alternate between easterly and westerly regimes. Via thermal wind balance these winds induce temperature anomalies, and both wind and temperature signals reach the tropopause. Recent observational results show a remarkably strong link between the MJO and the QBO during boreal winter: the MJO is stronger and more predictable when QBO winds in the lower stratosphere are easterly than when winds are westerly. Despite its important implications for MJO theory and prediction, the physical processes driving the MJO-QBO interaction are not well-understood. In this thesis, we use a hierarchy of models – including a cloud-resolving model, a forecast model, and a global climate model – to examine whether models can reproduce the MJO-QBO link, and better understand the possible mechanisms driving the connection. Based in part on our modeling findings, we further explore observed QBO temperature signals thought to be important for the MJO-QBO link. After providing necessary background and context in the first two chapters, the third chapter looks at the MJO-QBO link in a small-domain, cloud-resolving model. The model successfully simulates convection associated with two MJO events that occurred during the DYNAMO field campaign. To examine the effect of QBO, we add various QBO temperature and wind anomalies into the model. We find that QBO temperature anomalies alone, without wind anomalies, qualitatively affect the model MJO similarly to the observed MJO-QBO connection. QBO wind anomalies have no clear effect on the modeled MJO. We note however that the MJO response is quite sensitive to the vertical structure of the QBO temperature anomalies, and for realistic temperature signals the model response is very small. In the fourth chapter, we look at the MJO-QBO link in a state-of-the-art global forecast model with a good representation of the MJO. We conduct 84 hind-cast experiments initialized on dates across winters from 1989-2017. For each of these dates, we artificially impose an easterly and a westerly QBO in the stratospheric initial conditions, and examine the resulting changes to the simulated MJO under different stratospheric states. We find that the effect of the QBO on the model MJO is of the same sign as observations, but is much smaller. A large sample size is required to capture any QBO signal, and tropospheric initial conditions seem more important than the stratosphere in determining the behavior of the simulated MJO. Despite the weak signal, we find that simulations with stronger QBO temperature anomalies have a stronger MJO response. In the fifth chapter, we conduct experiments in recent versions of a NASA general circulation model. We find that a version with a high vertical resolution generates a reasonable QBO and MJO, but has no MJO-QBO link. However, this model has weaker-than-observed QBO temperature anomalies, which may explain the lack of an MJO impact. To explore this potential bias, we impose the QBO by nudging the model stratospheric winds towards reanalysis, leading to more realistic simulation of QBO temperature anomalies. Despite this, the model still fails to show a strong MJO-QBO link across several ensemble experiments and sensitivity tests. We conclude with discussion of possible reasons why the model fails to capture the MJO-QBO connection. The sixth chapter examines QBO temperature signals in a range of observational and reanalysis datasets. In particular, we are motivated by two elements of the MJO-QBO relationship which are especially puzzling: the seasonality (i.e. that the MJO-QBO link is only significant in boreal winter) and long-term trend (i.e. that the MJO-QBO link seems to have only emerged since the 1980s). By examining QBO temperature signals around the tropopause, we highlight changes to the strength and structure of QBO temperature anomalies both in boreal winter and in recent decades. Whether these changes are linked to the MJO-QBO relationship, and what more generally might explain them, is not presently clear. Overall, we demonstrate that capturing the MJO-QBO relationship in a variety of models is a difficult task. The majority of evidence indicates that QBO-induced temperature anomalies are a plausible pathway through which the QBO might modulate the MJO, but the theoretical description of precisely how these temperature anomalies may impact convection is lacking and likely more nuanced than the literature to date suggests. Most models show only a weak modulation of the MJO associated with changes in upper-tropospheric temperatures, and even when those temperature signals are artificially enhanced, comprehensive GCMs still fail to show a significant MJO-QBO connection. Our observational study indicates that temperature anomalies associated with the QBO show striking modulations on various timescales of relevance to the MJO-QBO link, but do not conclusively demonstrate a clear connection to the MJO. This difficulty simulating a strong MJO-QBO connection suggests that models may lack a key process in driving the MJO and coupling the tropical stratosphere and troposphere. It is further possible that the observed link may be in some regards different than is currently theorized -- for example statistically not robust, due to non-stratospheric processes, or driven by some mechanism that has not been suitably explored.

Antarctic Wind Engineering deals with the effects of wind on the built environment. The assessment of wind induced forces, wind resource and wind driven snowdrifts are the main tasks for a wind engineer when participating on the design of an Antarctic building. While conventional Wind Engineering techniques are generally applicable to the Antarctic environment, there are some aspects that require further analysis due to the special characteristics of the Antarctic wind climate and its boundary layer meteorology. <p>The first issue in remote places like Antarctica is the lack of site wind measurements and meteorological information in general. In order to complement this shortage of information various meteorological databases have been surveyed. Global Reanalyses, produced by the European Met Office ECMWF, and RACMO/ANT mesoscale model simulations, produced by the Institute for Marine and Atmospheric Research of Utrecht University (IMAU), have been validated versus independent observations from a network of 115 automatic weather stations. The resolution of these models, of some tens of kilometers, is sufficient to characterize the wind climate in areas of smooth topography like the interior plateaus or the coastal ice shelves. In contrast, in escarpment and coastal areas, where the terrain gets rugged and katabatic winds are further intensified in confluence zones, the models lack resolution and underestimate the wind velocity. <p>The Antarctic atmospheric boundary layer (ABL) is characterized by the presence of strong katabatic winds that are generated by the presence of surface temperature inversions in sloping terrain. This inversion is persistent in Antarctica due to an almost continuous cooling by longwave radiation, especially during the winter night. As a result, the ABL is stably stratified most of the time and, only when the wind speed is high it becomes near neutrally stratified. This thesis also aims at making a critical review of the hypothesis underlying wind engineering models when extreme boundary layer situations are faced. It will be shown that the classical approach of assuming a neutral log-law in the surface layer can hold for studies of wind loading under strong winds but can be of limited use when detailed assessments are pursued. <p>The Antarctic landscape, mostly composed of very long fetches of ice covered terrain, makes it an optimum natural laboratory for the development of homogeneous boundary layers, which are a basic need for the formulation of ABL theories. Flux-profile measurements, made at Halley Research Station in the Brunt Ice Shelf by the British Antarctic Survery (BAS), have been used to analyze boundary layer similarity in view of formulating a one-dimensional ABL model. A 1D model of the neutral and stable boundary layer with a transport model for blowing snow has been implemented and verified versus test cases of the literature. A validation of quasi-stationary homogeneous profiles at different levels of stability confirms that such 1D models can be used to classify wind profiles to be used as boundary conditions for detailed 3D computational wind engineering studies. <p>A summary of the wind engineering activities carried out during the design of the Antarctic Research Station is provided as contextual reference and point of departure of this thesis. An elevated building on top of sloping terrain and connected to an under-snow garage constitutes a challenging environment for building design. Building aerodynamics and snowdrift management were tested in the von Karman Institute L1B wind tunnel for different building geometries and ridge integrations. Not only for safety and cost reduction but also for the integration of renewable energies, important benefits in the design of a building can be achieved if wind engineering is considered since the conceptual phase of the integrated building design process.<p> / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished