Dynamics of an Idealized Fluid Model for Investigating Convective-scale Data Assimilation

An idealized fluid model of convective-scale numerical weather prediction, intended for use in inexpensive data assimilation experiments, is described here and its distinctive dynamics are investigated. The model modifies the rotating shallow water equations to include some simplified dynamics of cumulus convection and associated precipitation, extending and improving the model of Würsch and Craig. Changes to this original model are the removal of ad hoc diffusive terms and the addition of Coriolis rotation terms, leading to a so-called 1.5-dimensional model. Despite the non-trivial modifications to the parent equations, it is shown that this shallow water type model remains hyperbolic in character and can be integrated accordingly using a discontinuous Galerkin finite element method for nonconservative hyperbolic systems of partial differential equations. Combined with methods to ensure well-balancedness and non-negativity, the resulting numerical solver is novel, efficient and robust. Classical numerical experiments in the shallow water theory, such as the Rossby geostrophic adjustment and flow over topography, are reproduced for the standard shallow water model and used to highlight the modified dynamics of the new model. In particular, it exhibits important aspects of convective-scale dynamics relating to the disruption of large-scale balance and is able to simulate other features related to convecting and precipitating weather systems. Our analysis here and preliminary results suggest that the model is well suited for efficiently and robustly investigating data assimilation schemes in an idealized ‘convective-scale’ forecast assimilation framework

An idealised fluid model of Numerical Weather Prediction: dynamics and data assimilation

The dynamics of the atmosphere span a tremendous range of spatial and temporal scales which presents a great challenge to those who seek to forecast the weather. To aid understanding of and facilitate research into such complex physical systems, `idealised' models can be developed that embody essential characteristics of these systems. This thesis concerns the development of an idealised fluid model of convective-scale Numerical Weather Prediction (NWP) and its use in inexpensive data assimilation (DA) experiments. The model modifies the rotating shallow water equations to include some simplified dynamics of cumulus convection and associated precipitation, extending the model of Wuersch and Craig (2014). Despite the non-trivial modifications to the parent equations, it is shown that the model remains hyperbolic in character and can be integrated accordingly using a discontinuous Galerkin finite element method for nonconservative hyperbolic systems of partial differential equations. Combined with methods to ensure well-balancedness and non-negativity, the resulting numerical solver is novel, efficient, and robust. Classical numerical experiments in shallow water theory, based on the Rossby geostrophic adjustment problem and non-rotating flow over topography, elucidate the model's distinctive dynamics, including the disruption of large-scale balanced flows and other features of convecting and precipitating weather systems. When using such intermediate-complexity models for DA research, it is important to justify their relevance in the context of NWP. A well-tuned observing system and filter configuration is achieved using the ensemble Kalman filter that adequately estimates the forecast error and has an average observational influence similar to NWP. Furthermore, the resulting error-doubling time statistics reflect those of convection-permitting models in a cycled forecast-assimilation system, further demonstrating the model's suitability for conducting DA experiments in the presence of convection and precipitation. In particular, the numerical solver arising from this research provides a useful tool to the community and facilitates other studies in the field of convective-scale DA research

On the relevance of rotational and divergent modes of motion to mesoscale dynamics and upscale error growth

The atmospheric mesoscales encompass dynamical and thermodynamical processes that are characterized by length scales between a few and a couple of hundred kilometers and temporal scales of several minutes to one day. These processes are associated with mid-latitudinal weather and their skillful prediction is a major aim of meteorological research. In there, two fundamental issues arise: first, there is no consensus about the principal dynamical agent on the mesoscales that gives rise to the observed kinetic energy spectrum. Second, a dominant scale-interaction mechanism that governs the growth of initially small-scale errors to large scales remains undetermined. This thesis contributes to an improved understanding of these two aspects with an emphasis on the relevance of rotational and divergent modes of motion and their interplay. An important observational test of theoretical studies regarding the horizontal mesoscale kinetic energy spectrum is decoupling its rotational and divergent constituents from one-dimensional atmospheric wind measurements. Such a one-dimensional Helmholtz-decomposition method was recently suggested. The first part of this dissertation addresses the validity of the strong mathematical homogeneity and isotropy assumptions underlying this method. To that end, new high-resolution global atmospheric numerical simulations are employed. Rotational and divergent modes of motion are derived by applying the one-dimensional Helmholtz-decomposition method to one-dimensional transects of the horizontal wind field. The results are then compared to the divergent and rotational components obtained from the unambiguous decomposition of the two-dimensional wind field. The mathematical assumptions are found to be fulfilled such that the mesoscale ratio of divergent to rotational kinetic energy can be derived correctly with the one-dimensional Helmholtz-decomposition method. The results suggest a significant dependence of the horizontal divergent- and rotational kinetic energy spectra on the considered height- and latitude ranges. This finding points to the non-universality of the dynamics governing the mesoscale kinetic energy spectrum. Recent studies suggest that small-scale errors in numerical weather predictions quickly amplify through the convective instability and the release of latent heat of condensation within clouds. These errors then propagate to larger scales, whereby their dynamics transition from significantly divergent to mainly rotational. The second part of this dissertation explores the possibility that geostrophic adjustment following deep moist convection is the dominant dynamical process governing this transition with an analytical- and a numerical approach. An analytical framework for the geostrophic adjustment of an initial point-like pulse of heat (representing the error within the prediction of a cloud) is developed based on the linearized, hydrostatic Boussinesq-equations. The solution includes the Green's function of the problem and contains the full temporal evolution of all transient and balanced flow components. Characteristic spatial and temporal scales of the geostrophic adjustment mechanism are deduced and three diagnostics that can be used to identify this process in numerical simulations are proposed. These predictions are then tested in the framework of error growth experiments in highly idealized numerical simulations of a convective cloud field in a rotating environment. The error growth characteristics feature a high level of agreement with the analytical predictions. The results of this thesis suggest that the geostrophic adjustment following convective heating governs upscale error growth through the atmospheric mesoscales.Die atmosphärischen Mesoskalen beinhalten dynamische und thermodynamische Prozesse, die durch Längenskalen von einigen bis zu einigen hundert Kilometern und Zeitskalen von Minuten bis zu einem Tag charakterisiert werden. Atmosphärische Strömungen auf diesem Skalenbereich werden als Wetter der mittleren Breiten verstanden und ihre verlässliche Vorhersage ist ein Hauptziel meteorologischer Forschung. Dabei treten zwei grundlegende Probleme auf: Erstens besteht kein Konsens darüber, welcher Prozess die mesoskalige Dynamik dominiert und insbesondere dem beobachteten horizontalen kinetischen Energiespektrum zugrunde liegt. Zweitens konnte bisher kein dominanter Skalenwechselwirkungsmechanismus bestimmt werden, auf dem das Anwachsen zunächst kleinskaliger Fehler zu großen Skalen basiert. Die vorliegende Dissertation trägt zu einem verbesserten Verständnis dieser beiden Aspekte bei, wobei der Fokus auf dem relativen Beitrag rotationeller und divergenter Moden des horizontalen Geschwindigkeitsfeldes und deren Wechselwirkung liegt. Eine fundamentale Überprüfung existierender Theorien bezüglich des horizontalen mesoskaligen Energiespektrums wird durch die Aufspaltung eindimensionaler atmosphärischer Windmessungen in rotationelle und divergente Anteile ermöglicht. Eine dementsprechende eindimensionale Helmholtz-Zerlegungsmethode wurde kürzlich veröffentlicht. Diese Aufspaltung basiert auf den mathematischen Annahmen der Homogenität und Isotropie, deren Gültigkeit im ersten Teil der vorliegenden Dissertation getestet wird. Dazu werden neue, hochaufgelöste globale numerische Simulationen der Atmosphäre verwendet. Die rotationellen- und divergenten Strömungsanteile werden mit der Helmholtz-Zerlegungsmethode aus eindimensionalen Segmenten des Windfeldes abgeleitet. Diese werden dann mit den rotationellen und divergenten Beiträgen des zweidimensionalen Windfeldes, welche als Referenz verwendet werden, verglichen. Die mathematischen Annahmen der eindimensionalen Helmholtz-Zerlegungsmethode sind auf den Mesoskalen hinreichend gut erfüllt, so dass hier das mesoskalige Verhältnis rotationeller zu divergenten Geschwindigkeitsmoden korrekt reproduziert werden kann. Beide Anteile des horizontalen Windfeldes zeigen des Weiteren eine signifikante Abhängigkeit von dem betrachteten Höhen- und Breitengradbereich. Die Ergebnisse deuten darauf hin, dass die mesoskalige Dynamik und das damit verbundene horizontale kinetische Energiespektrum nicht universell sind. Aktuelle Studien zeigen, dass das schnelle Anwachsen kleinskaliger Fehler in numerischen Wettervorhersagen vor allem mit der konvektiven Instabilität und dem Freisetzen latenter Kondensationswärme in Wolken zusammenhängt. Während die Fehler auf größere Skalen expandieren, ändert sich die dominante Dynamik von signifikant divergent zu primär rotationell. Der zweite Teil dieser Dissertation erforscht, ob diesem dynamischen Übergang die geostrophische Anpassung nach dem Einsetzen von Feuchtkonvektion zugrunde liegt. Dabei wird sowohl ein analytischer- als auch ein numerischer Ansatz verfolgt. Zunächst wird ein analytisches Modell für die geostrophische Anpassung einer instantanen Wärmefreisetzung (repräsentativ für den Fehler innerhalb der Vorhersage einer Wolke) entwickelt. Die gefundene Lösung ist die Greensche Funktion der betrachteten linearisierten, hydrostatischen Boussinesq-Gleichungen und enthält explizit die zeitliche Entwicklung aller transienten und balancierten Strömungsanteile. Die charakteristischen Raum- und Zeitskalen des geostrophischen Anpassungsprozesses werden aus dieser Lösung bestimmt. Ferner werden drei Diagnostiken entwickelt, mithilfe derer dieser Mechanismus in numerischen Simulationen identifiziert werden kann. Die analytischen Ergebnisse werden danach mit Fehlerwachstumsexperimenten in idealisierten numerischen Simulationen eines konvektiven Wolkenfeldes in einer rotierenden Umgebung getestet. Die gefundenen Eigenschaften des Fehlerwachstums stimmen sehr gut mit den Vorhersagen des analytischen Modells überein. Damit unterstützen die Ergebnisse dieser Dissertation die Hypothese, dass die geostrophische Anpassung konvektiver Wärmefreisetzung das Fehlerwachstum durch die atmosphärischen Mesoskalen bestimmt

On the generation of waves during frontogenesis

Density fronts are ubiquitous features of the ocean and atmosphere boundary layers. Boundary layers are characterised by strong surface fluxes of heat, water and momentum, and exhibit intense eddy fields that are associated with strong horizontal strains. Such boundary layer phenomena can drive the generation and sharpening of frontal density gradients in a process known as frontogenesis. Analytic models of frontogenesis have typically employed the `two-dimensional front' configuration where the density front is assumed to be infinitely long and straight, such that gradients along the front may be neglected, and the mathematical problem reduced to two spatial dimensions. Hoskins and Bretherton (1972) used this configuration to demonstrate how a weak background strain flow, associated with a large scale weather system, can drive the collapse of a boundary front to a discontinuity in the inviscid equations in finite time. More recently, Blumen (2000) has used the same configuration to demonstrate how an unbalanced initial state --- associated with a rapidly applied boundary flux --- can trigger an adjustment process which drives frontogenesis on the boundary. These two types of frontogenesis are known as `forced' and `spontaneous', respectively. Forced and spontaneous frontogenesis have typically been studied in isolation, despite it being well established that they can and do occur simultaneously. Furthermore, neither the Hoskins and Bretherton (1972) nor Blumen (2000) models include propagating inertia-gravity waves, despite recent observations and numerical simulations showing that these waves are often generated during active frontogenesis. Here we formulate a generalised mathematical model for the classical two-dimensional density front subject to a simple background strain flow, as studied by Hoskins and Bretherton (1972) . This model firstly unifies the disparate frontogenesis theories of Hoskins and Bretherton (1972) and Blumen (2000). Secondly, the model extends these theories by permitting arbitrary initial conditions, stratification and strong strains. Thirdly, the model incorporates non-hydrostatic effects and unbounded domains. An important novel feature of the model is the accurate description of inertia-gravity wave generation during frontogenesis. We show that these waves can be generated both by the geostrophic adjustment of initial imbalances in a stratified ambient, and spontaneously due to the acceleration of the strain flow around the front. The generalised model thus provides a unified theory capable of describing frontogenesis and wave generation in the atmosphere and ocean boundary layers on a vast range of scales. In particular, the inclusion of strong strains permits the description of frontogenesis on the ocean submesoscale. The predictions of the generalised model are confirmed by comparison with a suite of fully non-linear numerical simulations

Balanced and transient aspects of the intertropical convergence zone

Includes bibliographical references.2015 Summer.The Intertropical Convergence Zone (ITCZ) is one of the primary drivers of tropical circulations and because of its interactions with the extratropics, contributes significantly to Earth's general circulation. This dissertation investigates dynamical aspects of the ITCZ using a variety of analytical and numerical models. In the first chapter, we learn that deep and shallow balanced Hadley circulations are forced by deep diabatic heating and Ekman pumping at the top of the boundary layer, respectively. Also, when the ITCZ is located off of the equator there is an inherent asymmetry between the winter and summer Hadley cells due to the anisotropic nature of the inertial stability. The second study examines shallow and deep vertical motions over the eastern Pacific Ocean (80°W--150°W) using the Year of Tropical Convection reanalysis (YOTC). Vertical motions in the eastern Pacific tend to be bimodal, with both shallow and deep vertical motions occurring throughout the year. Shallow vertical motions are typically narrow and restricted to low latitudes (ITCZ-like) while deep vertical motions tend to be broad and are located poleward of shallow regimes, except during El Niño conditions. The study of balanced Hadley circulations is also extended to investigate the role of transient aspects of the Hadley circulation. The solutions illustrate that inertia-gravity wave packets emanate from the ITCZ and bounce off a spectrum of turning latitudes when the ITCZ is switched on at various rates. These equatorially trapped wave packets cause the Hadley cells to pulsate with periods of 1--3 days. In the last part of this dissertation, we focus on boundary layer aspects of the formation of the ITCZ. Since the ITCZ boundary layer is a region of significant meridional convergence, meridional advection should not be neglected. Using a zonally symmetric slab boundary layer model, shock-like structures appear in the form of near discontinuities in the horizontal winds and near singularities in the vorticity and Ekman pumping after 1--2 days. The numerical model also agrees well with dynamical fields in YOTC while adding important details about the boundary layer pumping and vorticity. In closing, we believe that the ITCZ is a highly transient region vital to the general circulation of the atmosphere, and many of its features can be explained by dry dynamics

Dynamique, interactions et instabilités de structures cohérentes agéostrophiques dans les modèles en eau peu profonde

Coherent structures are ubiquitous features of atmospheric and oceanic flows. Their associated meso- and large scale circulation is in geostrophic equilibrium. However, at increasing Rossby numbers, ageostrophic effects may push the structures away from this equilibrium, and new types of instabilities can also disturb their dynamics. In this thesis, the properties of ageostrophic coherent structures are investigated, mainly by means of direct numerical simulations. This is done in the framework of simplified conceptual models of meso- and large scale oceanic and atmospheric flows, namely Rotating Shallow Water models. The instability of intense vortices (isolated anticyclonic vortices and tropical cyclones) in one-layer and two-layer shallow water models are studied. Direct numerical simulations of the nonlinear saturation of these instabilities allow us to study the properties of the ageostrophic part of the flow, such as the inertia-gravity wave emission and the formation of shocks. Then, quasi-stationary ageostrophic structures are obtained by means of numerical simulations in one-layer and two-layer models. It consists of vortex dipoles or tripoles, either baroclinic or barotropic, which are stable and whose ageostrophic component does not imply inertia-gravity waves emission. Finally, decaying vortex and wave turbulence is studied in the one-layer model. The evolution of the flow for very different initial conditions is discussed and we put the emphasis on the ageostrophic properties of the flow, the wave-vortex coupling and the sensitivity to initial conditions.Les structures cohérentes sont fréquemment observées dans les écoulements océaniques et atmosphériques. A moyenne et grande échelle, ces structures sont souvent proches de l'équilibre géostrophique. Cependant, pour des nombres de Rossby plus grands, les effets agéostrophiques entrent en jeu et modifient leur dynamique. Les propriétés des structures cohérentes agéostrophiques sont étudiées dans cette thèse, principalement à l'aide de simulations numériques, dans des modèles conceptuels des écoulements océaniques et atmosphériques à grande et moyenne échelle : les modèles en eau peu profonde. L'instabilité de tourbillons intenses (tourbillons anticycloniques isolés et cyclones tropicaux) dans les modèles en eau peu profonde à une et deux couches est étudiée. L'impact des différents paramètres sur ces instabilités est quantifié, et des simulations numériques de leur saturation non linéaire permet de dégager l'importance des mouvements agéostrophiques associés. Dans un second temps, des structures quasi-stationnaires agéostrophiques sont obtenues numériquement dans les modèles à une et deux couches. Ces structures, consistant en des dipôles et tripôles de vorticité (barotropes ou baroclines) sont stables, et la circulation agéostrophique qui leur est associée n'entraîne pas d'émission d'ondes d'inertie-gravité. Enfin, la turbulence d'ondes et de tourbillons en déclin dans un modèle à une couche est étudiée. L'évolution de l'écoulement à partir de conditions initiales très différentes est discutée, notamment en ce qui concerne les propriétés agéostrophiques de l'écoulement, le couplage ondes-tourbillons et la sensibilité aux conditions initiales

Dynamique, interactions et instabilités de structures cohérentes agéostrophiques dans les modèles en eau peu profonde

Coherent structures are ubiquitous features of atmospheric and oceanic flows. The cor- responding meso- and large scale circulation is in geostrophic equilibrium. However, at larger Rossby numbers, ageostrophic effects may push the structures away from this equi- librium, and new types of instabilities can also disturb their dynamics. In this thesis, the properties of ageostrophic coherent structures are investigated, mainly by means of direct numerical simulations. This is done in the framework of simplified conceptual models of meso- and large scale oceanic and atmospheric flows, namely the Rotating Shallow Wa- ter models. The instability of intense vortices (isolated anticyclonic vortices and tropical cyclones) in one-layer and two-layer shallow water models are studied. Direct numerical simulations of the nonlinear saturation of these instabilities allow us to study the proper- ties of the ageostrophic part of the flow, such as the inertia-gravity wave emission and the formation of shocks. Then, quasi-stationary ageostrophic structures are obtained by means of numerical simulations in one-layer and two-layer models. It consists of vortex dipoles or tripoles, either baroclinic or barotropic, which are stable and whose ageostrophic com- ponent does not imply inertia-gravity waves emission. Finally, decaying vortex and wave turbulence is studied in the one-layer model. The evolution of the flow for very different initial conditions is discussed. We put the emphasis on the ageostrophic properties of the flow, the wave-vortex coupling and the sensitivity to initial conditions.Les structures cohérentes sont fréquemment observées dans les écoulements océaniques et atmosphériques, et y ont un rôle important (transport, énergie...). A moyenne et grande échelle, ces structures sont souvent proches de l’équilibre géostrophique. Cependant, pour des nombres de Rossby plus grands, les effets agéostrophique – et parfois l’apparition de nouvelles instabilités – modifient leur dynamique. Les propriétés des structures cohérentes agéostrophiques sont étudiées dans cette thèse, principalement à l’aide de simulations nu- mériques, dans des modèles conceptuels des écoulements océaniques et atmosphériques à grande et moyenne échelle : les modèles en eau peu profonde. L’instabilité de tourbillons intenses – instabilités centrifuges et barotrope dans le cas de tourbillons anticycloniques isolés et instabilité barotrope radiative pour des cyclones tropicaux – dans les modèles en eau peu profonde à une et deux couches est étudiée. L’impact des différents paramètres sur ces instabilités est quantifié, et des simulations numériques de leur saturation non linéaire permettent de dégager l’importance des mouvements agéostrophiques associés. Dans un second temps, des structures quasi-stationnaires agéostrophiques sont obtenues numéri- quement dans les modèles à une et deux couches. Il s’agit de dipôles et tripôles de vor- ticité (barotropes ou baroclines) stables. Leur composante agéostrophique n’entraîne pas d’émission d’ondes d’inertie-gravité, et un découplage robuste ondes-tourbillons est ob- servé. Enfin, la turbulence d’ondes et de tourbillons en déclin dans un modèle à une couche est étudiée. L’évolution de l’écoulement à partir de conditions initiales très différentes est discutée, notamment en ce qui concerne les propriétés agéostrophiques de l’écoulement, le couplage ondes-tourbillons et la sensibilité aux conditions initiales

Role of inner-core and boundary layer dynamics on tropical cyclone structure and intensification, The

2018 Spring.Includes bibliographical references.Inner-core and boundary layer dynamics play a vital role in the tropical cyclone life cycle. This study makes use of analytical solutions and numerical models to gain insight into the role of dynamical processes involved with the incipient, rapidly intensifying, and eyewall replacement stages. A simplified, axisymmetric, one-layer, analytical model of tropical cyclone intensification is developed. Rather than formulating the model with the gradient balance approximation, the model uses the wave-vortex approximation, an assumption to the kinetic energy of the system, which limits its use to flows with small Froude numbers. Through filtering the inertia-gravity waves and adding a mass sink so that potential vorticity is not conserved in the system, the model is solved and provides analytical, time-evolving solutions that provide insight into long incubation periods prior to rapid intensification, potential vorticity tower development without frictional effects, and storm evolution in time through the maximum tangential velocity, total energy phase space. To understand the applicability of the forced, balance model for tropical cyclone intensification, the model is compared to a model using gradient balance. The comparison shows that the model based on the wave-vortex approximation is appropriate for fluids with flow speeds indicative of the external vertical normal mode in which case the deviation to the fluid depth is small. To understand another aspect of the inner-core dynamics that influence the radial location of the mass sink associated with the eyewall convection in the tropical cyclone, boundary-layer dynamics are considered. Motivated by abrupt jumps in the horizontal wind fields observed in flight-level aircraft reconnaissance data collected in Hurricanes Allen (1980) and Hugo (1989), an axisymmetric, f-plane slab boundary layer numerical model with a prescribed pressure forcing is developed. From this model, two simple analytic models are formulated in addition to two local, steady-state models. These models allow for the role of shock dynamics in the tropical cyclone boundary layer to be assessed. Two local models are also developed to evaluate the role of the nonlinear terms in the full numerical slab model. The local models adequately describe the boundary layer winds outside of the eyewall region. If a storm is weak or broad, the local models can explain a portion of the structure that develops in the eyewall region. This result shows that, to capture the hyperbolic nature of the eyewall region, the nonlinear terms are needed. The nonlinear response allows for the boundary-layer Ekman pumping to shift radially inward into the region of high inertial stability. The results from the local models and full numerical model also show that as the vortex wind field broadens, the convergence associated with the primary eyewall decays and that a secondary maximum displaced radially outward forms, a feature indicative of the formation of a secondary eyewall

On the relevance of rotational and divergent modes of motion to mesoscale dynamics and upscale error growth

The atmospheric mesoscales encompass dynamical and thermodynamical processes that are characterized by length scales between a few and a couple of hundred kilometers and temporal scales of several minutes to one day. These processes are associated with mid-latitudinal weather and their skillful prediction is a major aim of meteorological research. In there, two fundamental issues arise: first, there is no consensus about the principal dynamical agent on the mesoscales that gives rise to the observed kinetic energy spectrum. Second, a dominant scale-interaction mechanism that governs the growth of initially small-scale errors to large scales remains undetermined. This thesis contributes to an improved understanding of these two aspects with an emphasis on the relevance of rotational and divergent modes of motion and their interplay. An important observational test of theoretical studies regarding the horizontal mesoscale kinetic energy spectrum is decoupling its rotational and divergent constituents from one-dimensional atmospheric wind measurements. Such a one-dimensional Helmholtz-decomposition method was recently suggested. The first part of this dissertation addresses the validity of the strong mathematical homogeneity and isotropy assumptions underlying this method. To that end, new high-resolution global atmospheric numerical simulations are employed. Rotational and divergent modes of motion are derived by applying the one-dimensional Helmholtz-decomposition method to one-dimensional transects of the horizontal wind field. The results are then compared to the divergent and rotational components obtained from the unambiguous decomposition of the two-dimensional wind field. The mathematical assumptions are found to be fulfilled such that the mesoscale ratio of divergent to rotational kinetic energy can be derived correctly with the one-dimensional Helmholtz-decomposition method. The results suggest a significant dependence of the horizontal divergent- and rotational kinetic energy spectra on the considered height- and latitude ranges. This finding points to the non-universality of the dynamics governing the mesoscale kinetic energy spectrum. Recent studies suggest that small-scale errors in numerical weather predictions quickly amplify through the convective instability and the release of latent heat of condensation within clouds. These errors then propagate to larger scales, whereby their dynamics transition from significantly divergent to mainly rotational. The second part of this dissertation explores the possibility that geostrophic adjustment following deep moist convection is the dominant dynamical process governing this transition with an analytical- and a numerical approach. An analytical framework for the geostrophic adjustment of an initial point-like pulse of heat (representing the error within the prediction of a cloud) is developed based on the linearized, hydrostatic Boussinesq-equations. The solution includes the Green's function of the problem and contains the full temporal evolution of all transient and balanced flow components. Characteristic spatial and temporal scales of the geostrophic adjustment mechanism are deduced and three diagnostics that can be used to identify this process in numerical simulations are proposed. These predictions are then tested in the framework of error growth experiments in highly idealized numerical simulations of a convective cloud field in a rotating environment. The error growth characteristics feature a high level of agreement with the analytical predictions. The results of this thesis suggest that the geostrophic adjustment following convective heating governs upscale error growth through the atmospheric mesoscales.Die atmosphärischen Mesoskalen beinhalten dynamische und thermodynamische Prozesse, die durch Längenskalen von einigen bis zu einigen hundert Kilometern und Zeitskalen von Minuten bis zu einem Tag charakterisiert werden. Atmosphärische Strömungen auf diesem Skalenbereich werden als Wetter der mittleren Breiten verstanden und ihre verlässliche Vorhersage ist ein Hauptziel meteorologischer Forschung. Dabei treten zwei grundlegende Probleme auf: Erstens besteht kein Konsens darüber, welcher Prozess die mesoskalige Dynamik dominiert und insbesondere dem beobachteten horizontalen kinetischen Energiespektrum zugrunde liegt. Zweitens konnte bisher kein dominanter Skalenwechselwirkungsmechanismus bestimmt werden, auf dem das Anwachsen zunächst kleinskaliger Fehler zu großen Skalen basiert. Die vorliegende Dissertation trägt zu einem verbesserten Verständnis dieser beiden Aspekte bei, wobei der Fokus auf dem relativen Beitrag rotationeller und divergenter Moden des horizontalen Geschwindigkeitsfeldes und deren Wechselwirkung liegt. Eine fundamentale Überprüfung existierender Theorien bezüglich des horizontalen mesoskaligen Energiespektrums wird durch die Aufspaltung eindimensionaler atmosphärischer Windmessungen in rotationelle und divergente Anteile ermöglicht. Eine dementsprechende eindimensionale Helmholtz-Zerlegungsmethode wurde kürzlich veröffentlicht. Diese Aufspaltung basiert auf den mathematischen Annahmen der Homogenität und Isotropie, deren Gültigkeit im ersten Teil der vorliegenden Dissertation getestet wird. Dazu werden neue, hochaufgelöste globale numerische Simulationen der Atmosphäre verwendet. Die rotationellen- und divergenten Strömungsanteile werden mit der Helmholtz-Zerlegungsmethode aus eindimensionalen Segmenten des Windfeldes abgeleitet. Diese werden dann mit den rotationellen und divergenten Beiträgen des zweidimensionalen Windfeldes, welche als Referenz verwendet werden, verglichen. Die mathematischen Annahmen der eindimensionalen Helmholtz-Zerlegungsmethode sind auf den Mesoskalen hinreichend gut erfüllt, so dass hier das mesoskalige Verhältnis rotationeller zu divergenten Geschwindigkeitsmoden korrekt reproduziert werden kann. Beide Anteile des horizontalen Windfeldes zeigen des Weiteren eine signifikante Abhängigkeit von dem betrachteten Höhen- und Breitengradbereich. Die Ergebnisse deuten darauf hin, dass die mesoskalige Dynamik und das damit verbundene horizontale kinetische Energiespektrum nicht universell sind. Aktuelle Studien zeigen, dass das schnelle Anwachsen kleinskaliger Fehler in numerischen Wettervorhersagen vor allem mit der konvektiven Instabilität und dem Freisetzen latenter Kondensationswärme in Wolken zusammenhängt. Während die Fehler auf größere Skalen expandieren, ändert sich die dominante Dynamik von signifikant divergent zu primär rotationell. Der zweite Teil dieser Dissertation erforscht, ob diesem dynamischen Übergang die geostrophische Anpassung nach dem Einsetzen von Feuchtkonvektion zugrunde liegt. Dabei wird sowohl ein analytischer- als auch ein numerischer Ansatz verfolgt. Zunächst wird ein analytisches Modell für die geostrophische Anpassung einer instantanen Wärmefreisetzung (repräsentativ für den Fehler innerhalb der Vorhersage einer Wolke) entwickelt. Die gefundene Lösung ist die Greensche Funktion der betrachteten linearisierten, hydrostatischen Boussinesq-Gleichungen und enthält explizit die zeitliche Entwicklung aller transienten und balancierten Strömungsanteile. Die charakteristischen Raum- und Zeitskalen des geostrophischen Anpassungsprozesses werden aus dieser Lösung bestimmt. Ferner werden drei Diagnostiken entwickelt, mithilfe derer dieser Mechanismus in numerischen Simulationen identifiziert werden kann. Die analytischen Ergebnisse werden danach mit Fehlerwachstumsexperimenten in idealisierten numerischen Simulationen eines konvektiven Wolkenfeldes in einer rotierenden Umgebung getestet. Die gefundenen Eigenschaften des Fehlerwachstums stimmen sehr gut mit den Vorhersagen des analytischen Modells überein. Damit unterstützen die Ergebnisse dieser Dissertation die Hypothese, dass die geostrophische Anpassung konvektiver Wärmefreisetzung das Fehlerwachstum durch die atmosphärischen Mesoskalen bestimmt

Observational and theoretical study of squall line evolution, An

May 29,1992.Includes bibliographical references.Sponsored by National Oceanic and Atmospheric Administration NA90RAH00077.Sponsored by National Science Foundation ATM-9015485