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Joseph Egger

Abstract

Cyclogenesis in the lee of long north-south barriers is studied by use of a numerical weather prediction model. Lee-side development is simulated by the model if an initial situation is chosen, which is favorable for lee cyclogenesis, i.e., a low approaching the barrier from the west in a baroclinic current. Cyclogenesis is investigated in the lee of a barrier of 4000 km length and 2000 m height, which is comparable to the Rocky Mountains, and of another one, which is similar to the massif of Greenland. In both cases, the divergence equation and the vorticity equation are analyzed at the point of greatest pressure fall in the Ice to find out the causes of the lee-side development.

Pressure fall begins when the parent low approaches the barrier. It is caused by the warm air that is crossing the barrier in front of the approaching center of low pressure. Vorticity advection aloft is of no importance in the Rocky Mountains case and influences the surface pressure only during the final period of pressure fall in the Greenland case. The development is terminated when the cold front of the parent low passes over the new center of low pressure in the lee. An attempt is made to compare the predictions of the model to observations in the lee of the Rocky Mountains and of Greenland.

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Joseph Egger

Abstract

The mechanism of baroclinic instability in the Eady model is interpreted by explicitly calculating the ageostrophic circulations related to the model’s hyperbolic basic functions. It is advantageous to perform the analysis at the midlevel where the model’s “barotropic” mode provides the streamfunction and the “baroclinic” mode represents the temperature. These modes interact and instability occurs if the horizontal advection of background potential temperature by the barotropic mode dominates over the vertical one because of the same mode at the midlevel. A rather simple picture of the stable as well as the unstable flow configurations emerges. Other interpretations are discussed briefly.

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Joseph Egger

Abstract

Coriolis terms proportional to cosφ are omitted in the conventional theory of inertial motions, which predicts horizontal oscillations of frequency f for f-plane geometries in the absence of horizontal and vertical pressure gradients. If this approximation is removed, an oscillation is found within the framework of linear theory that comes rather close to the conventional inertial mode. Motions are quasi-horizontal and the frequency is almost equal to f. However, oscillations vanish at the ground in contrast to the standard theory. Gravity, compressibility, and, in particular, pressure gradient forces are important to this oscillation in addition to Coriolis forces.

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Joseph Egger

Abstract

The spurious numerical generation and/or destruction of various types of entropies in models is investigated. It is shown that entropy s θ of dry matter tends to be generated if potential temperature is advected by a damping scheme. There is no mean tendency of entropy if the reversible leapfrog scheme is used. Generalized entropies can be assigned to conserved quantities. In particular, the generalized entropy s ζ of the vorticity of two-dimensional nondivergent flow is shown to grow in presence of irreversible diffusive processes. This entropy increases numerically if the vorticity equation is integrated with an upstream scheme. There are weak oscillations of s ζ if a leapfrog time step is combined with the Arakawa scheme. Similar results are obtained for an entropy s p related to potential vorticity. Information entropy provides a gross measure of the information contained in ensemble forecasts. It is shown that information entropy decreases spuriously if schemes are used that are contracting in phase space. It is argued that the evaluation of entropies provides a useful check of the quality of numerical schemes.

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Joseph Egger

Abstract

It is proposed to monitor the conservation of “material” volumes in the phase space of a numerical model. In principle, strict volume conservation is required for reversible flow problems. In particular, the phase space volume occupied by the initial distribution of an ensemble forecast should not change in time for such flows. It is not obvious to what extent numerical schemes satisfy this requirement. A corresponding test for volume conservation is designed. Euler, upstream, Lax–Wendroff and Runge–Kutta schemes are exposed to this test as well as a time centered implicit scheme and the leapfrog method. Members of the former group are numerically irreversible, while those of the latter are reversible in time. Tests are performed for gridpoint representations of advection equations and of one-dimensional inviscid shallow-water flow. The numerically irreversible schemes exhibit spurious contraction or expansion. The error is O(C) for the upstream scheme and O(C 2) for all the other irreversible schemes except fourth-order Runge–Kutta (C is the Courant number). The implicit scheme conserves volume for reversible flow problems. It is a surprising result that the leapfrog scheme conserves volume for any type of equations. Applications to Monte Carlo forecasts are presented. It is shown that clouds of initial states contract or expand indeed as predicted by the test in the early stages of an integration. This affects the quality of the Monte Carlo forecast.

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Joseph Egger

Abstract

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Joseph Egger

Abstract

Lateral momentum transport by gravity waves is investigated within the framework of a linear steady-state model of inviscid, nonrotating flow over and around orography. Obstacles protruding laterally from massifs are considered as well as more conventional shallow mountains. For flow around obstacles, an analytic solution to the three-dimensional gravity wave equations with a lateral radiation condition is derived for constant zonal mean flow and stability. Laterally propagating gravity waves transport momentum toward the mountain if a rigid lid is imposed. Downward transports are important as well if the lid is removed. These results are compared to those obtained on the basis of the shallow mountain approximation.

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Joseph Egger

Abstract

A shallow inversion layer with southeasterly outflow and a cyclonic vortex in the troposphere are the basic characteristics of the Antarctic mean circulation. An attempt is made to model this pattern in a two-layer representation of the atmosphere where all equations are averaged horizontally over the Antarctic domain. Cooling at the slope drives a direct circulation that acts as a source of westerly angular momentum. This momentum is transferred out of Antarctica by topographically modified large-scale waves, enforced at the northern boundary of the model. Two types of steady states are found for fixed frequency and zonal wavenumber: one where the wave is quite effective in performing the required momentum transport so that a qualitatively realistic circulation results and another one with strong upper-level westerlies but virtually no surface easterlies. A model climatology can be derived if stochastic forcing is added to the equations. It turns out that the distribution of the flow states is centered near a “realistic” equilibrium if a wave spectrum is prescribed at the northern boundary according to observations.

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Joseph Egger

Abstract

The stochastic model of Weickmann et al. for the global angular momentum budget is modified to become applicable to latitude belts. In particular, a Langevin equation is added for the flux divergence of angular momentum in a belt. The friction torque Tf is assumed to be purely damping with respect to angular momentum M. The mountain torque To is generated by red noise but also damps angular momentum directly as suggested by recent stochastic models. The model parameters are tuned such that the variances of all model variables come close to the observations. The corresponding equations for the covariance functions of all variables are solved analytically. The results are compared to observations for selected belts. It is found that the model captures the observed decay rates of all covariance functions. The covariance of the flux divergence and the angular momentum is simulated successfully for positive lags but rarely for negative ones. The covariance of friction torque and angular momentum is reproduced reasonably well. The model is also successful with respect to the covariance of mountain torque and M in the Tropics, but there are large discrepancies at midlatitudes because the observed mountain torque events are accompanied by flux divergences in these belts.

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Joseph Egger

Abstract

Although mountains are generally thought to exert forces on the atmosphere, the related transfers of energy between earth and atmosphere are not represented in standard energy equations of the atmosphere. It is shown that the axial rotation of the atmosphere must be included in the energy budget in order to resolve this issue. The energy transfer resulting from mountains turns out to be closely related to mountain torques. The energetic effects of a changing rotation of the earth are discussed, as well as those of friction torques and those of the nonspherical shape of the earth.

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