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Edwin F. Danielsen

Abstract

Vertical cross sections of potential vorticity, computed and contoured by band, and hemispheric distributions of potential vorticity, computed and contoured by machine, are compared to both discrete and continuous measurements of radioactivity made during Project Springfield. Comparisons made in the upper troposphere and lower stratosphere show a positive correlation between potential vorticity and radioactivity of stratospheric origin. The radioactivity measurements and machine-computed isentropic trajectories prove that stratospheric air from high latitudes is transported southward and downward into the troposphere as the tropopause folds. Changes in potential vorticity and the concentration of radioactivity along the trajectories also prove that subsynoptic-scale mixing destroys the extruded stratospheric layer in the troposphere. The mass outflow from stratosphere to troposphere associated with tropopause folding is compensated by a quasi-steady inflow along the tropopause. This inflow is necessary to maintain the large radioactivity gradients observed at the tropopause and to amount for the observed mixing of stratosphere and tropospheric tracers on the stratospheric side of the tropopause. Tropospheric air entering the stratosphere at low latitudes with large values of potential temperature acquires radioactivity, ozone and potential vorticity by mixing in the stratosphere. Radiative cooling at high latitudes systematically moves the mixture to lower potential temperature levels in the cyclonic stratosphere, where the large-scale baroclinic waves transport it southward and the amplifying vortices fold it into the troposphere.

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Edwin F. Danielsen

Abstract

A potential vorticity theorem and its two summary statements published by Haynes and McIntyre are challenged conceptually by equations, discussions and examples. The apparent simplification proposed by the authors to convert from a mass to volume integral, i.e., by cancelling density against the specific volume in the potential vorticity, changes the physical significance of the integrand. It no longer is the potential vorticity. The resulting mean for either a bulk Eulerian or Lagrangian system is then not analogous to a mixing ratio and therefore not independent of the broad spectrum of internal waves, the independence that makes Ertel's potential vorticity so valuable either as a stratospheric tracer or as a predictive or diagnostic, large scale, meteorological variable.

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Edwin F. Danielsen

Abstract

An objective method for deriving the components of a generalized transport tensor for a two-dimensional model is presented. The method uses representative meridional and vertical velocities and thermodynamic scalars at a uniform grid to reduce the problem to solving two flux equations for two unknowns. One unknown is the streamfunction, coefficient of an antisymmetric tensor, which corrects the Eulerian mean motions for Stokes drift. The other is a time constant, which converts the deviatory velocity tensor (Reynold's stress tensor for temporal averaging) to a symmetric transport tensor. The complete asymmetric tensor is called a transport rather than a diffusion tensor because its divergence yields both advection and diffusion by the deviatory velocities. Advantages and disadvantages of Lagrangian and Eulerian averages are also discussed.

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Edwin F. Danielsen

Abstract

Vertical and horizontal deviations between an air trajectory and isobaric and isentropic trajectories are presented in a convenient form for order-of-magnitude comparisons and interpretation. Also, an objective method for computing isentropic trajectories is developed which is based on the total-energy equation.

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Edwin F. Danielsen
and
Rainer Bleck

Abstract

The mountain lee-wave problem is solved for a steady-state linearized model yielding both real and complex resonance modes. Filters applied to the wind and potential temperature determine the mean conditions and the number of layers required. Continuity of the wavenumber at the layer interfaces excludes spurious resonance modes. For multilayer models the solutions usually include six to nine waves ducted in the stratosphere and one wave ducted in the troposphere. Changing the tropospheric duct changes the tropospheric resonant wavelength and modulates the amplitude of the stratospheric waves. Progressive lowering of the top of the stratospheric duct from infinity changes the horizontal wavenumber of the longest waves from real to complex. These radiating waves dampen downstream from the mountain. Rotor pairs and steps in the stratospheric streamlines, generated when the ducting is strong, suggest sources of clear air turbulence. Large-amplitude tropospheric waves, thought to produce shock waves and strong surface winds, are shown to be caused by a strong shear of the mean wind in the lower troposphere and by horizontal wavelengths approaching 2π times the half-width of the mountain barrier.

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E. Paul McClain
and
Edwin F. Danielsen

Abstract

The thermal structure of the troposphere and lower stratosphere during the movement eastward of several Pacific troughs is examined primarily from the standpoint of the distribution of baroclinity within a vertical plane extending across the northwestern and north central United States. Baroclinity is defined and then expressed in a form suitable to the potential-temperature cross-sections employed in this study. Dominating features of the thermal field are two types of baroclinic zones: (1) broad and essentially non-frontal zones which form the leading and trailing edges of deep, rapidly moving cold domes in the middle and upper troposphere; (2) narrow, frontal type zones comprising the leading or trailing edges of either slowly-moving, low-level cold domes or rapidly-moving, upper-level ones. There is evidence that the non-frontal baroclinic zones are equally as important, both dynamically and synoptically, as the frontal ones.

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DALE A. LOWRY
and
EDWIN F. DANIELSEN

Abstract

The most striking shortcomings of previous 1000-mb. forecast models have been over-intensification of pressure systems, especially anticyclones, and inferior predictions in and near mountains. In this article a graphical-numerical two-level prediction model that incorporates a variable mean stability is developed and tested. When the mean stability is small, the 1000-mb. prediction is determined primarily by the 500-mb. steering and height changes. As the stability increases the 500-mb. control decreases and the effective mountain wind exerts more control over the 1000-mb. changes, Since the stability is generally larger in anticyclones than cyclones the anticyclones are steered by a smaller percentage of the 500-mb. wind and are more influenced by the mountain topography.

Twenty-four-hour forecasts were handproduced daily for the month of September 1965. Predictions were also prepared using a constant stability model, and the forecasts of the two models were compared statistically by rigorous verification techniques. It was found that a definite improvement in the overall product can be expected by application of the variable stability model as opposed to the constant stability technique, especially in the mountainous areas and around anticyclones.

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