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John W. Miles

Abstract

A variational principle and an associated integral invariant are constructed for two-dimensional (non-divergent) waves of permanent form in a Rossby β-plane. A solitary-wave solution is obtained, and it is shown that the effects of cubic nonlinearity may be comparable with those of quadratic nonlinearity and may limit the amplitude of the wave.

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John W. Miles

Abstract

A zonal-wind configuration in which wind speed is proportional to pressure-altitude and stability is proportional to the square of the density is posed. A solution to the eigenvalue problem governing the stability of this configuration with respect to small disturbances is obtained in terms of hypergeometric functions. It is proved that one and only one (exponentially) unstable mode exists for each point in a wavelength, wind-shear plane.

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John W. Miles

Abstract

An approximate solution of the eigenvalue problem governing the stability of the zonal wind with respect to small disturbances of long wavelength is developed for profiles with strong, positive-definite vertical shear. It is found that certain disturbances, characterized by positive phase velocities, appear to be stable on the basis of a first approximation but are unstable in higher approximations. The results, together with the previously established instability for short wavelengths and/or weak vertical shear, support the conjecture that typical zonal-wind configurations are unstable with respect to small disturbances of almost all wavelengths at almost all windspeeds.

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John W. Miles

Abstract

The baroclinic instability problem is reformulated to include diffusion of both heat and momentum through conduction and viscosity. A priori arguments suggest that the effects of heat conduction should dominate those of viscosity in the critical layer, where local wind speed equals wave speed and the adiabatic model for small disturbances is not uniformly valid. An asymptotic solution of the singular perturbation problem (based on the hypothesis that the Peclet and Reynolds numbers tend to infinity) supports this conjecture but also implies that the effects of diffusion on baroclinic instability are negligible insofar as the critical layer is within the geostrophic regime of the mean flow. This last condition is satisfied for the disturbances of principal meteorological interest.

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Bryan G. White
,
Jan Paegle
,
W. James Steenburgh
,
John D. Horel
,
Robert T. Swanson
,
Louis K. Cook
,
Daryl J. Onton
, and
John G. Miles

Abstract

The short-term forecast accuracy of six different forecast models over the western United States is described for January, February, and March 1996. Four of the models are operational products from the National Centers for Environmental Prediction (NCEP) and the other two are research models with initial and boundary conditions obtained from NCEP models. Model resolutions vary from global wavenumber 126 (∼100 km equivalent horizontal resolution) for the Medium Range Forecast model (MRF) to about 30 km for the Meso Eta, Utah Local Area Model (Utah LAM), and Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model Version 5 (MM5). Forecast errors are described in terms of bias error and mean square error (mse) as computed relative to (i) gridded objective analyses and (ii) rawinsonde observations. Bias error and mse fields computed relative to gridded analyses show considerable variation from model to model, with the largest errors produced by the most highly resolved models. Using this approach, it is impossible to separate real forecast errors from possibly correct, highly detailed forecast information because the forecast grids are of higher resolution than the observations used to generate the gridded analyses. Bias error and mse calculated relative to rawinsonde observations suggest that the Meso Eta, which is the most highly resolved and best developed operational model, produces the most accurate forecasts at 12 and 24 h, while the MM5 produces superior forecasts relative to the Utah LAM. At 36 h, the MRF appears to produce superior mass and wind field forecasts. Nevertheless, a preliminary validation of precipitation performance for fall 1997 suggests the more highly resolved models exhibit superior skill in predicting larger precipitation events. Although such results are valid when skill is averaged over many simulations, forecast errors at individual rawinsonde locations, averaged over subsets of the total forecast period, suggest more variability in forecast accuracy. Time series of local forecast errors show large variability from time to time and generally similar maximum error magnitudes among the different models.

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