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John R. Anderson

Abstract

The local spectral method is a minimum aliasing technique for the discretization and numerical integration of prognostic systems consisting of nonlinear partial differential equations. The technique embodies many features of both spectral transform methods and conventional finite difference techniques. The method is derived by applying a digital filtering approximation to a formulation of the nonlinear problem similar to the formulation that leads to the spectral transform method, and shares many of the desirable performance characteristics of that method. In contrast to the spectral transform method, the local spectral method can be implemented on a parallel processing computer system without requiring each processor to have a global knowledge of the values of variables in order to compute spatial derivatives. In addition to the computational virtues of the scheme, the local spectral method should have considerable promise as a high performance scheme for limited area models as appropriate boundary conditions are developed.

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John R. Anderson
and
John R. Gyakum

Abstract

The interannual and intraseasonal track variability of cold season extratropical cyclones in the Pacific basin is examined using an 8 year cyclone track dataset. An EOF technique incorporating VARIMAX rotation in time is used to objectively describe the regime nature of the variations. Based upon this analysis we conclude that the cyclone behavior can be classified into six major regime types, corresponding to the positive and negative amplitude excursions of each of the first three rotated EOFS. Each of these rotated EOFs explains approximately equal fractions of the total variance. A study of the cyclone tracks for individual extreme periods confirms the existence of times where each of these patterns dominate. The average 500 mb height fields for these extreme periods have been examined and are generally consistent with the cyclone track anomalies. The resultant regime description shows strong interannual variability; however, there appears to be little obvious correlation with the ENSO signal, suggesting that a significant fraction of the interannual variability may be generated within the middle and high latitudes.

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Jerry M. Straka
and
John R. Anderson

Abstract

The minimal aliasing local spectral (LS) method is a numerical technique that embodies features of both finite-difference (FD) and spectral transform (ST) methods. Anderson first described this method in the context of the one-dimensional advection-diffusion equation. In the current paper, we describe the extension of the LS method to multidimensions. First, we review the one-dimensional version of the LS method from a more rigorous view. In addition, we describe interpolation, differentiation, and dealiasing fitters for the LS method based on Lagrange polynomials. Without the dealiasing filters, this version of the LS method collapses to a standard high-order Taylor series FD scheme. When filter lengths span the integration domain and the dealiasing stage is retained, the LS method becomes an ST method, as described by Anderson. Issues concerning the implementation of the LS method in multidimensions are also discussed. These issues include the form of the high-resolution grid, the implementation of the interpolation stage, and the implementation of the dealiasing stage. Then, we test the LS method with a two-dimensional nonlinear density current problem using idealized boundary conditions. Comparisons are made with a high-resolution reference solution from a reference model, as well as with solutions from a high-order FD model. Results from simulations of the test problem demonstrate that the LS method is more accurate than high-order FD schemes at coarse grid resolutions, and as accurate at finer grid resolutions. Furthermore, the results show that solutions from LS models are more robust than solutions from FD models. After this, we show that dealiasing the nonlinear advection tendencies plays an important role in the success of the LS method, especially for simulations with sharp boundaries that are marginally resolved. For adequately resolved flows, dealiasing does not necessarily improve solutions for the short-term integrations that are presented. However, aliasing errors still must be controlled to prevent a catastrophic buildup of energy at the smallest resolvable wavelengths. Finally, the LS method is tested using open lateral boundary conditions. As the LS method is a higher-order scheme, special treatment of the vertical and lateral boundaries is required. One possibility is to use lower-order versions of the LS method as boundaries are approached, and outflow conditions at the lateral boundaries. This simple treatment results in solutions that compare very favorably to the reference solution of the test problem.

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Leigh G. Orf
and
John R. Anderson

Abstract

An analysis of traveling microbursts in unidirectionally sheared environments is undertaken using a three-dimensional numerical model with 50-m resolution in a 19 × 12 × 4 km domain. For each run, the cooling source is centered at a height of 2 km and travels in an eastward direction of C m , where C m = 3, 6, 9, 12, and 15 m s−1. Environmental winds above 2 km are equal to C m and decay linearly to 0 m s−1 below 2 km. The authors examine the kinetic energy budget of each run, focusing on the dynamic features that are not found in a static microburst simulation. As the source speed C m increases from 0 to 9 m s−1, the magnitude of the surface horizontal winds increase in the direction of source movement. An examination of the dynamic pressure equation shows that rotationally induced pressure work forces are primarily responsible for increasing surface horizontal winds for the moving-source microbursts. In a similar form to previous studies of vertical perturbations in a sheared environment, elevated horizontal vorticity is generated by tilting of environmental vorticity and is strengthened by stretching imposed by the downdraft. The authors’ results suggest that the magnitude of the damaging surface winds of a microburst can be enhanced significantly when the parent cloud is moving in a unidirectionally sheared environment.

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John R. Anderson
,
Duane E. Stevens
, and
Paul R. Julian

Abstract

In recent years there has been a great deal of interest in a quasi-periodic tropical oscillation of zonal winds, which was first reported by Madden and Julian. An attempt to determine the temporal variation of the oscillation parameters is presented here. Using a 4-year duration global time series and a 25-year station time series, we find that although the nonseasonal variations are large, any seasonal cycle in the oscillation amplitude and frequency must be very small. The small seasonal signal in the oscillation frequency seems to argue against explanations for the time scale based on Doppler-shifted traveling waves.

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John R. Gyakum
,
John R. Anderson
,
Richard H. Grumm
, and
Elissa L. Gruner

Abstract

An eight year sample of cold-season (1 October through 31 March) extratropical cyclones in the, Pacific Ocean basin is used to study central pressure changes and life cycle characteristics.

We find that over 90% of the cyclones passing through the area of the Kuroshio Current intensify in this region. Corresponding percentages in excess of 60% extend from the Kuroshio, south of 45°N, eastward to 130°W. Mean 24-h central pressure falls of all cyclones exceed 9 mb through the entire basin west of 140°W in the latitude band 30° to 50°N.

A statistical analysis of 24-h central pressure changes is performed on all cyclones within our domain. A frequency distribution of 1996 cases of 24-h maximum deepening reveals statistically significant departures from a Gaussian distribution, with the coefficient of skewness substantially negative. We also find similarly significant departures from normal in a frequency distribution of all 24-h central pressure changes, in spite of the fact that this distribution would be expected to have relatively fewer nonlinear interactions of processes associated with maximum deepening. A stratification of these data into ten degree latitude bands reveals that the ocean-dominated areas south of 60°N all have significant departures from the normal distributions with significantly large negative values of skewness. The land and ice-dominated region between 60° and 70°N has a deepening rate distribution that is approximately Gaussian with coefficients of skewness and kurtosis within the confidence limits of a normal distribution. These results suggest that the underlying ocean surface may be responsible for the significant departures of the pressure change distribution from a normal distribution.

We find that explosively developing cyclones (defined as those systems whose central pressure falls at least 24 mb in 24 h at 45°N) have longer lifetimes than the more conventional lows. Approximately 74% of the explosive cyclones last for at least four days. Only 21% of the nonexplosive cases exist for as long as four days. The vast majority of rapid deepeners commence their maximum intensification within 24 h of their initial formation. Thus, a correct analysis and forecast of a newly formed cyclone appears crucial to a successful explosive cyclone simulation.

Although cyclone formation areas cover vast areas of the Pacific, especially those east of Japan, south of Alaska, and the surroundings of the Kamchatka Peninsula, explosive cyclone formation positions are almost exclusively south of 50°N, concentrated east of the Asiatic continent, and in an area between 150° and 160°W. The “bomb” maximum deepening positions are located in areas slightly to the north and east of their formation positions. Dissipation positions, while concentrated in the Gulf of Alaska, the northeast Pacific, and in an area west of Kamchatka for all systems, are almost exclusively confined to areas north of 50°N for the rapidly deepening cyclones.

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