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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

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This paper discusses signal processing techniques being developed for making Doppler wind velocity measurements using airport surveillance radars. Techniques are presented and evaluated for velocity estimation using fast-rotating radars. In addition to their fast rotation rates airport surveillance radars employ block-staggered pulse repetition rates to enhance their detection of aircraft. The effect of this transmission strategy on the weather processor clutter filter is examined. The performance of the proposed algorithms are examined as a function of the weather signal spectral width and the ground clutter/weather signal ratio.

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John R. Anderson and John R. Gyakum

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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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John R. Christy, Kevin E. Trenberth, and John R. Anderson

Abstract

Seven years of daily global surface pressure (Ps,) analyses derived from European Centre for Medium Range Forecasts (ECMWF) data are examined to describe more fully interhemispheric mass exchanges and intraseasonal variability. Extreme events in hemispheric mean Ps are determined, and composited grid point differences show that hemispheric anomalies are mainly determined by pressures in the North Pacific, western North Atlantic, northern Asia and the Southern Hemisphere (SH) circumpolar trough. Seasonal differences in the composites indicate that the regional anomalies occur farther poleward in the winter hemisphere, and the tropical anomalies tend to have the same sign as that of the summer hemispheric mean anomaly.

Long-lasting, localized, extreme Ps anomalies are identified in 18 significant events of hemispheric mass imbalance, and are found to be highly favored when the hemispheric mean departs significantly from normal. The result implies that regionally persistent anomalies are related to global-scale mass redistributions, rather than being totally the result of more localized redistributions.

The global atmospheric angular momentum exhibits significant changes during interhemispheric mass imbalances that exceed one standard deviation (about 0.4 mb). There is a strong tendency for the hemisphere in which a deficit of mass occurs to experience, on average, a 5% increase in hemispheric angular momentum.

Zonal complex empirical orthogonal functions are used to describe the Ps cos ϕ anomalies, filtered for 30–75 day fluctuations. Dominant modes are found in which each hemisphere, independently, produced intrahemispheric exchanges between polar and temperate latitudes. An interhemispheric mode indicates exchanges of mass between the midlatitudes of the Northern Hemisphere and the entire tropics plus the SH subtropics. The interhemispheric mode displays a southward propagation of anomalies from the tropical belt into the SH.

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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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Jerry M. Straka and John R. Anderson

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In the first part of this paper, the characteristics of microburst-producing storms are examined with a three-dimensional cloud model using soundings from the Cooperative Huntsville Meteorological Experiment (COHMEX). With a grid resolution of 500 m, it is shown that the general characteristics of observed vertical velocities, vertical draft sizes, water contents, radar reflectivities, and surface outflow strengths can be simulated. In addition, observed microburst precursors such as midlevel convergence and descending precipitation cores can also be simulated. Using a grid resolution of 250 m, the observed structure of a particularly well-documented storm on 20 July 1986 during COHMEX is simulated, including a hail shaft 1–2 km wide that descended to the ground.

In the second part of this paper, the influence of microphysical processes in the production of low-level downdrafts in simulated COHMEX storms is investigated. It is shown that low-level downdrafts are in some cases stronger and deeper in simulations made with the ice phase than in simulations made without the ice phase. These differences are due, in part, to the additional cooling associated with the melting of ice, and are consistent with findings of several other recent studies of low-level downdraft production in deep convective storms.

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Leigh G. Orf and John R. Anderson

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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 and Duane E. Stevens

Abstract

The tropical response to a localized thermal forcing with approximately 45-day period is investigated for several models of increasing complexity consisting of two equivalent shallow water system and two fully stratified systems. The fully stratified models appear to be able to reproduce a number of observed features of the tropical 40–50 day oscillation including the modulation of the subtropical jet and the eastward and poleward propagation of zonal wind anomalies.

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John R. Anderson and Richard D. Rosen

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Quasi-periodic variations in the relative angular momentum of the atmosphere on time scales of around 40–50 days have been observed by Langley et al. (1981). A description of the two-dimensional (latitude-height) structure of the winds responsible for these changes is constructed here from five years of NMC twice-daily global analyses. Using cross-spectral and amplitude-phase eigenvector techniques, we find these variations are associated with wavelike motions in the tropical upper troposphere that propagate and downward in phase within the tropics. A coherently connected midlatitude Northern Hemisphere component is also present whose phase is essentially independent of height. We believe the tropical component to be the zonally averaged part of the motions described by Madden and Julian (1971, 1972). The Northern Hemisphere midlatitude component may be a direct response to the tropical motions or both motions may be the common response to an as yet unidentified tropical forcing.

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John R. Anderson and Duane E. Stevens

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The linear, zonally symmetric modes of the basic state of a Hadley cell are examined. We find that the inclusion of the divergent basic state leads to the formation of a new class of slowly oscillating modes, some of which have periods in the range of 40–50 days. The modes have many features in common with the observed tropical 40–50-day oscillation; however, an explanation for the observed fluctuations in convective cloudiness remains a topic for future work.

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