Unresolved Waves Research Articles

Modulation of microwave radiance by internal waves: critical point modeling of ocean observations

Microwave polarimetric radiance measurements of the ocean surface have revealed some characteristic modulations in response to strong internal waves. This paper demonstrates that the major features of these modulations are all consistent with a model that evaluates the response of radiance to the modulation of surface roughness. This is a two-scale model that divides the spectrum of unresolved waves into a short and a long wavelength domain. The short wave "critical point" model, which evaluates resonant interactions occurring when the surface roughness scale and microwave wavelengths are comparable, is based on the solution of Gershenzon et al. (1986), to the simpler problem of determining the effect on the emissivity of a monochromatic wave propagating in direction /spl phi/ with respect to the incidence plane. The model of the response of radiance to the modulation of long unresolved waves uses the Kirchhoff approximation and Gaussian slope probability function. This second contribution to the radiance modulation is not significant with respect to the dominant features of the observations, but it could contribute to some of the more subtle features.

Comprehensive simulation of the middle atmospheric climate: some recent results

This study discusses the results of comprehensive time-dependent, three-dimensional numerical modelling of the circulation in the middle atmosphere obtained with the GFDL “SKYHI” troposphere-stratosphere-mesosphere general circulation model (GCM). The climate in a long control simulation with an intermediate resolution version (≈3° in horizontal) is briefly reviewed. While many aspects of the simulation are quite realistic, the focus in this study is on remaining first-order problems with the modelled middle atmospheric general circulation, notably the very cold high latitude temperatures in the Southern Hemisphere (SH) winter/spring, and the virtual absence of a quasi-biennial oscillation (QBO) in the tropical stratosphere. These problems are shared by other extant GCMs. It was noted that the SH cold pole problem is somewhat ameliorated with increasing horizontal resolution in the model. This suggests that improved resolution increases the vertical momentum fluxes from the explicitly resolved gravity waves in the model, a point confirmed by detailed analysis of the spectrum of vertical eddy momentum flux in the winter SH extratropics. This result inspired a series of experiments with the 3° SKYHI model modified by adding a prescribed zonally-symmetric zonal drag on the SH winter westerlies. The form of the imposed momentum source was based on the simple assumption that the mean flow drag produced by unresolved waves has a spatial distribution similar to that of the Eliassen-Palm flux divergence associated with explicitly resolved gravity waves. It was found that an appropriately-chosen drag confined to the top six model levels (above 0.35 mb) can lead to quite realistic simulations of the SH winter flow (including even the stationary wave fields) through August, but that problems still remain in the late-winter/springtime simulation. While the imposed momentum source was largely confined to the extratropics, it produced considerable improvement in the simulation of the equatorial semiannual oscillation, with both the easterly and westerly phases being somewhat more intense than in the control simulation. A separate experiment was conducted in which the SKYHI model was simplified so that it had no topography and so that the seasonal cycle was frozen in perpetual equinox conditions. These changes result in a model that has much reduced interhemispheric asymmetry. This model spontaneously produces a long period mean flow oscillation of considerable amplitude in the tropical upper stratopause. The implication of this result for the general issue of obtaining a QBO in comprehensive GCMs is discussed.

Eddy Rossby wave frequency in β-plane turbulence

The concept of eddy viscosity is generalized to include an ‘‘eddy β-term’’ that accounts for the effect of unresolved turbulence and Rossby waves on the resolved modes in the subgrid-scale representation of β-plane turbulence.

Galerkin/least-squares finite element methods for the reduced wave equation with non-reflecting boundary conditions in unbounded domains

Finite element methods are constructed for the reduced wave equation in unbounded domains. Exterior boundary conditions for a computational problem are derived from an exact relation between the solution and its derivatives on an artificial boundary by the DtN method, precluding singular behavior in finite element models. Galerkin and Galerkin/least-squares finite element methods are presented. Model problems of radiation with inhomogeneous Neumann boundary conditions in plane and spherical configurations are employed to design and evaluate the numerical methods in the entire range of propagation and decay. The Galerkin/least-squares method with DtN boundary conditions is designed to exhibit superior behavior for problems of acoustics, providing accurate solutions with relatively low mesh resolution and allowing numerical damping of unresolved waves. General convergence results guarantee the good performance of Galerkin/least-squares methods on all configurations of practical interest. Numerical tests validate these conclusions.

Estimates of Time and Space Scales at 300 Meters in the Midlatitude North Pacific from the TRANSPAC XBT Program

Estimates of length and time scales of temperature variability at 300 meters in the midlatitude North Pacific are made. Data are XBT traces collected from 1976 to 1984 in the TRANSPAC Volunteer Observing Ship program. Temperatures at 300 meters are grouped in two-mouth bins and gridded using the Surface II mapping program. Temperature variance about the time mean is largest in the Kuroshio Extension and nearly constant in the eastern North Pacific. A cooling trend occurred in the eastern North Pacific over the eight years of the dataset. In the western Pacific, the annual cycle is most intense 1°–2° north of the Kuroshio Extension, with an indication of meridional propagation away from the region of most intense variability. Propagation of annual waves in the eastern Pacific was predominantly northwestward. Wavenumber and frequency spectra are computed from normalized temperatures with the mean and bimonthly average removed in order to eliminate the dominant annual cycle. Based on the overall temperature variance, the North Pacific was divided into western and eastern regions. Zonal wavenumber and frequency spectra and two-dimensional ω/k spectra were computed for a number of latitudes in the eastern and western regions. Two-dimensional k/l spectra were also computed for the western and eastern regions. The spectra indicate westward propagation throughout the midlatitude North Pacific with additional eastward propagation in the Kuroshio Extension region, shorter length and time scales in the Kuroshio Extension compared with other regions, and slight dominance of southwestward propagation in bath the eastern and western North Pacific. Tests to determine the effective spatial resolution of the dataset indicate that local average-station spacing is a good measure of local Nyquist wavelength. However, because of the nearly random sampling in a spatially limited region, an unresolved wave is aliased more or less in a band stretching towards low wavenumber rather than folded in coherent, predictable locations in the spectrum. With the choice of a two-month time bin, spectra are about equally aliased in space and time, with Nyquist wavelength and period close to the beginning of energy rolloff reported in other surveys, which have better spatial resolution but less degrees of freedom.

The use of geomagnetic pulsations in determining magnetospheric plasma properties

The existence of cold or cool heavy ions in the magnetospheric plasma of the earth has been known since early GEOS-I ion composition experiment results in 1977 (Geiss et al. 1978). Helium (He+) and oxygen (O+) relative concentrations of up to 50% of the total ion concentration were found. The reliability of these particle concentrations are difficult to estimate. Unresolved wave modulations, giving rise to plasma flows and other problems including spacecraft charging. make concentration measurements difficult. Mauk (1984) has recently shown, by computer simulation, that particle concentrations measured in association with linear interaction between a wave and He+ ions may be artificially inflated by an order of magnitude. An extremely simple and sensitive measure of heavy ion (He+, O+) relative ion concentrations can be made using the bounding surfaces associated with the propagation of ion cyclotron waves in a multicomponent cold plasma. Obviously, measurements can be made only in thc prcsence of ion cyclotron wave energy which occurs in the Pcl?2 geomagnctic pulsation frequency range (0.1?5 Hz).

Structure and dynamics of Saturn's rings as seen by the Voyager stellar occultation

The stellar occultation of δ Scorpii by Saturn's rings shows radial structure in Saturn's rings down to the resolution element of ~100m. Density waves, embedded moonlets, and other proposed mechanisms are insufficient to explain the observed structure. A limit of less than 100 density waves are likely to be found in the rings in the current data. Unresolved waves do not seem to play a major role, either. A detailed search and histogram of optical depth in the outer B ring show no evidence of embedded moonlets. The mass of Saturn's rings is 5(±3) x 10-8of Saturn's mass. Power spectra of the rings show no dominant individual wavelengths: we do not see any preferred size for radical structure in the rings. A straightforward comparison of earth-based photometry and the viscosity and mass density of the rings inferred from density wave observations leads to a model of the rings that is many-particles thick. The vertical thickness of the rings would be about 50 m.