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NASA NTRS1990

Integration of the shallow water equations on the sphere using a vector semi-Lagrangian scheme with a multigrid solver

A vector semi-Lagrangian semi-implicit two-time-level finite-difference integration scheme for the shallow water equations on the sphere is presented. A C-grid is used for the spatial differencing. The trajectory-centered discretization of the momentum equation in vector form eliminates pole problems and, at comparable cost, gives greater accuracy than a previous semi-Lagrangian finite-difference scheme which used a rotated spherical coordinate system. In terms of the insensitivity of the results to increasing timestep, the new scheme is as successful as recent spectral semi-Lagrangian schemes. In addition, the use of a multigrid method for solving the elliptic equation for the geopotential allows efficient integration with an operation count which, at high resolution, is of lower order than in the case of the spectral models. The properties of the new scheme should allow finite-difference models to compete with spectral models more effectively than has previously been possible.

Bates, J. R.↗

NASA NTRS1979

Explicit large time-step schemes for the shallow water equations

Modifications to explicit finite difference schemes for solving the shallow water equations for meteorological applications by increasing the time step for the fast gravity waves are analyzed. Terms associated with the gravity waves in the shallow water equations are treated on a coarser grid than those associated with the slow Rossby waves, which contain much more of the available energy and must be treated with higher accuracy, enabling a several-fold increase in time step without degrading the accuracy of the solution. The method is presented in Cartesian and spherical coordinates for a rotating earth, using generalized leapfrog, frozen coefficient, and Fourier filtering finite difference schemes. Computational results verify the numerical stability of the approach.

Turkel, E.↗

NASA NTRS2003

Deviation of Long-Period Tides from Equilibrium: Kinematics and Geostrophy

New empirical estimates of the long-period fortnightly (Mf) tide obtained from TOPEX/Poseidon (T/P) altimeter data confirm significant basin-scale deviations from equilibrium. Elevations in the low-latitude Pacific have reduced amplitude and lag those in the Atlantic by 30 deg or more. These interbasin amplitude and phase variations are robust features that are reproduced by numerical solutions of the shallow-water equations, even for a constant-depth ocean with schematic interconnected rectangular basins. A simplified analytical model for cooscillating connected basins also reproduces the principal features observed in the empirical solutions. This simple model is largely kinematic. Zonally averaged elevations within a simple closed basin would be nearly in equilibrium with the gravitational potential, except for a constant offset required to conserve mass. With connected basins these offsets are mostly eliminated by interbasin mass flux. Because of rotation, this flux occurs mostly in a narrow boundary layer across the mouth and at the western edge of each basin, and geostrophic balance in this zone supports small residual offsets (and phase shifts) between basins. The simple model predicts that this effect should decrease roughly linearly with frequency, a result that is confirmed by numerical modeling and empirical T/P estimates of the monthly (Mm) tidal constituent. This model also explains some aspects of the anomalous nonisostatic response of the ocean to atmospheric pressure forcing at periods of around 5 days.

Egbert, Gary D.↗

NASA NTRS2016

Traveling Weather Disturbances in Mars Southern Extratropics: Sway of the Great Impact Basins

As on Earth, between late autumn and early spring on Mars middle and high latitudes within its atmosphere support strong mean thermal contrasts between the equator and poles (i.e. "baroclinicity"). Data collected during the Viking era and observations from both the Mars Global Surveyor (MGS) and Mars Reconnaissance Orbiter (MRO) indicate that this strong baroclinicity supports vigorous, large-scale eastward traveling weather systems (i.e. transient synoptic-period waves). Within a rapidly rotating, differentially heated, shallow atmosphere such as on Earth and Mars, such large-scale, extratropical weather disturbances are critical components of the global circulation. These wave-like disturbances act as agents in the transport of heat and momentum, and moreover generalized tracer quantities (e.g., atmospheric dust, water vapor and water-ice clouds) between low and high latitudes of the planet. The character of large-scale, traveling extratropical synoptic-period disturbances in Mars' southern hemisphere during late winter through early spring is investigated using a high-resolution Mars global climate model (Mars GCM). This global circulation model imposes interactively lifted (and radiatively active) dust based on a threshold value of the instantaneous surface stress. Compared to observations, the model exhibits a reasonable "dust cycle" (i.e. globally averaged, a more dusty atmosphere during southern spring and summer occurs). In contrast to their northern-hemisphere counterparts, southern synoptic-period weather disturbances and accompanying frontal waves have smaller meridional and zonal scales, and are far less intense synoptically. Influences of the zonally asymmetric (i.e. east-west varying) topography on southern large-scale weather disturbances are examined. Simulations that adapt Mars' full topography compared to simulations that utilize synthetic topographies emulating essential large-scale features of the southern middle latitudes indicate that Mars' transient barotropic/baroclinic eddies are significantly influenced by the great impact basins of this hemisphere (e.g., Argyre and Hellas). In addition, the occurrence of a southern storm zone in late winter and early spring is keyed particularly to the western hemisphere via orographic influences arising from the Tharsis highlands, and the Argyre and Hellas impact basins. Geographically localized transient-wave activity diagnostics are constructed that illuminate fundamental differences amongst such simulations and these are described.

Weather disturbances↗

NASA NTRS2017

Extratropical Weather Systems on Mars: Radiatively-Active Water Ice Effects

Extratropical, large-scale weather disturbances, namely transient, synoptic-period,baroclinic barotropic eddies - or - low- (high-) pressure cyclones (anticyclones), are components fundamental to global circulation patterns for rapidly rotating, differentially heated, shallow atmospheres such as Earth and Mars. Such "wave-like" disturbances that arise via (geophysical) fluid shear instability develop, mature and decay, and travel west-to-east in the middle and high latitudes within terrestrial-like planetary atmospheres. These disturbances serve as critical agents in the transport of heat and momentum between low and high latitudes of the planet. Moreover, they transport trace species within the atmosphere (e.g., water vapor/ice, other aerosols (dust), chemical species, etc). Between early autumn through early spring, middle and high latitudes on Mars exhibit strong equator-to-pole mean temperature contrasts (i.e., "baroclinicity"). Data collected during the Viking era and observations from both the Mars Global Surveyor (MGS) and Mars Reconnaissance Orbiter (MRO) indicate that such strong baroclinicity supports vigorous, large-scale eastward traveling weather systems [Banfield et al., 2004; Barnes et al., 1993]. A good example of traveling weather systems, frontal wave activity and sequestered dust activity from MGS/MOC image analyses is provided in Figure 1 (cf. Wang et al. [2005]). Utilizing an upgraded and evolving version of the NASA Ames Research Center (ARC) Mars global climate model, investigated here are key dynamical and physical aspects of simulated northern hemisphere (NH) large-scale extratropica lweather systems,with and without radiatively-active water ice clouds. Mars Climate Model:

cyclones↗

NASA NTRS1983

An analytic solution for the response of the neutral atmosphere to the high-latitude convection pattern

The analytic solutions to a two-dimensional, shallow-water model of the high-latitude thermosphere are developed. The equations are a linearized representation of the response of the neutral atmosphere to the momentum source due to the plasma convection pattern. The obtained results show how the neutral winds depend on the Pedersen and Hall ion drag coefficients and the horizontal wave number. The response depends on the dimensionless scale as it appears in the product of the Rossby radius of deformation and the wave number. The flow pattern is shifted in local time from the plasma flow pattern by an amount that depends on the average electron density. At the largest scales there is a 180 deg phase shift between the rotational flow components in the E and F regions. The model applies to quiet magnetic conditions and below 200 km of altitude.

Mikkelsen, I. S.↗

NASA NTRS2014

Modeling Mars Cyclogenesis and Frontal Waves: Seasonal Variations and Implications on Dust Activity

Between late autumn through early spring,middle and high latitudes onMars exhibit strong equator-to-polemean temperature contrasts (i.e., "baroclinicity"). Data collected during the Viking era and observations from both the Mars Global Surveyor (MGS) and Mars Reconnaissance Orbiter (MRO) indicate that such strong baroclinicity supports vigorous, large-scale eastward traveling weather systems (i.e., transient synoptic period waves) [1, 2]. For a rapidly rotating, differentially heated, shallow atmosphere such as on Earth and Mars, these large-scale, extratropical weather disturbances are critical components of the global circulation. The wave-like disturbances serve as agents in the transport of heat and momentum between low and high latitudes of the planet. Through cyclonic/anticyclonic winds, intense shear deformations, contractions-dilatations in temperature and density, and sharp perturbations amongst atmospheric tracers (i.e., dust, volatiles (e.g., water vapor) and condensates (e.g., water-ice cloud particles)), Mars' extratropical weather systems have significant sub-synoptic scale ramifications by supporting atmospheric frontal waves (Fig. 1).

Mars Global Surveyor (MGS)↗

DOE OSTI2023

Semi-Implicit Computation of Fast Modes in a Scheme Integrating Slow Modes by a Leapfrog Method Based on a Selective Implicit Time Filter

Abstract A scheme for integration of atmospheric equations containing terms with differing time scales is developed. The method employs a filtered leapfrog scheme utilizing a fourth-order implicit time filter with one function evaluation per time step to compute slow-propagating phenomena such as advection and rotation. The terms involving fast-propagating modes are handled implicitly with an unconditionally stable method that permits application of larger time steps and faster computations compared to fully explicit treatment. Implementation using explicit and recurrent formulation is provided. Stability analysis demonstrates that the method is conditionally stable for any combination of frequencies involved in the slow and fast terms as they approach the origin. The implicit filter used in the method damps the computational modes without noticeably sacrificing the accuracy of the physical mode. TheO[(Δt 4 )] accuracy for amplitude errors achieved by the implicitly filtered leapfrog is preserved in applications where terms responsible for fast propagation are integrated with a semi-implicit method. Detailed formulation of the method for soundproof nonhydrostatic anelastic equations is provided. Procedures for implementation in global spectral shallow-water models are also given. Examples comparing numerical and analytical solutions for linear gravity waves demonstrate the accuracy of the scheme. The performance is also shown in more practical nonlinear applications, where numerical solutions accomplished by the method are evaluated against those computed from a scheme where the slow terms are handled by the third-order Runge–Kutta scheme. It demonstrates that the method is able to accurately resolve fine-scale dynamics of Kelvin–Helmholtz shear instabilities, the evolution of density current, and nonlinear drifts of twin tropical cyclones.

Meteorology & Atmospheric Sciences↗