Abstract

The scale-dependent characteristics of the optimal perturbations in a zonally asymmetric barotropic model are examined. The dependence of the optimal energy growth on the initial scale is investigated through the calculations of spectrally constrained optimal perturbations. Considering an optimization time of τ = 3 days, and a basic state containing an idealized Asian jet, the optimal amplification factor generally increases with the decrease of the imposed initial scale. In the absence of diffusion, the most amplifying scale becomes the smallest scale in the model. An energetics analysis shows that the energy conversion in the optimal excitation process is dominated by the shear straining term, with a sharp increase in the scale of the perturbation accompanying the explosive energy growth. These results show the similarity between the optimally growing process in the zonally asymmetric system and the shear straining process in a parallel shear flow. Except when a small τ is considered or a sufficiently strong diffusion is used in the system, the optimal energy growth for small-scale disturbances sensitively depends on the zonally varying feature of the basic state. With τ = 3 days, the optimal amplification factors for small-scale disturbances are reduced significantly when the idealized Asian jet is shortened by only one-fifth. At the same time, those for medium- and large-scale disturbances are almost unaffected by the change of the basic state. The reasons for this contrast of the sensitivity property between the small and large scales are discussed.

Abstract

The dynamics of two-dimensional turbulence on a rotating sphere are examined. The anisotropic Rhines scale is derived and verified in decaying turbulence simulations. Due to the anisotropic nature of the Rossby waves, the Rhines barrier is displaced toward small total wavenumber n with decreasing zonal wavenumber m. Up-scale energy transfer along the zonal axis (m = 0) is not directly arrested by beta. A forced dissipative model with high-wavenumber forcing is used to investigate the dynamics of persistent zonal jets. Persistent jets form in the low energy (strong rotation) cases with the root-mean-square velocity V*_rms ≪ aΩ. Under a fixed rotation rate, the jet scale decreases with the energy. The equilibrated jets generally stay at fixed latitudes. The zonal bands are nearly uniformly distributed in latitude, except that bands in the high latitudes tend to be wider and weaker, as clearly affected by a decreasing beta with latitude. The time-mean zonal winds in the forced simulations appear to be stable, with their absolute vorticity gradient dominated by beta. The increase of the jet scale with energy as required by stability is consistent with the simulated results.

Diagnostic analysis shows that the persistent jets are primarily maintained by the shear-straining mechanism involving small-scale eddies and large-scale zonal jets, with a clear scale separation between them. Although large-scale eddies, those at scales near the Rhines scale, possess most of the eddy energy, in the time mean they contribute little to the maintenance of the zonal jets. Thus, despite the similarity between the Rhines scale and the jet scale, their dynamical link is not obvious in the time-mean statistics. The presence of persistent zonal jets modifies the normal modes of the system. Pure Rossby–Haurwitz modes at small and medium scales are severely modified and fall into the continuum. Large-scale modes, however, may remain discrete. The discreteness of the large-scale modes limits their ability to exchange energy with the zonal jets in the time mean.

Abstract

This study performs an updated analysis of Northern Hemisphere retrograde disturbances that were first identified by classical observational studies as one of the dominating coherent structures in the higher latitudes on the submonthly time scale. Analyzing 8–30-day bandpass-filtered data based on reanalysis, a set of criteria on the phase and amplitude of zonal wave-1 Fourier coefficients of geopotential height anomalies at 250 mb (1 mb = 1 hPa) and 60°N are used to identify strong retrograde-wave events in the spirit of Madden and Speth. The new catalog of retrograde-wave events from 1979 to 2017 is used to extract basic statistics and structures of retrograde waves across all major events. The results broadly agree with those reported in the classical observational studies, reaffirming the robustness of the phenomenon. The new catalog can be used to aid further studies on the mechanisms and predictability of retrograde waves. As an example, an analysis of isentropic potential vorticity over the Pacific sector for selected retrograde-wave events reveals the common occurrence of an extrusion of low-PV air into the higher latitudes, followed by a westward shift of the low-PV patch and vortex shedding. Future directions of research surrounding the retrograde-wave phenomenon are discussed.

Abstract

Branstator–Kushnir-type large-scale westward propagating waves are investigated using linear and nonlinear global barotropic models with an idealized zonally asymmetric basic state. Retrograde waves are found in the most unstable normal mode of the zonally asymmetric basic state with a jet in the Northern Hemisphere. West-ward propagating waves also exist in nonlinear equilibrium states under a wide range of supercriticality and in both periodic and chaotic regimes. The frequency of the most unstable mode remains as a peak in the frequency spectrum through the nonlinear equilibration process. That frequency matches the frequency of the westward propagating waves in the nonlinear equilibrium states. Local energetics analyses of the linear and nonlinear cases show that the barotropic energy conversion concentrated in the jet exit supplies the perturbation energy of the disturbances all over the globe. Under a traditional spherical-harmonic decomposition, the westward propagating waves consist of several spherical-harmonic components. In the weakly chaotic nonlinear equilibrium states, these components show higher regularity in time than the others and may possess higher predictability.

Abstract

Due to the variety of periodic or quasi-periodic deterministic forcings (e.g., diurnal cycle, seasonal cycle, Milankovitch cycles, etc.), most climate fluctuations may be modeled as cyclostationary processes since their properties are modulated by these cycles. Difficulties in using conventional spectral analysis to explore the seasonal variation of climate fluctuations have indicated the need for some new statistical techniques. It is suggested here that the cyclic spectral analysis he used for interpreting such fluctuations. The technique is adapted from cyclostationarity theory in signal processing. To demonstrate the usefulness of this technique, a very simple cyclostationarity stochastic climate model is constructed. The results show that the seasonal cycle strongly modulates the amplitude of the covariance and spectrum. The seasonal variation of intraseasonal oscillations in the Tropics has also been studied on a zonally symmetric all-land planet in the absence of external forcing. The idealized planet has no ocean no topography. A 15-year length seasonal run of the atmosphere is analyzed with the NCAR Community Climate Model (CCM2, R15). Analysis of the simulation data indicates the presence of intraseaonal oscillations in the Tropics, which are also localized in the time of year.

Both examples suggest that these techniques might be useful for analysis of fluctuations that exhibit locality in both frequency and season.

Abstract

Cloud longwave scattering is generally neglected in general circulation models (GCMs), but it plays a significant and highly uncertain role in the atmospheric energy budget as demonstrated in recent studies. To reduce the errors caused by neglecting cloud longwave scattering, two new radiance adjustment methods are developed that retain the computational efficiency of broadband radiative transfer simulations. In particular, two existing scaling methods and the two new adjustment methods are implemented in the Rapid Radiative Transfer Model (RRTM). The results are then compared with those based on the Discrete Ordinate Radiative Transfer model (DISORT) that explicitly accounts for multiple scattering by clouds. The two scaling methods are shown to improve the accuracy of radiative transfer simulations for optically thin clouds but not effectively for optically thick clouds. However, the adjustment methods reduce computational errors over a wide range, from optically thin to thick clouds. With the adjustment methods, the errors resulting from neglecting cloud longwave scattering are reduced to less than 2 W m⁻² for the upward irradiance at the top of the atmosphere and less than 0.5 W m⁻² for the surface downward irradiance. The adjustment schemes prove to be more accurate and efficient than a four-stream approximation that explicitly accounts for multiple scattering. The neglect of cloud longwave scattering results in an underestimate of the surface downward irradiance (cooling effect), but the errors are almost eliminated by the adjustment methods (warming effect).