Parabolic resonances and instabilities in near-integrable two degrees of freedom Hamiltonian flows

When an integrable two-degrees-of-freedom Hamiltonian system possessing a circle of parabolic fixed points is perturbed, a parabolic resonance occurs. It is proved that its occurrence is generic for one parameter families (co-dimension one phenomenon) of near-integrable, t.d.o. systems. Numerical experiments indicate that the motion near a parabolic resonance exhibits new type of chaotic behavior which includes instabilities in some directions and long trapping times in others. Moreover, in a degenerate case, near a {\it flat parabolic resonance}, large scale instabilities appear. A model arising from an atmospherical study is shown to exhibit flat parabolic resonance. This supplies a simple mechanism for the transport of particles with {\it small} (i.e. atmospherically relevant) initial velocities from the vicinity of the equator to high latitudes. A modification of the model which allows the development of atmospherical jets unfolds the degeneracy, yet traces of the flat instabilities are clearly observed

Extension of Ekman (1905) wind-driven transport theory to the <i>β</i> plane

The seminal Ekman (1905) f-plane theory of wind-driven transport at the ocean surface is extended to the β plane by substituting the pseudo-angular momentum for the zonal velocity in the Lagrangian equation. When the β term is added, the equations become nonlinear, which greatly complicates the analysis. Though rotation relates the momentum equations in the zonal and the meridional directions, the transformation to pseudo-angular momentum greatly simplifies the longitudinal dynamics, which yields a clear description of the meridional dynamics in terms of a slow drift compounded by fast oscillations; this can then be applied to describe the motion in the zonal direction. Both analytical expressions and numerical calculations highlight the critical role of the Equator in determining the trajectories of water columns forced by eastward-directed (in the Northern Hemisphere) wind stress even when the water columns are initiated far from the Equator. Our results demonstrate that the averaged motion in the zonal direction depends on the amplitude of the meridional oscillations and is independent of the direction of the wind stress. The zonal drift is determined by a balance between the initial conditions and the magnitude of the wind stress, so it can be as large as the mean meridional motion; i.e., the averaged flow direction is not necessarily perpendicular to the wind direction.</p

Polynomial cointegration tests of anthropogenic impact on global warming

We use statistical methods for nonstationary time series to test the anthropogenic interpretation of global warming (AGW), according to which an increase in atmospheric greenhouse gas concentrations raised global temperature in the 20th century. Specifically, the methodology of polynomial cointegration is used to test AGW since during the observation period (1880–2007) global temperature and solar irradiance are stationary in 1st differences, whereas greenhouse gas and aerosol forcings are stationary in 2nd differences. We show that although these anthropogenic forcings share a common stochastic trend, this trend is empirically independent of the stochastic trend in temperature and solar irradiance. Therefore, greenhouse gas forcing, aerosols, solar irradiance and global temperature are not polynomially cointegrated, and the perceived relationship between these variables is a spurious regression phenomenon. On the other hand, we find that greenhouse gas forcings might have had a temporary effect on global temperature

A QBO Cookbook: Sensitivity of the Quasi-Biennial Oscillation to Resolution, Resolved Waves, and Parameterized Gravity Waves

An intermediate complexity moist general circulation model is used to investigate the sensitivity of the quasi-biennial oscillation (QBO) to resolution, diffusion, tropical tropospheric waves, and parameterized gravity waves. Finer horizontal resolution is shown to lead to a shorter period, while finer vertical resolution is shown to lead to a longer period and to a larger amplitude in the lowermost stratosphere. More scale-selective diffusion leads to a faster and stronger QBO, while enhancing the sources of tropospheric stationary wave activity leads to a weaker QBO. In terms of parameterized gravity waves, broadening the spectral width of the source function leads to a longer period and a stronger amplitude although the amplitude effect saturates in the mid-stratosphere when the half-width exceeds (Formula presented.) m/s. A stronger gravity wave source stress leads to a faster and stronger QBO, and a higher gravity wave launch level leads to a stronger QBO. All of these sensitivities are shown to result from their impact on the resultant wave-driven momentum torque in the tropical stratosphere. Atmospheric models have struggled to accurately represent the QBO, particularly at moderate resolutions ideal for long climate integrations. In particular, capturing the amplitude and penetration of QBO anomalies into the lower stratosphere (which has been shown to be critical for the tropospheric impacts) has proven a challenge. The results provide a recipe to generate and/or improve the simulation of the QBO in an atmospheric model

A Practical, Hybrid Model for Predicting the Trajectories of Near-Surface Ocean Drifters

A hybrid Lagrangian-Eulerian model for calculating the trajectories of near-surface drifters in the ocean is developed in this study. The model employs climatological, near-surface currents computed from a spline fit of all available drifter velocities observed in the Pacific Ocean between 1988 and 1996. It also incorporates contemporaneous wind fields calculated by either the U.S. Navy [the Navy Operational Global Atmospheric Prediction System (NOGAPS)] or the European Centre for Medium-Range Weather Forecasts (ECMWF). The model was applied to 30 drifters launched in the tropical Pacific Ocean in three clusters during 1990, 1993, and 1994. For 10-day-long trajectories the forecasts computed by the hybrid model are up to 164% closer to the observed trajectories compared to the trajectories obtained by advecting the drifters with the climatological currents only. The best-fitting trajectories are computed with ECMWF fields that have a temporal resolution of 6 h. The average improvement over all 30 drifters of the hybrid model trajectories relative to advection by the climatological currents is 21%, but in the open-ocean clusters (1990 and 1993) the improvement is 42% with ECMWF winds (34% with NOGAPS winds). This difference between the open-ocean and coastal clusters is due to the fact that the model does not presently include the effect of horizontal boundaries (coastlines). For zero initial velocities the trajectories generated by the hybrid model are significantly more accurate than advection by the mean currents on time scales of 5-15 days. For 3-day-long trajectories significant improvement is achieved if the drifter's initial velocity is known, in which case the model-generated trajectories are about 2 times closer to observations than persistence. The model's success in providing more accurate trajectories indicates that drifters' motion can deviate significantly from the climatological current and that the instantaneous winds are more relevant to their trajectories than the mean surface currents. It also demonstrates the importance of an accurate initial velocity, especially for short trajectories on the order of 1-3 days. A possible interpretation of these results is that winds affect drifter motion more than the water velocity since drifters do not obey continuity