Quantum Ergodicity and Localization in Conservative Systems: the Wigner Band Random Matrix Model

First theoretical and numerical results on the global structure of the energy shell, the Green function spectra and the eigenfunctions, both localized and ergodic, in a generic conservative quantum system are presented. In case of quantum localization the eigenfunctions are shown to be typically narrow and solid, with centers randomly scattered within the semicircle energy shell while the Green function spectral density (local spectral density of states) is extended over the whole shell, but sparse.Comment: 4 pages in RevTex and 4 Postscript figures; presented to Phys. Lett.

Parametric Evolution for a Deformed Cavity

We consider a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where (Q,P) describes a particle moving inside a cavity, and x controls a deformation of the boundary. The quantum-eigenstates of the system are |n(x)>. We describe how the parametric kernel P(n|m) = , also known as the local density of states, evolves as a function of x-x0. We illuminate the non-unitary nature of this parametric evolution, the emergence of non-perturbative features, the final non-universal saturation, and the limitations of random-wave considerations. The parametric evolution is demonstrated numerically for two distinct representative deformation processes.Comment: 13 pages, 8 figures, improved introduction, to be published in Phys. Rev.

Vertical profiles of droplet effective radius in shallow convective clouds

Conventional satellite retrievals can only provide information on cloud-top droplet effective radius (<i>r</i><sub>e</sub>). Given the fact that cloud ensembles in a satellite snapshot have different cloud-top heights, Rosenfeld and Lensky (1998) used the cloud-top height and the corresponding cloud-top <i>r</i><sub>e</sub> from the cloud ensembles in the snapshot to construct a profile of <i>r</i><sub>e</sub> representative of that in the individual clouds. This study investigates the robustness of this approach in shallow convective clouds based on results from large-eddy simulations (LES) for clean (aerosol mixing ratio <i>N</i><sub>a</sub> = 25 mg<sup>−1</sup>), intermediate (<i>N</i><sub>a</sub> = 100 mg<sup>−1</sup>), and polluted (<i>N</i><sub>a</sub> = 2000 mg<sup>−1</sup>) conditions. The cloud-top height and the cloud-top <i>r</i><sub>e</sub> from the modeled cloud ensembles are used to form a constructed <i>r</i><sub>e</sub> profile, which is then compared to the in-cloud <i>r</i><sub>e</sub> profiles. For the polluted and intermediate cases where precipitation is negligible, the constructed <i>r</i><sub>e</sub> profiles represent the in-cloud <i>r</i><sub>e</sub> profiles fairly well with a low bias (about 10 %). The method used in Rosenfeld and Lensky (1998) is therefore validated for nonprecipitating shallow cumulus clouds. For the clean, drizzling case, the in-cloud <i>r</i><sub>e</sub> can be very large and highly variable, and quantitative profiling based on cloud-top <i>r</i><sub>e</sub> is less useful. The differences in <i>r</i><sub>e</sub> profiles between clean and polluted conditions derived in this manner are however, distinct. This study also investigates the subadiabatic characteristics of the simulated cumulus clouds to reveal the effect of mixing on <i>r</i><sub>e</sub> and its evolution. Results indicate that as polluted and moderately polluted clouds develop into their decaying stage, the subadiabatic fraction <i>f</i><sub>ad</sub> becomes smaller, representing a higher degree of mixing, and <i>r</i><sub>e</sub> becomes smaller (~10 %) and more variable. However, for the clean case, smaller <i>f</i><sub>ad</sub> corresponds to larger <i>r</i><sub>e</sub> (and larger <i>r</i><sub>e</sub> variability), reflecting the additional influence of droplet collision-coalescence and sedimentation on <i>r</i><sub>e</sub>. Finally, profiles of the vertically inhomogeneous clouds as simulated by the LES and those of the vertically homogeneous clouds are used as input to a radiative transfer model to study the effect of cloud vertical inhomogeneity on shortwave radiative forcing. For clouds that have the same liquid water path, <i>r</i><sub>e</sub> of a vertically homogeneous cloud must be about 76–90 % of the cloud-top <i>r</i><sub>e</sub> of the vertically inhomogeneous cloud in order for the two clouds to have the same shortwave radiative forcing

Statistical Properties of Random Banded Matrices with Strongly Fluctuating Diagonal Elements

The random banded matrices (RBM) whose diagonal elements fluctuate much stronger than the off-diagonal ones were introduced recently by Shepelyansky as a convenient model for coherent propagation of two interacting particles in a random potential. We treat the problem analytically by using the mapping onto the same supersymmetric nonlinear $\sigma-$model that appeared earlier in consideration of the standard RBM ensemble, but with renormalized parameters. A Lorentzian form of the local density of states and a two-scale spatial structure of the eigenfunctions revealed recently by Jacquod and Shepelyansky are confirmed by direct calculation of the distribution of eigenfunction components.Comment: 7 pages,RevTex, no figures Submitted to Phys.Rev.

Investigating potential biases in observed and modeled metrics of aerosol-cloud-precipitation interactions

This study utilizes large eddy simulation, aircraft measurements, and satellite observations to identify factors that bias the absolute magnitude of metrics of aerosol-cloud-precipitation interactions for warm clouds. The metrics considered are precipitation susceptibility <i>S</i><sub>o</sub>, which examines rain rate sensitivity to changes in drop number, and a cloud-precipitation metric, χ, which relates changes in rain rate to those in drop size. While wide ranges in rain rate exist at fixed cloud drop concentration for different cloud liquid water amounts, χ and <i>S</i><sub>o</sub> are shown to be relatively insensitive to the growth phase of the cloud for large datasets that include data representing the full spectrum of cloud lifetime. Spatial resolution of measurements is shown to influence the liquid water path-dependent behavior of <i>S</i><sub>o</sub> and χ. Other factors of importance are the choice of the minimum rain rate threshold, and how to quantify rain rate, drop size, and the cloud condensation nucleus proxy. Finally, low biases in retrieved aerosol amounts owing to wet scavenging and high biases associated with above-cloud aerosol layers should be accounted for. The paper explores the impact of these effects for model, satellite, and aircraft data

On the link between Amazonian forest properties and shallow cumulus cloud fields

During the dry season the Amazon forest is frequently covered by shallow cumulus clouds fields, referred to here as forest cumulus (FCu). These clouds are shown to be sensitive to land cover and exhibit a high level of spatial organization. In this study we use satellite data to perform a morphological classification and examine the link between FCu cloud field occurrence and the enhanced vegetation index (EVI), which is commonly used as a measure for forest density and productivity. Although weaker than first-order effects of meteorology, a clear positive linear relation between EVI (i.e., surface properties) and FCu field occurrence is seen over forest land cover, implying a strong coupling between forest surface fluxes and the cloud organization above. Over non-forest land cover the relationship between EVI and FCu occurrence is nonlinear, showing a reduction of FCu for high EVI values. We find that forest to non-forest transition zones display a superposition of the two different land cover dependencies

Spherical nonparametric estimators applied to the UGAMP model integration for AMIP

The aim of this paper is essentially twofold: first, to describe the use of spherical nonparametric estimators for determining statistical diagnostic fields from ensembles of feature tracks on a global domain, and second, to report the application of these techniques to data derived from a modern general circulation model. New spherical kernel functions are introduced that are more efficiently computed than the traditional exponential kernels. The data-driven techniques of cross-validation to determine the amount elf smoothing objectively, and adaptive smoothing to vary the smoothing locally, are also considered. Also introduced are techniques for combining seasonal statistical distributions to produce longer-term statistical distributions. Although all calculations are performed globally, only the results for the Northern Hemisphere winter (December, January, February) and Southern Hemisphere winter (June, July, August) cyclonic activity are presented, discussed, and compared with previous studies. Overall, results for the two hemispheric winters are in good agreement with previous studies, both for model-based studies and observational studies

On clocks and clouds

Cumulus clouds exhibit a life cycle that consists of (a) the growth phase (increasing size, most notably in the vertical direction); (b) the mature phase (growth ceases; any precipitation that develops is strongest during this period); and (c) the dissipation phase (cloud dissipates because of precipitation and/or entrainment; no more dynamical support). Although radar can track clouds over time and give some sense of the age of a cloud, most aircraft in situ measurements lack temporal context. We use large eddy simulations of trade wind cumulus cloud fields from cases during the Barbados Oceanographic and Meteorological Experiment (BOMEX) and Rain In Cumulus over the Ocean (RICO) campaigns to demonstrate a potential cumulus cloud "clock." We find that the volume-averaged total water mixing ratio rt is a useful cloud clock for the 12 clouds studied. A cloud's initial rt is set by the subcloud mixed-layer mean rt and decreases monotonically from the initial value due primarily to entrainment. The clock is insensitive to aerosol loading, environmental sounding and extrinsic cloud properties such as lifetime and volume. In some cases (more commonly for larger clouds), multiple pulses of buoyancy occur, which complicate the cumulus clock by replenishing rt. The clock is most effectively used to classify clouds by life phase