Coupled Kelvin-wave and mirage-wave instabilities in semigeostrophic dynamics

A weak instability mode, associated with phase-locked counterpropagating coastal Kelvin waves in horizontal anticyclonic shear, is found in the semigeostrophic (SG) equations for stratified flow in a channel. This SG instability mode approximates a similar mode found in the Euler equations in the limit in which particle-trajectory slopes are much smaller than f/N, where f is the Coriolis frequency and N > f the buoyancy frequency. Though weak under normal parameter conditions, this instability mode is of theoretical interest because its existence accounts for the failure of an Arnol’d-type stability theorem for the SG equations. In the opposite limit, in which the particle motion is purely vertical, the Euler equations allow only buoyancy oscillations with no horizontal coupling. The SG equations, on the other hand, allow a physically spurious coastal “mirage wave,” so called because its velocity field vanishes despite a nonvanishing disturbance pressure field. Counterpropagating pairs of these waves can phase-lock to form a spurious “mirage-wave instability.” Closer examination shows that the mirage wave arises from failure of the SG approximations to be self-consistent for trajectory slopes f/N.

Nonlinear system identification using particle swarm optimisation tuned radial basis function models

A novel particle swarm optimisation (PSO) tuned radial basis function (RBF) network model is proposed for identification of non-linear systems. At each stage of orthogonal forward regression (OFR) model construction process, PSO is adopted to tune one RBF unit's centre vector and diagonal covariance matrix by minimising the leave-one-out (LOO) mean square error (MSE). This PSO aided OFR automatically determines how many tunable RBF nodes are sufficient for modelling. Compared with the-state-of-the-art local regularisation assisted orthogonal least squares algorithm based on the LOO MSE criterion for constructing fixed-node RBF network models, the PSO tuned RBF model construction produces more parsimonious RBF models with better generalisation performance and is often more efficient in model construction. The effectiveness of the proposed PSO aided OFR algorithm for constructing tunable node RBF models is demonstrated using three real data sets.

Particle swarm optimization aided orthogonal forward regression for unified data modeling

We propose a unified data modeling approach that is equally applicable to supervised regression and classification applications, as well as to unsupervised probability density function estimation. A particle swarm optimization (PSO) aided orthogonal forward regression (OFR) algorithm based on leave-one-out (LOO) criteria is developed to construct parsimonious radial basis function (RBF) networks with tunable nodes. Each stage of the construction process determines the center vector and diagonal covariance matrix of one RBF node by minimizing the LOO statistics. For regression applications, the LOO criterion is chosen to be the LOO mean square error, while the LOO misclassification rate is adopted in two-class classification applications. By adopting the Parzen window estimate as the desired response, the unsupervised density estimation problem is transformed into a constrained regression problem. This PSO aided OFR algorithm for tunable-node RBF networks is capable of constructing very parsimonious RBF models that generalize well, and our analysis and experimental results demonstrate that the algorithm is computationally even simpler than the efficient regularization assisted orthogonal least square algorithm based on LOO criteria for selecting fixed-node RBF models. Another significant advantage of the proposed learning procedure is that it does not have learning hyperparameters that have to be tuned using costly cross validation. The effectiveness of the proposed PSO aided OFR construction procedure is illustrated using several examples taken from regression and classification, as well as density estimation applications.

Transport in the low-latitude tropopause zone diagnosed using particle trajectories

Recent literature has described a “transition zone” between the average top of deep convection in the Tropics and the stratosphere. Here transport across this zone is investigated using an offline trajectory model. Particles were advected by the resolved winds from the European Centre for Medium-Range Weather Forecasts reanalyses. For each boreal winter clusters of particles were released in the upper troposphere over the four main regions of tropical deep convection (Indonesia, central Pacific, South America, and Africa). Most particles remain in the troposphere, descending on average for every cluster. The horizontal components of 5-day trajectories are strongly influenced by the El Niño–Southern Oscillation (ENSO), but the Lagrangian average descent does not have a clear ENSO signature. Tropopause crossing locations are first identified by recording events when trajectories from the same release regions cross the World Meteorological Organization lapse rate tropopause. Most crossing events occur 5–15 days after release, and 30-day trajectories are sufficiently long to estimate crossing number densities. In a further two experiments slight excursions across the lapse rate tropopause are differentiated from the drift deeper into the stratosphere by defining the “tropopause zone” as a layer bounded by the average potential temperature of the lapse rate tropopause and the profile temperature minimum. Transport upward across this zone is studied using forward trajectories released from the lower bound and back trajectories arriving at the upper bound. Histograms of particle potential temperature (θ) show marked differences between the transition zone, where there is a slow spread in θ values about a peak that shifts slowly upward, and the troposphere below 350 K. There forward trajectories experience slow radiative cooling interspersed with bursts of convective heating resulting in a well-mixed distribution. In contrast θ histograms for back trajectories arriving in the stratosphere have two distinct peaks just above 300 and 350 K, indicating the sharp change from rapid convective heating in the well-mixed troposphere to slow ascent in the transition zone. Although trajectories slowly cross the tropopause zone throughout the Tropics, all three experiments show that most trajectories reaching the stratosphere from the lower troposphere within 30 days do so over the west Pacific warm pool. This preferred location moves about 30°–50° farther east in an El Niño year (1982/83) and about 30° farther west in a La Niña year (1988/89). These results could have important implications for upper-troposphere–lower-stratosphere pollution and chemistry studies.