Projected gradient approach to the numerical solution of the SCoTLASS

The SCoTLASS problem-principal component analysis modified so that the components satisfy the Least Absolute Shrinkage and Selection Operator (LASSO) constraint-is reformulated as a dynamical system on the unit sphere. The LASSO inequality constraint is tackled by exterior penalty function. A globally convergent algorithm is developed based on the projected gradient approach. The algorithm is illustrated numerically and discussed on a well-known data set. (c) 2004 Elsevier B.V. All rights reserved.

A kinematically distorted flux rope model for magnetic clouds

Constant-α force-free magnetic flux rope models have proven to be a valuable first step toward understanding the global context of in situ observations of magnetic clouds. However, cylindrical symmetry is necessarily assumed when using such models, and it is apparent from both observations and modeling that magnetic clouds have highly noncircular cross sections. A number of approaches have been adopted to relax the circular cross section approximation: frequently, the cross-sectional shape is allowed to take an arbitrarily chosen shape (usually elliptical), increasing the number of free parameters that are fit between data and model. While a better “fit” may be achieved in terms of reducing the mean square error between the model and observed magnetic field time series, it is not always clear that this translates to a more accurate reconstruction of the global structure of the magnetic cloud. We develop a new, noncircular cross section flux rope model that is constrained by observations of CMEs/ICMEs and knowledge of the physical processes acting on the magnetic cloud: The magnetic cloud is assumed to initially take the form of a force-free flux rope in the low corona but to be subsequently deformed by a combination of axis-centered self-expansion and heliocentric radial expansion. The resulting analytical solution is validated by fitting to artificial time series produced by numerical MHD simulations of magnetic clouds and shown to accurately reproduce the global structure.

Lagrangian validation of numerical drifter trajectories using drifting buoys: Application to the Agulhas system

The skill of numerical Lagrangian drifter trajectories in three numerical models is assessed by comparing these numerically obtained paths to the trajectories of drifting buoys in the real ocean. The skill assessment is performed using the two-sample Kolmogorov–Smirnov statistical test. To demonstrate the assessment procedure, it is applied to three different models of the Agulhas region. The test can either be performed using crossing positions of one-dimensional sections in order to test model performance in specific locations, or using the total two-dimensional data set of trajectories. The test yields four quantities: a binary decision of model skill, a confidence level which can be used as a measure of goodness-of-fit of the model, a test statistic which can be used to determine the sensitivity of the confidence level, and cumulative distribution functions that aid in the qualitative analysis. The ordering of models by their confidence levels is the same as the ordering based on the qualitative analysis, which suggests that the method is suited for model validation. Only one of the three models, a 1/10° two-way nested regional ocean model, might have skill in the Agulhas region. The other two models, a 1/2° global model and a 1/8° assimilative model, might have skill only on some sections in the region