Factors Influencing Ensemble Sensitivity–Based Targeted Observing Predictions at Convection-Allowing Resolutions

Ensemble sensitivity analysis (ESA) is applied to select types of observations, in various locations and in advance of forecast convection, to systematically evaluate the effectiveness of ESA-based observation targeting for 10 convection forecasts. To facilitate the analysis, observing system simulation experiments and perfect models are utilized to generate synthetic targeted observations of temperature and pressure for future assimilation with an ensemble prediction system. Various observation assimilation experiments are carried out to assess the impacts of nonlinearity, covariance localization, and numerical noise on ESA-based observation-impact predictions. It is discovered that localization applied during data assimilation restricts targeted-observation increments onto the forecast responses of composite reflectivity and 3-hourly accumulated precipitation, making impact predictions poor. In addition, numerical noise introduced by nonlinear perturbation evolution tends to reduce the correlations between observed and predicted impacts; small, random-perturbation experiments often yielded similar impacts on forecasts as targeted observations. Nonlinearity also manifests in the observation impacts when comparing targeted observations with nontargeted, randomly chosen observations; random observations have seemingly the same impact on forecasts as targeted observations. The results, under idealized conditions and simplified ensemble configurations, demonstrate that ESA-based targeting for nonlinear convection forecasts may be most applicable at short time scales. Important implications for ESA-based targeting methods employed with real-time ensemble systems are also discussed.

A Postverification Method for Solving Forced Duffing Oscillator Problems without Prescribed Periods

This paper proposes a postverification method (PVM) for solving forced Duffing oscillator problems without prescribed periods. Comprising a postverification procedure and small random perturbation, the proposed PVM improves the sensitivity of the convergence of Newton’s iteration. Numerical simulations revealed that the PVM is more accurate and robust than Kubíček’s approach. We applied the PVM to previous research on bifurcation problems.

METASTABILITY FOR RANDOM PERTURBATIONS OF NEARLY-HAMILTONIAN SYSTEMS

We characterize the phenomenon of metastability for a small random perturbation of a nearly-Hamiltonian dynamical system. We use the averaging principle and the theory of large deviations to prove that the metastable "state" is, in general, not a single state but rather a nondegenerate probability measure across the stable equilibrium points of the unperturbed Hamiltonian system. The set of all possible "metastable distributions" is a finite set that is independent of the stochastic perturbation.

Automatic detection of molecular symmetry in the Cambridge Structural Database

A method for the detection of approximate molecular symmetry in crystal structures has been developed. The point-group symmetry is assigned to each molecule and the relevant symmetry elements can be visualized, superimposed on the molecule. The method has been validated against reference structures with exact symmetry subjected to small random perturbation.