The influence of physical processes on extratropical singular vectors

An investigation is made of the impact of a full linearized physical (moist) parameterization package on extratropical singular vectors (SVs) using the ECMWF integrated forecasting system (IFS). Comparison is made for one particular period with a dry physical package including only vertical diffusion and surface drag. The crucial extra ingredient in the full package is found to be the large-scale latent heat release. Consistent with basic theory, its inclusion results in a shift to smaller horizontal scales and enhanced growth for the SVs. Whereas, for the dry SVs, T42 resolution is sufficient, the moist SVs require T63 to resolve their structure and growth. A 24-h optimization time appears to be appropriate for the moist SVs because of the larger growth of moist SVs compared with dry SVs. Like dry SVs, moist SVs tend to occur in regions of high baroclinicity, but their location is also influenced by the availability of moisture. The most rapidly growing SVs appear to enhance or reduce large-scale rain in regions ahead of major cold fronts. The enhancement occurs in and ahead of a cyclonic perturbation and the reduction in and ahead of an anticyclonic perturbation. Most of the moist SVs for this situation are slightly modified versions of the dry SVs. However, some occur in new locations and have particularly confined structures. The most rapidly growing SV is shown to exhibit quite linear behavior in the nonlinear model as it grows from 0.5 to 12 hPa in 1 day. For 5 times this amplitude the structure is similar but the growth is about half as the perturbation damps a potential vorticity (PV) trough or produces a cutoff, depending on its sign.

Estimating climatically relevant singular vectors for decadal predictions of the Atlantic Ocean

A key aspect in designing an ecient decadal prediction system is ensuring that the uncertainty in the ocean initial conditions is sampled optimally. Here, we consider one strategy to address this issue by investigating the growth of optimal perturbations in the HadCM3 global climate model (GCM). More specically, climatically relevant singular vectors (CSVs) - the small perturbations which grow most rapidly for a specic initial condition - are estimated for decadal timescales in the Atlantic Ocean. It is found that reliable CSVs can be estimated by running a large ensemble of integrations of the GCM. Amplication of the optimal perturbations occurs for more than 10 years, and possibly up to 40 years. The identi ed regions for growing perturbations are found to be in the far North Atlantic, and these perturbations cause amplication through an anomalous meridional overturning circulation response. Additionally, this type of analysis potentially informs the design of future ocean observing systems by identifying the sensitive regions where small uncertainties in the ocean state can grow maximally. Although these CSVs are expensive to compute, we identify ways in which the process could be made more ecient in the future.

The system identification and control of Hammerstein system using non-uniform rational B-spline neural network and particle swarm optimization

In this paper a new system identification algorithm is introduced for Hammerstein systems based on observational input/output data. The nonlinear static function in the Hammerstein system is modelled using a non-uniform rational B-spline (NURB) neural network. The proposed system identification algorithm for this NURB network based Hammerstein system consists of two successive stages. First the shaping parameters in NURB network are estimated using a particle swarm optimization (PSO) procedure. Then the remaining parameters are estimated by the method of the singular value decomposition (SVD). Numerical examples including a model based controller are utilized to demonstrate the efficacy of the proposed approach. The controller consists of computing the inverse of the nonlinear static function approximated by NURB network, followed by a linear pole assignment controller.

On the stability radius of a generalized state-space system

The concept of “distance to instability” of a system matrix is generalized to system pencils which arise in descriptor (semistate) systems. Difficulties arise in the case of singular systems, because the pencil can be made unstable by an infinitesimal perturbation. It is necessary to measure the distance subject to restricted, or structured, perturbations. In this paper a suitable measure for the stability radius of a generalized state-space system is defined, and a computable expression for the distance to instability is derived for regular pencils of index less than or equal to one. For systems which are strongly controllable it is shown that this measure is related to the sensitivity of the poles of the system over all feedback matrices assigning the poles.