A numerical scheme to solve unstable boundary value problems

A new iterative scheme for solving boundary value problems is presented. It consists of the introduction of an artificial time dependence into a modified version of the system of equations. Then explicit forward integrations in time are followed by explicit integrations backwards in time. The method converges under much more general conditions than schemes based in forward time integrations (false transient schemes). In particular it can attain a steady state solution of an elliptical system of equations even if the solution is unstable, in which case other iterative schemes fail to converge. The simplicity of its use makes it attractive for solving large systems of nonlinear equations

Optimal design of measurement network for neutronic activity field reconstruction by data assimilation

Using data assimilation framework, to merge information from model and measurement, an optimal reconstruction of the neutronic activity field can be determined for a nuclear reactor core. In this paper, we focus on solving the inverse problem of determining an optimal repartition of the measuring instruments within the core, to get the best possible results from the data assimilation reconstruction procedure. The position optimisation is realised using Simulated Annealing algorithm, based on the Metropolis-Hastings one. Moreover, in order to address the optimisation computing challenge, algebraic improvements of data assimilation have been developed and are presented here.Comment: 24 pages, 10 figure

A study of the dynamics of the Intertropical Convergence Zone (ITCZ) in a symmetric atmosphere-ocean model

A numerical model of the circulation of a coupled axisymmetric atmosphere-ocean system was constructed to investigate the physical factors governing the location and intensity of the Intertropical Convergence Zone (ITCZ) over oceans and over land. The results of several numerical integrations are presented to illustrate the interaction of the individual atmospheric and oceanic circulations. It is shown that the ITCA cannot be located at the equator because the atmosphere-ocean system is unstable for lateral displacements of the ITCA from an equilibrium position at the equator

A method to estimate trends in distributions of 1 min rain rates from numerical weather prediction data

It is known that the rain rate exceeded 0.01% of the time in the UK has experienced an increasing trend over the last 20 years. It is very likely that rain fade and outage experience a similar trend. This paper presents a globally applicable method to estimate these trends, based on the widely accepted Salonen-Poiares Baptista model. The input data are parameters easily extracted from numerical weather prediction reanalysis data. The method is verified using rain gauge data from the UK, and the predicted trend slopes of 0.01% exceeded rain rate are presented on a global grid

Particle filtering in high-dimensional chaotic systems

We present an efficient particle filtering algorithm for multiscale systems, that is adapted for simple atmospheric dynamics models which are inherently chaotic. Particle filters represent the posterior conditional distribution of the state variables by a collection of particles, which evolves and adapts recursively as new information becomes available. The difference between the estimated state and the true state of the system constitutes the error in specifying or forecasting the state, which is amplified in chaotic systems that have a number of positive Lyapunov exponents. The purpose of the present paper is to show that the homogenization method developed in Imkeller et al. (2011), which is applicable to high dimensional multi-scale filtering problems, along with important sampling and control methods can be used as a basic and flexible tool for the construction of the proposal density inherent in particle filtering. Finally, we apply the general homogenized particle filtering algorithm developed here to the Lorenz'96 atmospheric model that mimics mid-latitude atmospheric dynamics with microscopic convective processes.Comment: 28 pages, 12 figure