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

Documentation of the Fourth Order Band Model

A general circulation model is presented which uses quadratically conservative, fourth order horizontal space differences on an unstaggered grid and second order vertical space differences with a forward-backward or a smooth leap frog time scheme to solve the primitive equations of motion. The dynamic equations for motion, finite difference equations, a discussion of the structure and flow chart of the program code, a program listing, and three relevent papers are given

A stochastic-dynamic model for global atmospheric mass field statistics

A model that yields the spatial correlation structure of atmospheric mass field forecast errors was developed. The model is governed by the potential vorticity equation forced by random noise. Expansion in spherical harmonics and correlation function was computed analytically using the expansion coefficients. The finite difference equivalent was solved using a fast Poisson solver and the correlation function was computed using stratified sampling of the individual realization of F(omega) and hence of phi(omega). A higher order equation for gamma was derived and solved directly in finite differences by two successive applications of the fast Poisson solver. The methods were compared for accuracy and efficiency and the third method was chosen as clearly superior. The results agree well with the latitude dependence of observed atmospheric correlation data. The value of the parameter c sub o which gives the best fit to the data is close to the value expected from dynamical considerations

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

The impact of scatterometer wind data on global weather forecasting

The impact of SEASAT-A scatterometer (SASS) winds on coarse resolution atmospheric model forecasts was assessed. The scatterometer provides high resolution winds, but each wind can have up to four possible directions. One wind direction is correct; the remainder are ambiguous or "aliases'. In general, the effect of objectively dealiased-SASS data was found to be negligible in the Northern Hemisphere. In the Southern Hemisphere, the impact was larger and primarily beneficial when vertical temperature profile radiometer (VTPR) data was excluded. However, the inclusion of VTPR data eliminates the positive impact, indicating some redundancy between the two data sets

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

Energetics, skeletal dynamics and long-term predictions in Kolmogorov-Lorenz systems

We study a particular return map for a class of low dimensional chaotic models called Kolmogorov Lorenz systems, which received an elegant general Hamiltonian description and includes also the famous Lorenz63 case, from the viewpoint of energy and Casimir balance. In particular it is considered in detail a subclass of these models, precisely those obtained from the Lorenz63 by a small perturbation on the standard parameters, which includes for example the forced Lorenz case in Ref.[6]. The paper is divided into two parts. In the first part the extremes of the mentioned state functions are considered, which define an invariant manifold, used to construct an appropriate Poincare surface for our return map. From the experimental observation of the simple orbital motion around the two unstable fixed points, together with the circumstance that these orbits are classified by their energy or Casimir maximum, we construct a conceptually simple skeletal dynamics valid within our sub class, reproducing quite well the Lorenz map for Casimir. This energetic approach sheds some light on the physical mechanism underlying regime transitions. The second part of the paper is devoted to the investigation of a new type of maximum energy based long term predictions, by which the knowledge of a particular maximum energy shell amounts to the knowledge of the future (qualitative) behaviour of the system. It is shown that, in this respect, a local analysis of predictability is not appropriate for a complete characterization of this behaviour. A perspective on the possible extensions of this type of predictability analysis to more realistic cases in (geo)fluid dynamics is discussed at the end of the paper.Comment: 21 pages, 14 figure