Influence sampling of trailing variables of dynamical systems

• Autorzy: Paul Krause
• Języki publikacji: EN

Abstrakty

EN

For dealing with dynamical instability in predictions, numerical models should be provided with accurate initial values on the attractor of the dynamical system they generate. A discrete control scheme is presented to this end for trailing variables of an evolutive system of ordinary differential equations. The Influence Sampling (IS) scheme adapts sample values of the trailing variables to input values of the determining variables in the attractor. The optimal IS scheme has affordable cost for large systems. In discrete data assimilation runs conducted with the Lorenz 1963 equations and a nonautonomous perturbation of the Lorenz equations whose dynamics shows on-off intermittency the optimal IS was compared to the straightforward insertion method and the Ensemble Kalman Filter (EnKF). With these unstable systems the optimal IS increases by one order of magnitude the maximum spacing between insertion times that the insertion method can handle and performs comparably to the EnKF when the EnKF converges. While the EnKF converges for sample sizes greater than or equal to 10, the optimal IS scheme does so fromsample size 1. This occurs because the optimal IS scheme stabilizes the individual paths of the Lorenz 1963 equations within data assimilation processes.

Słowa kluczowe

EN

data assimilation; determining variables; Dyson’s formula

Kategorie tematyczne

• 34F05: Equations and systems with randomness
• 37M05: Simulation
• 34K35: Control problems
• 58J45: Hyperbolic equations
• 86-08: Computational methods

• Wydawca: De Gruyter Open
• Czasopismo: Mathematics of Climate and Weather Forecasting
• Rocznik: 2017
• Tom: 3
• Numer: 1
• Strony: 51-63

Daty

wydano

2017-11-27

otrzymano

2017-07-11

zaakceptowano

2017-10-29

online

2017-11-24

Twórcy

autor

Paul Krause

• , SC,

Identyfikatory

DOI

10.1515/mcwf-2017-0003