Some theoretical considerations on predictability of linear stochastic dynamics

Publication Status is "Submitted" Or "In Press: 
LDEO Publication: 
Publication Type: 
Year of Publication: 
2003
Editor: 
Journal Title: 
Tellus Series a-Dynamic Meteorology and Oceanography
Journal Date: 
Mar
Place Published: 
Tertiary Title: 
Volume: 
55
Issue: 
2
Pages: 
148-157
Section / Start page: 
Publisher: 
ISBN Number: 
0280-6495
ISSN Number: 
Edition: 
Short Title: 
Accession Number: 
ISI:000181378300003
LDEO Publication Number: 
Call Number: 
Abstract: 

Predictability is a measure of prediction error relative to observed variability and so depends on both the physical and prediction systems. Here predictability is investigated for climate phenomena described by linear stochastic dynamics and prediction systems with perfect initial conditions and perfect linear prediction dynamics. Predictability is quantified using the predictive information matrix constructed from the prediction error and climatological covariances. Predictability measures defined using the eigenvalues of the predictive information matrix are invariant under linear state-variable transformations and for univariate systems reduce to functions of the ratio of prediction error and climatological variances. The predictability of linear stochastic dynamics is shown to be minimized for stochastic forcing that is uncorrelated in normal-mode space. This minimum predictability depends only on the eigenvalues of the dynamics, and is a lower bound for the predictability of the system with arbitrary stochastic forcing. Issues related to upper bounds for predictability are explored in a simple theoretical example.

Notes: 

652KLTimes Cited:5Cited References Count:20

DOI: