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| Quantifying Dynamical Predictability: the Pseudo-Ensemble Approach |
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Citation： |
Jianbo GAO,Wenwen TUNG,Jing HU.Quantifying Dynamical Predictability: the Pseudo-Ensemble Approach[J].Chinese Annals of Mathematics B,2009,30(5):569~588 |
| Page view： 1792
Net amount： 1176 |
Authors： |
Jianbo GAO; Wenwen TUNG; Jing HU; |
Foundation： |
the National Science Foundation (Nos. CMMI-0825311, CMMI-0826119). |
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| Abstract： |
The ensemble technique has been widely used in numerical weather prediction
and extended-range forecasting. Current approaches to evaluate the predictability using
the ensemble technique can be divided into two major groups. One is dynamical, includ-
ing generating Lyapunov vectors, bred vectors, and singular vectors, sampling the fastest
error-growing directions of the phase space, and examining the dependence of prediction
efficiency on ensemble size. The other is statistical, including distributional analysis and
quantifying prediction utility by the Shannon entropy and the relative entropy. Currently,
with simple models, one could choose as many ensembles as possible, with each ensemble
containing a large number of members. When the forecast models become increasingly
complicated, however, one would only be able to afford a small number of ensembles, each
with limited number of members, thus sacrificing estimation accuracy of the forecast errors.
To uncover connections between different information theoretic approaches and between
dynamical and statistical approaches, we propose an (?, τ )-entropy and scale-dependent
Lyapunov exponent—based general theoretical framework to quantify information loss in
ensemble forecasting. More importantly, to tremendously expedite computations, reduce
data storage, and improve forecasting accuracy, we propose a technique for constructing
a large number of “pseudo” ensembles from one single solution or scalar dataset. This
pseudo-ensemble technique appears to be applicable under rather general conditions, one
important situation being that observational data are available but the exact dynamical
model is unknown. |
Keywords： |
Dynamical predictability, Ensemble forecasting, Relative entropy,
Kolmogorov entropy, Scale-dependent Lyapunov exponent |
Classification： |
37, 60, 86 |
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