how long can an atmospheric model predict? peter c chu and leonid ivanov naval ocean-atmospheric...
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How Long Can an Atmospheric Model Predict?
Peter C Chu and Leonid IvanovNaval Ocean-Atmospheric Prediction Laboratory
Naval Postgraduate SchoolMonterey, California 93943, USA
[email protected]://www.oc.nps.navy.mil/~chu
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References Chu, P.C., L.M. Ivanov, T. M. Margolina, and O.V. Melnichenko, On
probabilistic stability of an atmospheric model to various amplitude perturbations. Journal of the Atmospheric Sciences, 59, 2860-2873.
Chu, P.C., L.M. Ivanov, C.W. Fan, 2002: Backward Fokker-Planck equation for determining model valid prediction period. Journal of Geophysical Research, 107, C6, 10.1029/2001JC000879.
Chu, P.C., L. Ivanov, L. Kantha, O. Melnichenko, and Y. Poberezhny, 2002: Power law decay in model predictability skill. Geophysical Research Letters, 29 (15), 10.1029/2002GLO14891.
Chu, P.C., L.M. Ivanov, L.H. Kantha, T.M. Margolina, and O.M. Melnichenko, and Y.A, Poberenzhny, 2004: Lagrangian predictabilty of high-resolution regional ocean models. Nonlinear Processes in Geophysics, 11, 47-66.
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Physical Reality Y
Physical Law: dY/dt = h(y, t)
Initial Condition: Y(t0) = Y0
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Atmospheric Models
X is the prediction of Y
d X/ dt = f(X, t) + q(t) X
Initial Condition: X(t0) = X0
Stochastic Forcing: <q(t)> = 0 <q(t)q(t’)> = q2δ(t-t’)
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Model Error Z = X – Y
Initial: Z0 = X0 - Y0
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One Overlooked Parameter
Tolerance Level
Maximum accepted error
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Valid Predict Period (VPP)
VPP is defined as the time period when the prediction error first exceeds a pre-determined criterion (i.e., the tolerance level ).
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First-Passage Time
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Conditional Probability Density Function Initial Error: Z0
(t – t0) Random Variable
Conditional PDF of (t – t0) with given Z0
P[(t – t0) |Z0]
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Two Approaches to Obtain PDF of VPP
Analytical (Backward Fokker-Planck Equation)
Practical
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Backward Fokker-Planck Equation
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Moments
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Example: Maximum Growing Maniford of Lorenz System (Nicolis, 1992)
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Mean and Variance of VPP
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Analytical Solutions
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Dependence of tau1 & tau2 on Initial Condition Error ( )
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Practical Approach
Gulf of Mexico Ocean Prediction System
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Gulf of Mexico Forecast System University of Colorado Version of
POM 1/12o Resolution Real-Time SSH Data (TOPEX, ESA
ERS-1/2) Assimilated Real Time SST Data (MCSST, NOAA
AVHRR) Assimilated Six Months Four-Times Daily Data
From July 9, 1998 for Verification
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Model Generated Velocity Vectors at 50 m on 00:00 July 9, 1998
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(Observational) Drifter Data at 50 m on 00:00 July 9, 1998
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Statistical Characteristics of VPP for zero initial error and 22 km tolerance level (Non-Gaussion)
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Conclusions (1) VPP (i.e., FPT) is an effective
prediction skill measure (scalar).
(2) Theoretical framework for FPT (such as Backward Fokker-Planck equation) can be directly used for model predictability study.