Ensemble forecasting and data assimilation in coupled systems
Eugenia Kalnay
Department of Meteorology and the Chaos Group
University of Maryland

References and thanks:

"An ensemble forecast starts from..."

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The errors of the day are instabilities of the background flow. At the same verification time, the forecast uncertainties have the same shape

Strong instabilities of the background tend to have simple shapes (perturbations lie in a low-dimensional subspace)

Errors of the day

One approach to create initial perturbations for ensemble forecasting with errors of the day: breeding

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Data assimilation: combine a forecast with observations. We make a temperature forecast Tb and then take an observation To.
A popular way to optimally estimate the truth (analysis) is to minimize the “3D-Var” cost function:

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The solution: Ensemble Kalman Filtering

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This advantage continues into the 3-day forecasts

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Results with Lorenz 40 variable model

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Preliminary LEKF results with NCEP’s global model

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However, two remaining problems…

"The atmosphere has coupled instabilities..."

To help understand the problem in coupled systems, test breeding in a coupled system. The results should be valid for other nonlinear approaches such as EnKF.

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The two rules are very robust, with threat scores >90%

Breeding in a coupled system

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Results from Lorenz coupled models

Example of bred vectors (contours) associated with equatorial unstable waves (color) in the NASA coupled GCM. The bred vectors (contours) give the most unstable perturbations, a powerful tool for a dynamical analysis. (Yang et al, 2003)

Experiments with coupled systems

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Breeding with the NSIPP
coupled GCM (10 year run)

Regression maps with BV NINO3 index

Regression maps with BV NINO3 index

Background ENSO vs. ENSO “embryo”

Summary about breeding in a coupled system

Tentative conclusions about data assimilation in coupled systems with multiple time scales