**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..."**

**Slide 4**

**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**

**Slide 9**

**Slide 10**

**Data assimilation:
combine a forecast with observations. We make a temperature forecast T**_{b}
and then take an observation T_{o}.

A popular way to optimally estimate the truth (analysis) is to minimize the
“3D-Var” cost function:

**Slide 12**

**Slide 13**

**The solution: Ensemble
Kalman Filtering**

**Slide 15**

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**This advantage continues
into the 3-day forecasts**

**Slide 26**

**Results with Lorenz 40
variable model**

**Slide 28**

**Slide 29**

**Slide 30**

**Preliminary LEKF results
with NCEP’s global model**

**Slide 32**

**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.**

**Slide 36**

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**Slide 39**

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

**Breeding in a coupled
system**

**Slide 42**

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**Slide 48**

**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**

**Slide 52**

**Slide 53**

**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**