"Sky and Water I", M.C. Escher |
Ross Bannister
Data Assimilation Research Centre Univ. of Reading Oxford / RAL Spring School 2004 |
Observation space |
Model space |
One variableGauss |
Two or more variables |
Bayes |
Optimal Interpolation equation:
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Example: Geostrophic error covariances
Geostrophic balance: Pressure-pressure covariances assumption: |
from Ingleby (2001)
The 'N.M.C.' method
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The 'ensemble' method
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Model space,
Cost function (let ) Hessian
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Control space,
Cost function (let ) By design let Hessian
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Operator | Name | Form | Input vector | Output vector |
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As above | As above | model variables, , | , | |
Parameter trans. | See later | " | uncorr. parameters, | |
Vertical trans. | uncorr. parameters, | uncorr. parameters, | ||
Horiz. trans. | uncorr. parameters, | uncorr. parameters, |
Example orthogonalization
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In practice, find global average matrix
Vertically (nearly) uncorrelated modes for this parameter are eigenvectors (EOFs), , of
From Ingleby (2001)
Compute horizontal variances for each parameter and vertical mode
NMC tends to predict length scales that are too long (statistics need to be massaged) |
Zonal wind standard deviation | Streamfunction vertical correlation | |
Measured | ||
Implied |