Modelling static 3-D spatial background error covariances – the effect of vertical and horizontal transform order
A major difference in the formulation of the univariate part of static background error covariance models for use in global operational 4DVAR arises from the order in which the horizontal and vertical transforms are applied. This is because the atmosphere is non-separable with large horizontal scale...
Main Authors: | , |
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Format: | Article |
Language: | English |
Published: |
Copernicus Publications
2014-06-01
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Series: | Advances in Science and Research |
Online Access: | http://www.adv-sci-res.net/11/63/2014/asr-11-63-2014.pdf |
Summary: | A major difference in the formulation of the univariate part of
static background error covariance models for use in global operational 4DVAR
arises from the order in which the horizontal and vertical transforms are
applied. This is because the atmosphere is non-separable with large
horizontal scales generally tied to large vertical scales and small
horizontal scales tied to small vertical scales. Also horizontal length
scales increase dramatically as one enters the stratosphere. A study is
presented which evaluates the strengths and weaknesses of each approach with
the Met Office Unified Model.
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It is shown that if the vertical transform is applied as a function of horizontal wavenumber then the
horizontal globally-averaged variance and the homogenous, isotropic length
scale on each model level for each control variable of the training data is
preserved by the covariance model. In addition the wind variance and
associated length scales are preserved as the scheme preserves the variances
and length scales of horizontal derivatives. If the vertical transform is
applied in physical space, it is possible to make it a function of latitude
at the cost of not preserving the variances and length scales of the
horizontal derivatives.
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Summer and winter global 4DVAR trials have
been run with both background error covariance models. A clear benefit is
seen in the fit to observations when the vertical transform is in spectral
space and is a function of total horizontal wavenumber. |
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ISSN: | 1992-0628 1992-0636 |