14:00 〜 14:15
[MGI30-02] Accounting for non-locality of vertical error correlation within ETKF through eigen-spectral localization
★Invited Papers
キーワード：データ同化、共分散局所化、アンサンブル・カルマンフィルタ
Covariance localization is an indispensable component of any EnKF and
it is most straightforwardly formulated as tapering of the sampled
background error covariance matrix by means of Schur product
(B-loc). However, within most (L)ETKF implementations, this operation
is substituted by artificial inflation of R-matrix for observations
distant from the analyzed grid-point (R-loc) due to the computational
the difficulty of B-loc approach. Recently studies (Bocquet et al. 2016;
Bishop et al. 2017) have derived an efficient way to implement B-loc
within an ETKF, so that B-loc within ETKF is now a feasible option.
The author's recent work has focused on clarifying the differences
between B-loc and R-loc, and showed with idealized 1D models that
B-loc can increase the effective rank of the background covariance
while R-loc cannot and that B-loc can more faithfully reproduce
canonical KF analysis than R-loc does when the observation operator is
non-local, suggesting that B-loc is particularly advantageous in cases
where the desired amount of assimilated observations are much larger
than the affordable ensemble size and/or the observation operator is
highly non-local.
This work extends the B-loc approach to accommodate situations where
the true background error covariance is not well localized (i.e., the
correlation between two grid-points is not given in terms of the
physical distance between them). In the proposed scheme, the state
vector of each background ensemble is first linearly transformed into
the space spanned by the (truncated) eigenbasis of the climatological
background error covariance prior to performing data assimilation. The
transformed ensemble is then used to form sample covariance to which
we apply localization (i.e., control on sampling noises) by
neglecting all the off-diagonal components. This method reposes on two
assumptions: (1) the true covariance, when expressed in its
eigen-space, is diagonal, so that, in this space, any off-diagonal
component present in the sample covariance from ensemble is a sign of
sampling error, and (2) the eigenstructure of the true covariance is
close to its climatological expectation.
In this presentation, I will show several preliminary verifications of
this approach using an idealized 1-dimensional system and discuss its
promise and limitations.
it is most straightforwardly formulated as tapering of the sampled
background error covariance matrix by means of Schur product
(B-loc). However, within most (L)ETKF implementations, this operation
is substituted by artificial inflation of R-matrix for observations
distant from the analyzed grid-point (R-loc) due to the computational
the difficulty of B-loc approach. Recently studies (Bocquet et al. 2016;
Bishop et al. 2017) have derived an efficient way to implement B-loc
within an ETKF, so that B-loc within ETKF is now a feasible option.
The author's recent work has focused on clarifying the differences
between B-loc and R-loc, and showed with idealized 1D models that
B-loc can increase the effective rank of the background covariance
while R-loc cannot and that B-loc can more faithfully reproduce
canonical KF analysis than R-loc does when the observation operator is
non-local, suggesting that B-loc is particularly advantageous in cases
where the desired amount of assimilated observations are much larger
than the affordable ensemble size and/or the observation operator is
highly non-local.
This work extends the B-loc approach to accommodate situations where
the true background error covariance is not well localized (i.e., the
correlation between two grid-points is not given in terms of the
physical distance between them). In the proposed scheme, the state
vector of each background ensemble is first linearly transformed into
the space spanned by the (truncated) eigenbasis of the climatological
background error covariance prior to performing data assimilation. The
transformed ensemble is then used to form sample covariance to which
we apply localization (i.e., control on sampling noises) by
neglecting all the off-diagonal components. This method reposes on two
assumptions: (1) the true covariance, when expressed in its
eigen-space, is diagonal, so that, in this space, any off-diagonal
component present in the sample covariance from ensemble is a sign of
sampling error, and (2) the eigenstructure of the true covariance is
close to its climatological expectation.
In this presentation, I will show several preliminary verifications of
this approach using an idealized 1-dimensional system and discuss its
promise and limitations.