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| Titel |
Estimation and calibration of observation impact signals using the Lanczos method in NOAA/NCEP data assimilation system |
| VerfasserIn |
M. Wei, M. S. F. V. Pondeca, Z. Toth, D. Parrish |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 19, no. 5 ; Nr. 19, no. 5 (2012-09-25), S.541-557 |
| Datensatznummer |
250014245
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| Publikation (Nr.) |
 copernicus.org/npg-19-541-2012.pdf |
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| Zusammenfassung |
Despite the tremendous progress that has been made in data assimilation (DA)
methodology, observing systems that reduce observation errors, and model
improvements that reduce background errors, the analyses produced by the
best available DA systems are still different from the truth. Analysis error
and error covariance are important since they describe the accuracy of the
analyses, and are directly related to the future forecast errors, i.e., the
forecast quality. In addition, analysis error covariance is critically
important in building an efficient ensemble forecast system (EFS).
Estimating analysis error covariance in an ensemble-based Kalman filter DA
is straightforward, but it is challenging in variational DA systems, which
have been in operation at most NWP (Numerical Weather Prediction) centers.
In this study, we use the Lanczos method in the NCEP (the National Centers
for Environmental Prediction) Gridpoint Statistical Interpolation (GSI) DA
system to look into other important aspects and properties of this method
that were not exploited before. We apply this method to estimate the
observation impact signals (OIS), which are directly related to the analysis
error variances. It is found that the smallest eigenvalue of the transformed
Hessian matrix converges to one as the number of minimization iterations
increases. When more observations are assimilated, the convergence becomes
slower and more eigenvectors are needed to retrieve the observation impacts.
It is also found that the OIS over data-rich regions can be represented by
the eigenvectors with dominant eigenvalues.
Since only a limited number of eigenvectors can be computed due to
computational expense, the OIS is severely underestimated, and the analysis
error variance is consequently overestimated. It is found that the mean OIS
values for temperature and wind components at typical model levels are
increased by about 1.5 times when the number of eigenvectors is doubled. We
have proposed four different calibration schemes to compensate for the
missing trailing eigenvectors. Results show that the method with calibration
for a small number of eigenvectors cannot pick up the observation impacts
over the regions with fewer observations as well as a benchmark with a large
number of eigenvectors, but proper calibrations do enhance and improve the
impact signals over regions with more data.
When compared with the observation locations, the method generally captures
the OIS over regions with more observation data, including satellite data
over the southern oceans. Over the tropics, some observation impacts may be
missed due to the smaller background errors specified in the GSI, which is
not related to the method. It is found that a large number of eigenvectors
are needed to retrieve impact signals that resemble the banded structures
from satellite observations, particularly over the tropics. Another benefit
from the Lanczos method is that the dominant eigenvectors can be used in
preconditioning the conjugate gradient algorithm in the GSI to speed up the
convergence. |
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