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Toward Sequential Data Assimilation for NWP Models Using Kalman Filter Tools
Stockholm University, Faculty of Science, Department of Mathematics.
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The aim of the meteorological data assimilation is to provide an initial field for Numerical Weather Prediction (NWP) and to sequentially update the knowledge about it using available observations. Kalman filtering is a robust technique for the sequential estimation of the unobservable model state based on the linear regression concept. In the iterative use together with Kalman smoothing, it can easily be extended to work powerfully in the non-Gaussian and/or  non-linear framework. The huge dimensionality of the model state variable for high resolution NWP models (magnitude 108) makes it impossible with any explicit manipulations of the forecast error covariance matrix required for Kalman filter and Kalman smoother recursions. For NWP models the technical implementation of a Kalman filtering becomes the main challenge which provokes developments of novel data assimilation algorithms.

This thesis is concerned with extensions of the Kalman filtering when the assumptions on linearity and Gaussianity of the state space model are violated. The research includes both theoretical studies of the properties of such extensions, within the framework of idealized small-dimensional models, and the development of the data assimilation algorithms for a full scale limited area high resolution NWP forecasting system.

This thesis shows that non-Gaussian state space models can efficiently be approximated by a Gaussian state space model with an adaptively estimated variance of the stochastic forcing. That results in a type of local smoothing, in contrast to the global smoothing provided by Gaussian state space models. With regards to NWP models, the thesis shows that the sequential update of the uncertainty about the model state estimate is essential for efficient extraction of information from observations. The Ensemble Kalman filters can be used to represent both flow- and observation-network-dependent structures of the forecast error covariance matrix, in spite of a severe rank-deficiency of the Ensemble Kalman filters. As a culmination of this research the hybrid variational data assimilation has been developed on top of the HIRLAM variational data assimilation system. It provides the possibility of utilizing, during the data assimilation process, the error-of-the-day structure of the forecast error covariance, estimated from the ensemble of perturbations, at the same time as the full rank of the variational data assimilation is preserved.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University , 2010. , 115 p.
Keyword [en]
non-Gaussian state space models, Kalman filtering, ETKF, 3D-Var, data assimilation, NWP
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:su:diva-38820ISBN: 978-91-7447-093-2 (print)OAI: oai:DiVA.org:su-38820DiVA: diva2:315880
Public defence
2010-06-04, sal 14, hus 5, Kräftriket, Roslagsvägen 101, Stockholm, 10:00 (English)
Opponent
Supervisors
Note
At the time of the doctoral defense, the following papers were unpublished  and had a status as follows: Paper 1: Manuscript. Paper 2: Manuscript. Paper 3: Accepted. Paper 4: Manuscript.Available from: 2010-05-12 Created: 2010-04-29 Last updated: 2010-05-12Bibliographically approved
List of papers
1. The EKTF rescaling scheme in HIRLAM
Open this publication in new window or tab >>The EKTF rescaling scheme in HIRLAM
2011 (English)In: Tellus. Series A, Dynamic meteorology and oceanography, ISSN 0280-6495, E-ISSN 1600-0870, Vol. 63, no 3, 685-401 p.Article in journal (Other academic) Published
Abstract [en]

The ETKF rescaling scheme has been implemented into the HIRLAM forecasting system in order to estimate the uncertainty of the model state. The main purpose is to utilize this uncertainty information for modelling of flow-dependent background error covariances within the framework of a hybrid variational ensemble data assimilation scheme. The effects of rank-deficiency in the ETKF formulation is explained and the need for variance inflation as a way to compensate for these effects is justified. A filter spin-up algorithm is proposed as a refinement of the variance inflation. The proposed spin-up algorithm will also act to prevent ensemble collapse since the ensemble will receive ‘fresh blood’ in the form of additional perturbation components, generated on the basis of a static background error covariance matrix. The resulting ETKF-based ensemble perturbations are compared with ensemble perturbations based on targeted singular vectors and are shown to have more realistic spectral characteristics.

National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-38811 (URN)10.1111/j.1600-0870.2011.00513.x (DOI)
Available from: 2010-04-29 Created: 2010-04-29 Last updated: 2017-12-12Bibliographically approved
2. A hybrid variational ensemble data assimilation for the HIgh Resolution Limited Area Model (HIRLAM)
Open this publication in new window or tab >>A hybrid variational ensemble data assimilation for the HIgh Resolution Limited Area Model (HIRLAM)
(English)Manuscript (preprint) (Other academic)
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics; Meteorology
Identifiers
urn:nbn:se:su:diva-38814 (URN)
Available from: 2010-04-29 Created: 2010-04-29 Last updated: 2010-05-12
3. Non-Gaussian state space models in decomposition of ice core time series in long and short time-scales
Open this publication in new window or tab >>Non-Gaussian state space models in decomposition of ice core time series in long and short time-scales
2010 (English)In: Environmetrics, ISSN 1180-4009, E-ISSN 1099-095X, Vol. 21, no 6, 562-587 p.Article in journal (Refereed) Published
Abstract [en]

Statistical modelling of six time series of geological ice core chemical data from Greenland is discussed. We decompose the total variation into long time-scale (trend) and short time-scale variations (fluctuations around the trend), and a pure noise component. Too heavy tails of the short-term variation makes a standard time-invariant linear Gaussian model inadequate. We try non-Gaussian state space models, which can be efficiently approximated by time-dependent Gaussian models. In essence, these time-dependent Gaussian models result in a local smoothing, in contrast to the global smoothing provided by the time-invariant model. To describe the mechanism of this local smoothing, we utilise the concept of a local variance function derived from a heavy-tailed density. The time-dependent error variance expresses the uncertainty about the dynamical development of the model state, and it controls the influence of observations on the estimates of the model state components. The great advantage of the derived time-dependent Gaussian model is that the Kalman filter and the Kalman smoother can be used as efficient computational tools for performing the variation decomposition. One of the main objectives of the study is to investigate how the distributional assumption on the model error component of the short time-scale variation affects the decomposition.

Keyword
On-line estimation, Kalman filter and Kalman smoother, variation decomposition, local linear Gaussian model, non-Gaussian state space model, GISP2, NGRIP
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-38810 (URN)10.1002/env.1012 (DOI)000282913900002 ()
Available from: 2010-04-29 Created: 2010-04-29 Last updated: 2017-12-12Bibliographically approved
4. Aspects of non-linearities for data assimilation by Kalman filtering in a shallow water model
Open this publication in new window or tab >>Aspects of non-linearities for data assimilation by Kalman filtering in a shallow water model
(English)Manuscript (preprint) (Other academic)
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-38806 (URN)
Available from: 2010-04-29 Created: 2010-04-29 Last updated: 2010-05-12

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