Evaluation of the New Background Covariance Model for the Ionospheric Data Assimilation

Radio Science ◽  
2021 ◽  
Author(s):  
Victoriya V. Forsythe ◽  
Irfan Azeem ◽  
Ryan Blay ◽  
Geoff Crowley ◽  
Federico Gasperini ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Covariance Model ◽  
Ionospheric Data Assimilation

Ionospheric data assimilation: recovery of strong mid-latitudinal density gradients

2003 ◽  
Vol 65 (10) ◽  
pp. 1087-1097 ◽  
Author(s):  
Jan J. Sojka ◽  
Donald C. Thompson ◽  
Robert W. Schunk ◽  
J.Vincent Eccles ◽  
Jonathan J. Makela ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Density Gradients ◽  
Ionospheric Data Assimilation

scholarly journals SymPKF (v1.0): a symbolic and computational toolbox for the design of parametric Kalman filter dynamics

2021 ◽  
Author(s):  
Olivier Pannekoucke ◽  
Philippe Arbogast
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Burgers Equation ◽  
Covariance Matrices ◽  
Covariance Model ◽  
Local Anisotropy ◽  
Code Generator ◽  
Univariate Statistics ◽  
Automatic Code ◽  
Python Package

Abstract. Recent researches in data assimilation lead to the introduction of the parametric Kalman filter (PKF): an implementation of the Kalman filter, where the covariance matrices are approximated by a parameterized covariance model. In the PKF, the dynamics of the covariance during the forecast step relies on the prediction of the covariance parameters. Hence, the design of the parameter dynamics is crucial while it can be tedious to do this by hand. This contribution introduces a python package, SymPKF, able to compute PKF dynamics for univariate statistics and when the covariance model is parameterized from the variance and the local anisotropy of the correlations. The ability of SymPKF to produce the PKF dynamics is shown on a non-linear diffusive advection (Burgers equation) over a 1D domain and the linear advection over a 2D domain. The computation of the PKF dynamics is performed at a symbolic level, but an automatic code generator is also introduced to perform numerical simulations. A final multivariate example illustrates the potential of SymPKF to go beyond the univariate case.

scholarly journals Ionospheric assimilation of radio occultation and ground-based GPS data using non-stationary background model error covariance

2014 ◽  
Vol 7 (3) ◽  
pp. 2631-2661 ◽  
Author(s):  
C. Y. Lin ◽  
T. Matsuo ◽  
J. Y. Liu ◽  
C. H. Lin ◽  
H. F. Tsai ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Electron Density ◽  
Radio Occultation ◽  
Model Error ◽  
Background Model ◽  
Ionospheric Electron Density ◽  
Error Covariance ◽  
Ionospheric Data Assimilation ◽  
Stationary Location ◽  
Assimilation Model

Abstract. Ionospheric data assimilation is a powerful approach to reconstruct the 3-D distribution of the ionospheric electron density from various types of observations. We present a data assimilation model for the ionosphere, based on the Gauss–Markov Kalman filter with the International Reference Ionosphere (IRI) as the background model, to assimilate two different types of total electron content (TEC) observations from ground-based GPS and space-based FORMOSAT-3/COSMIC (F3/C) radio occultation. Covariance models for the background model error and observational error play important roles in data assimilation. The objective of this study is to investigate impacts of stationary (location-independent) and non-stationary (location-dependent) classes of the background model error covariance on the quality of assimilation analyses. Location-dependent correlations are modeled using empirical orthogonal functions computed from an ensemble of the IRI outputs, while location-independent correlations are modeled using a Gaussian function. Observing System Simulation Experiments suggest that assimilation of TEC data facilitated by the location-dependent background model error covariance yields considerably higher quality assimilation analyses. Results from assimilation of real ground-based GPS and F3/C radio occultation observations over the continental United States are presented as TEC and electron density profiles. Validation with the Millstone Hill incoherent scatter radar data and comparison with the Abel inversion results are also presented. Our new ionospheric data assimilation model that employs the location-dependent background model error covariance outperforms the earlier assimilation model with the location-independent background model error covariance, and can reconstruct the 3-D ionospheric electron density distribution satisfactorily from both ground- and space-based GPS observations.

scholarly journals SymPKF (v1.0): a symbolic and computational toolbox for the design of parametric Kalman filter dynamics

2021 ◽  
Vol 14 (10) ◽  
pp. 5957-5976
Author(s):  
Olivier Pannekoucke ◽  
Philippe Arbogast
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Burgers Equation ◽  
Covariance Matrices ◽  
Covariance Model ◽  
Local Anisotropy ◽  
Code Generator ◽  
Univariate Statistics ◽  
Automatic Code ◽  
Python Package

Abstract. Recent research in data assimilation has led to the introduction of the parametric Kalman filter (PKF): an implementation of the Kalman filter, whereby the covariance matrices are approximated by a parameterized covariance model. In the PKF, the dynamics of the covariance during the forecast step rely on the prediction of the covariance parameters. Hence, the design of the parameter dynamics is crucial, while it can be tedious to do this by hand. This contribution introduces a Python package, SymPKF, able to compute PKF dynamics for univariate statistics and when the covariance model is parameterized from the variance and the local anisotropy of the correlations. The ability of SymPKF to produce the PKF dynamics is shown on a nonlinear diffusive advection (the Burgers equation) over a 1D domain and the linear advection over a 2D domain. The computation of the PKF dynamics is performed at a symbolic level, but an automatic code generator is also introduced to perform numerical simulations. A final multivariate example illustrates the potential of SymPKF to go beyond the univariate case.

Uncertainties of Terrestrial Water Storage Anomalies for Global Basins – A Comparison Between Modelled and Formal Covariances

2020 ◽  
Author(s):  
Eva Boergens ◽  
Andreas Kvas ◽  
Henryk Dobslaw ◽  
Annette Eicker ◽  
Christoph Dahle ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Spherical Harmonic ◽  
Water Storage ◽  
Covariance Matrices ◽  
Model Parameters ◽  
Data Sets ◽  
Terrestrial Water Storage ◽  
Covariance Model ◽  
Terrestrial Water ◽  
Level 3

<p class="western">The application of GRACE and GRACE-FO observed gridded terrestrial water storage data (TWS) often requires realistic assumptions of the data variances and covariances. Such covariances are, e.g., needed for data assimilation in various models or combinations with other data sets. The formal variance-covariance matrices now provided with the Stokes coefficients can yield such spatial variances and covariances after variance propagating them through the various post-processing steps, including the filtering, and spherical harmonic synthesis. However, a rigorous variance propagation to the TWS grids is beyond the capabilities of most non-geodetic users.</p> <p class="western">That is why we developed a new spatial covariance model for global TWS grids. This covariance model is non-stationary (time-depending), non-homogeneous (location-depending), and anisotropic (direction-depending). Additionally, it allows latitudinal wave-like correlations caused by residual striping errors. The model is tested for both GFZ RL06 Level-3 TWS data as provided via the GravIS portal (gravis.gfz-potsdam.de) and ITSG-Grace2018 GravIS-like processed Level-3 TWS data. The model parameters are fitted to empirical correlations derived from both TWS fields. Both data sets yield the same model parameters within the uncertainty of the parameter estimation.</p> <p class="western">Now, the covariance model derived thereof can be used to estimate uncertainties of mean TWS time series of arbitrary regions such as river basins. Here, we use a global basin segmentation covering all continents. At the same time, such regional uncertainties can be derived from formal variance-covariance matrices as well. To this end, the formal ITSG-Grace2018 variance-covariance matrices of the spherical harmonic coefficients are used. Thus, the modelled and formal basin uncertainties can be compared against each other globally, both spatially and temporally. Further, external validation investigates the usefulness of the basin uncertainties for applications such as data assimilation into hydrological models. Our results show a high agreement between the modelled and the formal basin uncertainties proving our approach of modelled covariance to be a suitable surrogate for the formal variance-covariance matrices.</p>

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