scholarly journals Using the local ensemble Transform Kalman Filter for upper atmospheric modelling

2019 ◽  
Vol 9 ◽  
pp. A30 ◽  
Author(s):  
Sean Elvidge ◽  
Matthew J. Angling
Keyword(s):  
Kalman Filter ◽  
General Circulation ◽  
Computational Cost ◽  
Circulation Model ◽  
Electron Content ◽  
Total Electron ◽  
Rms Error ◽  
Ensemble Transform Kalman Filter ◽  
Assimilation Model ◽  
Ensemble Transform

The Advanced Ensemble electron density (Ne) Assimilation System (AENeAS) is a new data assimilation model of the ionosphere/thermosphere. The background model is provided by the Thermosphere Ionosphere Electrodynamics General Circulation Model (TIE-GCM) and the assimilation uses the local ensemble transform Kalman filter (LETKF). An outline derivation of the LETKF is provided and the equations are presented in a form analogous to the classic Kalman filter. An enhancement to the efficient LETKF implementation to reduce computational cost is also described. In a 3 day test in June 2017, AENeAS exhibits a total electron content (TEC) RMS error of 2.1 TECU compared with 5.5 TECU for NeQuick and 6.8 for TIE-GCM (with an NeQuick topside).

scholarly journals The Gaussian Approach to Adaptive Covariance Inflation and Its Implementation with the Local Ensemble Transform Kalman Filter

2011 ◽  
Vol 139 (5) ◽  
pp. 1519-1535 ◽  
Author(s):  
Takemasa Miyoshi
Keyword(s):  
Kalman Filter ◽  
General Circulation ◽  
Forecast Error ◽  
Grid Point ◽  
Circulation Model ◽  
Error Variance ◽  
Model Errors ◽  
Variable Model ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform

In ensemble Kalman filters, the underestimation of forecast error variance due to limited ensemble size and other sources of imperfection is commonly treated by empirical covariance inflation. To avoid manual optimization of multiplicative inflation parameters, previous studies proposed adaptive inflation approaches using observations. Anderson applied Bayesian estimation theory to the probability density function of inflation parameters. Alternatively, Li et al. used the innovation statistics of Desroziers et al. and applied a Kalman filter analysis update to the inflation parameters based on the Gaussian assumption. In this study, Li et al.’s Gaussian approach is advanced to include the variance of the estimated inflation as derived from the central limit theorem. It is shown that the Gaussian approach is an accurate approximation of Anderson’s general Bayesian approach. An advanced implementation of the Gaussian approach with the local ensemble transform Kalman filter is proposed, where the adaptive inflation parameters are computed simultaneously with the ensemble transform matrix at each grid point. The spatially and temporally varying adaptive inflation technique is implemented with the Lorenz 40-variable model and a low-resolution atmospheric general circulation model; numerical experiments show promising results both with and without model errors.

scholarly journals The local ensemble transform Kalman filter and the running-in-place algorithm applied to a global ocean general circulation model

2013 ◽  
Vol 20 (6) ◽  
pp. 1031-1046 ◽  
Author(s):  
S. G. Penny ◽  
E. Kalnay ◽  
J. A. Carton ◽  
B. R. Hunt ◽  
K. Ide ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
General Circulation ◽  
Initial Conditions ◽  
Circulation Model ◽  
Global Ocean ◽  
Observation Data ◽  
Background Error ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform

Abstract. The most widely used methods of data assimilation in large-scale oceanography, such as the Simple Ocean Data Assimilation (SODA) algorithm, specify the background error covariances and thus are unable to refine the weights in the assimilation as the circulation changes. In contrast, the more computationally expensive Ensemble Kalman Filters (EnKF) such as the Local Ensemble Transform Kalman Filter (LETKF) use an ensemble of model forecasts to predict changes in the background error covariances and thus should produce more accurate analyses. The EnKFs are based on the approximation that ensemble members reflect a Gaussian probability distribution that is transformed linearly during the forecast and analysis cycle. In the presence of nonlinearity, EnKFs can gain from replacing each analysis increment by a sequence of smaller increments obtained by recursively applying the forecast model and data assimilation procedure over a single analysis cycle. This has led to the development of the "running in place" (RIP) algorithm by Kalnay and Yang (2010) and Yang et al. (2012a,b) in which the weights computed at the end of each analysis cycle are used recursively to refine the ensemble at the beginning of the analysis cycle. To date, no studies have been carried out with RIP in a global domain with real observations. This paper provides a comparison of the aforementioned assimilation methods in a set of experiments spanning seven years (1997–2003) using identical forecast models, initial conditions, and observation data. While the emphasis is on understanding the similarities and differences between the assimilation methods, comparisons are also made to independent ocean station temperature, salinity, and velocity time series, as well as ocean transports, providing information about the absolute error of each. Comparisons to independent observations are similar for the assimilation methods but the observation-minus-background temperature differences are distinctly lower for LETKF and RIP. The results support the potential for LETKF to improve the quality of ocean analyses on the space and timescales of interest for seasonal prediction and for RIP to accelerate the spin up of the system.

scholarly journals A Unification of Ensemble Square Root Kalman Filters

2012 ◽  
Vol 140 (7) ◽  
pp. 2335-2345 ◽  
Author(s):  
Lars Nerger ◽  
Tijana Janjić ◽  
Jens Schröter ◽  
Wolfgang Hiller
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Kalman Filters ◽  
Numerical Experiments ◽  
Computational Cost ◽  
Square Root ◽  
Symmetric Square ◽  
Ensemble Transform Kalman Filter ◽  
Filter Algorithms ◽  
Ensemble Transform

Abstract In recent years, several ensemble-based Kalman filter algorithms have been developed that have been classified as ensemble square root Kalman filters. Parallel to this development, the singular “evolutive” interpolated Kalman (SEIK) filter has been introduced and applied in several studies. Some publications note that the SEIK filter is an ensemble Kalman filter or even an ensemble square root Kalman filter. This study examines the relation of the SEIK filter to ensemble square root filters in detail. It shows that the SEIK filter is indeed an ensemble square root Kalman filter. Furthermore, a variant of the SEIK filter, the error subspace transform Kalman filter (ESTKF), is presented that results in identical ensemble transformations to those of the ensemble transform Kalman filter (ETKF), while having a slightly lower computational cost. Numerical experiments are conducted to compare the performance of three filters (SEIK, ETKF, and ESTKF) using deterministic and random ensemble transformations. The results show better performance for the ETKF and ESTKF methods over the SEIK filter as long as this filter is not applied with a symmetric square root. The findings unify the separate developments that have been performed for the SEIK filter and the other ensemble square root Kalman filters.

scholarly journals Spatial and temporal variation of total electron content as revealed by principal component analysis

2016 ◽  
Vol 34 (12) ◽  
pp. 1109-1117 ◽  
Author(s):  
Elsayed R. Talaat ◽  
Xun Zhu
Keyword(s):  
Principal Component Analysis ◽  
Total Electron Content ◽  
General Circulation ◽  
Circulation Model ◽  
Principal Component ◽  
Component Analysis ◽  
Total Variance ◽  
Spatial And Temporal Variation ◽  
Electron Content ◽  
Total Electron

Abstract. Eleven years of global total electron content (TEC) data derived from the assimilated thermosphere–ionosphere electrodynamics general circulation model are analyzed using empirical orthogonal function (EOF) decomposition and the corresponding principal component analysis (PCA) technique. For the daily averaged TEC field, the first EOF explains more than 89 % and the first four EOFs explain more than 98 % of the total variance of the TEC field, indicating an effective data compression and clear separation of different physical processes. The effectiveness of the PCA technique for TEC is nearly insensitive to the horizontal resolution and the length of the data records. When the PCA is applied to global TEC including local-time variations, the rich spatial and temporal variations of field can be represented by the first three EOFs that explain 88 % of the total variance. The spectral analysis of the time series of the EOF coefficients reveals how different mechanisms such as solar flux variation, change in the orbital declination, nonlinear mode coupling and geomagnetic activity are separated and expressed in different EOFs. This work demonstrates the usefulness of using the PCA technique to assimilate and monitor the global TEC field.

scholarly journals Non-Gaussian statistics in global atmospheric dynamics: a study with a 10 240-member ensemble Kalman filter using an intermediate AGCM

2018 ◽  
Author(s):  
Keiichi Kondo ◽  
Takemasa Miyoshi
Keyword(s):  
Kalman Filter ◽  
General Circulation ◽  
Circulation Model ◽  
Tropical Regions ◽  
Highly Nonlinear ◽  
Gaussian Statistics ◽  
Ensemble Transform Kalman Filter ◽  
Analysis Error ◽  
Non Gaussian ◽  
Analysis Errors

Abstract. We previously performed local ensemble transform Kalman filter experiments with up to 10 240 ensemble members using an intermediate atmospheric general circulation model. While the previous study focused on the localization impact on the analysis accuracy, the present study focuses on the probability density functions (PDFs) represented by the 10 240-member ensemble. The 10 240-member ensemble can resolve the detailed structures of the PDFs and indicates that the non-Gaussian PDF is caused by multimodality and outliers. The results show that the spatial patterns of the analysis errors correspond well with the non-Gaussianity. While the outliers appear randomly, large multimodality corresponds well with large analysis error, mainly in the tropical regions where highly nonlinear convective processes appear frequently. Therefore, we further investigate the lifecycle of multimodal PDFs, and show that the multimodal PDFs are generated by the on-off switch of convective parameterization and disappear naturally. Sensitivity to the ensemble size suggests that approximately 1000 ensemble members be necessary to capture the detailed structures of the non-Gaussian PDF.

The influence of ionospheric neutral wind variations on the propagation of a MSTID event

2021 ◽  
Author(s):  
Ji Luo ◽  
Jiyao Xu ◽  
Kun Wu ◽  
Wenbin Wang ◽  
Chao Xiong ◽  
...  
Keyword(s):  
General Circulation ◽  
Circulation Model ◽  
Propagation Direction ◽  
Electron Content ◽  
Total Electron ◽  
Neutral Winds ◽  
Fabry Perot ◽  
Inclination Angles ◽  
Swarm Satellite ◽  
Special Case

<p>The event reports a special case of the propagation and morphology of medium scale travelling ionospheric disturbances (MSTIDs) over middle–latitude China. The MSTIDs were simultaneously observed by the all-sky imager, Swarm satellite, as well as the total electron content (TEC) from global positioning system (GPS). In addition, the MSTIDs lasted for about 6 hours of the field view of airglow imager, the continuous imagers show that the inclination angles of phase fronts were decreasing gradually during the propagation process, resulting in the propagation direction changed from southwestward to nearly westward. More interestingly, the MSTIDs began to dissipate in the airglow observation when they propagated to lower latitudes with the MSTIDs at higher latitudes still visible in the later times. The simulation results from the Thermosphere-Ionosphere-Electrodynamics General Circulation Model (TIEGCM) and the Fabry-Perot Interferometer (FPI) wind observations suggest that the variations of background neutral winds and the ionospheric density might play important roles in the changes of propagation direction and the dissipation of MSTIDs.</p>

Strongly coupled ensemble transform Kalman filter estimation of ocean optical parameters in a coupled GCM

2021 ◽  
Author(s):  
Vassili Kitsios ◽  
Paul Sandery ◽  
Terence O'Kane ◽  
Russell Fiedler
Keyword(s):  
Kalman Filter ◽  
Sea Ice ◽  
General Circulation ◽  
Optical Parameters ◽  
Length Scale ◽  
Strongly Coupled ◽  
Climate Forecasts ◽  
Cycle Lengths ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform

<p>Coupled general circulation models (GCM) of the atmosphere, ocean, land and sea-ice have many parameters. Some of which govern the numerics of the dynamical core, whilst others represent the influence of unresolved subgrid process based on our current fundamental physical understanding. The spatio-temporal structure of many of these parameters are known with little precision, which contributes to the inherent model biases in the underlying GCM. To address this problem we use the CSIRO Climate re-Analysis and Forecast Ensemble (CAFE) system to estimate both the climate state (atmosphere, ocean, sea-ice) and also spatio-temporally varying parameter maps of the ocean surface albedo and shortwave radiation e-folding length scale in a coupled climate GCM of CMIP resolution and complexity. The CAFE system adopts a 96 member ensemble transform Kalman filter within a strongly coupled data assimilation (DA) framework. The parameters (and states) are determined by minimising the error between short term DA cycle forecasts of the climate model and a network of real world atmospheric, oceanic, and sea-ice observations.  Several DA cycle lengths are tested between 3 to 28 days. The DA system has an improved fit to observations over the period from 2010 to 2012, when estimating both of the ocean optical parameters either individually or simultaneously. However, only individually estimated maps of shortwave e-folding length scale attain systematically reduced bias in multi-year climate forecasts during the out-of-sample period from 2012 to 2020. Parameter maps determined from longer DA cycle lengths also have further reduced multi-year forecast bias. Such improved climate forecasts would potentially enable policy makers to make better informed decisions on water, energy and agricultural infrastructure and planning.</p>

scholarly journals Comparison between Local Ensemble Transform Kalman Filter and PSAS in the NASA finite volume GCM – perfect model experiments

2008 ◽  
Vol 15 (4) ◽  
pp. 645-659 ◽  
Author(s):  
J. Liu ◽  
E. J. Fertig ◽  
H. Li ◽  
E. Kalnay ◽  
B. R. Hunt ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Finite Volume ◽  
Circulation Model ◽  
Forecast Errors ◽  
Global Circulation Model ◽  
Perfect Model ◽  
Grid Points ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform ◽  
Assimilation System

Abstract. This paper compares the performance of the Local Ensemble Transform Kalman Filter (LETKF) with the Physical-Space Statistical Analysis System (PSAS) under a perfect model scenario. PSAS is a 3D-Var assimilation system used operationally in the Goddard Earth Observing System Data Assimilation System (GEOS-4 DAS). The comparison is carried out using simulated winds and geopotential height observations and the finite volume Global Circulation Model with 72 grid points zonally, 46 grid points meridionally and 55 vertical levels. With forty ensemble members, the LETKF obtains analyses and forecasts with significantly lower RMS errors than those from PSAS, especially over the Southern Hemisphere and oceans. This observed advantage of the LETKF over PSAS is due to the ability of the 40-member ensemble LETKF to capture flow-dependent errors and thus create a good estimate of the evolving background uncertainty. An initial decrease of the forecast errors in the Northern Hemisphere observed in the PSAS but not in the LETKF suggests that the LETKF analysis is more balanced.

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