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 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 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 Estimating Surface Carbon Fluxes Based on a Local Ensemble Transform Kalman Filter with a Short Assimilation Window and a Long Observation Window

2017 ◽  
Author(s):  
Yun Liu ◽  
Eugenia Kalnay ◽  
Ning Zeng ◽  
Ghassem Asrar ◽  
Zhaohui Chen ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Grid Point ◽  
Carbon Fluxes ◽  
Transfer Model ◽  
Observation Window ◽  
Surface Carbon ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform ◽  
Assimilation System

Abstract. We developed a Carbon data assimilation system to estimate the surface carbon fluxes using the Local Ensemble Transform Kalman Filter and atmospheric transfer model of GEOS-Chem driven by the MERRA-1 reanalysis of the meteorological fields based on the Goddard Earth Observing System Model, Version 5 (GEOS-5). This assimilation system is inspired by the method of Kang et al. [2011, 2012], who estimated the surface carbon fluxes in an Observing System Simulation Experiment (OSSE) mode, as evolving parameters in the assimilation of the atmospheric CO2, using a short assimilation window of 6 hours. They included the assimilation of the standard meteorological variables, so that the ensemble provided a measure of the uncertainty in the CO2 transport. After introducing new techniques such as variable localization, and increased observation weights near the surface, they obtained accurate carbon fluxes at grid point resolution. We developed a new version of the LETKF related to the Running-in-Place (RIP) method used to accelerate the spin-up of EnKF data assimilation [Kalnay and Yang, 2010; Wang et al., 2013, Yang et al., 2014]. Like RIP, the new assimilation system uses the no-cost smoothing algorithm for the LETKF [Kalnay et al., 2007b], which allows shifting at no cost the Kalman Filter solution forward or backward within an assimilation window. In the new scheme a long observation window (e.g., 7-days or longer) is used to create an LETKF ensemble at 7-days. Then, the RIP smoother is used to obtain an accurate final analysis at 1-day. This analysis has the advantage of being based on a short assimilation window, which makes it more accurate, and of having been exposed to the future 7-days observations, which accelerates the spin up. The assimilation and observation windows are then shifted forward by one day, and the process is repeated. This reduces significantly the analysis error, suggesting that this method could be used in other data assimilation problems.

scholarly journals Soil Moisture Assimilation Using a Modified Ensemble Transform Kalman Filter Based on Station Observations in the Hai River Basin

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Guocan Wu ◽  
Bo Dan ◽  
Xiaogu Zheng
Keyword(s):  
Soil Moisture ◽  
Kalman Filter ◽  
Water Budget ◽  
Forecast Error ◽  
Estimation Accuracy ◽  
Surface Model ◽  
Common Land Model ◽  
Ensemble Transform Kalman Filter ◽  
Analysis Error ◽  
Ensemble Transform

Assimilating observations to a land surface model can further improve soil moisture estimation accuracy. However, assimilation results largely rely on forecast error and generally cannot maintain a water budget balance. In this study, shallow soil moisture observations are assimilated into Common Land Model (CoLM) to estimate the soil moisture in different layers. A proposed forecast error inflation and water balance constraint are adopted in the Ensemble Transform Kalman Filter to reduce the analysis error and water budget residuals. The assimilation results indicate that the analysis error is reduced and the water imbalance is mitigated with this approach.

scholarly journals Evaluation of a Strategy for the Assimilation of Satellite Radiance Observations with the Local Ensemble Transform Kalman Filter

2011 ◽  
Vol 139 (6) ◽  
pp. 1932-1951 ◽  
Author(s):  
José A. Aravéquia ◽  
Istvan Szunyogh ◽  
Elana J. Fertig ◽  
Eugenia Kalnay ◽  
David Kuhl ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Grid Point ◽  
Earth Observing System ◽  
Wind Analysis ◽  
Correction Technique ◽  
Ensemble Transform Kalman Filter ◽  
Environmental Prediction ◽  
Observation Bias ◽  
Ensemble Transform

Abstract This paper evaluates a strategy for the assimilation of satellite radiance observations with the local ensemble transform Kalman filter (LETKF) data assimilation scheme. The assimilation strategy includes a mechanism to select the radiance observations that are assimilated at a given grid point and an ensemble-based observation bias-correction technique. Numerical experiments are carried out with a reduced (T62L28) resolution version of the model component of the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS). The observations used for the evaluation of the assimilation strategy are AMSU-A level 1B brightness temperature data from the Earth Observing System (EOS) Aqua spacecraft. The assimilation of these observations, in addition to all operationally assimilated nonradiance observations, leads to a statistically significant improvement of both the temperature and wind analysis in the Southern Hemisphere. This result suggests that the LETKF, combined with the proposed data assimilation strategy for the assimilation of satellite radiance observations, can efficiently extract information from radiance observations.

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.

scholarly journals Estimating Surface Carbon Fluxes Based on a Local Ensemble Transform Kalman Filter with a Short Assimilation Window and a Long Observation Window

2017 ◽  
Author(s):  
Yun Liu ◽  
Eugenia Kalnay ◽  
Ning Zeng ◽  
Ghassem Asrar ◽  
Zhaohui Chen ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Grid Point ◽  
Carbon Fluxes ◽  
Transfer Model ◽  
Observation Window ◽  
Surface Carbon ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform ◽  
Assimilation System

Abstract. We developed a Carbon data assimilation system to estimate the surface carbon fluxes using the Local Ensemble Transform Kalman Filter and atmospheric transfer model of GEOS-Chem driven by the MERRA-1 reanalysis of the meteorological fields based on the Goddard Earth Observing System Model, Version 5 (GEOS-5). This assimilation system is inspired by the method of Kang et al. (2011, 2012), who estimated the surface carbon fluxes in an Observing System Simulation Experiment (OSSE) mode, as evolving parameters in the assimilation of the atmospheric CO2, using a short assimilation window of 6 hours. They included the assimilation of the standard meteorological variables, so that the ensemble provided a measure of the uncertainty in the CO2 transport. After introducing new techniques such as “variable localization”, and increased observation weights near the surface, they obtained accurate carbon fluxes at grid point resolution. We developed a new version of the LETKF related to the “Running-in-Place” (RIP) method used to accelerate the spin-up of EnKF data assimilation (Kalnay and Yang, 2010; Wang et al., 2013, Yang et al., 2014). Like RIP, the new assimilation system uses the “no-cost smoothing” algorithm for the LETKF (Kalnay et al., 2007b), which allows shifting at no cost the Kalman Filter solution forward or backward within an assimilation window. In the new scheme a long “observation window” (e.g., 7-days or longer) is used to create an LETKF ensemble at 7-days. Then, the RIP smoother is used to obtain an accurate final analysis at 1-day. This analysis has the advantage of being based on a short assimilation window, which makes it more accurate, and of having been exposed to the future 7-days observations, which accelerates the spin up. The assimilation and observation windows are then shifted forward by one day, and the process is repeated. This reduces significantly the analysis error, suggesting that this method could be used in other data assimilation problems. The newly developed assimilation method can be used with other Earth system models, especially for greater use of observations in conjunction with models.

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