scholarly journals Applying an ensemble Kalman filter to the assimilation of AERONET observations in a global aerosol transport model

2009 ◽  
Vol 9 (6) ◽  
pp. 23835-23873 ◽  
Author(s):  
N. A. J. Schutgens ◽  
T. Miyoshi ◽  
T. Takemura ◽  
T. Nakajima
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Transport Model ◽  
Current Model ◽  
Aerosol Transport ◽  
Model Uncertainties ◽  
Variable Model ◽  
Mixing Ratios ◽  
Observational Errors ◽  
Assimilation System

Abstract. We present a global aerosol assimilation system based on an ensemble Kalman filter, which we believe leads to a significant improvement in aerosol fields. The ensemble allows realistic, spatially and temporally variable model covariances (unlike other assimilation schemes). As the analyzed variables are mixing ratios (prognostic variables of the aerosol transport model), there is no need for the extra assumptions required by previous assimilation schemes analyzing aerosol optical thickness (AOT). We describe the implementation of this assimilation system and in particular the construction of the ensemble. This ensemble should represent our estimate of current model uncertainties. Consequently, we construct the ensemble around randomly modified emission scenarios. The system is tested with AERONET observations of AOT and Angström exponent (AE). Particular care is taken in the prescribing the observational errors. The assimilated fields (AOT and AE) are validated through independent AERONET, SKYNET and MODIS Aqua observations. We show that, in general, assimilation of AOT observations leads to improved modelling of global AOT, while assimilation of AE only improves modelling when the AOT is high.

scholarly journals Applying an ensemble Kalman filter to the assimilation of AERONET observations in a global aerosol transport model

2010 ◽  
Vol 10 (5) ◽  
pp. 2561-2576 ◽  
Author(s):  
N. A. J. Schutgens ◽  
T. Miyoshi ◽  
T. Takemura ◽  
T. Nakajima
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Transport Model ◽  
Current Model ◽  
Aerosol Transport ◽  
Model Uncertainties ◽  
Variable Model ◽  
Mixing Ratios ◽  
Observational Errors ◽  
Assimilation System

Abstract. We present a global aerosol assimilation system based on an Ensemble Kalman filter, which we believe leads to a significant improvement in aerosol fields. The ensemble allows realistic, spatially and temporally variable model covariances (unlike other assimilation schemes). As the analyzed variables are mixing ratios (prognostic variables of the aerosol transport model), there is no need for the extra assumptions required by previous assimilation schemes analyzing aerosol optical thickness (AOT). We describe the implementation of this assimilation system and in particular the construction of the ensemble. This ensemble should represent our estimate of current model uncertainties. Consequently, we construct the ensemble around randomly modified emission scenarios. The system is tested with AERONET observations of AOT and Angström exponent (AE). Particular care is taken in prescribing the observational errors. The assimilated fields (AOT and AE) are validated through independent AERONET, SKYNET and MODIS Aqua observations. We show that, in general, assimilation of AOT observations leads to improved modelling of global AOT, while assimilation of AE only improves modelling when the AOT is high.

scholarly journals Comparison of the ensemble Kalman filter and 4D-Var assimilation methods using a stratospheric tracer transport model

2014 ◽  
Vol 7 (4) ◽  
pp. 1451-1465 ◽  
Author(s):  
S. Skachko ◽  
Q. Errera ◽  
R. Ménard ◽  
Y. Christophe ◽  
S. Chabrillat
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Transport Model ◽  
Control Variable ◽  
Observation Data ◽  
Tracer Transport ◽  
Error Statistics ◽  
Data Set ◽  
Two Parameters ◽  
Assimilation System

Abstract. An ensemble Kalman filter (EnKF) assimilation method is applied to the tracer transport using the same stratospheric transport model as in the four-dimensional variational (4D-Var) assimilation system BASCOE (Belgian Assimilation System for Chemical ObsErvations). This EnKF version of BASCOE was built primarily to avoid the large costs associated with the maintenance of an adjoint model. The EnKF developed in BASCOE accounts for two adjustable parameters: a parameter α controlling the model error term and a parameter r controlling the observational error. The EnKF system is shown to be markedly sensitive to these two parameters, which are adjusted based on the monitoring of a χ2 test measuring the misfit between the control variable and the observations. The performance of the EnKF and 4D-Var versions was estimated through the assimilation of Aura-MLS (microwave limb sounder) ozone observations during an 8-month period which includes the formation of the 2008 Antarctic ozone hole. To ensure a proper comparison, despite the fundamental differences between the two assimilation methods, both systems use identical and carefully calibrated input error statistics. We provide the detailed procedure for these calibrations, and compare the two sets of analyses with a focus on the lower and middle stratosphere where the ozone lifetime is much larger than the observational update frequency. Based on the observation-minus-forecast statistics, we show that the analyses provided by the two systems are markedly similar, with biases less than 5% and standard deviation errors less than 10% in most of the stratosphere. Since the biases are markedly similar, they most probably have the same causes: these can be deficiencies in the model and in the observation data set, but not in the assimilation algorithm nor in the error calibration. The remarkably similar performance also shows that in the context of stratospheric transport, the choice of the assimilation method can be based on application-dependent factors, such as CPU cost or the ability to generate an ensemble of forecasts.

An ensemble Kalman filter data assimilation system for the martian atmosphere: Implementation and simulation experiments

Icarus ◽  
2010 ◽  
Vol 209 (2) ◽  
pp. 470-481 ◽  
Author(s):  
Matthew J. Hoffman ◽  
Steven J. Greybush ◽  
R. John Wilson ◽  
Gyorgyi Gyarmati ◽  
Ross N. Hoffman ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Martian Atmosphere ◽  
Simulation Experiments ◽  
Data Assimilation System ◽  
Assimilation System

scholarly journals A Global Carbon Assimilation System using a modified EnKF assimilation method

2014 ◽  
Vol 7 (5) ◽  
pp. 6519-6547
Author(s):  
S. Zhang ◽  
X. Zheng ◽  
Z. Chen ◽  
B. Dan ◽  
J. M. Chen ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Carbon Assimilation ◽  
Terrestrial Ecosystem ◽  
Carbon Fluxes ◽  
Ecosystem Model ◽  
Atmospheric Co2 ◽  
Forecast Errors ◽  
Global Carbon ◽  
Assimilation System

Abstract. A Global Carbon Assimilation System based on Ensemble Kalman filter (GCAS-EK) is developed for assimilating atmospheric CO2 abundance data into an ecosystem model to simultaneously estimate the surface carbon fluxes and atmospheric CO2 distribution. This assimilation approach is based on the ensemble Kalman filter (EnKF), but with several new developments, including using analysis states to iteratively estimate ensemble forecast errors, and a maximum likelihood estimation of the inflation factors of the forecast and observation errors. The proposed assimilation approach is tested in observing system simulation experiments and then used to estimate the terrestrial ecosystem carbon fluxes and atmospheric CO2 distributions from 2002 to 2008. The results showed that this assimilation approach can effectively reduce the biases and uncertainties of the carbon fluxes simulated by the ecosystem model.

scholarly journals Estimating surface CO<sub>2</sub> fluxes from space-borne CO<sub>2</sub> dry air mole fraction observations using an ensemble Kalman Filter

2009 ◽  
Vol 9 (8) ◽  
pp. 2619-2633 ◽  
Author(s):  
L. Feng ◽  
P. I. Palmer ◽  
H. Bösch ◽  
S. Dance
Keyword(s):  
Kalman Filter ◽  
Mole Fraction ◽  
Ensemble Kalman Filter ◽  
Transport Model ◽  
Co2 Flux ◽  
Surface Flux ◽  
Surface Fluxes ◽  
Co2 Fluxes ◽  
Dry Air ◽  
Geographical Regions

Abstract. We have developed an ensemble Kalman Filter (EnKF) to estimate 8-day regional surface fluxes of CO2 from space-borne CO2 dry-air mole fraction observations (XCO2) and evaluate the approach using a series of synthetic experiments, in preparation for data from the NASA Orbiting Carbon Observatory (OCO). The 32-day duty cycle of OCO alternates every 16 days between nadir and glint measurements of backscattered solar radiation at short-wave infrared wavelengths. The EnKF uses an ensemble of states to represent the error covariances to estimate 8-day CO2 surface fluxes over 144 geographical regions. We use a 12×8-day lag window, recognising that XCO2 measurements include surface flux information from prior time windows. The observation operator that relates surface CO2 fluxes to atmospheric distributions of XCO2 includes: a) the GEOS-Chem transport model that relates surface fluxes to global 3-D distributions of CO2 concentrations, which are sampled at the time and location of OCO measurements that are cloud-free and have aerosol optical depths <0.3; and b) scene-dependent averaging kernels that relate the CO2 profiles to XCO2, accounting for differences between nadir and glint measurements, and the associated scene-dependent observation errors. We show that OCO XCO2 measurements significantly reduce the uncertainties of surface CO2 flux estimates. Glint measurements are generally better at constraining ocean CO2 flux estimates. Nadir XCO2 measurements over the terrestrial tropics are sparse throughout the year because of either clouds or smoke. Glint measurements provide the most effective constraint for estimating tropical terrestrial CO2 fluxes by accurately sampling fresh continental outflow over neighbouring oceans. We also present results from sensitivity experiments that investigate how flux estimates change with 1) bias and unbiased errors, 2) alternative duty cycles, 3) measurement density and correlations, 4) the spatial resolution of estimated flux estimates, and 5) reducing the length of the lag window and the size of the ensemble. At the revision stage of this manuscript, the OCO instrument failed to reach its orbit after it was launched on 24 February 2009. The EnKF formulation presented here is also applicable to GOSAT measurements of CO2 and CH4.

Evaluating Ensemble Kalman Filter Analyses of Severe Hailstorms on 8 May 2017 in Colorado: Effects of State Variable Updating and Multimoment Microphysics Schemes on State Variable Cross Covariances

2020 ◽  
Vol 148 (6) ◽  
pp. 2365-2389
Author(s):  
Jonathan Labriola ◽  
Nathan Snook ◽  
Youngsun Jung ◽  
Ming Xue
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Forecast Error ◽  
Variable Cross ◽  
Background Error ◽  
Mixing Ratios ◽  
State Variable ◽  
Error Covariance ◽  
Thermodynamic Variables ◽  
The Impact

Abstract Ensemble Kalman filter (EnKF) analyses of the storms associated with the 8 May 2017 Colorado severe hail event using either the Milbrandt and Yau (MY) or the NSSL double-moment bulk microphysics scheme in the forecast model are evaluated. With each scheme, two experiments are conducted in which the reflectivity (Z) observations update in addition to dynamic and thermodynamic variables: 1) only the hydrometeor mixing ratios or 2) all microphysical variables. With fewer microphysical variables directly constrained by the Z observations, only updating hydrometeor mixing ratios causes the forecast error covariance structure to become unreliable, and results in larger errors in the analysis. Experiments that update all microphysical variables produce analyses with the lowest Z root-mean-square innovations; however, comparing the estimated hail size against hydrometeor classification algorithm output suggests that further constraint from observations is needed to more accurately estimate surface hail size. Ensemble correlation analyses are performed to determine the impact of hail growth assumptions in the MY and NSSL schemes on the forecast error covariance between microphysical and thermodynamic variables. In the MY scheme, Z is negatively correlated with updraft intensity because the strong updrafts produce abundant small hail aloft. The NSSL scheme predicts the growth of large hail aloft; consequently, Z is positively correlated with storm updraft intensity and hail state variables. Hail production processes are also shown to alter the background error covariance for liquid and frozen hydrometeor species. Results in this study suggest that EnKF analyses are sensitive to the choice of MP scheme (e.g., the treatment of hail growth processes).

scholarly journals Convective-Scale Data Assimilation for the Weather Research and Forecasting Model Using the Local Particle Filter

2017 ◽  
Vol 145 (5) ◽  
pp. 1897-1918 ◽  
Author(s):  
Jonathan Poterjoy ◽  
Ryan A. Sobash ◽  
Jeffrey L. Anderson
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Weather Prediction ◽  
Squall Line ◽  
Monte Carlo Data ◽  
Mixing Ratios ◽  
Convective Scale ◽  
Non Gaussian ◽  
Mean Square Errors

Abstract Particle filters (PFs) are Monte Carlo data assimilation techniques that operate with no parametric assumptions for prior and posterior errors. A data assimilation method introduced recently, called the local PF, approximates the PF solution within neighborhoods of observations, thus allowing for its use in high-dimensional systems. The current study explores the potential of the local PF for atmospheric data assimilation through cloud-permitting numerical experiments performed for an idealized squall line. Using only 100 ensemble members, experiments using the local PF to assimilate simulated radar measurements demonstrate that the method provides accurate analyses at a cost comparable to ensemble filters currently used in weather models. Comparisons between the local PF and an ensemble Kalman filter demonstrate benefits of the local PF for producing probabilistic analyses of non-Gaussian variables, such as hydrometeor mixing ratios. The local PF also provides more accurate forecasts than the ensemble Kalman filter, despite yielding higher posterior root-mean-square errors. A major advantage of the local PF comes from its ability to produce more physically consistent posterior members than the ensemble Kalman filter, which leads to fewer spurious model adjustments during forecasts. This manuscript presents the first successful application of the local PF in a weather prediction model and discusses implications for real applications where nonlinear measurement operators and nonlinear model processes limit the effectiveness of current Gaussian data assimilation techniques.

scholarly journals Mathematical Modeling of Immune Responses against SARS-CoV-2 Using an Ensemble Kalman Filter

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2427
Author(s):  
Rabih Ghostine ◽  
Mohamad Gharamti ◽  
Sally Hassrouny ◽  
Ibrahim Hoteit
Keyword(s):  
Kalman Filter ◽  
Viral Load ◽  
Immune Responses ◽  
Ensemble Kalman Filter ◽  
Plasma Cells ◽  
Equilibrium Points ◽  
Infected Cells ◽  
Many Sources ◽  
Antibody Levels ◽  
Assimilation System

In this paper, a mathematical model was developed to simulate SARS-CoV-2 dynamics in infected patients. The model considers both the innate and adaptive immune responses and consists of healthy cells, infected cells, viral load, cytokines, natural killer cells, cytotoxic T-lymphocytes, B-lymphocytes, plasma cells, and antibody levels. First, a mathematical analysis was performed to discuss the model’s equilibrium points and compute the basic reproduction number. The accuracy of such mathematical models may be affected by many sources of uncertainties due to the incomplete representation of the biological process and poorly known parameters. This may strongly limit their performance and prediction skills. A state-of-the-art data assimilation technique, the ensemble Kalman filter (EnKF), was then used to enhance the model’s behavior by incorporating available data to determine the best possible estimate of the model’s state and parameters. The proposed assimilation system was applied on the real viral load datasets of six COVID-19 patients. The results demonstrate the efficiency of the proposed assimilation system in improving the model predictions by up to 40%.

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