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

2014 ◽  
Vol 7 (1) ◽  
pp. 339-377 ◽  
Author(s):  
S. Skachko ◽  
Q. Errera ◽  
R. Ménard ◽  
Y. Christophe ◽  
S. Chabrillat
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Transport Model ◽  
Control Variable ◽  
Tracer Transport ◽  
Error Statistics ◽  
Proper Comparison ◽  
Antarctic Ozone ◽  
Two Parameters ◽  
Update Frequency

Abstract. The Ensemble Kalman filter (EnKF) assimilation method is applied to the tracer transport using the same stratospheric transport model as in the 4D-Var assimilation system BASCOE. 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 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 smaller than 5% and standard deviation errors smaller than 10% in most of the stratosphere. Since the biases are markedly similar, they have most probably the same causes: these can be deficiencies in the model and in the observation dataset, 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.

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.

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.

scholarly journals Assimilation with an Ensemble Kalman Filter of Synthetic Radial Wind Data in Anisotropic Turbulence: Perfect Model Experiments

2006 ◽  
Vol 134 (2) ◽  
pp. 618-637 ◽  
Author(s):  
Martin Charron ◽  
P. L. Houtekamer ◽  
Peter Bartello
Keyword(s):  
Kalman Filter ◽  
Vertical Velocity ◽  
Ensemble Kalman Filter ◽  
Grid Point ◽  
Synthetic Data ◽  
Wind Data ◽  
Error Statistics ◽  
Boussinesq Model ◽  
Analysis Error ◽  
The Impact

Abstract The ensemble Kalman filter (EnKF) developed at the Meteorological Research Branch of Canada is used in the context of synthetic radial wind data assimilation at the mesoscale. A dry Boussinesq model with periodic boundary conditions is employed to provide a control run, as well as two ensembles of first guesses. Synthetic data, which are interpolated from the control run, are assimilated and simulate Doppler radar wind measurements. Nine “radars” with a range of 120 km are placed evenly on the horizontal 1000 km × 1000 km domain. These radars measure the radial wind with assumed Gaussian error statistics at each grid point within their range provided that there is sufficient upward motion (a proxy for precipitation). These data of radial winds are assimilated every 30 min and the assimilation period extends over 4 days. Results show that the EnKF technique with 2 × 50 members performed well in terms of reducing the analysis error for horizontal winds and temperature (even though temperature is not an observed variable) over a period of 4 days. However the analyzed vertical velocity shows an initial degradation. During the first 2 days of the assimilation period, the analysis error of the vertical velocity is greater when assimilating radar observations than when scoring forecasts initialized at t = 0 without assimilating any data. The type of assimilated data as well as the localization of the impact of the observations is thought to be the cause of this degradation of the analyzed vertical velocity. External gravity modes are present in the increments when localization is performed. This degradation can be eliminated by filtering the external gravity modes of the analysis increments. A similar set of experiments is realized in which the model dissipation coefficient is reduced by a factor of 10. This shows the level of sensitivity of the results to the kinetic energy power spectrum, and that the quality of the analyzed vertical wind is worse when dissipation is small.

scholarly journals Performance Characteristics of a Pseudo-Operational Ensemble Kalman Filter

2008 ◽  
Vol 136 (10) ◽  
pp. 3947-3963 ◽  
Author(s):  
Ryan D. Torn ◽  
Gregory J. Hakim
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Prediction Models ◽  
North Pacific Ocean ◽  
Weather Prediction ◽  
Limited Area ◽  
Observation Data ◽  
Error Statistics ◽  
Ensemble Forecasts ◽  
Ensemble Mean

The 2-yr performance of a pseudo-operational (real time) limited-area ensemble Kalman filter (EnKF) based on the Weather Research and Forecasting Model is described. This system assimilates conventional observations from surface stations, rawinsondes, the Aircraft Communications Addressing and Reporting System (ACARS), and cloud motion vectors every 6 h on a domain that includes the eastern North Pacific Ocean and western North America. Ensemble forecasts from this system and deterministic output from operational numerical weather prediction models during this same period are verified against rawinsonde and surface observation data. Relative to operational forecasts, the forecast from the ensemble-mean analysis has slightly larger errors in wind and temperature but smaller errors in moisture, even though satellite radiances are not assimilated by the EnKF. Time-averaged correlations indicate that assimilating ACARS and cloud wind data with flow-dependent error statistics provides corrections to the moisture field in the absence of direct observations of that field. Comparison with a control experiment in which a deterministic forecast is cycled without observation assimilation indicates that the skill in the EnKF’s forecasts results from assimilating observations and not from lateral boundary conditions or the model formulation. Furthermore, the ensemble variance is generally in good agreement with the ensemble-mean error and the spread increases monotonically with forecast hour.

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 Expanding the validity of the ensemble Kalman filter without the intrinsic need for inflation

2015 ◽  
Vol 22 (6) ◽  
pp. 645-662 ◽  
Author(s):  
M. Bocquet ◽  
P. N. Raanes ◽  
A. Hannart
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Ad Hoc ◽  
Finite Size ◽  
Practical Interest ◽  
Sampling Errors ◽  
Jeffreys Prior ◽  
Error Statistics ◽  
Additional Information

Abstract. The ensemble Kalman filter (EnKF) is a powerful data assimilation method meant for high-dimensional nonlinear systems. But its implementation requires somewhat ad hoc procedures such as localization and inflation. The recently developed finite-size ensemble Kalman filter (EnKF-N) does not require multiplicative inflation meant to counteract sampling errors. Aside from the practical interest in avoiding the tuning of inflation in perfect model data assimilation experiments, it also offers theoretical insights and a unique perspective on the EnKF. Here, we revisit, clarify and correct several key points of the EnKF-N derivation. This simplifies the use of the method, and expands its validity. The EnKF is shown to not only rely on the observations and the forecast ensemble, but also on an implicit prior assumption, termed hyperprior, that fills in the gap of missing information. In the EnKF-N framework, this assumption is made explicit through a Bayesian hierarchy. This hyperprior has so far been chosen to be the uninformative Jeffreys prior. Here, this choice is revisited to improve the performance of the EnKF-N in the regime where the analysis is strongly dominated by the prior. Moreover, it is shown that the EnKF-N can be extended with a normal-inverse Wishart informative hyperprior that introduces additional information on error statistics. This can be identified as a hybrid EnKF–3D-Var counterpart to the EnKF-N.

scholarly journals Regional scale ozone data assimilation using an ensemble Kalman filter and the CHIMERE chemical transport model

2014 ◽  
Vol 7 (1) ◽  
pp. 283-302 ◽  
Author(s):  
B. Gaubert ◽  
A. Coman ◽  
G. Foret ◽  
F. Meleux ◽  
A. Ung ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Transport Model ◽  
Regional Scale ◽  
Chemical Transport ◽  
Quality Analysis ◽  
Observation Error ◽  
Chemical Transport Model ◽  
Sensitivity Tests

Abstract. An ensemble Kalman filter (EnKF) has been coupled to the CHIMERE chemical transport model in order to assimilate ozone ground-based measurements on a regional scale. The number of ensembles is reduced to 20, which allows for future operational use of the system for air quality analysis and forecast. Observation sites of the European ozone monitoring network have been classified using criteria on ozone temporal variability, based on previous work by Flemming et al. (2005). This leads to the choice of specific subsets of suburban, rural and remote sites for data assimilation and for evaluation of the reference run and the assimilation system. For a 10-day experiment during an ozone pollution event over Western Europe, data assimilation allows for a significant improvement in ozone fields: the RMSE is reduced by about a third with respect to the reference run, and the hourly correlation coefficient is increased from 0.75 to 0.87. Several sensitivity tests focus on an a posteriori diagnostic estimation of errors associated with the background estimate and with the spatial representativeness of observations. A strong diurnal cycle of both these errors with an amplitude up to a factor of 2 is made evident. Therefore, the hourly ozone background error and the observation error variances are corrected online in separate assimilation experiments. These adjusted background and observational error variances provide a better uncertainty estimate, as verified by using statistics based on the reduced centered random variable. Over the studied 10-day period the overall EnKF performance over evaluation stations is found relatively unaffected by different formulations of observation and simulation errors, probably due to the large density of observation sites. From these sensitivity tests, an optimal configuration was chosen for an assimilation experiment extended over a three-month summer period. It shows a similarly good performance as the 10-day experiment.

Ensemble Kalman Filter Data Assimilation in a 1D Numerical Model Used for Fog Forecasting

2010 ◽  
Vol 138 (5) ◽  
pp. 1792-1810 ◽  
Author(s):  
Samuel Rémy ◽  
Thierry Bergot
Keyword(s):  
Kalman Filter ◽  
Numerical Model ◽  
Ensemble Kalman Filter ◽  
Initial Conditions ◽  
Specific Humidity ◽  
Error Statistics ◽  
Background Error ◽  
Fog Forecasting ◽  
Low Clouds ◽  
The Impact

Abstract Because poor visibility conditions have a considerable influence on airport traffic, a need exists for accurate and updated fog and low-cloud forecasts. Couche Brouillard Eau Liquide (COBEL)-Interactions between Soil, Biosphere, and Atmosphere (ISBA), a boundary layer 1D numerical model, has been developed for the very short-term forecast of fog and low clouds. This forecast system assimilates local observations to produce initial profiles of temperature and specific humidity. The initial conditions have a great impact on the skill of the forecast. In this work, the authors first estimated the background error statistics; they varied greatly with time, and cross correlations between temperature and humidity in the background were significant. This led to the implementation of an ensemble Kalman filter (EnKF) within COBEL-ISBA. The new assimilation system was evaluated with temperature and specific humidity scores, as well as in terms of its impact on the quality of fog forecasts. Simulated observations were used and focused on the modeling of the atmosphere before fog formation and also on the simulation of the life cycle of fog and low clouds. For both situations, the EnKF brought a significant improvement in the initial conditions and the forecasts. The forecast of the onset and burn-off times of fogs was also improved. The EnKF was also tested with real observations and gave good results. The size of the ensemble did not have much impact when simulated observations were used, thanks to an adaptive covariance inflation algorithm, but the impact was greater when real observations were used.

scholarly journals Expanding the validity of the ensemble Kalman filter without the intrinsic need for inflation

2015 ◽  
Vol 2 (4) ◽  
pp. 1091-1136 ◽  
Author(s):  
M. Bocquet ◽  
P. N. Raanes ◽  
A. Hannart
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Finite Size ◽  
Practical Interest ◽  
Sampling Errors ◽  
Jeffreys Prior ◽  
Error Statistics ◽  
Perfect Model ◽  
Key Points

Abstract. The ensemble Kalman filter (EnKF) is a powerful data assimilation method meant for high-dimensional nonlinear systems. But its implementation requires fixes such as localization and inflation. The recently developed finite-size ensemble Kalman filter (EnKF-N) does not require multiplicative inflation meant to counteract sampling errors. Aside from the practical interest of avoiding the tuning of inflation in perfect model data assimilation experiments, it also offers theoretical insights and a unique perspective on the EnKF. Here, we revisit, clarify and correct several key points of the EnKF-N derivation. This simplifies the use of the method, and expands its validity. The EnKF is shown to not only rely on the observations and the forecast ensemble but also on an implicit prior assumption, termed hyperprior, that fills in the gap of missing information. In the EnKF-N framework, this assumption is made explicit through a Bayesian hierarchy. This hyperprior has been so far chosen to be the uninformative Jeffreys' prior. Here, this choice is revisited to improve the performance of the EnKF-N in the regime where the analysis strongly relaxes to the prior. Moreover, it is shown that the EnKF-N can be extended with a normal-inverse-Wishart informative hyperprior that additionally introduces climatological error statistics. This can be identified as a hybrid 3D-Var/EnKF counterpart to the EnKF-N.

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