scholarly journals Estimation of the error covariance matrix for IASI radiances and its impact on ozone analyses

2020 ◽  
Author(s):  
Mohammad El Aabaribaoune ◽  
Emanuele Emili ◽  
Vincent Guidard
Keyword(s):  
Covariance Matrix ◽  
Atmospheric Chemistry ◽  
Transport Model ◽  
Weather Prediction ◽  
Computational Cost ◽  
Observation Error ◽  
Chemical Transport Model ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
Estimated Error

Abstract. In atmospheric chemistry retrievals and data assimilation systems, observation errors associated with satellite radiances are chosen empirically and generally treated as uncorrelated. In this work, we estimate inter-channel error covariances for the Infrared Atmospheric Sounding Interferometer (IASI) and evaluate their impact on ozone assimilation with the chemical transport model MOCAGE (MOdèle de Chime Atmospheric à Grand Echelle). The method used to calculate observation errors is a diagnostic based on the observation and analysis residual statistics already adopted in numerical weather prediction centers. We used a subset of 280 channels covering the spectral range between 980 and 1100 cm−1 to estimate the observation error covariance matrix. We computed hourly 3D-Var analyses and compared the resulting O3 fields against ozonesondes and the measurements provided by the Microwave Limb Sounder (MLS). The results show significant differences between using the estimated error covariance matrix with respect to the empirical diagonal matrix employed in previous studies. The validation of the analyses against independent data reports a significant improvement especially in the tropical stratosphere. The computational cost has also been reduced when the estimated covariance is employed in the assimilation system.

scholarly journals Estimation of the error covariance matrix for IASI radiances and its impact on the assimilation of ozone in a chemistry transport model

2021 ◽  
Vol 14 (4) ◽  
pp. 2841-2856
Author(s):  
Mohammad El Aabaribaoune ◽  
Emanuele Emili ◽  
Vincent Guidard
Keyword(s):  
Covariance Matrix ◽  
Spectral Range ◽  
Atmospheric Chemistry ◽  
Transport Model ◽  
Weather Prediction ◽  
Computational Cost ◽  
Observation Error ◽  
Chemistry Transport Model ◽  
Error Covariance Matrix ◽  
Error Covariance

Abstract. In atmospheric chemistry retrievals and data assimilation systems, observation errors associated with satellite radiances are chosen empirically and generally treated as uncorrelated. In this work, we estimate inter-channel error covariances for the Infrared Atmospheric Sounding Interferometer (IASI) and evaluate their impact on ozone assimilation with the chemistry transport model MOCAGE (Modèle de Chimie Atmosphérique à Grande Echelle). The method used to calculate observation errors is a diagnostic based on the observation and analysis residual statistics already adopted in many numerical weather prediction centres. We used a subset of 280 channels covering the spectral range between 980 and 1100 cm−1 to estimate the observation-error covariance matrix. This spectral range includes ozone-sensitive and atmospheric window channels. We computed hourly 3D-Var analyses and compared the resulting O3 fields against ozonesondes and the measurements provided by the Microwave Limb Sounder (MLS) and by the Ozone Monitoring Instrument (OMI). The results show significant differences between using the estimated error covariance matrix with respect to the empirical diagonal matrix employed in previous studies. The validation of the analyses against independent data reports a significant improvement, especially in the tropical stratosphere. The computational cost has also been reduced when the estimated covariance matrix is employed in the assimilation system, by reducing the number of iterations needed for the minimizer to converge.

scholarly journals Ozone-sensitive channel selection over IASI full spectrum with correlated observation errors for NWP

2019 ◽  
Author(s):  
Olivier Coopmann ◽  
Vincent Guidard ◽  
Béatrice Josse ◽  
Virginie Marécal ◽  
Nadia Fourrié
Keyword(s):  
Covariance Matrix ◽  
Weather Prediction ◽  
Channel Selection ◽  
Spectral Interval ◽  
Observation Error ◽  
Full Spectrum ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
One Year ◽  
Selection Of

Abstract. The Infrared Atmospheric Sounding Interferometer (IASI) onboard the Metop satellites provides 8461 channels in the infrared spectrum, covering the spectral interval 645–2760 cm−1 at a resolution of 0.5 cm−1. The high volume of data observation resulting from IASI presents many challenges. In current Numerical Weather Prediction (NWP) models, assimilating all channels is not feasible, due to data transmission, data storage and significant computational costs. One of the methods for reducing the data volume is the channel selection. Many NWP centres use a subset of 314 IASI channels including 15 ozone-sensitive channels. However, this channel selection has been carried out assuming uncorrelated observation errors. In addition, these ozone-sensitive channels have been selected only for ozone information. The objective of this study is to carry out a new selection of IASI ozone-sensitive channels from the full spectrum over a spectral range of 1000–1070 cm−1, in a direct radiance assimilation framework. This selection is done with a full observation error covariance matrix to take into account cross-channel error correlations. A sensitivity method based on the channel spectral sensitivity to variables and a statistical approach based on the Degrees of Freedom for Signal (DFS) have been chosen. To be representative of atmospheric variability, 345 profiles from around the world over a one-year period were selected. The new selection, is evaluated in a One-Dimensional Variational (1D-Var) analyses framework. This selection highlights a new set of 15 IASI ozone-sensitive channels. The results are very encouraging since by adding these 15 channels to 122 operational channels, temperature and humidity analyses are improved by 13.8 % and 20.9 % respectively. Obviously, these 15 channels significantly improve ozone analyses. In addition to considering inter-channel observation error correlations, the channel selection method uses a robust background error covariance matrix that takes into account temperature, humidity and ozone errors using a lagged forecast method over a one-year period. The new selection of IASI ozone-sensitive channels will be soon used in the global 4D-Var ARPEGE (Action de Recherche Petite Echelle Grande Echelle) data assimilation system.

scholarly journals Balance and Ensemble Kalman Filter Localization Techniques

2011 ◽  
Vol 139 (2) ◽  
pp. 511-522 ◽  
Author(s):  
Steven J. Greybush ◽  
Eugenia Kalnay ◽  
Takemasa Miyoshi ◽  
Kayo Ide ◽  
Brian R. Hunt
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Covariance Matrix ◽  
Ensemble Kalman Filter ◽  
Weather Prediction ◽  
Length Scale ◽  
Observation Error ◽  
Long Distance ◽  
Error Covariance Matrix ◽  
Error Covariance

Abstract In ensemble Kalman filter (EnKF) data assimilation, localization modifies the error covariance matrices to suppress the influence of distant observations, removing spurious long-distance correlations. In addition to allowing efficient parallel implementation, this takes advantage of the atmosphere’s lower dimensionality in local regions. There are two primary methods for localization. In B localization, the background error covariance matrix elements are reduced by a Schur product so that correlations between grid points that are far apart are removed. In R localization, the observation error covariance matrix is multiplied by a distance-dependent function, so that far away observations are considered to have infinite error. Successful numerical weather prediction depends upon well-balanced initial conditions to avoid spurious propagation of inertial-gravity waves. Previous studies note that B localization can disrupt the relationship between the height gradient and the wind speed of the analysis increments, resulting in an analysis that can be significantly ageostrophic. This study begins with a comparison of the accuracy and geostrophic balance of EnKF analyses using no localization, B localization, and R localization with simple one-dimensional balanced waves derived from the shallow-water equations, indicating that the optimal length scale for R localization is shorter than for B localization, and that for the same length scale R localization is more balanced. The comparison of localization techniques is then expanded to the Simplified Parameterizations, Primitive Equation Dynamics (SPEEDY) global atmospheric model. Here, natural imbalance of the slow manifold must be contrasted with undesired imbalance introduced by data assimilation. Performance of the two techniques is comparable, also with a shorter optimal localization distance for R localization than for B localization.

Including the spatial observation error correlation in data assimilation of AMSU-A radiances

2021 ◽  
Author(s):  
Koji Terasaki ◽  
Takemasa Miyoshi
Keyword(s):  
Data Assimilation ◽  
Covariance Matrix ◽  
Weather Prediction ◽  
Computation Time ◽  
Horizontal Resolution ◽  
Observation Error ◽  
Correlated Errors ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
Error Correlation

<p>Recent developments in sensing technology increased the number of observations both in space and time. It is essential to effectively utilize the information from observations to improve numerical weather prediction (NWP). It is known to have correlated errors in observations measured with a single instrument, such as satellite radiances. The observations with the horizontal error correlation are usually thinned to compensate for neglecting the error correlation in data assimilation. This study explores to explicitly include the horizontal observation error correlation of Advanced Microwave Sounding Unit-A (AMSU-A) radiances using a global atmospheric data assimilation system NICAM-LETKF, which comprises the Nonhydrostatic ICosahedral Atmospheric Model (NICAM) and the Local Ensemble Transform Kalman Filter (LETKF). This study performs the data assimilation experiments at 112-km horizontal resolution and 38 vertical layers up to 40 km and with 32 ensemble members.</p><p>In this study, we estimate the horizontal observation error correlation of AMSU-A radiances using innovation statistics. The computation cost of inverting the observation error covariance matrix will increase when non-zero off-diagonal terms are included. In this study, we assume uncorrelated observation errors between different instruments and observation variables, so that the observation error covariance matrix becomes block diagonal with only horizontal error correlations included. The computation time of the entire LETKF analysis procedure is increased only by up to 10 % compared with the case using the diagonal observation error covariance matrix. The analyses and forecasts of temperature and zonal wind in the mid- and upper-troposphere are improved by including the horizontal error correlations. We will present the most recent results at the workshop.</p>

Enhancing the impact of IASI observations through an updated observation-error covariance matrix

2016 ◽  
Vol 142 (697) ◽  
pp. 1767-1780 ◽  
Author(s):  
Niels Bormann ◽  
Massimo Bonavita ◽  
Rossana Dragani ◽  
Reima Eresmaa ◽  
Marco Matricardi ◽  
...  
Keyword(s):  
Covariance Matrix ◽  
Observation Error ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
The Impact

scholarly journals EnKF and 4D-Var data assimilation with chemical transport model BASCOE (version 05.06)

2016 ◽  
Vol 9 (8) ◽  
pp. 2893-2908 ◽  
Author(s):  
Sergey Skachko ◽  
Richard Ménard ◽  
Quentin Errera ◽  
Yves Christophe ◽  
Simon Chabrillat
Keyword(s):  
Data Assimilation ◽  
Transport Model ◽  
Chemical Transport ◽  
Error Variance ◽  
Model Error ◽  
Chemical Processes ◽  
Observation Error ◽  
Chemical Transport Model ◽  
Error Covariance ◽  
Chemical Tracer

Abstract. We compare two optimized chemical data assimilation systems, one based on the ensemble Kalman filter (EnKF) and the other based on four-dimensional variational (4D-Var) data assimilation, using a comprehensive stratospheric chemistry transport model (CTM). This work is an extension of the Belgian Assimilation System for Chemical ObsErvations (BASCOE), initially designed to work with a 4D-Var data assimilation. A strict comparison of both methods in the case of chemical tracer transport was done in a previous study and indicated that both methods provide essentially similar results. In the present work, we assimilate observations of ozone, HCl, HNO3, H2O and N2O from EOS Aura-MLS data into the BASCOE CTM with a full description of stratospheric chemistry. Two new issues related to the use of the full chemistry model with EnKF are taken into account. One issue is a large number of error variance parameters that need to be optimized. We estimate an observation error variance parameter as a function of pressure level for each observed species using the Desroziers method. For comparison purposes, we apply the same estimate procedure in the 4D-Var data assimilation, where both scale factors of the background and observation error covariance matrices are estimated using the Desroziers method. However, in EnKF the background error covariance is modelled using the full chemistry model and a model error term which is tuned using an adjustable parameter. We found that it is adequate to have the same value of this parameter based on the chemical tracer formulation that is applied for all observed species. This is an indication that the main source of model error in chemical transport model is due to the transport. The second issue in EnKF with comprehensive atmospheric chemistry models is the noise in the cross-covariance between species that occurs when species are weakly chemically related at the same location. These errors need to be filtered out in addition to a localization based on distance. The performance of two data assimilation methods was assessed through an 8-month long assimilation of limb sounding observations from EOS Aura MLS. This paper discusses the differences in results and their relation to stratospheric chemical processes. Generally speaking, EnKF and 4D-Var provide results of comparable quality but differ substantially in the presence of model error or observation biases. If the erroneous chemical modelling is associated with moderately fast chemical processes, but whose lifetimes are longer than the model time step, then EnKF performs better, while 4D-Var develops spurious increments in the chemically related species. If, however, the observation biases are significant, then 4D-Var is more robust and is able to reject erroneous observations while EnKF does not.

scholarly journals Estimating model error covariance matrix parameters in extended Kalman filtering

2014 ◽  
Vol 21 (5) ◽  
pp. 919-927 ◽  
Author(s):  
A. Solonen ◽  
J. Hakkarainen ◽  
A. Ilin ◽  
M. Abbas ◽  
A. Bibov
Keyword(s):  
Covariance Matrix ◽  
Weather Prediction ◽  
Estimation Method ◽  
Model Error ◽  
Tuning Parameter ◽  
Extended Kalman Filtering ◽  
Error Covariance Matrix ◽  
Nonlinear Dynamical ◽  
Error Covariance

Abstract. The extended Kalman filter (EKF) is a popular state estimation method for nonlinear dynamical models. The model error covariance matrix is often seen as a tuning parameter in EKF, which is often simply postulated by the user. In this paper, we study the filter likelihood technique for estimating the parameters of the model error covariance matrix. The approach is based on computing the likelihood of the covariance matrix parameters using the filtering output. We show that (a) the importance of the model error covariance matrix calibration depends on the quality of the observations, and that (b) the estimation approach yields a well-tuned EKF in terms of the accuracy of the state estimates and model predictions. For our numerical experiments, we use the two-layer quasi-geostrophic model that is often used as a benchmark model for numerical weather prediction.

scholarly journals Efficient Adaptive Error Parameterizations for Square Root or Ensemble Kalman Filters: Application to the Control of Ocean Mesoscale Signals

2010 ◽  
Vol 138 (3) ◽  
pp. 932-950 ◽  
Author(s):  
Jean-Michel Brankart ◽  
Emmanuel Cosme ◽  
Charles-Emmanuel Testut ◽  
Pierre Brasseur ◽  
Jacques Verron
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
Error Estimates ◽  
Forecast Error ◽  
Observation Error ◽  
Square Root ◽  
Error Statistics ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
Optimal Estimates

Abstract In Kalman filter applications, an adaptive parameterization of the error statistics is often necessary to avoid filter divergence, and prevent error estimates from becoming grossly inconsistent with the real error. With the classic formulation of the Kalman filter observational update, optimal estimates of general adaptive parameters can only be obtained at a numerical cost that is several times larger than the cost of the state observational update. In this paper, it is shown that there exists a few types of important parameters for which optimal estimates can be computed at a negligible numerical cost, as soon as the computation is performed using a transformed algorithm that works in the reduced control space defined by the square root or ensemble representation of the forecast error covariance matrix. The set of parameters that can be efficiently controlled includes scaling factors for the forecast error covariance matrix, scaling factors for the observation error covariance matrix, or even a scaling factor for the observation error correlation length scale. As an application, the resulting adaptive filter is used to estimate the time evolution of ocean mesoscale signals using observations of the ocean dynamic topography. To check the behavior of the adaptive mechanism, this is done in the context of idealized experiments, in which model error and observation error statistics are known. This ideal framework is particularly appropriate to explore the ill-conditioned situations (inadequate prior assumptions or uncontrollability of the parameters) in which adaptivity can be misleading. Overall, the experiments show that, if used correctly, the efficient optimal adaptive algorithm proposed in this paper introduces useful supplementary degrees of freedom in the estimation problem, and that the direct control of these statistical parameters by the observations increases the robustness of the error estimates and thus the optimality of the resulting Kalman filter.

scholarly journals Assimilation of Stratospheric Temperature and Ozone with an Ensemble Kalman Filter in a Chemistry–Climate Model

2011 ◽  
Vol 139 (11) ◽  
pp. 3389-3404 ◽  
Author(s):  
Thomas Milewski ◽  
Michel S. Bourqui
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Covariance Matrix ◽  
Ensemble Kalman Filter ◽  
Climate Model ◽  
Observation Error ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
Analysis Error

Abstract A new stratospheric chemical–dynamical data assimilation system was developed, based upon an ensemble Kalman filter coupled with a Chemistry–Climate Model [i.e., the intermediate-complexity general circulation model Fast Stratospheric Ozone Chemistry (IGCM-FASTOC)], with the aim to explore the potential of chemical–dynamical coupling in stratospheric data assimilation. The system is introduced here in a context of a perfect-model, Observing System Simulation Experiment. The system is found to be sensitive to localization parameters, and in the case of temperature (ozone), assimilation yields its best performance with horizontal and vertical decorrelation lengths of 14 000 km (5600 km) and 70 km (14 km). With these localization parameters, the observation space background-error covariance matrix is underinflated by only 5.9% (overinflated by 2.1%) and the observation-error covariance matrix by only 1.6% (0.5%), which makes artificial inflation unnecessary. Using optimal localization parameters, the skills of the system in constraining the ensemble-average analysis error with respect to the true state is tested when assimilating synthetic Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) retrievals of temperature alone and ozone alone. It is found that in most cases background-error covariances produced from ensemble statistics are able to usefully propagate information from the observed variable to other ones. Chemical–dynamical covariances, and in particular ozone–wind covariances, are essential in constraining the dynamical fields when assimilating ozone only, as the radiation in the stratosphere is too slow to transfer ozone analysis increments to the temperature field over the 24-h forecast window. Conversely, when assimilating temperature, the chemical–dynamical covariances are also found to help constrain the ozone field, though to a much lower extent. The uncertainty in forecast/analysis, as defined by the variability in the ensemble, is large compared to the analysis error, which likely indicates some amount of noise in the covariance terms, while also reducing the risk of filter divergence.

scholarly journals Coupled Stratospheric Chemistry-Meteorology Data Assimilation. Part I: Modeling Chemistry-Dynamics Interactions

2019 ◽  
Author(s):  
Richard Ménard ◽  
Simon Chabrillat ◽  
Alain Robichaud ◽  
Jean de Grandpré ◽  
Martin Charron ◽  
...  
Keyword(s):  
Atmospheric Chemistry ◽  
Transport Model ◽  
Model Simulation ◽  
Weather Prediction ◽  
Coupled Model ◽  
Horizontal Resolution ◽  
Chemical Transport Model ◽  
Stratospheric Chemistry ◽  
Temperature Bias ◽  
Meteorological Analysis

A coupled stratospheric chemistry-meteorology model was developed by combining the Canadian operational weather prediction model Global Environmental Multiscale (GEM) with a comprehensive stratospheric photochemistry model from the Belgian Assimilation System for Chemical ObsErvations (BASCOE). The coupled model was called GEM-BACH for GEM-Belgian Atmospheric CHemistry. The coupling was made across a chemical interface that preserves time splitting while being modular, allowing GEM to run with or without chemistry. An evaluation of the coupling was performed by comparing the coupled model, refreshed by meteorological analyses every 6 hours, against the standard offline chemical transport model (CTM) approach. Results show that the dynamical meteorological consistency between meteorological analysis times far outweighs the error created by the jump resulting from the meteorological analysis increments at regular time intervals, irrespective whether a 3D-Var or 4D-Var meteorological analysis is used. GEM-BACH forecast refreshed by meteorological analyses every 6 hours were compared against independent measurements of temperature, long-lived species, ozone and water vapor. The comparison showed a relatively good agreement throughout the stratosphere except for an upper-level warm temperature bias and an ozone deficit of nearly 15%. Arguments in favor of using the same horizontal resolution for chemistry, meteorology, and meteorological analysis increments are also presented. In particular, the coupled model simulation during an ozone hole event gives better ozone concentrations than a 4D-Var chemical assimilation at a lower resolution.

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