scholarly journals Biogeochemical Oceanographic Data Assimilation: Dimensionality Reduced Kalman Filter For Mediterranean Sea Forecasting

2018 ◽  
Author(s):  
Simone K. Spada ◽  
Gianpiero Cossarini ◽  
Stefano Salon ◽  
Stefano Maset
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Mediterranean Sea ◽  
Computational Efficiency ◽  
Transport Model ◽  
Computational Cost ◽  
Principal Component ◽  
Covariance Matrices ◽  
Background Error ◽  
Biological Variables

Data assimilation is a key element to improve the performance of biogeochemical ocean/marine forecasting systems. Handling the very big dimension of the state vector of the system (often of the order of 10 6 ) remains an issue, also considering the computational efficiency of operational systems. Indeed, simple product operations involving the covariance matrices are too heavy to be computed for operational forecasting purposes. Various attempts have been made in literature to reduce the complexity of this task, often adding strong hypotheses to simplify the problem and decrease the computational cost. The MedBFM model system, which is responsible for monitoring and forecasting the biogeochemical state of the Mediterranean Sea within the European Copernicus Marine Services (see http://marine.copernicus.eu/ ) assimilates surface chlorophyll data through a 3D Variational algorithm, that decomposes the background error covariance matrix into sequential operators to reduce complexity. In this work, we developed a novel Kalman Filter for the MedBFM system. The novel Kalman Filter scheme starts from a SEIK approach but benefits from advanced Principal Component Analysis to reduce the dimension of covariance matrices and improve the computational efficiency. We compared the standard SEIK filter and the new Kalman filter implementations in a one dimensional transport model with 2 biological variables in terms of root mean square distance. In the vast majority of the experiments, the new Kalman filter had better performances.

scholarly journals Regional scale ozone data assimilation using an Ensemble Kalman Filter and the CHIMERE Chemical-Transport Model

2013 ◽  
Vol 6 (2) ◽  
pp. 3033-3083
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 ◽  
Random Variable ◽  
Chemical Transport ◽  
Chemical Transport Model ◽  
Background Error ◽  
Filter Performance

Abstract. The Ensemble Kalman Filter is an efficient algorithm for data assimilation; it allows for an estimation of forecast and analysis error by updating the model error covariance matrices at the analysis step. This algorithm has been coupled to the CHIMERE chemical transport model in order to assimilate ozone ground measurements at the regional scale. The analyzed ozone field is evaluated using a consistent set of observations and shows a reduction of the quadratic error by about a third and an improvement of the hourly correlation coefficient despite of a low ensemble size designed for operational purposes. A classification of the European observation network is derived from the ozone temporal variability in order to qualitatively determine the observation spatial representativeness. Then, an estimation of the temporal behavior of both model and observations error variances of the assimilated stations is checked using a posteriori Desroziers diagnostics. The amplitude of the additive noise applied to the ozone fields can be diagnosed and tuned online. The evaluation of the obtained background error variance distribution through the Reduced Centered Random Variable standard deviation shows improved statistics. The use of the diagnostics indicates a strong diurnal cycle of both the model and the representativeness errors. Another design of the ensemble is constructed by perturbing model parameter, but does not allow creating enough variability if used solely. Finally, the overall filter performance over evaluation stations is found to be relatively unaffected by different formulations of observation and simulation errors.

An Efficient Dual-Resolution Approach for Ensemble Data Assimilation and Tests with Simulated Doppler Radar Data

2008 ◽  
Vol 136 (3) ◽  
pp. 945-963 ◽  
Author(s):  
Jidong Gao ◽  
Ming Xue
Keyword(s):  
High Resolution ◽  
Data Assimilation ◽  
Radial Velocity ◽  
Computational Cost ◽  
Radar Data ◽  
Horizontal Resolution ◽  
Velocity Data ◽  
Background Error ◽  
Cross Covariance ◽  
Radial Velocity Data

Abstract A new efficient dual-resolution (DR) data assimilation algorithm is developed based on the ensemble Kalman filter (EnKF) method and tested using simulated radar radial velocity data for a supercell storm. Radar observations are assimilated on both high-resolution and lower-resolution grids using the EnKF algorithm with flow-dependent background error covariances estimated from the lower-resolution ensemble. It is shown that the flow-dependent and dynamically evolved background error covariances thus estimated are effective in producing quality analyses on the high-resolution grid. The DR method has the advantage of being able to significantly reduce the computational cost of the EnKF analysis. In the system, the lower-resolution ensemble provides the flow-dependent background error covariance, while the single-high-resolution forecast and analysis provides the benefit of higher resolution, which is important for resolving the internal structures of thunderstorms. The relative smoothness of the covariance obtained from the lower 4-km-resolution ensemble does not appear to significantly degrade the quality of analysis. This is because the cross covariance among different variables is of first-order importance for “retrieving” unobserved variables from the radar radial velocity data. For the DR analysis, an ensemble size of 40 appears to be a reasonable choice with the use of a 4-km horizontal resolution in the ensemble and a 1-km resolution in the high-resolution analysis. Several sensitivity tests show that the DR EnKF system is quite robust to different observation errors. A 4-km thinned data resolution is a compromise that is acceptable under the constraint of real-time applications. A data density of 8 km leads to a significant degradation in the analysis.

Evaluation of Surface Analyses and Forecasts with a Multiscale Ensemble Kalman Filter in Regions of Complex Terrain

2011 ◽  
Vol 139 (6) ◽  
pp. 2008-2024 ◽  
Author(s):  
Brian C. Ancell ◽  
Clifford F. Mass ◽  
Gregory J. Hakim
Keyword(s):  
Kalman Filter ◽  
High Resolution ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Complex Terrain ◽  
Error Variance ◽  
Small Scale ◽  
Observation Error ◽  
Grid Spacing ◽  
Background Error

Abstract Previous research suggests that an ensemble Kalman filter (EnKF) data assimilation and modeling system can produce accurate atmospheric analyses and forecasts at 30–50-km grid spacing. This study examines the ability of a mesoscale EnKF system using multiscale (36/12 km) Weather Research and Forecasting (WRF) model simulations to produce high-resolution, accurate, regional surface analyses, and 6-h forecasts. This study takes place over the complex terrain of the Pacific Northwest, where the small-scale features of the near-surface flow field make the region particularly attractive for testing an EnKF and its flow-dependent background error covariances. A variety of EnKF experiments are performed over a 5-week period to test the impact of decreasing the grid spacing from 36 to 12 km and to evaluate new approaches for dealing with representativeness error, lack of surface background variance, and low-level bias. All verification in this study is performed with independent, unassimilated observations. Significant surface analysis and 6-h forecast improvements are found when EnKF grid spacing is reduced from 36 to 12 km. Forecast improvements appear to be a consequence of increased resolution during model integration, whereas analysis improvements also benefit from high-resolution ensemble covariances during data assimilation. On the 12-km domain, additional analysis improvements are found by reducing observation error variance in order to address representativeness error. Removing model surface biases prior to assimilation significantly enhances the analysis. Inflating surface wind and temperature background error variance has large impacts on analyses, but only produces small improvements in analysis RMS errors. Both surface and upper-air 6-h forecasts are nearly unchanged in the 12-km experiments. Last, 12-km WRF EnKF surface analyses and 6-h forecasts are shown to generally outperform those of the Global Forecast System (GFS), North American Model (NAM), and the Rapid Update Cycle (RUC) by about 10%–30%, although these improvements do not extend above the surface. Based on these results, future improvements in multiscale EnKF are suggested.

E4DVar: Coupling an Ensemble Kalman Filter with Four-Dimensional Variational Data Assimilation in a Limited-Area Weather Prediction Model

2012 ◽  
Vol 140 (2) ◽  
pp. 587-600 ◽  
Author(s):  
Meng Zhang ◽  
Fuqing Zhang
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Prediction Model ◽  
Ensemble Kalman Filter ◽  
Weather Prediction ◽  
Coupled System ◽  
Limited Area ◽  
Ensemble Forecasts ◽  
Background Error ◽  
Hybrid Data Assimilation

A hybrid data assimilation approach that couples the ensemble Kalman filter (EnKF) and four-dimensional variational (4DVar) methods is implemented for the first time in a limited-area weather prediction model. In this coupled system, denoted E4DVar, the EnKF and 4DVar systems run in parallel while feeding into each other. The multivariate, flow-dependent background error covariance estimated from the EnKF ensemble is used in the 4DVar minimization and the ensemble mean in the EnKF analysis is replaced by the 4DVar analysis, while updating the analysis perturbations for the next cycle of ensemble forecasts with the EnKF. Therefore, the E4DVar can obtain flow-dependent information from both the explicit covariance matrix derived from ensemble forecasts, as well as implicitly from the 4DVar trajectory. The performance of an E4DVar system is compared with the uncoupled 4DVar and EnKF for a limited-area model by assimilating various conventional observations over the contiguous United States for June 2003. After verifying the forecasts from each analysis against standard sounding observations, it is found that the E4DVar substantially outperforms both the EnKF and 4DVar during this active summer month, which featured several episodes of severe convective weather. On average, the forecasts produced from E4DVar analyses have considerably smaller errors than both of the stand-alone EnKF and 4DVar systems for forecast lead times up to 60 h.

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.

Heterogeneous Convective-Scale Background Error Covariances with the Inclusion of Hydrometeor Variables

2011 ◽  
Vol 139 (9) ◽  
pp. 2994-3015 ◽  
Author(s):  
Yann Michel ◽  
Thomas Auligné ◽  
Thibaut Montmerle
Keyword(s):  
Data Assimilation ◽  
Control Variable ◽  
The United States ◽  
Covariance Matrices ◽  
Specific Humidity ◽  
Matrix Formulation ◽  
Background Error ◽  
Error Matrix ◽  
Vertical Extension ◽  
Convective Scale

Convective-scale models used in NWP nowadays include detailed realistic parameterization for the representation of cloud and precipitation processes. Yet they still lack advanced data assimilation schemes able to efficiently use observations to initialize hydrometeor fields. This challenging task may benefit from a better understanding of the statistical structure of background errors in precipitating areas for both traditional and hydrometeor variables, which is the goal of this study. A special binning has been devised to compute separate background error covariance matrices for precipitating and nonprecipitating areas. This binning is based on bidimensional geographical masks defined by the vertical averaged rain content of the background error perturbations. The sample for computing the covariances is taken from an ensemble of short range forecasts run at 3-km resolution for the prediction of two specific cases of convective storms over the United States. The covariance matrices and associated diagnostics are built on the control variable transform formulation typical of variational data assimilation. The comparison especially highlights the strong coupling of specific humidity, cloud, and rain content with divergence. Shorter horizontal correlations have been obtained in precipitating areas. Vertical correlations mostly reflect the cloud vertical extension due to the convective processes. The statistics for hydrometeor variables show physically meaningful autocovariances and statistical couplings with other variables. Issues for data assimilation of radar reflectivity or more generally of observations linked to cloud and rain content with this kind of background error matrix formulation are thereon briefly discussed.

scholarly journals An Examination of the Incremental Balance in a Global Ensemble-Based 3D-Var Data Assimilation System

2010 ◽  
Vol 138 (10) ◽  
pp. 3946-3966 ◽  
Author(s):  
Jean-François Caron ◽  
Luc Fillion
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Three Dimensional ◽  
Vertical Motion ◽  
Variational Data Assimilation ◽  
Spatial Covariance ◽  
Background Error ◽  
Localization Technique ◽  
Vertical Localization

Abstract This study examines the modification to the balance properties of the analysis increments in a global three-dimensional variational data assimilation scheme when using flow-dependent background-error covariances derived from an operational ensemble Kalman filter instead of static homogenous and isotropic background-error covariances based on lagged forecast differences. It is shown that the degree of balance in the analysis increments is degraded when the former method is used. This change can be attributed in part to the reduced degree of rotational balance found in short-term ensemble Kalman filter perturbations as compared to lagged forecast differences based on longer-range forecasts. However, the use of a horizontal and vertical localization technique to increase the rank of the ensemble-based covariances are found to have a significant deleterious effect on the rotational balance with the largest detrimental impact coming from the vertical localization and affecting particularly the upper levels. The examination of the vertical motion part of the analysis increments revealed that the spatial covariance localization technique also produces unrealistic vertical structure of vertical motion increments with abnormally large increments near the surface. A comparison between the analysis increments from the ensemble Kalman filter and from the ensemble-based three-dimensional variational data assimilation (3D-Var) scheme showed that the balance characteristics of the analysis increments resulting from the two systems are very similar.

scholarly journals Construction of non-diagonal background error covariance matrices for global chemical data assimilation

2010 ◽  
Vol 3 (4) ◽  
pp. 1783-1827 ◽  
Author(s):  
K. Singh ◽  
M. Jardak ◽  
A. Sandu ◽  
K. Bowman ◽  
M. Lee ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Computational Procedure ◽  
Covariance Matrices ◽  
Chemical Data ◽  
Spatial Correlations ◽  
Transport Models ◽  
Background Error ◽  
Spatial Error ◽  
Background Error Covariance ◽  
Error Covariance

Abstract. Chemical data assimilation attempts to optimally use noisy observations along with imperfect model predictions to produce a better estimate of the chemical state of the atmosphere. It is widely accepted that a key ingredient for successful data assimilation is a realistic estimation of the background error distribution. Particularly important is the specification of the background error covariance matrix, which contains information about the magnitude of the background errors and about their correlations. Most models currently use diagonal background covariance matrices. As models evolve toward finer resolutions, the diagonal background covariance matrices become increasingly inaccurate, since they captures less of the spatial error correlations. This paper discusses an efficient computational procedure for constructing non-diagonal background error covariance matrices which account for the spatial correlations of errors. The benefits of using the non-diagonal covariance matrices for variational data assimilation with chemical transport models are illustrated.

scholarly journals Global NO<sub>x</sub> emission estimates derived from an assimilation of OMI tropospheric NO<sub>2</sub> columns

2011 ◽  
Vol 11 (12) ◽  
pp. 31523-31583 ◽  
Author(s):  
K. Miyazaki ◽  
H. J. Eskes ◽  
K. Sudo
Keyword(s):  
Data Assimilation ◽  
Transport Model ◽  
A Priori ◽  
Eastern China ◽  
Nox Emissions ◽  
Chemical Transport Model ◽  
Background Error ◽  
Tropospheric No2 ◽  
Data Assimilation System ◽  
Assimilation System

Abstract. A data assimilation system has been developed to estimate global nitrogen oxides (NOx) emissions using OMI tropospheric NO2 columns (DOMINO product) and a global chemical transport model (CTM), CHASER. The data assimilation system, based on an ensemble Kalman filter approach, was applied to optimize daily NOx emissions with a horizontal resolution of 2.8° during the years 2005 and 2006. The background error covariance estimated from the ensemble CTM forecasts explicitly represents non-direct relationships between the emissions and tropospheric columns caused by atmospheric transport and chemical processes. In comparison to the a priori emissions based on bottom-up inventories, the optimized emissions were higher over Eastern China, the Eastern United States, Southern Africa, and Central-Western Europe, suggesting that the anthropogenic emissions are mostly underestimated in the inventories. In addition, the seasonality of the estimated emissions differed from that of the a priori emission over several biomass burning regions, with a large increase over Southeast Asia in April and over South America in October. The data assimilation results were validated against independent data: SCIAMACHY tropospheric NO2 columns and vertical NO2 profiles obtained from aircraft and lidar measurements. The emission correction greatly improved the agreement between the simulated and observed NO2 fields; this implies that the data assimilation system efficiently derives NOx emissions from concentration observations. We also demonstrated that biases in the satellite retrieval and model settings used in the data assimilation largely affect the magnitude of estimated emissions. These dependences should be carefully considered for better understanding NOx sources from top-down approaches.

scholarly journals SymPKF (v1.0): a symbolic and computational toolbox for the design of parametric Kalman filter dynamics

2021 ◽  
Author(s):  
Olivier Pannekoucke ◽  
Philippe Arbogast
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Burgers Equation ◽  
Covariance Matrices ◽  
Covariance Model ◽  
Local Anisotropy ◽  
Code Generator ◽  
Univariate Statistics ◽  
Automatic Code ◽  
Python Package

Abstract. Recent researches in data assimilation lead to the introduction of the parametric Kalman filter (PKF): an implementation of the Kalman filter, where the covariance matrices are approximated by a parameterized covariance model. In the PKF, the dynamics of the covariance during the forecast step relies on the prediction of the covariance parameters. Hence, the design of the parameter dynamics is crucial while it can be tedious to do this by hand. This contribution introduces a python package, SymPKF, able to compute PKF dynamics for univariate statistics and when the covariance model is parameterized from the variance and the local anisotropy of the correlations. The ability of SymPKF to produce the PKF dynamics is shown on a non-linear diffusive advection (Burgers equation) over a 1D domain and the linear advection over a 2D domain. The computation of the PKF dynamics is performed at a symbolic level, but an automatic code generator is also introduced to perform numerical simulations. A final multivariate example illustrates the potential of SymPKF to go beyond the univariate case.

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