scholarly journals A Hybrid Kalman Filter Algorithm for Large-Scale Atmospheric Chemistry Data Assimilation

2007 ◽  
Vol 135 (1) ◽  
pp. 140-151 ◽  
Author(s):  
R. G. Hanea ◽  
G. J. M. Velders ◽  
A. J. Segers ◽  
M. Verlaan ◽  
A. W. Heemink
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Atmospheric Chemistry ◽  
Large Scale ◽  
Transport Model ◽  
Reduced Rank ◽  
Nonlinear Properties ◽  
Rank Approximation ◽  
Kalman Filter Algorithm ◽  
Better Than

Abstract In the past, a number of algorithms have been introduced to solve data assimilation problems for large-scale applications. Here, several Kalman filters, coupled to the European Operational Smog (EUROS) atmospheric chemistry transport model, are used to estimate the ozone concentrations in the boundary layer above Europe. Two Kalman filter algorithms, the reduced-rank square root (RRSQRT) and the ensemble Kalman filter (EnKF), were implemented in a prior study. To combine the best features of these two filters, a hybrid filter was constructed by making use of the reduced-rank approximation of the covariance matrix as a variance reducer for the EnKF. This hybrid algorithm, complementary orthogonal subspace filter for efficient ensembles (COFFEE), is coupled to the EUROS model. The performance of all algorithms is compared in terms of residual errors and number of EUROS model evaluations. The COFFEE results score somewhere between the EnKF and RRSQRT results for less than approximately 30 model evaluations. For more than approximately 30 model evaluations, the COFFEE results are, in all cases, better than the EnKF and RRSQRT results. The results of the COFFEE simulations with more than about 60 model evaluations proved to be significantly better than all the EnKF and RRSQRT simulations (even better than those with 100 and 200 modes or ensemble members). The performance of both the EnKF- and RRSQRT-type filters is affected by the nonlinear properties of the model and observation operator, because both rely on linearization to some extent. To further study this aspect, several measures of nonlinearity were calculated and linked with the performance of these algorithms.

TREATMENT OF THE ERROR DUE TO UNRESOLVED SCALES IN SEQUENTIAL DATA ASSIMILATION

2011 ◽  
Vol 21 (12) ◽  
pp. 3619-3626 ◽  
Author(s):  
ALBERTO CARRASSI ◽  
STÉPHANE VANNITSEM
Keyword(s):  
Dynamical System ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Large Scale ◽  
Model Error ◽  
Environmental Modeling ◽  
Sequential Data ◽  
Chaotic Dynamical System ◽  
Error Covariance ◽  
Sequential Data Assimilation

In this paper, a method to account for model error due to unresolved scales in sequential data assimilation, is proposed. An equation for the model error covariance required in the extended Kalman filter update is derived along with an approximation suitable for application with large scale dynamics typical in environmental modeling. This approach is tested in the context of a low order chaotic dynamical system. The results show that the filter skill is significantly improved by implementing the proposed scheme for the treatment of the unresolved scales.

scholarly journals A linear CO chemistry parameterization in a chemistry-transport model: evaluation and application to data assimilation

2010 ◽  
Vol 10 (13) ◽  
pp. 6097-6115 ◽  
Author(s):  
M. Claeyman ◽  
J.-L. Attié ◽  
L. El Amraoui ◽  
D. Cariolle ◽  
V.-H. Peuch ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Large Scale ◽  
Lower Stratosphere ◽  
Transport Model ◽  
Order Approximation ◽  
Chemical Transport Model ◽  
Long Run ◽  
Linear Scheme ◽  
Mean Differences ◽  
First Order Approximation

Abstract. This paper presents an evaluation of a new linear parameterization valid for the troposphere and the stratosphere, based on a first order approximation of the carbon monoxide (CO) continuity equation. This linear scheme (hereinafter noted LINCO) has been implemented in the 3-D Chemical Transport Model (CTM) MOCAGE (MOdèle de Chimie Atmospherique Grande Echelle). First, a one and a half years of LINCO simulation has been compared to output obtained from a detailed chemical scheme output. The mean differences between both schemes are about ±25 ppbv (part per billion by volume) or 15% in the troposphere and ±10 ppbv or 100% in the stratosphere. Second, LINCO has been compared to diverse observations from satellite instruments covering the troposphere (Measurements Of Pollution In The Troposphere: MOPITT) and the stratosphere (Microwave Limb Sounder: MLS) and also from aircraft (Measurements of ozone and water vapour by Airbus in-service aircraft: MOZAIC programme) mostly flying in the upper troposphere and lower stratosphere (UTLS). In the troposphere, the LINCO seasonal variations as well as the vertical and horizontal distributions are quite close to MOPITT CO observations. However, a bias of ~−40 ppbv is observed at 700 Pa between LINCO and MOPITT. In the stratosphere, MLS and LINCO present similar large-scale patterns, except over the poles where the CO concentration is underestimated by the model. In the UTLS, LINCO presents small biases less than 2% compared to independent MOZAIC profiles. Third, we assimilated MOPITT CO using a variational 3D-FGAT (First Guess at Appropriate Time) method in conjunction with MOCAGE for a long run of one and a half years. The data assimilation greatly improves the vertical CO distribution in the troposphere from 700 to 350 hPa compared to independent MOZAIC profiles. At 146 hPa, the assimilated CO distribution is also improved compared to MLS observations by reducing the bias up to a factor of 2 in the tropics. This study confirms that the linear scheme is able to simulate reasonably well the CO distribution in the troposphere and in the lower stratosphere. Therefore, the low computing cost of the linear scheme opens new perspectives to make free runs and CO data assimilation runs at high resolution and over periods of several years.

scholarly journals Scale-Dependent Representation of the Information Content of Observations in the Global Ensemble Kalman Filter Data Assimilation

2016 ◽  
Vol 144 (8) ◽  
pp. 2927-2945
Author(s):  
Nedjeljka Žagar ◽  
Jeffrey Anderson ◽  
Nancy Collins ◽  
Timothy Hoar ◽  
Kevin Raeder ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Information Content ◽  
Ensemble Kalman Filter ◽  
Large Scale ◽  
Variance Reduction ◽  
Weather Prediction ◽  
Current Data ◽  
Model Framework ◽  
The Tropics

Abstract Global data assimilation systems for numerical weather prediction (NWP) are characterized by significant uncertainties in tropical analysis fields. Furthermore, the largest spread of global ensemble forecasts in the short range on all scales is in the tropics. The presented results suggest that these properties hold even in the perfect-model framework and the ensemble Kalman filter data assimilation with a globally homogeneous network of wind and temperature profiles. The reasons for this are discussed by using the modal analysis, which provides information about the scale dependency of analysis and forecast uncertainties and information about the efficiency of data assimilation to reduce the prior uncertainties in the balanced and inertio-gravity dynamics. The scale-dependent representation of variance reduction of the prior ensemble by the data assimilation shows that the peak efficiency of data assimilation is on the synoptic scales in the midlatitudes that are associated with quasigeostrophic dynamics. In contrast, the variance associated with the inertia–gravity modes is less successfully reduced on all scales. A smaller information content of observations on planetary scales with respect to the synoptic scales is discussed in relation to the large-scale tropical uncertainties that current data assimilation methodologies do not address successfully. In addition, it is shown that a smaller reduction of the large-scale uncertainties in the prior state for NWP in the tropics than in the midlatitudes is influenced by the applied radius for the covariance localization.

Application of Adaptive Kalman Filter Technique in Initial Alignment of Single-Axial Rotation Strap-Down Inertial Navigation System

2012 ◽  
Vol 466-467 ◽  
pp. 617-621
Author(s):  
Song Tian Shang ◽  
Wen Shao Gao
Keyword(s):  
Kalman Filter ◽  
Axial Rotation ◽  
Estimation Accuracy ◽  
Initial Alignment ◽  
Adaptive Kalman Filter ◽  
Rotation System ◽  
Kalman Filter Algorithm ◽  
Axis Rotation ◽  
Single Axis Rotation ◽  
Better Than

In order to improve the accuracy of initial alignment which determines the accuracy of navigation, a Sage-Husa adaptive kalman filter algorithm is applied to SINS initial alignment of single-axis rotation system. The simulation result further shows that in the case of inaccurate statistical property of noise, the estimation accuracy of Sage-Husa adaptive kalman filter is better than the conventional kalman filter.

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 On the extraction of wind information from the assimilation of ozone profiles in Météo–France 4-D-Var operational NWP suite

2009 ◽  
Vol 9 (14) ◽  
pp. 4855-4867 ◽  
Author(s):  
N. Semane ◽  
V.-H. Peuch ◽  
S. Pradier ◽  
G. Desroziers ◽  
L. El Amraoui ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Degrees Of Freedom ◽  
Variance Reduction ◽  
Lower Stratosphere ◽  
Transport Model ◽  
Weather Prediction ◽  
Error Variance ◽  
Numerical Weather Prediction Model ◽  
Background Error ◽  
Better Than

Abstract. By applying four-dimensional variational data-assimilation (4-D-Var) to a combined ozone and dynamics Numerical Weather Prediction model (NWP), ozone observations generate wind increments through the ozone-dynamics coupling. The dynamical impact of Aura/MLS satellite ozone profiles is investigated using Météo-France operational ARPEGE NWP 4-D-Var assimilation system for a period of 3 months. A data-assimilation procedure has been designed and run on 6-h windows. The procedure includes: (1) 4-D-Var assimilating both ozone and operational NWP standard observations, (2) ARPEGE transporting ozone as a passive-tracer, (3) MOCAGE, the Météo–France chemistry and transport model re-initializing the ARPEGE ozone background at the beginning time of the assimilation window. Using observation minus forecast statistics, it is found that the ozone assimilation reduces the wind bias in the lower stratosphere. Moreover, the Degrees of Freedom for Signal diagnostics show that the MLS data covering the 68.1–31.6 hPa vertical pressure range are the most informative and their information content is nearly of the same order as tropospheric humidity-sensitive radiances. Furthermore, with the help of error variance reduction diagnostics, the ozone contribution to the reduction of the horizontal divergence background-error variance is shown to be better than tropospheric humidity-sensitive radiances.

scholarly journals Singular-Vector-Based Covariance Propagation in a Quasigeostrophic Assimilation System

2005 ◽  
Vol 133 (5) ◽  
pp. 1295-1310 ◽  
Author(s):  
Alexander Beck ◽  
Martin Ehrendorfer
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Variational Data Assimilation ◽  
Dynamic Information ◽  
Dynamic Background ◽  
Background Error ◽  
Singular Vectors ◽  
Reduced Rank ◽  
The Impact ◽  
Static Background

Abstract Variational data assimilation systems require the specification of the covariances of background and observation errors. Although the specification of the background-error covariances has been the subject of intense research, current operational data assimilation systems still rely on essentially static and thus flow-independent background-error covariances. At least theoretically, it is possible to use flow-dependent background-error covariances in four-dimensional variational data assimilation (4DVAR) through exploiting the connection between variational data assimilation and estimation theory. This paper reports on investigations concerning the impact of flow-dependent background-error covariances in an idealized 4DVAR system that, based on quasigeostrophic dynamics, assimilates artificial observations. The main emphasis is placed on quantifying the improvement in analysis quality that is achievable in 4DVAR through the use of flow-dependent background-error covariances. Flow dependence is achieved through dynamical error-covariance evolution based on singular vectors in a reduced-rank approach, referred to as reduced-rank Kalman filter (RRKF). The RRKF yields partly dynamic background-error covariances through blending static and dynamic information, where the dynamic information is obtained from error evolution in a subspace of dimension k (defined here through the singular vectors) that may be small compared to the dimension of the model’s phase space n, which is equal to 1449 in the system investigated here. The results show that the use of flow-dependent background-error covariances based on the RRKF leads to improved analyses compared to a system using static background-error statistics. That latter system uses static background-error covariances that are carefully tuned given the model dynamics and the observational information available. It is also shown that the performance of the RRKF approaches the performance of the extended Kalman filter, as k approaches n. Results therefore support the hypothesis that significant analysis improvement is possible through the use of flow-dependent background-error covariances given that a sufficiently large number (here on the order of n/10) of singular vectors is used.

Data assimilation in stand-level forest inventories

2013 ◽  
Vol 43 (12) ◽  
pp. 1104-1113 ◽  
Author(s):  
Sarah Ehlers ◽  
Anton Grafström ◽  
Kenneth Nyström ◽  
Håkan Olsson ◽  
Göran Ståhl
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Extended Kalman Filter ◽  
Large Scale ◽  
Prediction Models ◽  
Quality Data ◽  
Relative Advantage ◽  
Sources Of Information ◽  
Short Intervals ◽  
Forest Inventories

The development of remote sensing methods through research and large-scale application nowadays makes it possible to obtain stand-level estimates of forest variables at short intervals and at low cost. This offers substantial possibilities to forestry practitioners, but it also poses challenges regarding how cost-efficient data acquisition strategies should be developed. For example, should cheap but low-quality data be acquired and discarded whenever new data become available or should investments be made in high-quality data that are continuously updated to last over a longer period of time? We suggest that the solution could be to establish data assimilation (DA) procedures linked to forest inventories to make appropriate use of data from several sources. With DA, old information is updated through growth forecasts and when new information becomes available it is assimilated with the old information; the different sources of information are made use of to the extent motivated by their accuracy. In this study we made a general assessment of the usefulness of DA in connection with stand-level forest inventories and we compared two different methodological approaches, the extended Kalman filter and the Bayesian method. Not surprisingly, the relative advantage of DA was found to be largest for cases where low-precision estimates of growing stock volume were obtained at short intervals and forecasts were made with accurate growth prediction models. The methodological comparison revealed a tendency of the extended Kalman filter to underestimate the variance of the estimates.

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