Four-dimensional local ensemble transform Kalman filter: numerical experiments with a global circulation model

2007 ◽  
Author(s):  
John Harlim ◽  
Brian R. Hunt
Keyword(s):  
Kalman Filter ◽  
Numerical Experiments ◽  
Circulation Model ◽  
Global Circulation Model ◽  
Global Circulation ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform

scholarly journals Comparison between Local Ensemble Transform Kalman Filter and PSAS in the NASA finite volume GCM – perfect model experiments

2008 ◽  
Vol 15 (4) ◽  
pp. 645-659 ◽  
Author(s):  
J. Liu ◽  
E. J. Fertig ◽  
H. Li ◽  
E. Kalnay ◽  
B. R. Hunt ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Finite Volume ◽  
Circulation Model ◽  
Forecast Errors ◽  
Global Circulation Model ◽  
Perfect Model ◽  
Grid Points ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform ◽  
Assimilation System

Abstract. This paper compares the performance of the Local Ensemble Transform Kalman Filter (LETKF) with the Physical-Space Statistical Analysis System (PSAS) under a perfect model scenario. PSAS is a 3D-Var assimilation system used operationally in the Goddard Earth Observing System Data Assimilation System (GEOS-4 DAS). The comparison is carried out using simulated winds and geopotential height observations and the finite volume Global Circulation Model with 72 grid points zonally, 46 grid points meridionally and 55 vertical levels. With forty ensemble members, the LETKF obtains analyses and forecasts with significantly lower RMS errors than those from PSAS, especially over the Southern Hemisphere and oceans. This observed advantage of the LETKF over PSAS is due to the ability of the 40-member ensemble LETKF to capture flow-dependent errors and thus create a good estimate of the evolving background uncertainty. An initial decrease of the forecast errors in the Northern Hemisphere observed in the PSAS but not in the LETKF suggests that the LETKF analysis is more balanced.

scholarly journals A Unification of Ensemble Square Root Kalman Filters

2012 ◽  
Vol 140 (7) ◽  
pp. 2335-2345 ◽  
Author(s):  
Lars Nerger ◽  
Tijana Janjić ◽  
Jens Schröter ◽  
Wolfgang Hiller
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Kalman Filters ◽  
Numerical Experiments ◽  
Computational Cost ◽  
Square Root ◽  
Symmetric Square ◽  
Ensemble Transform Kalman Filter ◽  
Filter Algorithms ◽  
Ensemble Transform

Abstract In recent years, several ensemble-based Kalman filter algorithms have been developed that have been classified as ensemble square root Kalman filters. Parallel to this development, the singular “evolutive” interpolated Kalman (SEIK) filter has been introduced and applied in several studies. Some publications note that the SEIK filter is an ensemble Kalman filter or even an ensemble square root Kalman filter. This study examines the relation of the SEIK filter to ensemble square root filters in detail. It shows that the SEIK filter is indeed an ensemble square root Kalman filter. Furthermore, a variant of the SEIK filter, the error subspace transform Kalman filter (ESTKF), is presented that results in identical ensemble transformations to those of the ensemble transform Kalman filter (ETKF), while having a slightly lower computational cost. Numerical experiments are conducted to compare the performance of three filters (SEIK, ETKF, and ESTKF) using deterministic and random ensemble transformations. The results show better performance for the ETKF and ESTKF methods over the SEIK filter as long as this filter is not applied with a symmetric square root. The findings unify the separate developments that have been performed for the SEIK filter and the other ensemble square root Kalman filters.

scholarly journals Using the local ensemble Transform Kalman Filter for upper atmospheric modelling

2019 ◽  
Vol 9 ◽  
pp. A30 ◽  
Author(s):  
Sean Elvidge ◽  
Matthew J. Angling
Keyword(s):  
Kalman Filter ◽  
General Circulation ◽  
Computational Cost ◽  
Circulation Model ◽  
Electron Content ◽  
Total Electron ◽  
Rms Error ◽  
Ensemble Transform Kalman Filter ◽  
Assimilation Model ◽  
Ensemble Transform

The Advanced Ensemble electron density (Ne) Assimilation System (AENeAS) is a new data assimilation model of the ionosphere/thermosphere. The background model is provided by the Thermosphere Ionosphere Electrodynamics General Circulation Model (TIE-GCM) and the assimilation uses the local ensemble transform Kalman filter (LETKF). An outline derivation of the LETKF is provided and the equations are presented in a form analogous to the classic Kalman filter. An enhancement to the efficient LETKF implementation to reduce computational cost is also described. In a 3 day test in June 2017, AENeAS exhibits a total electron content (TEC) RMS error of 2.1 TECU compared with 5.5 TECU for NeQuick and 6.8 for TIE-GCM (with an NeQuick topside).

scholarly journals The Gaussian Approach to Adaptive Covariance Inflation and Its Implementation with the Local Ensemble Transform Kalman Filter

2011 ◽  
Vol 139 (5) ◽  
pp. 1519-1535 ◽  
Author(s):  
Takemasa Miyoshi
Keyword(s):  
Kalman Filter ◽  
General Circulation ◽  
Forecast Error ◽  
Grid Point ◽  
Circulation Model ◽  
Error Variance ◽  
Model Errors ◽  
Variable Model ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform

In ensemble Kalman filters, the underestimation of forecast error variance due to limited ensemble size and other sources of imperfection is commonly treated by empirical covariance inflation. To avoid manual optimization of multiplicative inflation parameters, previous studies proposed adaptive inflation approaches using observations. Anderson applied Bayesian estimation theory to the probability density function of inflation parameters. Alternatively, Li et al. used the innovation statistics of Desroziers et al. and applied a Kalman filter analysis update to the inflation parameters based on the Gaussian assumption. In this study, Li et al.’s Gaussian approach is advanced to include the variance of the estimated inflation as derived from the central limit theorem. It is shown that the Gaussian approach is an accurate approximation of Anderson’s general Bayesian approach. An advanced implementation of the Gaussian approach with the local ensemble transform Kalman filter is proposed, where the adaptive inflation parameters are computed simultaneously with the ensemble transform matrix at each grid point. The spatially and temporally varying adaptive inflation technique is implemented with the Lorenz 40-variable model and a low-resolution atmospheric general circulation model; numerical experiments show promising results both with and without model errors.

scholarly journals The local ensemble transform Kalman filter and the running-in-place algorithm applied to a global ocean general circulation model

2013 ◽  
Vol 20 (6) ◽  
pp. 1031-1046 ◽  
Author(s):  
S. G. Penny ◽  
E. Kalnay ◽  
J. A. Carton ◽  
B. R. Hunt ◽  
K. Ide ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
General Circulation ◽  
Initial Conditions ◽  
Circulation Model ◽  
Global Ocean ◽  
Observation Data ◽  
Background Error ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform

Abstract. The most widely used methods of data assimilation in large-scale oceanography, such as the Simple Ocean Data Assimilation (SODA) algorithm, specify the background error covariances and thus are unable to refine the weights in the assimilation as the circulation changes. In contrast, the more computationally expensive Ensemble Kalman Filters (EnKF) such as the Local Ensemble Transform Kalman Filter (LETKF) use an ensemble of model forecasts to predict changes in the background error covariances and thus should produce more accurate analyses. The EnKFs are based on the approximation that ensemble members reflect a Gaussian probability distribution that is transformed linearly during the forecast and analysis cycle. In the presence of nonlinearity, EnKFs can gain from replacing each analysis increment by a sequence of smaller increments obtained by recursively applying the forecast model and data assimilation procedure over a single analysis cycle. This has led to the development of the "running in place" (RIP) algorithm by Kalnay and Yang (2010) and Yang et al. (2012a,b) in which the weights computed at the end of each analysis cycle are used recursively to refine the ensemble at the beginning of the analysis cycle. To date, no studies have been carried out with RIP in a global domain with real observations. This paper provides a comparison of the aforementioned assimilation methods in a set of experiments spanning seven years (1997–2003) using identical forecast models, initial conditions, and observation data. While the emphasis is on understanding the similarities and differences between the assimilation methods, comparisons are also made to independent ocean station temperature, salinity, and velocity time series, as well as ocean transports, providing information about the absolute error of each. Comparisons to independent observations are similar for the assimilation methods but the observation-minus-background temperature differences are distinctly lower for LETKF and RIP. The results support the potential for LETKF to improve the quality of ocean analyses on the space and timescales of interest for seasonal prediction and for RIP to accelerate the spin up of the system.

scholarly journals A Comparative Evaluation of a Mesoscale Model and Atmospheric Global Circulation Model for Air Quality Simulation: A Multiscale, Multisite Evaluation

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
P. Goswami ◽  
J. Baruah
Keyword(s):  
High Resolution ◽  
Mesoscale Model ◽  
Large City ◽  
Circulation Model ◽  
Urban Pollution ◽  
Atmospheric Pollutants ◽  
Scale Model ◽  
Global Circulation Model ◽  
Global Circulation ◽  
Meso Scale

Concentrations of atmospheric pollutants are strongly influenced by meteorological parameters like rainfall, relative humidity and wind advection. Thus accurate specifications of the meteorological fields, and their effects on pollutants, are critical requirements for successful modelling of air pollution. In terms of their applications, pollutant concentration models can be used in different ways; in one, short term high resolution forecasts are generated to predict and manage urban pollution. Another application of dynamical pollution models is to generate outlook for a given airbasin, such as over a large city. An important question is application-specific model configuration for the meteorological simulations. While a meso-scale model provides a high-resolution configuration, a global model allows better simulation of large-sale fields through its global environment. Our objective is to comparatively evaluate a meso-scale atmospheric model (MM5) and atmospheric global circulation model (AGCM) in simulating different species of pollutants over different airbasins. In this study we consider four locations: ITO (Central Delhi), Sirifort (South Delhi), Bandra (Mumbai) and Karve Road (Pune). The results show that both the model configurations provide comparable skills in simulation of monthly and annual loads, although the skill of the meso-scale model is somewhat higher, especially at shorter time scales.

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