scholarly journals An Adaptive Compensatory Approach of the Fixed Localization in the EnKF

2015 ◽  
Vol 143 (11) ◽  
pp. 4714-4735 ◽  
Author(s):  
Xinrong Wu ◽  
Wei Li ◽  
Guijun Han ◽  
Lianxin Zhang ◽  
Caixia Shao ◽  
...  
Keyword(s):  
Multiscale Analysis ◽  
General Circulation ◽  
Computational Cost ◽  
Circulation Model ◽  
Adaptive Method ◽  
Background Error ◽  
Error Covariance ◽  
Incremental Improvement ◽  
Better Than

Abstract Although the fixed covariance localization in the ensemble Kalman filter (EnKF) can significantly increase the reliability of background error covariance, it has been demonstrated that extreme impact radii can cause the EnKF to lose some useful information. Tuning an optimal impact radius, on the other hand, is always difficult for a general circulation model. The EnKF multiscale analysis (MSA) approach was presented to make up for the above-mentioned drawback of the fixed localization. As a follow-up, this study presents an adaptive compensatory approach to further improve the performance of the EnKF-MSA. The new method adaptively triggers a multigrid analysis (MGA) to extract multiscale information from the observational residual after the EnKF without inflation is completed at each analysis step. Within a biased twin experiment framework consisting of a barotropic spectral model and an idealized observing system, the performance of the adaptive method is examined. Results show that the MGA reduces the computational cost of the MSA by 93%. On the assimilation quality, the adaptive method has an incremental improvement over the EnKF-MSA. That is, the adaptive EnKF-MGA reduces to the EnKF without inflation, which is better than the EnKF-MSA, for moderate impact radii. The proposed scheme works for a broader range of impact radii than the standard EnKF (i.e., the EnKF with inflation). For extreme impact radii, the adaptive EnKF-MGA can produce smaller assimilation errors than the standard EnKF and shorten the spinup period by 53%. In addition, the computational cost of the MGA is negligible relative to that of the standard EnKF.

scholarly journals A Compensatory Approach of the Fixed Localization in EnKF

2014 ◽  
Vol 142 (10) ◽  
pp. 3713-3733 ◽  
Author(s):  
Xinrong Wu ◽  
Wei Li ◽  
Guijun Han ◽  
Shaoqing Zhang ◽  
Xidong Wang
Keyword(s):  
General Circulation ◽  
Computational Cost ◽  
Circulation Model ◽  
Multiple Scale ◽  
Long Distance ◽  
Background Error ◽  
Weather Forecasts ◽  
Error Covariance ◽  
Analysis Technique ◽  
Cutoff Distance

Abstract While fixed covariance localization can greatly increase the reliability of the background error covariance in filtering by suppressing the long-distance spurious correlations evaluated by a finite ensemble, it may degrade the assimilation quality in an ensemble Kalman filter (EnKF) as a result of restricted longwave information. Tuning an optimal cutoff distance is usually very expensive and time consuming, especially for a general circulation model (GCM). Here the authors present an approach to compensate the demerit in fixed localization. At each analysis step, after the standard EnKF is done, a multiple-scale analysis technique is used to extract longwave information from the observational residual (referred to the EnKF ensemble mean). Within a biased twin-experiment framework consisting of a global barotropical spectral model and an idealized observing system, the performance of the new method is examined. Compared to a standard EnKF, the hybrid method is superior when an overly small/large cutoff distance is used, and it has less dependence on cutoff distance. The new scheme is also able to improve short-term weather forecasts, especially when an overly large cutoff distance is used. Sensitivity studies show that caution should be taken when the new scheme is applied to a dense observing system with an overly small cutoff distance in filtering. In addition, the new scheme has a nearly equivalent computational cost to the standard EnKF; thus, it is particularly suitable for GCM applications.

scholarly journals Using Temperature–Salinity Relations in a Global Ocean Implementation of a Multivariate Data Assimilation Scheme

2007 ◽  
Vol 135 (11) ◽  
pp. 3785-3807 ◽  
Author(s):  
A. Bellucci ◽  
S. Masina ◽  
P. DiPietro ◽  
A. Navarra
Keyword(s):  
Data Assimilation ◽  
General Circulation ◽  
Circulation Model ◽  
Ocean General Circulation Model ◽  
Global Ocean ◽  
Special Focus ◽  
Background Error ◽  
Background Error Covariance ◽  
Error Covariance ◽  
The Impact

Abstract In this paper results from the application of an ocean data assimilation (ODA) system, combining a multivariate reduced-order optimal interpolator (OI) scheme with a global ocean general circulation model (OGCM), are described. The present ODA system, designed to assimilate in situ temperature and salinity observations, has been used to produce ocean reanalyses for the 1962–2001 period. The impact of assimilating observed hydrographic data on the ocean mean state and temporal variability is evaluated. A special focus of this work is on the ODA system skill in reproducing a realistic ocean salinity state. Results from a hierarchy of different salinity reanalyses, using varying combinations of assimilated data and background error covariance structures, are described. The impact of the space and time resolution of the background error covariance parameterization on salinity is addressed.

The Met Office operational global ocean forecast system FOAM-ORCA12

2021 ◽  
Author(s):  
Ana Barbosa Aguiar ◽  
Jennifer Waters ◽  
Martin Price ◽  
Gordon Inverarity ◽  
Christine Pequignet ◽  
...  
Keyword(s):  
Computational Cost ◽  
Absolute Error ◽  
Global Ocean ◽  
Background Error ◽  
Verification Methods ◽  
Climate Simulations ◽  
Forecast Models ◽  
The Mean ◽  
Lower Continuous ◽  
Better Than

<div> <p>The importance of oceans for atmospheric forecasts as well as climate simulations is being increasingly recognised with the advent of coupled ocean / atmosphere forecast models. Having comparable resolutions in both domains maximises the benefits for a given computational cost. The Met Office has recently upgraded its operational global ocean-only model from an eddy permitting 1/4 degree tripolar grid (ORCA025) to the eddy resolving 1/12 degree ORCA12 configuration while retaining 1/4 degree data assimilation. </p> </div><div> <p>We will present a description of the ocean-only ORCA12 system, FOAM-ORCA12, alongside some initial results. Qualitatively, FOAM-ORCA12 seems to represent better (than FOAM-ORCA025) the details of mesoscale features in SST and surface currents. Overall, traditional statistical results suggest that the new FOAM-ORCA12 system performs similarly or slightly worse than the pre-existing FOAM-ORCA025. However, it is known that comparisons of models running at different resolutions suffer from a double penalty effect, whereby higher-resolution models are penalised more than lower-resolution models for features that are offset in time and space. Neighbourhood verification methods seek to make a fairer comparison using a common spatial scale for both models and it can be seen that, as neighbourhood sizes increase, ORCA12 consistently has lower continuous ranked probability scores (CRPS) than ORCA025. CRPS measures the accuracy of the pseudo-ensemble created by the neighbourhood method and generalises the mean absolute error measure for deterministic forecasts. </p> </div><div> <p>The focus over the next year will be on diagnosing the performance of both the model and assimilation. A planned development that is expected to enhance the system is the update of the background-error covariances used for data assimilation. </p> </div>

scholarly journals A Maximum Likelihood Ensemble Filter via a Modified Cholesky Decomposition for Non-Gaussian Data Assimilation

Sensors ◽  
2020 ◽  
Vol 20 (3) ◽  
pp. 877 ◽  
Author(s):  
Elias David Nino-Ruiz ◽  
Alfonso Mancilla-Herrera ◽  
Santiago Lopez-Restrepo ◽  
Olga Quintero-Montoya
Keyword(s):  
Maximum Likelihood ◽  
General Circulation ◽  
Circulation Model ◽  
Cholesky Decomposition ◽  
Practical Implementation ◽  
Square Root ◽  
Background Error ◽  
Modified Cholesky Decomposition ◽  
Highly Nonlinear ◽  
Maximum Likelihood Ensemble Filter

This paper proposes an efficient and practical implementation of the Maximum Likelihood Ensemble Filter via a Modified Cholesky decomposition (MLEF-MC). The method works as follows: via an ensemble of model realizations, a well-conditioned and full-rank square-root approximation of the background error covariance matrix is obtained. This square-root approximation serves as a control space onto which analysis increments can be computed. These are calculated via Line-Search (LS) optimization. We theoretically prove the convergence of the MLEF-MC. Experimental simulations were performed using an Atmospheric General Circulation Model (AT-GCM) and a highly nonlinear observation operator. The results reveal that the proposed method can obtain posterior error estimates within reasonable accuracies in terms of ℓ − 2 error norms. Furthermore, our analysis estimates are similar to those of the MLEF with large ensemble sizes and full observational networks.

scholarly journals A description of the FAMOUS (version XDBUA) climate model and control run

2008 ◽  
Vol 1 (1) ◽  
pp. 53-68 ◽  
Author(s):  
R. S. Smith ◽  
J. M. Gregory ◽  
A. Osprey
Keyword(s):  
General Circulation ◽  
High Performance ◽  
Climate Model ◽  
Computational Cost ◽  
Circulation Model ◽  
Cold Bias ◽  
Northern Latitudes ◽  
Climate Simulations ◽  
Atmosphere General Circulation Model ◽  
And Control

Abstract. FAMOUS is an ocean-atmosphere general circulation model of low resolution, capable of simulating approximately 120 years of model climate per wallclock day using current high performance computing facilities. It uses most of the same code as HadCM3, a widely used climate model of higher resolution and computational cost, and has been tuned to reproduce the same climate reasonably well. FAMOUS is useful for climate simulations where the computational cost makes the application of HadCM3 unfeasible, either because of the length of simulation or the size of the ensemble desired. We document a number of scientific and technical improvements to the original version of FAMOUS. These improvements include changes to the parameterisations of ozone and sea-ice which alleviate a significant cold bias from high northern latitudes and the upper troposphere, and the elimination of volume-averaged drifts in ocean tracers. A simple model of the marine carbon cycle has also been included. A particular goal of FAMOUS is to conduct millennial-scale paleoclimate simulations of Quaternary ice ages; to this end, a number of useful changes to the model infrastructure have been made.

scholarly journals A Comparison of HWRF Six-Hourly 4DEnVar and Hourly 3DEnVar Assimilation of Inner Core Tail Dopper Radar Observations for the Prediction of Hurricane Edouard (2014)

Atmosphere ◽  
2021 ◽  
Vol 12 (8) ◽  
pp. 942
Author(s):  
Benjamin Davis ◽  
Xuguang Wang ◽  
Xu Lu
Keyword(s):  
Inner Core ◽  
Doppler Radar ◽  
Three Dimensional ◽  
Weather Research And Forecasting ◽  
Location Error ◽  
Background Error ◽  
Error Covariance ◽  
Storm Center ◽  
The One ◽  
Better Than

Six-hourly three-dimensional ensemble variational (3DEnVar) (6H-3DEnVar) data assimilation (DA) assumes constant background error covariance (BEC) during a six-hour DA window and is, therefore, unable to account for temporal evolution of the BEC. This study evaluates the one-hourly 3DEnVar (1H-3DEnVar) and six-hourly 4DEnVar (6H-4DEnVar) DA methods for the analyses and forecasts of hurricanes with rapidly evolving BEC. Both methods account for evolving BEC in a hybrid EnVar DA system. In order to compare these methods, experiments are conducted by assimilating inner core Tail Doppler Radar (TDR) wind for Hurricane Edouard (2014) and by running the Hurricane Weather Research and Forecasting (HWRF) model. In most metrics, 1H-3DEnVar and 6H-4DEnVar analyses and forecasts verify better than 6H-3DEnVar. 6H-4DEnVar produces better thermodynamic analyses than 1H-3DEnVar. Radar reflectivity shows that 1H-3DEnVar produces better structure forecasts. For the first 24–48 h of the intensity forecast, 6H-4DEnVar forecast performs better than 1H-3DEnVar verified against the best track. Degraded 1H-3DEnVar forecasts are found to be associated with background storm center location error as a result of underdispersive ensemble storm center spread. Removing location error in the background improves intensity forecasts of 1H-3DEnVar.

scholarly journals A Comparison of Multiscale GSI-Based EnKF and 3DVar Data Assimilation Using Radar and Conventional Observations for Midlatitude Convective-Scale Precipitation Forecasts

2015 ◽  
Vol 143 (8) ◽  
pp. 3087-3108 ◽  
Author(s):  
Aaron Johnson ◽  
Xuguang Wang ◽  
Jacob R. Carley ◽  
Louis J. Wicker ◽  
Christopher Karstens
Keyword(s):  
Data Assimilation ◽  
Multiscale Analysis ◽  
Multiple Scales ◽  
Three Dimensional ◽  
Forecast Period ◽  
Background Error ◽  
Cold Pools ◽  
Error Covariance ◽  
Convective Scale

Abstract A GSI-based data assimilation (DA) system, including three-dimensional variational assimilation (3DVar) and ensemble Kalman filter (EnKF), is extended to the multiscale assimilation of both meso- and synoptic-scale observation networks and convective-scale radar reflectivity and velocity observations. EnKF and 3DVar are systematically compared in this multiscale context to better understand the impacts of differences between the DA techniques on the analyses at multiple scales and the subsequent convective-scale precipitation forecasts. Averaged over 10 diverse cases, 8-h precipitation forecasts initialized using GSI-based EnKF are more skillful than those using GSI-based 3DVar, both with and without storm-scale radar DA. The advantage from radar DA persists for ~5 h using EnKF, but only ~1 h using 3DVar. A case study of an upscale growing MCS is also examined. The better EnKF-initialized forecast is attributed to more accurate analyses of both the mesoscale environment and the storm-scale features. The mesoscale location and structure of a warm front is more accurately analyzed using EnKF than 3DVar. Furthermore, storms in the EnKF multiscale analysis are maintained during the subsequent forecast period. However, storms in the 3DVar multiscale analysis are not maintained and generate excessive cold pools. Therefore, while the EnKF forecast with radar DA remains better than the forecast without radar DA throughout the forecast period, the 3DVar forecast quality is degraded by radar DA after the first hour. Diagnostics revealed that the inferior analysis at mesoscales and storm scales for the 3DVar is primarily attributed to the lack of flow dependence and cross-variable correlation, respectively, in the 3DVar static background error covariance.

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 A Study of Coupling Parameter Estimation Implemented by 4D-Var and EnKF with a Simple Coupled System

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Guijun Han ◽  
Xinrong Wu ◽  
Shaoqing Zhang ◽  
Zhengyu Liu ◽  
Ionel Michael Navon ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
General Circulation ◽  
Coupling Parameter ◽  
Coupled Model ◽  
Circulation Model ◽  
Coupled System ◽  
Model Studies ◽  
Error Covariance ◽  
Estimated Parameters ◽  
Observing System Simulation Experiment

Coupling parameter estimation (CPE) that uses observations to estimate the parameters in a coupled model through error covariance between variables residing in different media may increase the consistency of estimated parameters in an air-sea coupled system. However, it is very challenging to accurately evaluate the error covariance between such variables due to the different characteristic time scales at which flows vary in different media. With a simple Lorenz-atmosphere and slab ocean coupled system that characterizes the interaction of two-timescale media in a coupled “climate” system, this study explores feasibility of the CPE with four-dimensional variational analysis and ensemble Kalman filter within a perfect observing system simulation experiment framework. It is found that both algorithms can improve the representation of air-sea coupling processes through CPE compared to state estimation only. These simple model studies provide some insights when parameter estimation is implemented with a coupled general circulation model for improving climate estimation and prediction initialization.

scholarly journals Emulation of an ensemble Kalman filter algorithm on a flood wave propagation model

2013 ◽  
Vol 10 (6) ◽  
pp. 6963-7001
Author(s):  
S. Barthélémy ◽  
S. Ricci ◽  
O. Pannekoucke ◽  
O. Thual ◽  
P. O. Malaterre
Keyword(s):  
Correlation Length ◽  
Computational Cost ◽  
Error Variance ◽  
Observation Point ◽  
Propagation Model ◽  
Length Scale ◽  
Background Error ◽  
Background Error Covariance ◽  
Covariance Functions ◽  
Error Covariance

Abstract. This study describes the emulation of an Ensemble Kalman Filter (EnKF) algorithm on a 1-D flood wave propagation model. This model is forced at the upstream boundary with a random variable with gaussian statistics and a correlation function in time with gaussian shape. This allows for, in the case without assimilation, the analytical study of the covariance functions of the propagated signal anomaly. This study is validated numerically with an ensemble method. In the case with assimilation with one observation point, where synthetical observations are generated by adding an error to a true state, the dynamic of the background error covariance functions is not straightforward and a numerical approach using an EnKF algorithm is prefered. First, those numerical experiments show that both background error variance and correlation length scale are reduced at the observation point. This reduction of variance and correlation length scale is propagated downstream by the dynamics of the model. Then, it is shown that the application of a Best Linear Unbiased Estimator (BLUE) algorithm using the background error covariance matrix converged from the EnKF algorithm, provides the same results as the EnKF but with a cheaper computational cost, thus allowing for the use of data assimilation in the context of real time flood forecasting. Moreover it was demonstrated that the reduction of background error correlation length scale and variance at the observation point depends on the error observation statistics. This feature is quantified by abacus built from linear regressions over a limited set of EnKF experiments. These abacus that describe the background error variance and the correlation length scale in the neighboring of the observation point combined with analytical expressions that describe the background error variance and the correlation length scale away from the observation point provide parametrized models for the variance and the correlation length scale. Using this parametrized variance and correlation length scale with a diffusion operator makes it possible to model the converged background error covariance matrix from the EnKF without actually integrating the EnKF algorithm. This method was finally applied to a case with two different observation point with different error statistics. It was shown that the results of this emulated EnKF (EEnKF) in terms of background error variance, correlation length scale and analyzed water level is close to those of the EnKF but with a significantly reduced computational cost.

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