scholarly journals An Investigation of Adaptive Radius for the Covariance Localization in Ensemble Data Assimilation

2021 ◽  
Vol 9 (11) ◽  
pp. 1156
Author(s):  
Xiang Xing ◽  
Bainian Liu ◽  
Weimin Zhang ◽  
Jianping Wu ◽  
Xiaoqun Cao ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Computational Cost ◽  
Adaptive Scheme ◽  
Model Parameter ◽  
Schur Product ◽  
Ensemble Data Assimilation ◽  
Localization Radius ◽  
Ensemble Data ◽  
Localization Scheme ◽  
Taper Function

The covariance matrix estimated from the ensemble data assimilation always suffers from filter collapse because of the spurious correlations induced by the finite ensemble size. The localization technique is applied to ameliorate this issue, which has been suggested to be effective. In this paper, an adaptive scheme for Schur product covariance localization is proposed, which is easy and efficient to implement in the ensemble data assimilation frameworks. A Gaussian-shaped taper function is selected as the localization taper function for the Schur product in the adaptive localization scheme, and the localization radius is obtained adaptively through a certain criterion of correlations with the background ensembles. An idealized Lorenz96 model with an ensemble Kalman filter is firstly examined, showing that the adaptive localization scheme helps to significantly reduce the spurious correlations in the small ensemble with low computational cost and provides accurate covariances that are similar to those derived from a much larger ensemble. The investigations of adaptive localization radius reveal that the optimal radius is model-parameter-dependent, vertical-level-dependent and nearly flow-dependent with weather scenarios in a realistic model; for example, the radius of model parameter zonal wind is generally larger than that of temperature. The adaptivity of the localization scheme is also illustrated in the ensemble framework and shows that the adaptive scheme has a positive effect on the assimilated analysis as the well-tuned localization.

scholarly journals Soil model parameter estimation with ensemble data assimilation

2009 ◽  
Vol 10 (2) ◽  
pp. 127-131 ◽  
Author(s):  
Biljana Orescanin ◽  
Borivoj Rajkovic ◽  
Milija Zupanski ◽  
Dusanka Zupanski
Keyword(s):  
Parameter Estimation ◽  
Data Assimilation ◽  
Model Parameter ◽  
Model Parameter Estimation ◽  
Ensemble Data Assimilation ◽  
Ensemble Data ◽  
Soil Model

Initiation of ensemble data assimilation

2006 ◽  
Author(s):  
M. Zupanski ◽  
S. J. Fletcher ◽  
I. M. Navon ◽  
B. Uzunoglu ◽  
R. P. Heikes ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Ensemble Data Assimilation ◽  
Ensemble Data

Using a machine learning proxy for localization in ensemble data assimilation

2021 ◽  
Vol 25 (3) ◽  
pp. 931-944
Author(s):  
Johann M. Lacerda ◽  
Alexandre A. Emerick ◽  
Adolfo P. Pires
Keyword(s):  
Machine Learning ◽  
Data Assimilation ◽  
Ensemble Data Assimilation ◽  
Ensemble Data

Maximum Likelihood Ensemble Filter: Theoretical Aspects

2005 ◽  
Vol 133 (6) ◽  
pp. 1710-1726 ◽  
Author(s):  
Milija Zupanski
Keyword(s):  
Maximum Likelihood ◽  
Data Assimilation ◽  
Cost Function ◽  
Ensemble Data Assimilation ◽  
Error Covariance ◽  
Ensemble Data ◽  
Analysis Error ◽  
Nonlinear Observation ◽  
The Cost ◽  
Maximum Likelihood Ensemble Filter

Abstract A new ensemble-based data assimilation method, named the maximum likelihood ensemble filter (MLEF), is presented. The analysis solution maximizes the likelihood of the posterior probability distribution, obtained by minimization of a cost function that depends on a general nonlinear observation operator. The MLEF belongs to the class of deterministic ensemble filters, since no perturbed observations are employed. As in variational and ensemble data assimilation methods, the cost function is derived using a Gaussian probability density function framework. Like other ensemble data assimilation algorithms, the MLEF produces an estimate of the analysis uncertainty (e.g., analysis error covariance). In addition to the common use of ensembles in calculation of the forecast error covariance, the ensembles in MLEF are exploited to efficiently calculate the Hessian preconditioning and the gradient of the cost function. A sufficient number of iterative minimization steps is 2–3, because of superior Hessian preconditioning. The MLEF method is well suited for use with highly nonlinear observation operators, for a small additional computational cost of minimization. The consistent treatment of nonlinear observation operators through optimization is an advantage of the MLEF over other ensemble data assimilation algorithms. The cost of MLEF is comparable to the cost of existing ensemble Kalman filter algorithms. The method is directly applicable to most complex forecast models and observation operators. In this paper, the MLEF method is applied to data assimilation with the one-dimensional Korteweg–de Vries–Burgers equation. The tested observation operator is quadratic, in order to make the assimilation problem more challenging. The results illustrate the stability of the MLEF performance, as well as the benefit of the cost function minimization. The improvement is noted in terms of the rms error, as well as the analysis error covariance. The statistics of innovation vectors (observation minus forecast) also indicate a stable performance of the MLEF algorithm. Additional experiments suggest the amplified benefit of targeted observations in ensemble data assimilation.

scholarly journals Convection-Permitting Forecasts Initialized with Continuously Cycling Limited-Area 3DVAR, Ensemble Kalman Filter, and “Hybrid” Variational–Ensemble Data Assimilation Systems

2014 ◽  
Vol 142 (2) ◽  
pp. 716-738 ◽  
Author(s):  
Craig S. Schwartz ◽  
Zhiquan Liu
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Three Dimensional ◽  
Skill Score ◽  
Limited Area ◽  
Computational Domain ◽  
Ensemble Data Assimilation ◽  
Ensemble Data ◽  
Precipitation Characteristics ◽  
High Precipitation

Abstract Analyses with 20-km horizontal grid spacing were produced from parallel continuously cycling three-dimensional variational (3DVAR), ensemble square root Kalman filter (EnSRF), and “hybrid” variational–ensemble data assimilation (DA) systems between 0000 UTC 6 May and 0000 UTC 21 June 2011 over a domain spanning the contiguous United States. Beginning 9 May, the 0000 UTC analyses initialized 36-h Weather Research and Forecasting Model (WRF) forecasts containing a large convection-permitting 4-km nest. These 4-km 3DVAR-, EnSRF-, and hybrid-initialized forecasts were compared to benchmark WRF forecasts initialized by interpolating 0000 UTC Global Forecast System (GFS) analyses onto the computational domain. While important differences regarding mean state characteristics of the 20-km DA systems were noted, verification efforts focused on the 4-km precipitation forecasts. The 3DVAR-, hybrid-, and EnSRF-initialized 4-km precipitation forecasts performed similarly regarding general precipitation characteristics, such as timing of the diurnal cycle, and all three forecast sets had high precipitation biases at heavier rainfall rates. However, meaningful differences emerged regarding precipitation placement as quantified by the fractions skill score. For most forecast hours, the hybrid-initialized 4-km precipitation forecasts were better than the EnSRF-, 3DVAR-, and GFS-initialized forecasts, and the improvement was often statistically significant at the 95th percentile. These results demonstrate the potential of limited-area continuously cycling hybrid DA configurations and suggest additional hybrid development is warranted.

scholarly journals Southern High-Latitude Ensemble Data Assimilation in the Antarctic Mesoscale Prediction System

2005 ◽  
Vol 133 (12) ◽  
pp. 3431-3449 ◽  
Author(s):  
D. M. Barker
Keyword(s):  
Data Assimilation ◽  
Sampling Error ◽  
Forecast Error ◽  
Weather Prediction ◽  
Forecast Errors ◽  
Prediction System ◽  
Spatial Covariance ◽  
Ensemble Data Assimilation ◽  
Ensemble Data ◽  
The Antarctic

Abstract Ensemble data assimilation systems incorporate observations into numerical models via solution of the Kalman filter update equations, and estimates of forecast error covariances derived from ensembles of model integrations. In this paper, a particular algorithm, the ensemble square root filter (EnSRF), is tested in a limited-area, polar numerical weather prediction (NWP) model: the Antarctic Mesoscale Prediction System (AMPS). For application in the real-time AMPS, the number of model integrations that can be run to provide forecast error covariances is limited, resulting in an ensemble sampling error that degrades the analysis fit to observations. In this work, multivariate, climatologically plausible forecast error covariances are specified via averaged forecast difference statistics. Ensemble representations of the “true” forecast errors, created using randomized control variables of the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5) three-dimensional variational (3DVAR) data assimilation system, are then used to assess the dependence of sampling error on ensemble size, data density, and localization of covariances using simulated observation networks. Results highlight the detrimental impact of ensemble sampling error on the analysis increment structure of correlated, but unobserved fields—an issue not addressed by the spatial covariance localization techniques used to date. A 12-hourly cycling EnSRF/AMPS assimilation/forecast system is tested for a two-week period in December 2002 using real, conventional (surface, rawinsonde, satellite retrieval) observations. The dependence of forecast scores on methods used to maintain ensemble spread and the inclusion of perturbations to lateral boundary conditions are studied.

Ensemble data assimilation in the presence of cloud

2011 ◽  
Vol 46 (1) ◽  
pp. 493-497 ◽  
Author(s):  
S. Vetra-Carvalho ◽  
S. Migliorini ◽  
N.K. Nichols
Keyword(s):  
Data Assimilation ◽  
Ensemble Data Assimilation ◽  
Ensemble Data
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