Ensemble Data Assimilation for Tropospheric Ozone Analysis Within the CHIMERE Regional Chemistry Transport Model

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.

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An adaptive covariance relaxation method for ensemble data assimilation

Quarterly Journal of the Royal Meteorological Society ◽

10.1002/qj.2576 ◽

2015 ◽

Vol 141 (692) ◽

pp. 2898-2906 ◽

Cited By ~ 24

Author(s):

Yue Ying ◽

Fuqing Zhang

Keyword(s):

Data Assimilation ◽

Relaxation Method ◽

Ensemble Data Assimilation ◽

Ensemble Data

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

Monthly Weather Review ◽

10.1175/mwr-d-13-00100.1 ◽

2014 ◽

Vol 142 (2) ◽

pp. 716-738 ◽

Cited By ~ 49

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.

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

Monthly Weather Review ◽

10.1175/mwr3042.1 ◽

2005 ◽

Vol 133 (12) ◽

pp. 3431-3449 ◽

Cited By ~ 43

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.

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A fault-tolerant HPC scheduler extension for large and operational ensemble data assimilation: Application to the Red Sea

Journal of Computational Science ◽

10.1016/j.jocs.2018.04.018 ◽

2018 ◽

Vol 27 ◽

pp. 46-56 ◽

Cited By ~ 1

Author(s):

Habib Toye ◽

Samuel Kortas ◽

Peng Zhan ◽

Ibrahim Hoteit

Keyword(s):

Data Assimilation ◽

Red Sea ◽

Fault Tolerant ◽

Ensemble Data Assimilation ◽

Ensemble Data

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Diagnosing the transition layer at extratropical latitudes using MLS O<sub>3</sub> and MOPITT CO analyses

Atmospheric Chemistry and Physics ◽

10.5194/acp-13-7225-2013 ◽

2013 ◽

Vol 13 (14) ◽

pp. 7225-7240 ◽

Cited By ~ 9

Author(s):

J. Barré ◽

L. El Amraoui ◽

P. Ricaud ◽

W. A. Lahoz ◽

J.-L. Attié ◽

...

Keyword(s):

Data Assimilation ◽

Transition Region ◽

Transition Layer ◽

Transport Model ◽

Global Scale ◽

British Isles ◽

Chemistry Transport Model ◽

Free Model ◽

The Relationship

Abstract. The behavior of the extratropical transition layer (ExTL) is investigated using a chemistry transport model (CTM) and analyses derived from assimilation of MLS (Microwave Limb Sounder) O3 and MOPITT (Measurements Of Pollution In The Troposphere) CO data. We firstly focus on a stratosphere–troposphere exchange (STE) case study that occurred on 15 August 2007 over the British Isles (50° N, 10° W). We evaluate the effect of data assimilation on the O3–CO correlations. It is shown that data assimilation disrupts the relationship in the transition region. When MLS O3 is assimilated, CO and O3 values are not consistent between each other, leading to unphysical correlations at the STE location. When MLS O3 and MOPITT CO assimilated fields are taken into account in the diagnostics the relationship happens to be more physical. We then use O3–CO correlations to quantify the effect of data assimilation on the height and depth of the ExTL. When the free-model run O3 and CO fields are used in the diagnostics, the ExTL distribution is found 1.1 km above the thermal tropopause and is 2.6 km wide (2σ). MOPITT CO analyses only slightly sharpen (by −0.02 km) and lower (by −0.2 km) the ExTL distribution. MLS O3 analyses provide an expansion (by +0.9 km) of the ExTL distribution, suggesting a more intense O3 mixing. However, the MLS O3 analyses ExTL distribution shows a maximum close to the thermal tropopause and a mean location closer to the thermal tropopause (+0.45 km). When MLS O3 and MOPITT CO analyses are used together, the ExTL shows a mean location that is the closest to the thermal tropopause (+0.16 km). We also extend the study at the global scale on 15 August 2007 and for the month of August 2007. MOPITT CO analyses still show a narrower chemical transition between stratosphere and troposphere than the free-model run. MLS O3 analyses move the ExTL toward the troposphere and broaden it. When MLS O3 analyses and MOPITT CO analyses are used together, the ExTL matches the thermal tropopause poleward of 50°.

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