Systematic Comparison of Four-Dimensional Data Assimilation Methods With and Without the Tangent Linear Model Using Hybrid Background Error Covariance: E4DVar versus 4DEnVar

Monthly Weather Review - Tập 143 Số 5 - Trang 1601-1621 - 2015
Jonathan Poterjoy1, Fuqing Zhang1
1Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania

Tóm tắt

Abstract Two ensemble formulations of the four-dimensional variational (4DVar) data assimilation technique are examined for a low-dimensional dynamical system. The first method, denoted E4DVar, uses tangent linear and adjoint model operators to minimize a cost function in the same manner as the traditional 4DVar data assimilation system. The second method, denoted 4DEnVar, uses an ensemble of nonlinear model trajectories to replace the function of linearized models in 4DVar, thus improving the parallelization of the data assimilation. Background errors for each algorithm are represented using a hybrid error covariance, which includes climatological errors as well as ensemble-estimated errors from an ensemble Kalman filter (EnKF). Numerical experiments performed over a range of scenarios suggest that both methods provide similar analysis accuracy for dense observation networks, and in perfect model experiments with large ensembles. Nevertheless, E4DVar has clear benefits over 4DEnVar when substantial covariance localization is required to treat sampling error. The greatest advantage of the tangent-linear approach is that it implicitly propagates a localized, full-rank ensemble covariance in time, thus avoiding the need to localize a time-dependent ensemble covariance. The tangent linear and adjoint model operators also provide a means of evolving flow-dependent information from the climate-based error component, which is found to be beneficial for treating model error. Challenges that need to be overcome before adopting a pure ensemble framework are illustrated through experiments estimating time covariances with four-dimensional ensembles and comparing results with those estimated with a tangent linear model.

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Tài liệu tham khảo

Bishop, 2011, Adaptive ensemble covariance localization in ensemble 4D-VAR state estimation, Mon. Wea. Rev., 139, 1241, 10.1175/2010MWR3403.1

Bishop, 2013, Hidden error variance theory. Part I: Exposition and analytic model, Mon. Wea. Rev., 141, 1454, 10.1175/MWR-D-12-00118.1

Buehner, 2005, Ensemble-derived stationary and flow-dependent background-error covariances: Evaluation in a quasi-operational NWP setting, Quart. J. Roy. Meteor. Soc., 131, 1013, 10.1256/qj.04.15

Buehner, 2010, Intercomparison of variational data assimilation and the ensemble Kalman filter for global deterministic NWP. Part I: Description and single-observation experiments, Mon. Wea. Rev., 138, 1550, 10.1175/2009MWR3157.1

Buehner, 2010, Intercomparison of variational data assimilation and the ensemble Kalman filter for global deterministic NWP. Part II: One-month experiments with real observations, Mon. Wea. Rev., 138, 1567, 10.1175/2009MWR3158.1

Clayton, 2013, Operational implementation of a hybrid ensemble/4D-Var global data assimilation system at the Met Office, Quart. J. Roy. Meteor. Soc., 139, 1445, 10.1002/qj.2054

Courtier, 1994, A strategy for operational implementation of 4D-Var, using an incremental approach, Quart. J. Roy. Meteor. Soc., 120, 1367, 10.1002/qj.49712051912

Etherton, 2004, Resilience of hybrid ensemble/3DVAR analysis schemes to model error and ensemble covariance error, Mon. Wea. Rev., 132, 1065, 10.1175/1520-0493(2004)132<1065:ROHDAS>2.0.CO;2

Evensen, 1994, Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics, J. Geophys. Res., 99, 10 143, 10.1029/94JC00572

Fairbairn, 2014, A comparison of 4DVar with ensemble data assimilation methods, Quart. J. Roy. Meteor. Soc., 140, 281, 10.1002/qj.2135

Fisher, 2001

Gustafsson, 2014, Four-dimensional ensemble variational (4D-En-Var) data assimilation for the HIgh Resolution Limited Area Model (HIRLAM), Nonlinear Processes Geophys., 21, 745, 10.5194/npg-21-745-2014

Hamill, 2000, A hybrid ensemble Kalman filter-3D variational analysis scheme, Mon. Wea. Rev., 128, 2905, 10.1175/1520-0493(2000)128<2905:AHEKFV>2.0.CO;2

Honda, 2005, A pre-operational variational data assimilation system for a non-hydrostatic model at the Japan Meteorological Agency: Formulation and preliminary results, Quart. J. Roy. Meteor. Soc., 131, 3465, 10.1256/qj.05.132

Houtekamer, 1998, Data assimilation using an ensemble Kalman filter technique, Mon. Wea. Rev., 126, 796, 10.1175/1520-0493(1998)126<0796:DAUAEK>2.0.CO;2

Huang, 2009, Four-dimensional variational data assimilation for WRF: Formulation and preliminary results, Mon. Wea. Rev., 137, 299, 10.1175/2008MWR2577.1

Kuhl, 2013, Comparison of hybrid ensemble/4DVar and 4DVar within the NAVDAS-AR data assimilation framework, Mon. Wea. Rev., 141, 2740, 10.1175/MWR-D-12-00182.1

Le Dimet, 1986, Variational algorithms for analysis and assimilation of meteorological observations: Theoretical aspects, Tellus, 38A, 97, 10.1111/j.1600-0870.1986.tb00459.x

Liu, 2013, An ensemble-based four-dimensional variational data assimilation scheme. Part III: Antarctic applications with Advanced Research WRF using real data, Mon. Wea. Rev., 141, 2721, 10.1175/MWR-D-12-00130.1

Liu, 2008, An ensemble-based four-dimensional variational data assimilation scheme. Part I: Technical formulation and preliminary test, Mon. Wea. Rev., 136, 3363, 10.1175/2008MWR2312.1

Liu, 2009, An ensemble-based four-dimensional variational data assimilation scheme. Part II: Observing System Simulation Experiments with Advanced Research WRF (ARW), Mon. Wea. Rev., 137, 1687, 10.1175/2008MWR2699.1

Lorenc, 1997, Development of an operational variational assimilation scheme, J. Meteor. Soc. Japan, 75, 339, 10.2151/jmsj1965.75.1B_339

Lorenc, 2003, The potential of the ensemble Kalman filter for NWP: A comparison with 4D-Var, Quart. J. Roy. Meteor. Soc., 129, 3183, 10.1256/qj.02.132

Lorenc, 2000, The Met Office global three-dimensional variational data assimilation scheme, Quart. J. Roy. Meteor. Soc., 126, 2991, 10.1002/qj.49712657002

Lorenc, 2014

Lorenz, 1996

Lorenz, 1998, Optimal sites for supplementary weather observations: Simulation with a small model, J. Atmos. Sci., 55, 399, 10.1175/1520-0469(1998)055<0399:OSFSWO>2.0.CO;2

Poterjoy, 2014, Intercomparison and coupling of ensemble and four-dimensional variational data assimilation methods for the analysis and forecasting of Hurricane Karl (2010), Mon. Wea. Rev., 10.1175/MWR-D-13-00394.1

Sun, 1997, Dynamical and microphysical retrieval from Doppler radar observations using a cloud model and its adjoint. Part I: Model development and simulated data experiments, J. Atmos. Sci., 54, 1642, 10.1175/1520-0469(1997)054<1642:DAMRFD>2.0.CO;2

Thepáut, 1991, Four-dimensional variational data assimilation using the adjoint of a multilevel primitive-equation model, Quart. J. Roy. Meteor. Soc., 117, 1225, 10.1002/qj.49711750206

Thepáut, 1996, Dynamical structure functions in a four-dimensional variational assimilation: A case study, Quart. J. Roy. Meteor. Soc., 122, 535, 10.1002/qj.49712253012

Tian, 2008, 10.1029/2008JD010358

Tian, 2009, 10.1029/2008JD011600

Wang, 2014, GSI-based four-dimensional ensemble-variational (4DEnsVar) data assimilation: Formulation and single-resolution experiments with real data for NCEP Global Forecast System, Mon. Wea. Rev., 142, 3303, 10.1175/MWR-D-13-00303.1

Wang, 2007, On the theoretical equivalence of differently proposed ensemble-3DVar hybrid analysis schemes, Mon. Wea. Rev., 135, 222, 10.1175/MWR3282.1

Zhang, 2004, Impacts of initial estimate and observation availability on convective-scale data assimilation with an ensemble Kalman filter, Mon. Wea. Rev., 132, 1238, 10.1175/1520-0493(2004)132<1238:IOIEAO>2.0.CO;2

Zhang, 2009, Coupling ensemble Kalman filter with four-dimensional variational data assimilation, Adv. Atmos. Sci., 26, 1, 10.1007/s00376-009-0001-8

Zhang, 2013, E3DVar: Coupling an ensemble Kalman filter with three-dimensional variational data assimilation in a limited-area weather prediction model and comparison to E4DVar, Mon. Wea. Rev., 141, 900, 10.1175/MWR-D-12-00075.1

Zhang, 2012, E4DVar: Coupling an ensemble Kalman filter with four-dimensional data assimilation in a limited-area weather prediction model, Mon. Wea. Rev., 140, 587, 10.1175/MWR-D-11-00023.1

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Monthly Weather Review

Tập 143 Số 5

1601-1621

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