A non-linear least squares enhanced POD-4DVar algorithm for data assimilation
By: Xiangjun Tian and Xiaobing Feng
References
-
. An ensemble adjustment Kalman filter for data assimilation. Mon. Weather Rev. 2001; 129: 2884– 2903. -
, , , , , co-authors. Implementation of 1D+4D-Var assimilation of precipitation affected microwave radiances at ECMWF II: 4D-Var. Q. J. Roy. Meteorol. Soc. 2006; 132: 2307– 2332. -
, . Singular-vector-based covariance propagation in a quasigeostrophic assimilation system. Mon. Weather Rev. 2005; 133: 1295– 1310. -
, . Impact of MODIS polar winds in ECMWF's 4DVAR data assimilation system. Mon. Weather Rev. 2004; 132: 929– 940. -
, , . A comparison between the 4DVAR and the ensemble Kalman filter techniques for radar data assimilation. Mon. Weather Rev. 2005; 133: 3081– 3094. -
, . Coupling an advanced land-surface/hydrology model with the Penn State/NCAR MM5 modeling system. Part I: Model description and implementation. Mon. Weather Rev. 2001; 129: 569– 585. -
, . A one-dimensional time dependent cloud model. J. Meteorol. Soc. Jpn. 2002; 80: 99– 118. -
, , , . A hybrid approach to estimating error covariances in variational data assimilation. Tellus A. 2010; 62: 288– 297. -
, , . Operational implementation of a hybrid ensemble/4D-Var global data assimilation system at the Met Office. Q. J. Roy. Meteorol. Soc. 2013; 139: 1445– 1461. -
, . Variational assimilation of meteorological observations with the adjoint vorticity equation II: numerical results. Q. J. Roy. Meteorol. Soc. 1987; 113: 1329– 1347. -
, , . A strategy for operational implementation of 4DVar using an incremental approach. Q. J. Roy. Meteorol. Soc. 1994; 120: 1367– 1387. -
, . Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics). -
. Numerical study of convection observed during the winter monsoon experiment using a mesoscale two-dimensional model. J. Atmos. Sci. 1989; 46: 3077– 3107. -
. Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res. 1994; 99( C5): 10143– 10162. -
. Sampling strategies and square root analysis schemes for the EnKF. Ocean Dynam. 2004; 54: 539– 560. -
, . An ensemble Kalman smoother for nonlinear dynamics. Mon. Weather Rev. 2000; 128: 1852– 1867. -
, . Construction of correlation functions in two and three dimensions. Q. J. Roy. Meteorol. Soc. 1999; 125: 723– 757. -
, , , , . Extension of 3DVAR to 4DVAR: implementation of 4DVAR at the meteorological service of Canada. Mon. Weather Rev. 2007; 135( 6): 2339– 2354. -
, . Four-dimensional local ensemble transform Kalman filter: numerical experiments with a global circulation model. Tellus A. 2007; 59: 731– 748. -
, , . A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Weather Rev. 2006; 134: 2318– 2341. -
, . Data assimilation using an ensemble Kalman filter technique. Mon. Weather Rev. 1998; 126: 796– 811. -
, . A sequential ensemble Kalman filter for atmospheric data assimilation. Mon. Weather Rev. 2001; 129: 123– 137. -
, , , . Efficient data assimilation spatiotemporal chaos: a local ensemble transform Kalman filter. Physica D. 2007; 230: 112– 126. -
. Data assimilation into a primitive-equation model with a parallel ensemble Kalman filter. Mon. Weather Rev. 2000; 128: 1971– 1981. -
, . Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus A. 1986; 38: 97– 110. -
, . The use of the adjoint equation to solve a variational adjustment problem with advective constraints. Tellus A. 1985; 37: 309– 322. -
, , . Bulk parameterization of the snow field in a cloud model. J. Clim. Appl. Meteorol. 1983; 22: 1065– 1092. -
, , . An ensemble-based four-dimensional variational data assimilation scheme. Part I: Technique formulation and preliminary test. Mon. Weather Rev. 2008; 136: 3363– 3373. -
. The potential of the ensemble Kalman Filter for NWP: a comparison with 4Dvar. Q. J. Roy. Meteorol. Soc. 2003; 129: 3183– 3203. -
, . Modeling and control of physical processes using proper orthogonal decomposition. Math. Comput. Model. 2001; 33: 223– 236. -
, . Proper orthogonal decomposition for flow calculations and optimal control in a horizontal CVD reactor. Q. Appl. Math. 2002; 60: 631– 656. -
, . Potential of an ensemble Kalman smoother for stratospheric chemical-dynamical data assimilation. Tellus A. 2013; 65: 18541. -
, , , , . Radiative transfer for inhomogeneous atmosphere: RRTM, a validated correlated-k model for the longwave. J. Geophys. Res. 1997; 102( D14): 16663– 16682. -
, , , , , co-authors. A local ensemble Kalman filter for atmospheric data assimilation. Tellus A. 2004; 56: 415– 428. -
, , , , , co-authors. Assimilating Doppler radar radial velocity and reflectivity observations in the weather research and forecasting model by a proper orthogonal decomposition based ensemble three-dimensional variational assimilation method. J. Geophys. Res. 2012; 117: D17113. -
, . Toward developing an objective 4DVAR BDA scheme for hurricane initialization based on TPC observed parameters. Mon. Weather Rev. 2004; 132( 8): 2054– 2069. -
, , , . Fitting model fields to observations by using singular value decomposition: an ensemble-based 4DVar approach. J. Geophys. Res. 2007; 112: D11105. -
, . Development of NAVDAS-AR: nonlinear formulation and outer loop tests. Tellus A. 2006; 58( 1): 45– 58. -
, . The mesoscale and microscale structure and organization of clouds and precipitation in midlatitude cyclones. XII: a diagnostic modeling study of precipitation development in narrow cloud-frontal rain bands. J. Atmos. Sci. 1984; 20: 2949– 2972. -
, , , , , co-authors. A Description of the Advanced Research WRF Version 3. -
, . Implementations of a square-root ensemble analysis and a hybrid localisation into the POD-based ensemble 4DVar. Tellus A. 2012; 64. -
, , . An ensemble-based explicit four-dimensional variational assimilation method. J. Geophys. Res. 2008; 113: D21124. -
, , , , . A microwave land data assimilation system: scheme and preliminary evaluation over China. J. Geophys. Res. 2010; 115: D21113. -
, , , , , co-authors. A dual-pass variational data assimilation framework for estimating soil moisture profiles from AMSR-E microwave brightness temperature. J. Geophys. Res. 2009; 114: D16102. -
, , , , , co-authors. A joint data assimilation system (Tan-Tracker) to simultaneously estimate surface CO2 fluxes and 3-D atmospheric CO2 concentrations from observations. Atmos. Chem. Phys. 2014; 14: 13281– 13293. -
, , . A POD-based ensemble four-dimensional variational assimilation method. Tellus A. 2011; 63: 805– 816. -
, , , , , co-authors. An economical approach to four-dimensional variational data assimilation. Adv. Atmos. Sci. 2010; 27( 4 ): 715– 727. -
, , , . A hybrid ETKF-3DVAR data assimilation scheme for the wrf model. Part I: Observing system simulation experiment. Mon. Weather Rev. 2008a; 136: 5116– 5131. -
, , , . A hybrid ETKF-3DVAR data assimilation scheme for the WRF model. Part II: Real observation experiments. Mon. Weather Rev. 2008b; 136: 5132– 5147. -
, , , . GSI 3DVar-based ensemble-variational hybrid data assimilation for NCEP global forecast system: single resolution experiments. Mon. Weather Rev. 2013; 141: 4098– 4117. -
, . Ensemble data assimilation without perturbed observations. Mon. Weather Rev. 2002; 130: 1913– 1924. -
. Generalized adjoint for physical processes with parameterized discontinuities. Part I: Basis issues and heuristic examples. J. Atmos. Sci. 1996; 53( 8): 1123– 1142. -
, , , co-authors. PODEn4DVar-based radar data assimilation scheme: formulation and preliminary results from real-data experiments with advanced research WRF (ARW). Tellus A. 2014 -
, , . Tests of an ensemble Kalman filter for convective-scale data assimilation: impact of initial estimate and observations. Mon. Weather Rev. 2004; 132: 1238– 1253. -
, , . Coupling ensemble Kalman filter with four dimensional variational data assimilation. Adv. Atmos. Sci. 2009; 26( 1 ): 1– 8. -
, . E4DVar: coupling an ensemble Kalman filter with four-dimensional variational data assimilation in a limited-area weather prediction model. Mon. Weather Rev. 2012; 140: 587– 600. -
, . Rainfall assimilation through an optimal control of initial and boundary conditions in a limited-area mesoscale model. Mon. Weather Rev. 1996; 124: 2859– 2882.
DOI: https://doi.org/10.3402/tellusa.v67.25340 | Journal eISSN: 3035-9554
Language: English
Page range: 25340 - 25340
Submitted on: Jul 1, 2014
Accepted on: Dec 1, 2014
Published on: Dec 1, 2015
Published by: Stockholm University Press
In partnership with: Paradigm Publishing Services
Keywords:
© 2015 Xiangjun Tian, Xiaobing Feng, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.