501
Views
4
CrossRef citations to date
0
Altmetric
Data assimilation and predictability

Representer-based variational data assimilation in a spectral element shallow water model on the cubed-sphere grid

, &
Article: 24493 | Received 30 Mar 2014, Accepted 10 Sep 2014, Published online: 27 Oct 2014

References

  • Bannister R. N . A review of forecast error covariance statistics in atmospheric variational data assimilation. I: characteristics and measurements of forecast error covariances. Q. J. Roy. Meteorol. Soc. 2008a; 134: 1951–1970.
  • Bannister R. N . A review of forecast error covariance statistics in atmospheric variational data assimilation. II: modeling the forecast error covariance statistics. Q. J. Roy. Meteorol. Soc. 2008b; 134: 1971–1996.
  • Bennett A. F . Inverse methods in physical oceanography, monographs on mechanics and applied mathematics. 1992; Cambridge University Press, Cambridge.
  • Bennett A. F . Inverse modeling of the ocean and atmosphere. 2002; New York: Cambridge University Press. 225 pp.
  • Bennett A. F. , McIntosh P. C . Open ocean modeling as an inverse problem: tidal theory. J. Phys. Oceanogr. 1982; 12: 1004–1018.
  • Bennett A. F. , Thorburn M. A . The generalized inverse of a nonlinear quasigeostrophic ocean circulation model. J. Phys. Oceanogr. 1992; 22: 213–230.
  • Bouttier F. , Courtier P . Data assimilation concepts and methods, ECMWF meteorological training lecture notes. 1999; ECMWF. 1–58.
  • Chua B. S. , Bennett A. F . An inverse ocean modeling system. Ocean. Model. 2001; 3: 137–165.
  • Chua B. S. , Zaron E. , Xu L. , Baker N. , Rosmond T . Park S. K. , Xu L . Recent applications in representer-based variational data assimilation. Data Assimilation in Atmospheric, Oceanic and Hydrologic Application. 2013; Berlin: Springer-Verlag. 287–301.
  • Courtier P . Dual formulation of four-dimensional data assimilation. Quart. J. Royal. Meteo. Soc. 1997; 123: 2449–2461.
  • Courtier P. , Talagrand O . Variational assimilation of meteorological observations with the direct and adjoint shallow-water equations. Tellus A. 1990; 42: 531–549.
  • Daley R . Atmospheric data analysis. 1991; New York: Cambridge University Press.
  • Dennis J. , Fournier A. , Spotz W. F. , St-Cyr A. , Taylor M. A. , co-authors . High resolution mesh convergence properties and parallel efficiency of a spectral element atmospheric dynamical core. High Perf. Comp. Appl. 2005; 19: 225–235.
  • Dennis J. M. , Edwards J. , Evans K. J. , Guba O. , Lauritzen P. H. , co-authors . CAM-SE: A scalable spectral element dynamical core for the Community Atmosphere Model. High Perf. Comp. Appl. 2012; 26: 74–89.
  • Derber J. , Rosati A . A global oceanic data assimilation system. J. Phys. Oceanogr. 1989; 19: 1333–1347.
  • Fisher M. , Andersson E . Developments in 4d-Var and Kalman filtering. 2001. ECMWF Tech. Memo. 347 (available from ECMWF, Shinfield Park, Reading, Berkshire, RG2 9AX, UK).
  • Giering R. , Kaminski T . Recipes for adjoint code construction. ACM Trans. Math. Software. 1997; 24: 437–474.
  • Hollingsworth A. , Lonnberg P . The statistical structure of short range forecast errors as determined from radiosonde data. Part I: the wind field. Tellus A. 1986; 38: 111–136.
  • Holm E. V . Lecture note on assimilation algorithms. 2008; ECMWF. 30p.
  • Kim S. , Jung B.-J. , Jo Y . Development of a tangent linear model (version 1.0) for the High-Order Method Modelling Environment dynamical core. Geosci. Model Dev. 2014; 7: 1175–1196.
  • Kurapov A. L. , Egbert G. D. , Allen J. S. , Miller R. N . Representer-based variational data assimilation in a nonlinear model of nearshore circulation. J. Geo. Res. C11019 . 2007; 1–18.
  • Kurapov A. L. , Egbert G. D. , Allen J. S. , Miller R. N . Representer-based analyses in the coastal upwelling system. Dynam. Atmos. Oceans. 2009; 48: 198–218.
  • Lawless A. S. , Nichols N. K. , Ballard S. P . A comparison of two methods for developing the linearization of a shallow-water model. Q. J. R. Meteorol. Soc. 2003; 129: 1237–1254.
  • Mandel J . Efficient implementation of the ensemble Kalman filter. 2006. CCM Report 231, University of Colorado Denver.
  • Moore A. M . Schiller A , Grassington G. B . Adjoint data assimilation methods. Operational Oceanography in the 21st Century. 2011; Springer. 351–380.
  • Moore A. M. , Hernan G. A. , Lorenzo E. D. , Cornuelle B. D. , Miller A. J. , co-authors . A comprehensive ocean prediction and analysis system based on the tangent linear and adjoint of a regional ocean model. Ocean Model. 2004; 7: 227–258.
  • Nair R. D. , Thomas S. J. , Loft R. D . A discontinuous galerkin global shallow water model. Mon. Wea. Rev. 2005; 133: 876–888.
  • Ngodock H. E. , Smith S. R. , Jacobs G. A . Cycling the representer algorithm for variational data assimilation with the Lorenz Attractor. Mon. Wea. Rev. 2007; 135: 373–386.
  • Ngodock H. E. , Smith S. R. , Jacobs G. A . Park S. K. , Xu L . Cycling the Representer Method with Nonlinear Models. Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications. 2009; Berlin: Springer-Verlag. 321–340.
  • Parrish D. F , Derber J. C . The National Meteorological Center's spectral statistical interpolation analysis system. Mon. Wea. Rev. 1992; 120: 1747–1763.
  • Rabier F . Overview of global data assimilation developments in numerical weather prediction centres. Q. J. Roy. Meteorol. Soc. 2005; 131: 3215–3233.
  • Rabier F. , Järvinen H. , Klinker E. , Mahfouf J.-F. , Simmons A . The ECMWF implementation of four-dimensional variational assimilation. I: experimental results with simplified physics. Q. J. Roy. Meteorol. Soc. 2000; 126: 1143–1170.
  • Ronchi C. , Iacono R. , Paolucci P. S . The “cubed sphere”: a new method for the solution of partial differential equations in spherical geometry. J. Comput. Phys. 1996; 124: 93–114.
  • Rosmond T. , Xu L . Development of NAVDAS-AR: nonlinear formulation and outer loop tests. Tellus A. 2006; 58A: 45–58.
  • Sadourny R . Conservative finite-difference approximations of the primitive equations on quasi-uniform spherical grids. Mon. Wea. Rev. 1972; 100: 136–144.
  • Smith S. R. , Ngodock H. E . Cycling the representer method for 4D-variational data assimilation with the Navy Coastal Ocean Model. Ocean Model. 2008; 24: 92–107.
  • Taylor M. , Tribbia J. , Iskandrani M . The spectral element method for the shallow water equations on the sphere. J. Comput. Phys. 1997; 130: 92–108.
  • Weaver A. , Courtier P . Correlation modelling on the sphere using a generalized diffusion equation. Q. J. R. Meteo. Soc. 2001; 127: 1815–1846.
  • Williamson D. L. , Drake J. B. , Hack J. J. , Jakob R. , Swarztrauber P. N . A standard test set for numerical approximations to the shallow water equations in spherical geometry. J. Comput. Phys. 1992; 102: 211–224.
  • Xu L. , Daley R . Towards a true 4-dimensional data assimilation algorithm: application of a cycling representer algorithm to a simple transport problem. Tellus A. 2000; 52: 109–128.
  • Xu L. , Daley R . Data assimilation with a barotropically unstable shallow water system using representer algorithms. Tellus. 2002; 54: 125–137.
  • Xu L. , Rosmond T. , Daley R . Development of NAVDAS-AR. Formulation and initial tests of the linear problem. Tellus. 2005; 57: 546–559.
  • Zhu K. , Navon I. M. , Zou X . Variational data assimilation with a variable resolution finite-element shallow-water equation model. Mon. Wea. Rev. 1994; 122: 946–965.
  • Zou X. , Vandenberghe F. , Pondeca M. , Kuo Y.-H . Introduction to adjoint techniques and the MM5 adjoint modeling system. 1997. NCAR Tech. Note NCAR/TN-435-STR.