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Data assimilation and predictability

Variational data assimilation via sparse regularisation

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Article: 21789 | Received 18 Jun 2013, Accepted 01 Jan 2014, Published online: 11 Feb 2014

References

  • Afshar A , Marino M. A . Model for simulating soil-water content considering evapotranspiration. J. Hydrol. 1978; 37: 309–322.
  • Anderson J. L . An ensemble adjustment Kalman Filter for data assimilation. Mon. Weather Rev. 2001; 129: 2884–2903.
  • Bai Z , Demmel J , Dongarra J , Ruhe A , Van Der Vorst H . Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide. 1987; 11 Philadelphia: SIAM.
  • Barnard J , McCulloch R , Meng X . Modeling covariance matrices in terms of standard deviations and correlations, with application to shrinkage. Stat. Sin. 2000; 10: 1281–1312.
  • Bennett A. F , McIntosh P. C . Open ocean modeling as an inverse problem: tidal theory. J. Phys. Oceanogr. 1982; 12: 1004–1018.
  • Bertsekas D . On the Goldstein-Levitin-Polyak gradient projection method. IEEE Trans. Automat. Contr. 1976; 21: 174–184.
  • Bertsekas D. P . Nonlinear Programming. 1999; Belmont, MA: Athena Scientific. 794. 2nd ed.
  • Boyd S , Vandenberghe L . Convex Optimization. 2004; New York: Cambridge University Press. 716.
  • Budd C , Freitag M , Nichols N . Regularization techniques for ill-posed inverse problems in data assimilation. Comput. Fluids. 2011; 46: 168–173.
  • Candes E , Tao T . Near-optimal signal recovery from random projections: universal encoding strategies?. IEEE Trans. Inform. Theor. 2006; 52: 5406–5425.
  • Chan R. H.-F , Jin X.-Q . An Introduction to Iterative Toeplitz Solvers. 2007; Philadelphia: SIAM.
  • Chapra S. C . Surface Water Quality Modeling. 2008; long grove, IL, USA: Waveland Press, Inc..
  • Chen S , Donoho D , Saunders M . Atomic decomposition by basis pursuit. SIAM Rev. 2001; 43: 129–159.
  • Chen S. S , Donoho D , Saunders M . Atomic decomposition by basis pursuit. SIAM J. Sci. Comput. 1998; 20: 33–61.
  • Courtier P , Talagrand O . Variational assimilation of meteorological observations with the direct and adjoint shallow-water equations. Tellus A. 1990; 42: 531–549.
  • Courtier P , Thépaut J.-N , Hollingsworth A . A strategy for operational implementation of 4D-VAR, using an incremental approach. Q. J. Roy. Meteorol. Soc. 1994; 120: 1367–1387.
  • Daley R . Atmospheric Data Analysis. 1993; New York, NY, USA: Cambridge University Press. 472.
  • Durrett R . Essentials of Stochastic Processes. 1999; New York, NY, USA: Springer-Verlag, New York Inc..
  • Ebtehaj A. M , Foufoula-Georgiou E . Statistics of precipitation reflectivity images and cascade of Gaussian-scale mixtures in the wavelet domain: a formalism for reproducing extremes and coherent multiscale structures. J. Geophys. Res. 2011; 116: D14110.
  • Ebtehaj A. M , Foufoula-Georgiou E . On variational downscaling, fusion and assimilation of hydro-meteorological states: a unified framework via regularization. 2013; 49: 5944–5963.
  • Ebtehaj A. M , Foufoula-Georgiou E , Lerman G . Sparse regularization for precipitation downscaling. J. Geophys. Res. 2012; 116: D22110.
  • Elad M . Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing. 2010; New York, NY, USA: Springer-Verlag, New York Inc.. 376.
  • Evensen G . Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res. 1994a; 99: 10143–10162.
  • Evensen G . Inverse methods and data assimilation in nonlinear ocean models. Physica D. 1994b; 77: 108–129.
  • Fetter C . Applied Hydrogeology. 1994; 4th ed, New Jersey: Prentice Hall.
  • Figueiredo M , Nowak R , Wright S . Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE J. Sel. Topics Signal Process. 2007; 1: 586–597.
  • Freitag M. A , Nichols N. K , Budd C. J . L1-regularisation for ill-posed problems in variational data assimilation. PAMM. 2010; 10: 665–668.
  • Freitag M. A , Nichols N. K , Budd C. J . Resolution of sharp fronts in the presence of model error in variational data assimilation. Q. J. Roy. Meteorol. Soc. 2012; 139: 742–757.
  • Gaspari G , Cohn S. E . Construction of correlation functions in two and three dimensions. Q. J. Roy. Meteorol. Soc. 1999; 125: 723–757.
  • Ghil M . Meteorological data assimilation for oceanographers. Part I: description and theoretical framework. Dynam. Atmos. Oceans. 1989; 13: 171–218.
  • Ghil M , Cohn S , Tavantzis J , Bube K , Isaacson E , Bengtsson L , Ghil M , Källén E . Applications of estimation theory to numerical weather prediction. Dynamic Meteorology: Data Assimilation Methods, Applied Mathematical Sciences. 1981; New York: Springer. 139–224. Vol. 36.
  • Ghil M , Malanotte-Rizzoli P . Data Assimilation in Meteorology and Oceanography. 1991; B.V. Amsterdam, Netherlands: Elsevier Science. 141–266.
  • Golub G , Hansen P , O'Leary D . Tikhonov regularization and total least squares. SIAM J. Matrix Anal. Appl. 1999; 21: 185–194.
  • Hansen P . Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion. 1998; 4 Philadelphia: Society for Industrial Mathematics (SIAM).
  • Hansen P . Discrete Inverse Problems: Insight and Algorithms Vol 7. 2010; Philadelphia, PA: Society for Industrial & Applied Mathematics (SIAM).
  • Hansen P , O'Leary D . The use of the L-curve in the regularization of discrete ill-posed problems. SIAM J Sci Comput. 1993; 14: 1487–1503.
  • Hansen P , Nagy J , O'Leary D . Deblurring Images: Matrices, Spectra, and Filtering Vol 3. 2006; Philadelphia, PA: Society for Industrial & Applied Mathematics (SIAM).
  • Hawkins D. M . The problem of overfitting. J. Chem. Inf. Comput. Sci. 2004; 44: 1–12.
  • Hu Z , Islam S . Prediction of ground surface temperature and soil moisture content by the force–restore method. Water Resour. Res. 1995; 31: 2531–2539.
  • Ide K , Courtier P , Gill M , Lorenc A . Unified notation for data assimilation: operational, sequential, and variational. J. Met. Soc. Japan. 1997; 75: 181–189.
  • Jochum M , Murtugudde R . Temperature advection by tropical instability waves. J. Phys. Oceanogr. 2006; 36: 592–605.
  • Johnson C , Hoskins B. J , Nichols N. K . A singular vector perspective of 4D-Var: filtering and interpolation. Q. J. Roy. Meteorol. Soc. 2005a; 131: 1–19.
  • Johnson C , Nichols N. K , Hoskins B. J . Very large inverse problems in atmosphere and ocean modelling. Int. J. Numer. Meth. Fluids. 2005b; 47: 759–771.
  • Kalnay E . Atmospheric Modeling, Data Assimilation, and Predictability. 2003; New York: Cambridge University Press. 341.
  • Kim S.-J , Koh K , Lustig M , Boyd S , Gorinevsky D . An interior-point method for large-scale l1-regularized least squares. IEEE J. Sel. Topics Signal Process. 2007; 1: 606–617.
  • Kleist D. T , Parrish D. F , Derber J. C , Treadon R , Wu W. S , co-authors . Introduction of the GSI into the NCEP global data assimilation system. Weather. Forecast. 2009; 24: 1691–1705.
  • Lanser D , Verwer J . Analysis of operator splitting for advection–diffusion–reaction problems from air pollution modelling. J. Comput. Appl. Math. 1999; 111: 201–216.
  • Law K. J. H , Stuart A. M . Evaluating data assimilation algorithms. Mon. Weather. Rev. 2012; 140(11): 3757–3782.
  • Levy B. C . Principles of Signal Detection and Parameter Estimation. 2008; 1st ed, New York: Springer Publishing Company. 639.
  • Lewicki M , Sejnowski T . Learning overcomplete representations. Neural Comput. 2000; 12: 337–365.
  • Liang X , Wood E. F , Lettenmaier D. P . Modeling ground heat flux in land surface parameterization schemes. J. Geophys. Res. 1999; 104: 9581–9600.
  • Lin Y.-L , Deal R. L , Kulie M. S . Mechanisms of cell regeneration, development, and propagation within a two-dimensional multicell storm. J. Atmos. Sci. 1998; 55: 1867–1886.
  • Lorenc A . Optimal nonlinear objective analysis. Q. J. Roy. Meteorol. Soc. 1988; 114: 205–240.
  • Lorenc A. C . Analysis methods for numerical weather prediction. Q. J. Roy. Meteorol. Soc. 1986; 112: 1177–1194.
  • Lorenc A. C , Ballard S. P , Bell R. S , Ingleby N. B , Andrews P. L. F , co-authors . The Met. Office global three-dimensional variational data assimilation scheme. Q. J. Roy. Meteorol. Soc. 2000; 126: 2991–3012.
  • Mallat S . A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Anal. Mach. Intell. 1989; 11: 674–693.
  • Mallat S . A Wavelet Tour of Signal Processing: The Sparse Way. 2009; 3rd ed, Elsevier. 805.
  • Moradkhani H , Hsu K.-L , Gupta H , Sorooshian S . Uncertainty assessment of hydrologic model states and parameters: sequential data assimilation using the particle filter. Water Resour. Res. 2005; 41: W05012.
  • Nadarajah S . A generalized normal distribution. J. Appl. Stat. 2005; 32: 685–694.
  • Neumaier A . Solving Ill-conditioned and singular linear systems: a tutorial on regularization. SIAM Rev. 1998; 40: 636–666.
  • Parrish D. F , Derber J. C . The National Meteorological Center's spectral statistical-interpolation analysis system. Mon. Weather Rev. 1992; 120: 1747–1763.
  • Peters-Lidard C. D , Zion M. S , Wood E. F . A soil–vegetation–atmosphere transfer scheme for modeling spatially variable water and energy balance processes. J. Geophys. Res. 1997; 102: 4303–4324.
  • Rabier F , Järvinen H , Klinker E , Mahfouf J.-F , Simmons A . The ECMWF operational implementation of four-dimensional variational assimilation. I: experimental results with simplified physics. Q. J. Roy. Meteorol. Soc. 2000; 126: 1143–1170.
  • Rao K , Yip P . Discrete Cosine Transform: Algorithms, Advantages, Applications. 1990; Boston: Academic Press.
  • Rasmussen C , Williams C . Gaussian Processes for Machine Learning Vol 1. 2006; Cambridge, MA: MIT press.
  • Rawlins F , Ballard S. P , Bovis K. J , Clayton A. M , Li D , co-authors . The Met Office global four-dimensional variational data assimilation scheme. Q. J. Roy. Meteorol. Soc. 2007; 133: 347–362.
  • Sasaki Y . Some basic formalisms in numerical variational analysis. Mon. Weather Rev. 1970; 98: 875–883.
  • Serafini T , Zanghirati G , Zanni L . Gradient projection methods for quadratic programs and applications in training support vector machines. Optim. Methods Softw. 2005; 20: 353–378.
  • Smith K. S , Marshall J . Evidence for enhanced Eddy mixing at middepth in the Southern ocean. J. Phys. Oceanogr. 2009; 39: 50–69.
  • Stein M. L . Interpolation of Spatial Data. 1999; Springer-Verlag, New York.
  • Tibshirani R . Regression shrinkage and selection via the Lasso. J. R. Stat. Soc. Ser. B Stat. Methodol. 1996; 58: 267–288.
  • Tikhonov A , Arsenin V , John F . Solutions of Ill-Posed Problems. 1977; Washington, DC: Winston & Sons.
  • Van Leeuwen P. J . Nonlinear data assimilation in geosciences: an extremely efficient particle filter. Q. J. Roy. Meteorol. Soc. 2010; 136: 1991–1999.
  • Wahba G , Wendelberger J . Some new mathematical methods for variational objective analysis using splines and cross validation. Mon. Weather. Rev. 1980; 108: 1122–1143.
  • Zhou Y , McLaughlin D , Entekhabi D . Assessing the performance of the ensemble Kalman filter for land surface data assimilation. Mon. Weather Rev. 2006; 134: 2128–2142.
  • Zupanski M . Regional four-dimensional variational data assimilation in a quasi-operational forecasting environment. Mon. Weather Rev. 1993; 121: 2396–2408.