On variational downscaling, fusion, and assimilation of hydrometeorological states: A unified framework via regularization

Water Resources Research

Volumn 49, Issue 9, 2013, Pages 5944-5963

  Ebtehaj, A M ^a   Foufoula Georgiou, E ^a  

^a University of Minnesota   (United States)

Author keywords

data fusion and assimilation; discrete inverse problems; downscaling; Maximum a posteriori estimator; regularization; sparse representation; variational principle

Indexed keywords

DATA FUSION; DIFFERENTIAL EQUATIONS; GAUSSIAN DISTRIBUTION; GAUSSIAN NOISE (ELECTRONIC); SURFACE MEASUREMENT;

DOWN-SCALING; MAXIMUM A POSTERIORI ESTIMATOR; REGULARIZATION; SPARSE REPRESENTATION; VARIATIONAL PRINCIPLES;

INVERSE PROBLEMS;

DATA ASSIMILATION; DOWNSCALING; ESTIMATION METHOD; FORECASTING METHOD; GAUSSIAN METHOD; HYDROMETEOROLOGY; NUMERICAL MODEL; OBSERVATIONAL METHOD; PARADIGM SHIFT;

EID: 84884368001     PISSN: 00431397     EISSN: 19447973     Source Type: Journal    
DOI: 10.1002/wrcr.20424     Document Type: Article

References (86)

1. Adler, R., et al. (2003), The version 2 global precipitation climatology project GPCP monthly precipitation analysis (1979-present), J. Hydrometeorol., 4 (6), 1147-1167. (Pubitemid 38162561)
2. AghaKouchak, A., A. Mehran, H. Norouzi, and, A. Behrangi, (2012), Systematic and random error components in satellite precipitation data sets, Geophys. Res. Lett., 39, L09406, doi: 10.1029/2012GL051592.
3. Badas, M. G., R. Deidda, and, E. Piga, (2006), Modulation of homogeneous space-time rainfall cascades to account for orographic influences, Nat. Hazard Earth. Syst. Sci., 6 (3), 427-437, doi: 10.5194/nhess-6-427-2006. (Pubitemid 44222006)
4. Bateni, S. M., and, D. Entekhabi, (2012), Surface heat flux estimation with the ensemble Kalman smoother: Joint estimation of state and parameters, Water Resour. Res., 48, W08521, doi: 10.1029/2011WR011542.
5. Bertsekas, D. P., (1999), Nonlinear Programming, 2nd ed., 794 pp., Athena Scientific, Belmont, Mass.
6. Bocchiola, D., (2007), Use of scale recursive estimation for assimilation of precipitation data from TRMM (PR and TMI) and NEXRAD, Adv. Water Resour., 30 (11), 2354-2372, doi: 10.1016/j.advwatres.2007.05.012. (Pubitemid 47335550)
7. Bouttier, F., and, P. Courtier, (2002), Data assimilation concepts and methods, Meteorological Training Course Lecture Series, ECMWF, p. 59.
8. Boyd, S., and, L. Vandenberghe, (2004), Convex Optimization, 716 pp., Cambridge Univ. Press, New York.
9. Candes, E. J., and, T. Tao, (2006), Near-optimal signal recovery from random projections: Universal encoding strategies?, IEEE Trans. Inf. Theory, 50 (12), 5406-5425, doi: 10.1109/TIT.2006.885507. (Pubitemid 46445381)
10. Castro, C. J., A. S. Pielke Roger, and, G. Leoncini, (2005), Dynamical downscaling: Assessment of value retained and added using the Regional Atmospheric Modeling System RAMS, J. Geophys. Res., 110, D05108, doi: 10.1029/2004JD004721.
11. Chen, S. S., D. L. Donoho, and, M. A. Saunders, (1998), Atomic decomposition by basis pursuit, SIAM J. Sci. Comput., 20, 33-61. (Pubitemid 128689501)
12. Chen, S., D. Donoho, and, M. Saunders, (2001), Atomic decomposition by basis pursuit, SIAM Rev., 43 (1), 129-159. (Pubitemid 32406896)
13. Ciach, G. J., and, W. F. Krajewski, (1999), On the estimation of radar rainfall error variance, Adv. Water Resour., 22 (6), 585-595. (Pubitemid 29253166)
14. Cooley, J. W., and, J. W. Tukey, (1965), An algorithm for the machine calculation of complex Fourier series, Math. Comput., 19 (90), 297-301.
15. Courtier, P., and, O. Talagrand, (1990), Variational assimilation of meteorological observations with the direct and adjoint shallow-water equations, Tellus, Ser. A, 42 (5), 531-549.
16. Courtier, P., J.-N. Thépaut, and, A. Hollingsworth, (1994), A strategy for operational implementation of 4D-VAR, using an incremental approach, Q. J. R. Meteorol. Soc., 120 (519), 1367-1387, doi: 10.1002/qj.49712051912.
17. Daley, R., (1993), Atmospheric Data Analysis, 472 pp., Cambridge Univ. Press, Cambridge, U.K.
18. Deidda, R., (2000), Rainfall downscaling in a space-time multifractal framework, Water Resour. Res., 36 (7), 1779-1794. (Pubitemid 30651194)
19. Drusch, M., and, P. Viterbo, (2007), Assimilation of screen-level variables in ECMWF's integrated forecast system: A study on the impact on the forecast quality and analyzed soil moisture, Mon. Weather Rev., 135 (2), 300-314, doi: 10.1175/MWR3309.1. (Pubitemid 46344361)
20. Ebtehaj, A. M., and, E. Foufoula-Georgiou, (2011a), Adaptive fusion of multisensor precipitation using Gaussian-scale mixtures in the wavelet domain, J. Geophys. Res., 116, D22110, doi: 10.1029/2011JD016219.
21. Ebtehaj, A. M., and, E. Foufoula-Georgiou, (2011b), 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., 116, D14110, doi: 10.1029/2010JD015177.
22. Ebtehaj, A. M., E. Foufoula-Georgiou, and, G. Lerman, (2012), Sparse regularization for precipitation downscaling, J. Geophys. Res., 116, D22110, doi: 10.1029/2011JD017057.
23. Elad, M., (2010), Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing, 376 pp., Springer, New York.
24. Elad, M., and, A. Feuer, (1997), Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images, IEEE Trans. Image Process., 6 (12), 1646-1658, doi: 10.1109/83.650118. (Pubitemid 127770520)
25. Entekhabi, D., H. Nakamura, and, E. Njoku, (1994), Solving the inverse problem for soil moisture and temperature profiles by sequential assimilation of multifrequency remotely sensed observations, IEEE Trans. Geosci. Remote Sens., 32 (2), 438-448, doi: 10.1109/36.295058.
26. Freitag, M. A., N. K. Nichols, and, C. J. Budd, (2010), L1-regularisation for ill-posed problems in variational data assimilation, Proc. Appl. Math. Mech., 10 (1), 665-668, doi: 10.1002/pamm.201010324.
27. Freitag, M. A., N. K. Nichols, and, C. J. Budd, (2012), Resolution of sharp fronts in the presence of model error in variational data assimilation, Q. J. R. Meteorol. Soc., 139, 742-757, doi: 10.1002/qj.2002.
28. Gaspari, G., and, S. E. Cohn, (1999), Construction of correlation functions in two and three dimensions, Q. J. R. Meteorol. Soc., 125 (554), 723-757, doi: 10.1002/qj.49712555417. (Pubitemid 29247364)
29. Geman, S., and, D. Geman, (1984), Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, IEEE Trans. Pattern Anal. Mach. Intell., 6 (6), 721-741. (Pubitemid 15453722)
30. Golub, G., P. Hansen, and, D. O'Leary, (1999), Tikhonov regularization and total least squares, SIAM J. Matrix Anal. Appl., 21 (1), 185-194.
31. Gorenburg, I. P., D. McLaughlin, and, D. Entekhabi, (2001), Scale-recursive assimilation of precipitation data, Adv. Water Resour., 24 (9-10), 941-953, doi: 10.1016/S0309-1708(01)00033-1. (Pubitemid 34057241)
32. Gupta, V., and, E. Waymire, (1993), A statistical analysis of mesoscale rainfall as a random cascade, J. Appl. Meteorol., 32, 251-251.
33. Hansen, P., (1998), Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion, vol. 4, Soc. for Ind. Math., Philadelphia, Pa.
34. Hansen, P., (2010), Discrete Inverse Problems: Insight and Algorithms, vol. 7, Soc. for Ind. and Appl. Math., Philadelphia, Pa.
35. Hong, Y., K. Hsu, S. Sorooshian, and, X. Gao, (2004), Precipitation estimation from remotely sensed imagery using an artificial neural network cloud classification system, J. Appl. Meteorol., 43 (12), 1834-1853.
36. Hossain, F., and, E. N. Anagnostou, (2005), Numerical investigation of the impact of uncertainties in satellite rainfall estimation and land surface model parameters on simulation of soil moisture, Adv. Water Resour., 28 (12), 1336-1350. (Pubitemid 41600490)
37. Hossain, F., and, E. N. Anagnostou, (2006), A two-dimensional satellite rainfall error model, IEEE Trans. Geosci. Remote Sens., 44 (6), 1511-1522. (Pubitemid 43824498)
38. Huber, P., (1964), Robust estimation of a location parameter, Ann. Math. Stat., 35 (1), 73-101.
39. Huber, P., (1981), Robust Statistics, vol. 1, John Wiley, New York.
40. Huffman, G., R. Adler, B. Rudolf, U. Schneider, and, P. Keehn, (1995), Global precipitation estimates based on a technique for combining satellite-based estimates, rain gauge analysis, and NWP model precipitation information, J. Clim., 8 (5), 1284-1295. (Pubitemid 26442033)
41. Huffman, G., R. Adler, M. Morrissey, D. Bolvin, S. Curtis, R. Joyce, B. McGavock, and, J. Susskind, (2001), Global precipitation at one-degree daily resolution from multisatellite observations, J. Hydrometeorol., 2 (1), 36-50.
42. Huffman, G., D. Bolvin, E. Nelkin, D. Wolff, R. Adler, G. Gu, Y. Hong, K. Bowman, and, E. Stocker, (2007), The TRMM multisatellite precipitation analysis (TMPA): Quasi-global, multiyear, combined-sensor precipitation estimates at fine scales, J. Hydrometeorol., 8 (1), 38-55. (Pubitemid 46444451)
43. Johnson, C., N. K. Nichols, and, B. J. Hoskins, (2005), Very large inverse problems in atmosphere and ocean modelling, Int. J. Numer. Methods Fluids, 47 (8-9), 759-771, doi: 10.1002/fld.869. (Pubitemid 40413112)
44. Kalnay, E., (2003), Atmospheric Modeling, Data Assimilation, and Predictability, 341 pp., Cambridge Univ. Press, New York.
45. Kim, G., and, A. Barros, (2002), Downscaling of remotely sensed soil moisture with a modified fractal interpolation method using contraction mapping and ancillary data, Remote Sens. Environ., 83 (3), 400-413. (Pubitemid 35337194)
46. Krajewski, W. F., B. Vignal, B. C. Seo, and, G. Villarini, (2011), Statistical model of the range-dependent error in radar-rainfall estimates due to the vertical profile of reflectivity, J. Hydrol., 402, 306-316, doi: 10.1016/j.jhydrol.2011.03.024.
47. Kumar, P., (1999), A multiple scale state-space model for characterizing subgrid scale variability of near-surface soil moisture, IEEE Trans. Geosci. Remote Sens., 37 (1), 182-197, doi: 10.1109/36.739153.
48. Kumar, P., and, E. Foufoula-Georgiou, (1993), A multicomponent decomposition of spatial rainfall fields. 2. Self-similarity in fluctuations, Water Resour. Res., 29 (8), 2533-2544. (Pubitemid 24397671)
49. Kummerow, C. D., S. Ringerud, J. Crook, D. Randel, and, W. Berg, (2010), An observationally generated a priori database for microwave rainfall retrievals, J. Atmos. Oceanic Technol., 28 (2), 113-130, doi: 10.1175/2010JTECHA1468.1.
50. Ledoit, O., and, M. Wolf, (2004), A well-conditioned estimator for large-dimensional covariance matrices, J. Multivariate Anal., 88 (2), 365-411. (Pubitemid 38033261)
51. Levy, B. C., (2008), Principles of Signal Detection and Parameter Estimation, 1st ed., 639 pp., Springer, New York, doi: 10.1007/978-0-387-76544- 0.
52. Lewicki, M., and, T. Sejnowski, (2000), Learning overcomplete representations, Neural Comput., 12(2), 337-365.
53. Liang, X., E. F. Wood, and, D. P. Lettenmaier, (1999), Modeling ground heat flux in land surface parameterization schemes, J. Geophys. Res., 104 (D8), 9581-9600. (Pubitemid 29370755)
54. Lorenc, A., (1988), Optimal nonlinear objective analysis, Q. J. R. Meteorol. Soc., 114 (479), 205-240.
55. Lorenc, A. C., (1986), Analysis methods for numerical weather prediction, Q. J. R. Meteorol. Soc., 112 (474), 1177-1194, doi: 10.1002/qj.49711247414.
56. Lovejoy, S., and, B. Mandelbrot, (1985), Fractal properties of rain, and a fractal model, Tellus, Ser. A, 37 (3), 209-232.
57. Lovejoy, S., and, D. Schertzer, (1990), Multifractals, universality classes and satellite and radar, J. Geophys. Res., 95 (D3), 2021-2034.
58. Maggioni, V., R. H. Reichle, and, E. N. Anagnostou, (2012), The impact of rainfall error characterization on the estimation of soil moisture fields in a land data assimilation system, J. Hydrometeorol., 13 (3), 1107-1118, doi: 10.1175/JHM-D-11-0115.1.
59. Margulis, S. A., and, D. Entekhabi, (2003), Variational assimilation of radiometric surface temperature and reference-level micrometeorology into a model of the atmospheric boundary layer and land surface, Mon. Weather Rev., 131 (7), 1272-1288, doi: 10.1175/1520-0493(2003)131 <1272:VAORST>2.0.CO;2. (Pubitemid 36953812)
60. Margulis, S. A., D. McLaughlin, D. Entekhabi, and, S. Dunne, (2002), Land data assimilation and estimation of soil moisture using measurements from the Southern Great Plains 1997 Field Experiment, Water Resour. Res., 38 (12), 1299, doi: 10.1029/2001WR001114.
61. Masunaga, H., and, C. Kummerow, (2005), Combined radar and radiometer analysis of precipitation profiles for a parametric retrieval algorithm, J. Atmos. Oceanic Technol., 22 (7), 909-929. (Pubitemid 41535040)
62. Merlin, O., A. Chehbouni, Y. Kerr, and, D. Goodrich, (2006), A downscaling method for distributing surface soil moisture within a microwave pixel: Application to the Monsoon'90 data, Remote Sens. Environ., 101 (3), 379-389.
63. Nichols, N. K., (2010), Mathematical concepts of data assimilation, in Data Assimilation: Making Sense of Observations, Part 1, pp. 13-39, Springer, Berlin.
64. Parrish, D. F., and, J. C. Derber, (1992), The National Meteorological Center's spectral statistical-interpolation analysis system, Mon. Weather Rev., 120 (8), 1747-1763, doi: 10.1175/1520-0493(1992)120 <1747: TNMCSS>2.0.CO;2. (Pubitemid 23375504)
65. Perica, S., and, E. Foufoula-Georgiou, (1996), Model for multiscale disaggregation of spatial rainfall based on coupling meteorological and scaling, J. Geophys. Res., 101 (D21), 26,347-26,361.
66. Peter-Lidard, C. D., M. S. Zion, and, E. F. Wood, (1997), A soil-vegetation-atmosphere transfer scheme for modeling spatially variable water and energy balance processes, J. Geophys. Res., 102 (D4), 4303-4324.
67. Rebora, N., L. Ferraris, J. Von Hardenberg, and, A. Provenzale, (2005), Stochastic downscaling of LAM predictions: An example in the Mediterranean area, Adv. Geosci., 2, 181-185. (Pubitemid 44294203)
68. Rebora, N., L. Ferraris, J. Von Hardenberg, and, A. Provenzale, (2006), Rainfall downscaling and flood forecasting: A case study in the Mediterranean area, Nat. Hazards Earth Syst. Sci., 6 (4), 611-619. (Pubitemid 44065372)
69. Reichle, R., D. Entekhabi, and, D. McLaughlin, (2001a), Downscaling of radio brightness measurements for soil moisture estimation: A four-dimensional variational data assimilation approach, Water Resour. Res., 37 (9), 2353-2364. (Pubitemid 32808505)
70. Reichle, R., D. McLaughlin, and, D. Entekhabi, (2001b), Variational data assimilation of microwave radio brightness observations for land surface hydrology applications, IEEE Trans. Geosci. Remote Sens., 39 (8), 1708-1718, doi: 10.1109/36.942549. (Pubitemid 32933010)
71. Sasaki, Y., (1958), An objective analysis based on variational method, J. Meteorol. Soc. Jpn., 36, 77-88.
72. Schultz, R., and, R. Stevenson, (1994), A Bayesian approach to image expansion for improved definition, IEEE Trans. Image Process., 3 (3), 233-242.
73. Siccardi, F., G. Boni, L. Ferraris, and, R. Rudari, (2005), A hydrometeorological approach for probabilistic flood forecast, J. Geophys. Res., 110, D05101, doi: 10.1029/2004JD005314.
74. Sorooshian, S., K. Hsu, G. Xiaogang, H. Gupta, B. Imam, and, D. Braithwaite, (2000), Evaluation of PERSIANN system satellite-based estimates of tropical rainfall, Bull. Am. Meteorol. Soc., 81 (9), 2035-2046.
75. Talagrand, O., and, P. Courtier, (1987), Variational assimilation of meteorological observations with the adjoint vorticity equation. I: Theory, Q. J. R. Meteorol. Soc., 113 (478), 1311-1328.
76. Tibshirani, R., (1996), Regression shrinkage and selection via the lasso, J. R. Stat. Soc. Ser. B, 58 (1), 267-288.
77. Tikhonov, A., V. Arsenin, and, F. John, (1977), Solutions of Ill-Posed Problems, Winston. Washington, D. C.
78. Tustison, B., E. Foufoula-Georgiou, and, D. Harris, (2003), Scale-recursive estimation for multisensor Quantitative Precipitation Forecast verification: A preliminary assessment, J. Geophys. Res, 107 (D8), 8377, doi: 10.1029/2001JD001073.
79. Van de Vyver, H., and, E. Roulin, (2009), Scale-recursive estimation for merging precipitation data from radar and microwave cross-track scanners, J. Geophys. Res., 114, D08104, doi: 10.1029/2008JD010709.
80. Veneziano, D., R. L. Bras, and, J. D. Niemann, (1996), Nonlinearity and self-similarity of rainfall in time and a stochastic model, J. Geophys. Res., 101 (D21), 26,371-26,392.
81. Wang, S., X. Liang, and, Z. Nan, (2011), How much improvement can precipitation data fusion achieve with a multiscale Kalman Smoother-based framework?, Water Resour. Res., 47, W00H12, doi: 10.1029/2010WR009953.
82. Wang, Z., A. Bovik, H. Sheikh, and, E. Simoncelli, (2004), Image quality assessment: From error visibility to structural similarity, IEEE Trans. Image Process., 13 (4), 600-612.
83. Wilby, R., T. Wigley, D. Conway, P. Jones, B. J. M. Hewitson, and, D. S. Wilks, (1998a), Statistical downscaling of general circulation model output: A comparison of methods, Water Resour. Res., 34 (11), 2995-3008, doi: 10.1029/98WR02577. (Pubitemid 28494932)
84. Wilby, R., H. Hassan, and, K. Hanaki, (1998b), Statistical downscaling of hydrometeorological variables using general circulation model output, J. Hydrol., 205 (1), 1-19. (Pubitemid 28190164)
85. Zupanski, D., S. Q. Zhang, M. Zupanski, A. Y. Hou, and, S. H. Cheung, (2010), A prototype WRF-based ensemble data assimilation system for dynamically downscaling satellite precipitation observations, J. Hydrometeorol., 12 (1), 118-134, doi: 10.1175/2010JHM1271.1.
86. Zupanski, M., (1993), Regional four-dimensional variational data assimilation in a quasi-operational forecasting environment, Mon. Weather Rev., 121 (8), 2396-2408. (Pubitemid 24398928)