Abstract
It is well known that retrieval of parameters is usually ill-posed and highly nonlinear, so parameter retrieval problems are very difficult. There are still many important theoretical issues under research, although great success has been achieved in data assimilation in meteorology and oceanography. This paper reviews the recent research on parameter retrieval, especially that of the authors. First, some concepts and issues of parameter retrieval are introduced and the state-of-the-art parameter retrieval technology in meteorology and oceanography is reviewed briefly, and then atmospheric and oceanic parameters are retrieved using the variational data assimilation method combined with the regularization techniques in four examples: retrieval of the vertical eddy diffusion coefficient; of the turbulivity of the atmospheric boundary layer; of wind from Doppler radar data, and of the physical process parameters. Model parameter retrieval with global and local observations is also introduced.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Cao Xiaoqun, Huang Sixun, and Du Huadong, 2005: Theoretical analysis and numerical experiments of single-Doppler wind retrieval. J. Hydrodynamics, 20B, 277–285.
Courtier, P., J. Derber, R. Errico, J.-F. Louis, and T. Vukicevic, 1993: Important literature on the use of adjoint, variational methods and the Kalman filter in meteorology. Tellus, 45A, 342–357.
Du Huadong, Huang Sixun, and Shi Hanqing, 2004: Theoretical analyses and numerical tests for one-dimensional semigeostrophic shallow water model. Journal of Hydrodynamics, 19A, 38-45.
Du Huadong, 2004: Studies on application of the adjoint method to some problems in the atmospheric sciences. M. S. thesis, PLA University of Science and Technology, 66pp. (in Chinese)
Evensen, G., 2003: The ensemble Kalman filter: Theoretical formulation and practical implementation. Ocean Dynamics, 53, 343–367.
Fang Hanxian, and Huang Sixun, 2004: Theoretical analysis and numerical experiments of retrieval of 2-D dropsonde’s motion. Progress in Natural Sciences, 14, 1257–1264.
Fang Hanxian, Huang Sixun, and Wang Tingfang, 2004: Retrieval study of 1-D dropsonde’s motion. Journal of Hydrodynamics, 19A, 53–60. (in Chinese)
Gal-Chen, T., and J. Zhang, 1993: On the optimal use of reflectivities and single Doppler radar velocities to deduce 3D motions. 26th International Conf. on Radar Meteorology, Norman, Amer. Meteor. Soc., 414-416.
Gao Jidong, and Chou Jifan, 1995: The impact of sensitivity of initial values of numerical models on 4-D assimilation. A case study of the Lorenz system. Acta Meteorologica Sinica, 53, 471–479.
Gelfand, I. M., and B. M. Levitan, 1951: On the determination of a differential equation from its spectral function. Amer. Math. Soci. Trans., 1, 253–304.
Groetsch, C. W., 1984: The Theory of Tikhonov Regularization for Fredholm Equation of the First Kind. Pitman Advanced Publishing Program, 104pp.
Groetsch, C. W., 1993: Inverse Problems in the Mathematical Sciences. Vieweg-Verlag, Wiesbaden, 152pp.
Guo Baoqi, 1988: Inverse Problem of Parabolic Partial Differential Equation. Heilongjiang Science and Technology Press, Harbin, 286pp. (in Chinese)
Huang Sixun, and Wu Rongsheng, 2001: Methods of Mathematical Physics in Atmospheric Science. China Meteorological Press, 540pp. (in Chinese)
Huang Sixun, and Han Wei, 2003: Application of techniques in inverse problems to variational data assimilation in meteorology and oceanography. Recent Development in Theories and Nunmerics, Int. Conf. on Inverse Problems, World Scientific, 349-355.
Huang Sixun, Han Wei, and Wu Rongsheng, 2004a: Theoretical analyses and numerical experiments of variational assimilation for one-dimensional ocean temperature model with techniques in inverse problems. Science in China (D), 47(7), 630–638.
Huang Sixun, Du Huadong, and Han Wei, 2004b: Generalized variational assimilation method and numerical experiment for non-differential system. Applied Mathematics and Mechanics, 25, 1061–1066.
Huang Sixun, Teng Jiajun, Lan Weiren, and Xiang Jie, 2005a: Variational adjustment of 3-D wind field combining with the regularization method and filtering. Chinese Journal of Theoretical and Applied Mechanics, 37(4), 399–407. (in Chinese)
Huang Sixun, Xiang Jie, Du Huadong, and Cao Xiaoqun, 2005b: Inverse problems in atmospheric science and their application. Journal of Physics: Conference Series, 12, 45–57.
Kirsch, A., 1996: An Introduction to the Mathematical Theory of Inverse Problems, Springer-Verlag, New York, 282pp.
Kress, R., 1989: Linear Integral Equations. Springer-Verlag, 250pp.
Lan Weiren, Huang Sixun, and Xiang Jie, 2004: Generalized method of variational analysis for 3-D flow. Adv. Atmos. Sci., 21, 730–740.
Le Dimet, F. X., and I. M. Navon, 1988: Variational and optimization methods in meteorology: A review. Tech. Rep. SCRI 144, Supercomputer Computations Research Institute, Florida State University, Tallahassee, FL, 83pp.
Le Dimet, F., and O. Talagrand, 1986: Variational algorithms for analysis and assimilation of meteorological observations: Theoretical aspects. Tellus, 38A, 97–110.
Le Dimet, F. X., and Yang Junqing, 2002: Models and data for the water cycle. Mathematical Problems in Environmental Science and Engineering, P. G. Ciarlet and Li Ta-tsien, Eds., Higher Education Press, 391pp. (in China).
Li Jun, and Huang Sixun, 2001: Application of improved discrepancy principle in retrieval of atmosphere infrared remote sensing. Science in China, 44D, 847–857.
Lorenc, A. C., 1988: A practical approximation to optimal 4-D objective analysis. Mon. Wea. Rev. 116, 730–745.
Louis, J.-F., and M. Zivkovi, 1994: Optimizing a local weather forecast system. AER Inc., Final Report, Cambridge, MA, 55pp.
Mu, Mu, and J. Wang, 2003: A method for adjoint variational data assimilation with physical “on-off” processes. J. Atmos. Sci., 60, 2010–2018.
Navon, I. M., 1997: Pratical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography. Dyn. Atmos. Oceans, 27, 55–79.
Pan Xiaoqiang, and Huang Sixun, 2004: Variational adjoint method for one-dimensional shallow water model: Theoretical analysis and numerical experiments. Chinese J. Atmos. Sci, 28, 175–186.
Panchang, V. G., J. J. O’Brien, 1989: On the determination of hydraulic model parameters using the strong constraint formulation. Modeling Marine Systems, A. M. Davies, Ed., CRC Press Inc., 5-18.
Qiu, C. J., and Q. Xu, 1992: A simple adjoint method of wind analysis for single-Doppler data. J. Atmos. Oceanic Technol., 9, 588–598.
Qiu Chongjian, Yu Jinxiang, and Q. Xu, 2000. Use of Doppler-radar data in improving short-term prediction of mesoscale weather. Acta Meteorologica Sinica, 58, 244–249.
Richardson, J. E., and V. G. Panchang, 1992: A modified adjoint method for inverse eddy viscosity estimation in coastal circulation models. Estuarine and Coastal Modeling, Proc. 2nd Internal. Conf. Amer. Soc. Civil Eng., Spaulding et al., Eds., New York, 733-745.
Romanov, V. G., 1987: Inverse Problem of Mathematical Physics. VNU Science Press BV Utrecht, 239pp.
Shapiro, A., S. Ellis, and J. Shaw, 1996: Single-Doppler velocity retrievals with Phoenix II data: Clear air and microburst wind retrievals in the planetary boundary layer. J. Atmos. Sci., 52, 1265–1287.
Smedstad, O. M., and J. J. O’Brien, 1991: Variational data assimilation and parameter estimation in an equatorial Pacific Ocean model. Progr. Oceanogr., 26, 179–241.
Stauffer, D. R., and J. Bao, 1993: Optimal determination of nudging coefficients using the adjoint equations. Tellus, 45A, 358–369.
Talagrand, O., and P. Courtier, 1987: Variational assimilation of meteorological observations with the adjoint vorticity equation. Part I: Theory. Quart. J. Roy. Meteor. Soc., 113, 1311–1328.
Tan Zhemin, 2000: Structure and Dynamics of Fronts in the Planetary Boundary Layer. Nanjing University, Ph. D. dissertation, 196pp. (in Chinese)
Tosaka, N., K. Onoshi, and M. Yamamoto, 1999: Mathematical Approach and Solution Methods for Inverse Problems: Inverse Analysis of Partial Differential Equation, University of Tokyo Press, 294pp. (in Japanese)
Wang, B., X. Zou, and J. Zhu, 2000: Data assimilation and its applications. Proc. Natl. Acad. Sci. U. S. A., 97, 11143–11144.
Wang Tingfang, Huang Sixun, and Xiang Jie, 2006: Studies on retrieval of the turbulivity of the atmospheric boundary layer. J. Hydrodynamics (B). (in Press)
Wang Jiafeng, Mu Mu, and Zheng Qin, 2002: Adjoint approach to VDA of “on-off” processes based on the nonlinear perturbation equation. Progress in Natural Sciences, 12, 869–873.
Wang, J. F., M. Mu, and Q. Zheng, 2005: Initial condition and parameter estimation in physical “on-off” processes by variational data assimilation. Tellus, 57A, 736–741.
Wang, Z., 1993: Variational data assimilation with 2-D shallow water equations and 3-D FSU global spectral models. Ph.D. Dissentation, Florida State University, Tallahassee, FL, 235pp.
Wang, Z., I. M. Navon, X. Zou, and F. X. Le Dimet, 1995: A truncated Newton optimization algorithm in meteorology applications with analytic Hessian/vector products. Comput. Optim. Appl. 4, 241–262.
Wei Ming, Dang Renqing, Ge Wenzhong, and Takao Takeda, 1998: Retrieval single-Doppler radar wind with variational assimilation method. Part I: Objective selection of functional weighting factors. Adv. Atmos. Sci., 15, 553–568.
Wu Shaorong, Xu Baoxiang, and Zhou Xiuji, 1997: Assimilation method of retieving horizontal wind from single-Doppler radar. Acta Meteorologica Sinica, 11, 469–477.
Xiang Jie, Wu Rongsheng, and Huang Sixun, 2004: Studies on application of the adjoint method to statistic-dynamical prediction model (SD-90) for Tropical cyclones. Progress in Natural Sciences, 14, 677–682. (in Chinese)
Xu, Q., 1996a: Generalized adjoint for physical processes with parameterized discontinuities. Part I: Basic issues and heuristic examples. J. Atmos. Sci., 53, 1123–1142.
Xu, Q., 1996b: Generalized adjoint for physical processes with parameterized discontinuities. Part II: Vector formulations and matching conditions. J. Atmos. Sci., 53, 1143–1155.
Xu, Q., 1997: Generalized adjoint forphysical processes with parameterized discontinuities. Part IV: Problems in time discretization. J. Atmos. Sci., 54, 2722–2728.
Xu, Q., 1998: Comments on “Tangent linear and adjoint of ‘on-off’ processes and their feasibility for use in 4-dimensional variational data assimilation”. Tellus, 50A, 653–656.
Xu, Q., and C. J. Qiu, 1994: Simple adjoint methods for single-Doppler wind analysis with a strong constraint of mass conservation. J. Atmos. Oceanic Technol., 11, 289–298.
Xu, Q., and Gao, J. D., 1999: Generalized adjoint for physical processes with parametrized discontinuities. Part VI: Minimization problems in multidimensional space. J. Atmos. Sci., 56, 994–1002.
Xu, Q., C. J. Qiu, and J. X. Yu, 1994: Adjoint-method retrievals of low-altitude wind fields from single-Doppler reflectivity measured during Phoenix II. J. Atmos. Oceanic Technol., 11, 275–288.
Yeh, W. W.-G., 1986: Review of parameter estimation procedures in groundwater hydrology. Water Res. Rev., 22, 95–108.
Zhu Jiang, Zeng Qingcun, Guo Dongjian, and Liu Zhuo, 1998: Estimating open boundary conditions from coastal tidal observations by adjoint approach. Science in China, 41D, 330–336.
Zou, X., I. M. Navon, F. X. Le Dimet, 1992: An optimal nudging data assimilation scheme using parameter estimation. Quart. J. Roy. Meteor. Soc., 118, 1163–1186.
Zou, X., 1997: Tangent linear and adjoint of “on-off” processes and their feasibility for use in four-dimensional variational data assimilation. Tellus, 49A, 3–31.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Huang, S., Cao, X., Du, H. et al. Retrieval of atmospheric and oceanic parameters and the relevant numerical calculation. Adv. Atmos. Sci. 23, 106–117 (2006). https://doi.org/10.1007/s00376-006-0011-8
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s00376-006-0011-8