海浪谱能量方程稳定性、敏感性分析与海浪变分同化研究
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摘要
本论文主要完成了以下几个方面的研究：
1）建立了推广形式的共轭变分同化方法，使之能够应用于LAGFD-WAM海浪数值
模式；
2）导出了扰动谱线性演化方程，分析了扰动谱增长、衰减机制，考察了涌浪情况下
扰动谱的持续时效问题及风浪情况下扰动的演变过程；
3）利用波谱共轭方程初步分析了同化模型中距离泛函的敏感性及敏感区域空间分
布；
4）将推广的共轭变分方法应用于海浪谱能量平衡方程，建立了连续形式的海浪同化
模型，特别是严格导出了风输入、破碎、底摩擦、波波非线性相互作用和波流相
互作用各源函数的共轭源函数表示式；
5）分别进行了波谱层次上和有效波高层次上的同化试验，并对数值结果进行了分
析。
创新之处主要有以下几个方面：
●利用算子半群理论对共轭变分方法进行了推广；
●首次导出扰动谱线性演化方程，并利用其考察波谱能量平衡方程的不稳定性问
题；
●在处理波波非线性相互作用时，将Hasselmann et al.[1985]离散参数化的6对相互
作用架组源函数表示用复数解析表示，并在此基础上导出其共轭源函数；
●建立了连续形式的基于初始波谱优化的海浪同化模型；
．针对观测资料类型的不同，给出了波谱层次上和有效波高层次上的同化处理方
法。
The following are the major work in this thesis which has been studied and still needs
to be studied further in the future:
1) An improved adjoint variational method is developed, thus it can be applied to the
LAGFD-WAM Wave Numerical Model for data assimilation;
2) A linear evolution equation of spectral perturbation is derived in order to analyze its
increasing or decreasing mechanism. The duration of spectral perturbation is
calculated under the swell situation after the linear evolution equation of spectral
perturbation is simplified. The evolution of perturbation under the wind sea situation is
also analyzed primarily;
3) The sensitivity of distance function in the wave assimilation model is studied with the
use of adjoint spectrum balance equation. Disregard its primary, the spacial value
distribution of sensitivity is important for oceanic convention observation, etc.
4) The improved adjoint variational method is applied to the wave energy spectrum
balance equation, and then the continuous wave data assimilation model is developed.
Especially the adjoint source functions of wind input function, wave breaking
dissipation function, bottom friction function, wave-wave nonlinear interaction and
wave-current interaction are derived rigorously;
5) The assimilation experiments based on the level of spectrum and significant wave
height are implemented and analyzed respectively.
The new ideas in this thesis are stated below:
The adjoint variational method is improved with the use of semigroups of linear
operators for wide application;
The linear evolution equation of spectral perturbation is derived, which is then used to
analyze the instability of wave energy spectrum balance equation;
The nonlinear interaction operator constructed by the superposition of a small number
of discrete-interaction configurations is formularized in order to derive its adjoint
operator. The adjoint operator is then derived and formularized as well;
The continuous wave data assimilation model is developed to optimize the initial
spectrum;
Two different assimilation processes are developed under the level that the observation
is spectrum by SAR or significant wave height by ALT.
1）建立了推广形式的共轭变分同化方法，使之能够应用于LAGFD-WAM海浪数值
模式；
2）导出了扰动谱线性演化方程，分析了扰动谱增长、衰减机制，考察了涌浪情况下
扰动谱的持续时效问题及风浪情况下扰动的演变过程；
3）利用波谱共轭方程初步分析了同化模型中距离泛函的敏感性及敏感区域空间分
布；
4）将推广的共轭变分方法应用于海浪谱能量平衡方程，建立了连续形式的海浪同化
模型，特别是严格导出了风输入、破碎、底摩擦、波波非线性相互作用和波流相
互作用各源函数的共轭源函数表示式；
5）分别进行了波谱层次上和有效波高层次上的同化试验，并对数值结果进行了分
析。
创新之处主要有以下几个方面：
●利用算子半群理论对共轭变分方法进行了推广；
●首次导出扰动谱线性演化方程，并利用其考察波谱能量平衡方程的不稳定性问
题；
●在处理波波非线性相互作用时，将Hasselmann et al.[1985]离散参数化的6对相互
作用架组源函数表示用复数解析表示，并在此基础上导出其共轭源函数；
●建立了连续形式的基于初始波谱优化的海浪同化模型；
．针对观测资料类型的不同，给出了波谱层次上和有效波高层次上的同化处理方
法。
The following are the major work in this thesis which has been studied and still needs
to be studied further in the future:
1) An improved adjoint variational method is developed, thus it can be applied to the
LAGFD-WAM Wave Numerical Model for data assimilation;
2) A linear evolution equation of spectral perturbation is derived in order to analyze its
increasing or decreasing mechanism. The duration of spectral perturbation is
calculated under the swell situation after the linear evolution equation of spectral
perturbation is simplified. The evolution of perturbation under the wind sea situation is
also analyzed primarily;
3) The sensitivity of distance function in the wave assimilation model is studied with the
use of adjoint spectrum balance equation. Disregard its primary, the spacial value
distribution of sensitivity is important for oceanic convention observation, etc.
4) The improved adjoint variational method is applied to the wave energy spectrum
balance equation, and then the continuous wave data assimilation model is developed.
Especially the adjoint source functions of wind input function, wave breaking
dissipation function, bottom friction function, wave-wave nonlinear interaction and
wave-current interaction are derived rigorously;
5) The assimilation experiments based on the level of spectrum and significant wave
height are implemented and analyzed respectively.
The new ideas in this thesis are stated below:
The adjoint variational method is improved with the use of semigroups of linear
operators for wide application;
The linear evolution equation of spectral perturbation is derived, which is then used to
analyze the instability of wave energy spectrum balance equation;
The nonlinear interaction operator constructed by the superposition of a small number
of discrete-interaction configurations is formularized in order to derive its adjoint
operator. The adjoint operator is then derived and formularized as well;
The continuous wave data assimilation model is developed to optimize the initial
spectrum;
Two different assimilation processes are developed under the level that the observation
is spectrum by SAR or significant wave height by ALT.
引文
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4． Bauer, E., Hasselmann, S., Hasselmann, K. and Graber, H. C. Validation and assimilation of Seasat altimeter wave heights using the WAM Wave Model, J. Geophys. Res., 1992,97: 12671-12682．
5． Courtier, P. and Talagrand, O. Variational assimilation of meteorological observations with the adjoint vorticity equation. Ⅱ : Numerical results, Q. J. R. Meteorol.Soc.1987,113: 1329-1347．
6． Courtier, P. and Talagrand, O. Variational assimilation of meteorological observations with the direct and adjoint shallow-water equations, Tellus, 1990, 42A: 531-549．
7． de las Heras, M. and P.A.E.M Janssen. Data assimilation with a coupled wind-wave model, J. Geophys. Res., 1992, 97: 20261-20270．
8． Derber, J. C. A variational continuous assimilation technique, Mon. Wea. Rev., 1989, 117:2437-2446．
9． Epstein, E. S. Stochastic dynamic prediction, Tellus, 1969, 21:739-759．
10． Esteva, D C. Evaluation of preliminary experiments assimilating Seasat significant wave height into a spectral wave model, J. Geophys. Res., 1988, 93: 14099-14105．
11． Gustafsson, N. and Huang Xiangyu. Sensitivity experiments with the spectral HIRLAM and its adjoint, Tellus, 1996,48A: 501-517．
12． Hall, M. C. G., Cacuci, D. G. and Schlesinger, M. E. Sensitivity analysis of a
radiative-convective model by the adjoint method, J. Atmos. Sci., 1982, 39: 2038-2050．
13． Hasselmann, K. and Hasselmann, S. On the nonlinear mapping of an ocean wave spectrum into a synthetic aperture radar image spectrum and its inversion, J. Geophys. Res., 1991,96:10713-10729．
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2． AVISO, AVISO user handbook: TOPEX/POSEIDON update product, AVI-NT-103-CN, 1996, Edition 1． 0．
3． Bauer, E., Hasselmann, K., Young, I. R. and Hasselmann, S. Assimilation of wave data into the wave model WAM using an impulse response function method, J. Geophys. Res., 1996,101: 3801-3816．
4． Bauer, E., Hasselmann, S., Hasselmann, K. and Graber, H. C. Validation and assimilation of Seasat altimeter wave heights using the WAM Wave Model, J. Geophys. Res., 1992,97: 12671-12682．
5． Courtier, P. and Talagrand, O. Variational assimilation of meteorological observations with the adjoint vorticity equation. Ⅱ : Numerical results, Q. J. R. Meteorol.Soc.1987,113: 1329-1347．
6． Courtier, P. and Talagrand, O. Variational assimilation of meteorological observations with the direct and adjoint shallow-water equations, Tellus, 1990, 42A: 531-549．
7． de las Heras, M. and P.A.E.M Janssen. Data assimilation with a coupled wind-wave model, J. Geophys. Res., 1992, 97: 20261-20270．
8． Derber, J. C. A variational continuous assimilation technique, Mon. Wea. Rev., 1989, 117:2437-2446．
9． Epstein, E. S. Stochastic dynamic prediction, Tellus, 1969, 21:739-759．
10． Esteva, D C. Evaluation of preliminary experiments assimilating Seasat significant wave height into a spectral wave model, J. Geophys. Res., 1988, 93: 14099-14105．
11． Gustafsson, N. and Huang Xiangyu. Sensitivity experiments with the spectral HIRLAM and its adjoint, Tellus, 1996,48A: 501-517．
12． Hall, M. C. G., Cacuci, D. G. and Schlesinger, M. E. Sensitivity analysis of a
radiative-convective model by the adjoint method, J. Atmos. Sci., 1982, 39: 2038-2050．
13． Hasselmann, K. and Hasselmann, S. On the nonlinear mapping of an ocean wave spectrum into a synthetic aperture radar image spectrum and its inversion, J. Geophys. Res., 1991,96:10713-10729．
14． Hasselmann, S., Hasselmann, K. et al. Computations and parameterizations of the nonlinear energy transfer in a gravity-wave spectrum, Part II, J. phys. Oceanogr., 1985,15: 1378-1391．
15． Hasselmann, S., Bruning, C., Hasselmann, S. and Heimbach, P. An improved algorithm for the retrieval of ocean wave spectra from synthetic aperture radar image spectra, J. Geophys. Res., 1996, 101: 16615-16629．
16． Hasselmann, S., Lionello, P. and Hasselmann, K. An optimal interpolation scheme for the assimilation of spectral wave data. J. Geophys. Res., 1997,102: 15823-15836．
17． Hersbach, H. Application of the adjoint of the WAM model to inverse wave modeling. J. Geophys. Res., 1998,103: 10469-10487．
18． Hoffman, B. N., Louis, J. N. and Nehrkorn, T. A method for implementing adjoint calculations in the discrete case, ECMWF Research Dept. Tech. Memo. 183, 1992．
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