Hostname: page-component-7b7567c8c-2n9c9 Total loading time: 0 Render date: 2026-11-15T21:50:55.362Z Has data issue: false hasContentIssue false
  • English
  • Français

The problem of data assimilationfor soil water movement

Published online by Cambridge University Press:  15 June 2004

François-Xavier Le Dimet,
Victor Petrovich Shutyaev,
Jiafeng Wang and
Mu Mu
François-Xavier Le Dimet
Affiliation:
LMC-IMAG, 38041 Grenoble Cedex 9, France.
Victor Petrovich Shutyaev
Affiliation:
Institute of Numerical Mathematics, Russian Academy of Sciences, Russia.
Jiafeng Wang
Affiliation:
LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, 100029, China.
Mu Mu
Affiliation:
LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, 100029, China.
Get access

Abstract

The soil water movement modelgoverned by the initial-boundary value problem for a quasilinear1-D parabolic equation with nonlinear coefficients is considered.The generalized statement of the problem is formulated. Thesolvability of the problem is proved in a certain class offunctional spaces. The data assimilation problem for this model isanalysed. The numerical results are presented.

Keywords

Variational data assimilationsoil water movementquasilinear parabolic problemsolvabilitynumerical analysis.

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 10 , Issue 3 , July 2004, pp. 331 - 345
Copyright
© EDP Sciences, SMAI, 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

V.I. Agoshkov and A.P. Mishneva, Calculation of the diffusion coefficient in a nonlinear parabolic equation. Preprint of the Department of Numerical Mathematics, USSR Acad. Sci., Moscow (1988), No. 200.
Agoshkov, V.I. and Marchuk, G.I., On the solvability and numerical solution of data assimilation problems. Russ. J. Numer. Anal. Math. Modelling 8 (1986) 1-16. CrossRef
Alt, H.W. and Luckhaus, S., Quasilinear elliptic-parabolic differential equations. Math. Zeitschrift 183 (1983) 311-341.
E. Blayo, J. Blum and J. Verron, Assimilation variationnelle de données en océanographie et réduction de la dimension de l'espace de contrôle. Équations aux Dérivées Partielles et Applications (Articles dédiées à Jacques-Louis Lions) (1998) 205-219.
Chao, W.C. and Chang, L.P., Development of a four-dimensional variational analysis system using the adjoint method at GLA. Part I: Dynamics. Mon. Wea. Rev. 120 (1992) 1661-1673. 2.0.CO;2>CrossRef
Derber, J.C., Variational four-dimensional analysis using quasigeostrophic constraints. Mon. Wea. Rev. 115 (1987) 998-1008. 2.0.CO;2>CrossRef
Gilbert, J.-C. and Lemarechal, C., Some numerical experiments with variable storage quasi-Newton algorithms. Math. Program. B25 (1989) 408-435.
P.E. Gill, W. Murray and M.H. Wright, Practical Optimization. Academic Press (1981).
D. Henry, Geometric Theory of Semilinear Parabolic Equations. New York, Springer (1981).
Ladyzhenskaya, O.A. and Uraltseva, N.N., A survey on solvability of boundary value problems for uniformly elliptic and parabolic equations of the second order. Uspekhi Math. Nauk 41 (1986) 59-83.
O.A. Ladyzhenskaya, V.A. Solonnikov and N.N. Uraltseva, Linear and Quasilinear Parabolic Equations. Moscow, Nauka (1967).
M.M. Lavrentiev, A priori Estimates and Existence Theorems for Nonlinear Parabolic Equations. Novosibirsk, Nauka (1982).
F.-X. Le Dimet and I. Charpentier, Méthodes de second ordre en assimilation de données. Équations aux Dérivées Partielles et Applications (Articles dédiées à Jacques-Louis Lions) (1998) 623-639.
Le Dimet, F.-X., Ngodock, H.E. and Luong, B., Sensitivity analysis in variational data assimilation. J. Met. Soc. Japan 75 (1997) 245-255. CrossRef
Le Dimet, F.-X. and Talagrand, O., Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus A 38 (1986) 97-110. CrossRef
Zh. Lei and Sh. Yang, The Dynamics of Soil Water. Tsinghua University Press (1986).
Li, Y., Navon, I.M., Yang, W., Zou, X., Bates, J.R., Moorthi, S. and Higgins, R.W., Four-dimensional variational data assimilation experiments with a multilevel semi-Lagrangian semi-implicit general circulation model. Mon. Wea. Rev. 122 (1994) 966-983. 2.0.CO;2>CrossRef
J.-L. Lions, Optimal Control of Systems Governed by Partial Differential Equations. New York, Springer (1970).
J.-L. Lions, Some Methods for Solving Nonlinear Problems. Moscow, Mir (1972).
J.-L. Lions and E. Magenes, Problémes aux limites non homogènes et applications. Paris, Dunod (1968).
G.I. Marchuk, V.I. Agoshkov and V.P. Shutyaev, Adjoint Equations and Perturbation Algorithms in Nonlinear Problems. CRC Press Inc. New York (1996).
Global, M. Mu smooth solutions of two-dimensional Euler equations. Chin. Sci. Bull. 35 (1990) 1895-1900.
Navon, I.M., Zou, X., Derber, J. and Variational da, J. Selata assimilation with an adiabatic version of the NMC spectral model. Mon. Wea. Rev. 120 (1992) 1433-1446. 2.0.CO;2>CrossRef
Oleinik, O.A. and Radkevich, E.V., Method of introducing a parameter for study of evolution equations. Uspehi Math. Nauk 33 (1978) 7-76.
Penenko, V. and Obraztsov, N.N., A variational initialization method for the fields of meteorological elements. Meteorol. Gidrol. 11 (1976) 1-11.
Shutyaev, V.P., Some properties of the control operator in the problem of data assimilation and iterative algorithms. Russ. J. Numer. Anal. Math. Modelling 10 (1995) 357-371. CrossRef
T.I. Zelenyak, M.M. Lavrentiev and M.P. Vishnevski, Qualitative Theory of Parabolic Equations. Utrecht, VSP Publishers (1997).
T.I. Zelenyak and V.P. Michailov, Asymptotical behaviour of solutions of mathematical physics. Partial Diff. Eqs. (1970) 96-110.
Zou, X., Navon, I. and Le Dimet, F.-X., Incomplete observations and control of gravity waves in variational data assimilation. Tellus A 44 (1992) 273-296. CrossRef