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Four-dimensional Variational Data Assimilation For Limited-area Models: Lateral Boundary Conditions, Solution Uniqueness, and Numerical Convergence


Mathematical issues arising when applying four-dimensional variational (4DVAR) data assimilation to limited-area problems are studied. The derivation of the adjoint system for the initial-boundary value problem for a general hyperbolic system using the standard variational approach requires that the inflow adjoint variables at an open boundary be zero. However, in general, these ``natural'' boundary conditions will lead to a different solution than that provided by the global assimilation problem. The impact of using natural boundary conditions when there are errors (on the boundary) in the initial guess on the assimilated initial conditions is discussed. A proof of the uniqueness of the solution for both forward and adjoint equations in the presence of open boundaries at each iteration of the minimization procedure is provided, along with an assessment of the convergence of numerical solutions. Numerical experiments with a simple advection equation support the theoretical analyses. Numerical results show that if observational data are perfect, 4DVAR data assimilation using a limited-area model can produce a reasonable initial condition. However, if there are errors in the observational data at the open boundaries and if natural boundary conditions are assumed, boundary errors can contaminate the assimilated solutions.}

Article / Publication Data
Available Metadata
Accepted On
April 29, 1999
Fiscal Year
Publication Name
Journal of The Atmospheric Sciences
Published On
April 29, 1999
Publisher Name
Amer Meteorological Soc
Print Volume
Print Number
Submitted On
September 24, 1998


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Authors who have authored or contributed to this publication.

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