Variational data assimilation with the Lorenz model.
Xiang-Yu Huang and Xiaohua Yang
Danish Meteorological Institute, Denmark
This note is intended as an introduction to various aspects of
variational data assimilation using the adjoint model technique, in particular
the principles and formulation of an adjoint model. A complete assimilation
system for the Lorenz equations is formulated. The Lorenz model
is chosen for its simplicity in structure and the dynamic similarities with
the nonlinear atmospheric system. Detailed derivations are performed to
introduce basic concepts of the adjoint model method, and the general
procedure to construct an adjoint variational assimilation is discussed.
The coding process to construct the Lorenz assimilation is demonstrated
in detail, in which the line-by-line approach for adjoint model coding is
introduced. With the Lorenz assimilation model, various numerical
experiments including coding checks are performed and results discussed.
The FORTRAN source code for the constructed assimilation is given
in an appendix. It is believed that by designing, coding and running the
variational data assimilation for the Lorenz model, newcomers may gain
useful insights and experiences which will be beneficial for the research
and development work of a more complicated variational assimilation
system, such as the four dimensional data assimilation of an operational
weather prediction model.