Abstract
A generalized method of multivariate optimum interpolation method is shown. Generalization is done in two points. The first is that homogeneous linear constraints are incorporated in formulation explicitly. The second is that the generalized method makes use of both climatological information (climatological mean data and their covariance) and forecast data in an integrated way, while multivariate optimum interpolation makes use of either climatological information (climatological mean data and their covariance) or forecast data as its first guess.
The role of covariance matrix is made clear in a different way from that of Phillips (1982) . It is shown that covariance matrix consistent with linear constrains works as a projection operator or as a filter, just as explicit linear constrains in variational objective analysis do.
The method is considered to be an improved method of variational objective analysis in two points. The first is that the method produces statistically optimum analyzed data while statistical meaning is vague in variational objective analysis. The second is that the method gets analyzed data on grid points directly from randomly distributed observed data, while variational objective analysis needs pre-interpolation of observed data onto grid points.
Some examples of application of the method is shown. The statistical meaning of weak constraint in variational objective analysis is illustrated in an example. A divergent covariance model is also discussed.
The method includes both multivariate optimum interpolation method and variational objective analysis with linear constraints as its special cases. Via the method, the relationship between multivariate optimum interpolation method and variational objective analysis can be understood basically.
