Abstract :
The problem of deriving tidal fields from observations by reason of incompleteness and
imperfectness of every data set practically available has an infinitely large number of allowable
solutions fitting the data within measurement errors and hence can be treated as ill-posed. Therefore,
interpolating the data always relies on some a priori assumptions concerning the tides, which provide
a rule of sampling or, in other words, a regularization of the ill-posed problem. Data assimilation
procedures used in large scale tidemodeling are viewed in a commonmathematical framework as such
regularizations. It is shown that they all (basis functions expansion, parameter estimation, nudging,
objective analysis, general inversion, and extended general inversion), including those (objective
analysis and general inversion) originally formulated in stochastic terms, may be considered as
utilizations of one of the three general methods suggested by the theory of ill-posed problems. The
problem of grid refinement critical for inverse methods and nudging is discussed.
