  We propose a modification of a maximum likelihood procedure for tuning
parameter values in models, based upon the comparison of their output to field
data. Our methodology, which uses polynomial approximations of the sample space
to increase the computational efficiency, differs from similar Bayesian
estimation frameworks in the use of an alternative likelihood distribution, is
shown to better address problems in which covariance information is lacking,
than its more conventional counterpart.
  Lack of covariance information is a frequent challenge in large-scale
geophysical estimation. This is the case in the geophysical problem considered
here. We use a nearshore model for long shore currents and observational data
of the same to show the contrast between both maximum likelihood methodologies.
  Beyond a methodological comparison, this study gives estimates of parameter
values for the bottom drag and surface forcing that make the particular model
most consistent with data; furthermore, we also derive sensitivity estimates
that provide useful insights regarding the estimation procedure as well as of
the model itself.
