  A lubrication model describes the dynamics of a thin layer of fluid spreading
over a solid substrate. But to make forecasts we need to supply correct initial
conditions to the model. Remarkably, the initial fluid thickness is not the
correct initial thickness for the lubrication model. Theory recently developed
in \cite{Roberts89b,Roberts97b} provides the correct projection of initial
conditions onto a model of a dynamical system. The correct projection is
determined by requiring that the model's solution exponentially quickly
approaches that of the actual fluid dynamics. For lubrication we show that
although the initial free surface shape contributes the most to the model's
initial conditions, the initial velocity field is also an influence. The
projection also gives a rationale for incorporating miscellaneous small forcing
effects into the lubrication model; gravitational forcing is given as one
example.
