  In this manuscript we present a method for the quantitative comparison of two
surfaces, applicable to temporal and/or spatial extent in one or two
dimensions. Often surface comparisons are simply overlaid graphs of results
from different methodologies that are qualitative at best; it is the purpose of
this work to facilitate quantitative evaluation. The surfaces can be
analytical, numerical, and/or experimental, and the result returned by the
method, termed surface similarity parameter or normalized error, has been
normalized so that its value lies between zero and one. When the parameter has
a value of zero, the surfaces are in perfect agreement, whereas a value of one
is indicative of perfect disagreement. To provide insight regarding the
magnitude of the parameter, several canonical cases are presented, followed by
results from breaking water wave experimental measurements with numerical
simulations, and by a comparison of a prescribed, periodic, square-wave surface
profile and the subsequent manufactured surface.
