  Space-based observations of solar-like oscillations present an opportunity to
constrain stellar models using individual mode frequencies. However, current
stellar models are inaccurate near the surface, which introduces a systematic
difference that must be corrected. We introduce and evaluate two
parametrizations of the surface corrections based on formulae given by Gough
(1990). The first we call a cubic term proportional to $\nu^3/\mathcal{I}$ and
the second has an additional inverse term proportional to
$\nu^{-1}/\mathcal{I}$, where $\nu$ and $\mathcal{I}$ are the frequency and
inertia of an oscillation mode. We first show that these formulae accurately
correct model frequencies of two different solar models ... We then incorporate
the parametrizations into a modelling pipeline that simultaneously fits the
surface effects and the underlying stellar model parameters. We apply this
pipeline to synthetic observations of a Sun-like stellar model, solar
observations degraded to typical asteroseismic uncertainties, and observations
of the well-studied CoRoT target HD52265. For comparison, we also run the
pipeline with the scaled power-law correction proposed by Kjeldsen et al.
(2008). The fits to synthetic and degraded solar data show that the method is
unbiased and produces best-fit parameters that are consistent with the input
models and known parameters of the Sun. Our results for HD52265 are consistent
with previous modelling efforts and the magnitude of the surface correction is
similar to that of the Sun. The fit using a scaled power-law correction is
significantly worse but yields consistent parameters ... We find that the cubic
term alone is suitable for asteroseismic applications and it is easy to
implement in an existing pipeline. ... This parametrization is thus a useful
new way to correct model frequencies so that observations of individual mode
frequencies can be exploited.
