  Accurate modelling of solar-like oscillators requires that modelled mode
frequencies are corrected for the systematic shift caused by improper modelling
of the near-surface layers, known as the surface effect. ... We investigate how
much additional uncertainty is introduced to stellar model parameters by our
uncertainty about the functional form of the surface effect. At the same time,
we test whether any of the parametrizations is significantly better or worse at
modelling observed subgiants and low-luminosity red giants. We model six stars
observed by Kepler that show clear mixed modes. We fix the input physics of the
stellar models and vary the choice of surface correction ... Models using a
solar-calibrated power law correction consistently fit the observations more
poorly than the other four corrections. Models with the remaining four
corrections generally fit ... about equally well, with the combined surface
correction by Ball & Gizon perhaps being marginally superior. The fits broadly
agree on the model parameters within about the $2\sigma$ uncertainties, with
discrepancies between the modified Lorentzian and free power law corrections
occasionally exceeding the $3\sigma$ level. Relative to the best-fitting
values, the total uncertainties on the masses, radii and ages of the stars are
all less than 2, 1 and 6 per cent, respectively. A solar-calibrated power law
... appears unsuitable for use with more evolved solar-like oscillators. Among
the remaining surface corrections, the uncertainty in the model parameters
introduced by the surface effects is about twice as large as the uncertainty in
the individual fits for these six stars. Though the fits are thus somewhat less
certain because of our uncertainty of how to manage the surface effect, these
results also demonstrate that it is feasible to model the individual mode
frequencies of subgiants and low-luminosity red giants. ...
