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 $2sigma$ uncertainties, with discrepancies between the modified Lorentzian and free power law corrections occasionally exceeding the $3sigma$ 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. ...
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