  State-of-the-art stellar structure and evolution codes fail to adequately
describe turbulent convection. For stars with convective envelopes, such as red
giants, this leads to an incomplete depiction of the surface layers. As a
result, the predicted stellar oscillation frequencies are haunted by systematic
errors, the so-called surface effect. Different empirically and theoretically
motivated correction relations have been proposed to deal with this issue. In
this paper, we compare the performance of these surface correction relations
for red giant branch stars. For this purpose, we apply the different surface
correction relations in asteroseismic analyses of eclipsing binaries and open
clusters. In accordance with previous studies of main-sequence stars, we find
that the use of different surface correction relations biases the derived
global stellar properties, including stellar age, mass, and distance estimates.
We furthermore demonstrate that the different relations lead to the same
systematic errors for two different open clusters. Our results overall
discourage from the use of surface correction relations that rely on reference
stars to calibrate free parameters. Due to the demonstrated systematic biasing
of the results, the use of appropriate surface correction relations is
imperative to any asteroseismic analysis of red giants. Accurate mass, age, and
distance estimates for red giants are fundamental when addressing questions
that deal with the chemo-dynamical evolution of the Milky Way galaxy. In this
way, our results also have implications for fields, such as galactic
archaeology, that draw on findings from stellar physics.
