  The effective temperature (Teff) distribution of stellar evolution models
along the red giant branch (RGB) is sensitive to a number of parameters
including the overall metallicity, elemental abundance patterns, the efficiency
of convection, and the treatment of the surface boundary condition. Recently
there has been interest in using observational estimates of the RGB Teff to
place constraints on the mixing length parameter, a_MLT, and possible variation
with metallicity. Here we use 1D MESA stellar evolution models to explore the
sensitivity of the RGB Teff to the treatment of the surface boundary condition.
We find that different surface boundary conditions can lead to +/- 100 K
metallicity-dependent offsets on the RGB relative to one another in spite of
the fact that all models can reproduce the properties of the Sun. Moreover, for
a given atmosphere T-tau relation, we find that the RGB Teff is also sensitive
to the optical depth at which the surface boundary condition is applied in the
stellar model. Nearly all models adopt the photosphere as the location of the
surface boundary condition but this choice is somewhat arbitrary. We compare
our models to stellar parameters derived from the APOGEE-Kepler sample of first
ascent red giants and find that systematic uncertainties in the models due to
treatment of the surface boundary condition place a limit of ~100 K below which
it is not possible to make firm conclusions regarding the fidelity of the
current generation of stellar models.
