We check how the change in surface conditions between the Sun and red giant
branch stars changes the characteristic surface convection length scale to be
used in models. We investigate the question in the case of the mixing length
theory and of the phenomenology of full spectrum of turbulence. For the
observational part, we rely on independent measurements of effective
temperatures and interferometric radii of nearby red giants. We find that the
local red giant branch cannot be explained taking into account the solar
calibrated convective length scale.Comment: In the proceedings of the French Astronomical Society meeting SF2A
201