  We present new synthetic broad-band photometric colors for late-type giants
based on synthetic spectra calculated with the PHOENIX model atmosphere code.
The grid covers effective temperatures T_eff=3000...5000K, gravities log
g=-0.5...+3.5, and metallicities [M/H]=+0.5...-4.0. We show that individual
broad-band photometric colors are strongly affected by model parameters such as
molecular opacities, gravity, microturbulent velocity, and stellar mass. Our
exploratory 3D modeling of a prototypical late-type giant shows that convection
has a noticeable effect on the photometric colors too, as it alters
significantly both the vertical and horizontal thermal structures in the outer
atmosphere. The differences between colors calculated with full 3D
hydrodynamical and 1D model atmospheres are significant (e.g., \Delta(V-K)~0.2
mag), translating into offsets in effective temperature of up to ~70K. For a
sample of 74 late-type giants in the Solar neighborhood, with interferometric
effective temperatures and broad-band photometry available in the literature,
we compare observed colors with a new PHOENIX grid of synthetic photometric
colors, as well as with photometric colors calculated with the MARCS and ATLAS
model atmosphere codes. (abridged)
