  We study the local and global roughness scaling in growth models with grains
at the film surfaces. The local roughness, measured as a function of window
size r, shows a crossover at a characteristic length r_c, from a rapid increase
with exponent \alpha_1 to a slower increase with exponent \alpha_2. The result
\alpha_1\approx 1 is explained by the large height differences in the borders
of the grains when compared to intragrain roughness, and must not be
interpreted as a consequence of a diffusion dominated intragrain dynamics. This
exponent shows a weak dependence on the shape and size distribution of the
grains, and typically ranges from 0.85 for rounded grain surfaces to 1 for the
sharpest ones. The scaling corrections of exactly solvable models suggest the
possibility of slightly smaller values due to other smoothing effects of the
surface images. The crossover length r_c provides a reasonable estimate of the
average grain size in all model systems, including the cases of wide grain size
distributions. In Kardar-Parisi-Zhang growth, very different values of \alpha_2
are obtained, ranging from 0.4 for the films with smoothest surfaces to values
in the range 0.1\lesssim \alpha_2 \lesssim 0.2 for systems with large cliffs
separating the grains. Possible applications to real systems which show this
crossover with similar exponents are discussed.
