The evolution of surface roughness during growth of Ge(001) by molecular beam epitaxy at 155 degrees C is characterized using in situ scanning tunneling microscopy. The range of film thickness studied spans more than three orders of magnitude, 0.1-200 nm. Beginning at a film thickness near 100 nm, a periodic pattern of growth mounds is observed. The average in-plane separation of growth features d evolves continuously with film thickness t, following a power law d=t(0.42). The vertical roughness of the film does not follow a single power-law behavior over this range of film thickness.