The possibility to detect solar oscillations in the low frequency doma
in depends crucially on the power contrast among the oscillation signa
l and other time dependent signals in the same frequency range. The si
gnal to noise ratio is increased by our ability to understand and remo
ve solar sources of noise. In measurements of the mean Doppler velocit
y shift of the integrated solar disk, the solar noise has a line compo
nent spectrum with a major peak at 13.1 days, and a second less promin
ent peak at 27.2 days. Active region modulation is believed almost com
pletely responsible for this signal. We develop simulations of the flu
x and velocity fluctuations produced by different solar active region
distributions, based on an analytical description of their action. Fro
m a grid of models of active regions and from their spatial distributi
on over the disk, we calculate the synthetic flux profile in the Na I
D-1 line and determine the velocity measure of a resonance spectromete
r. Our velocity results are compared with the offset velocities from t
he IRIS network. There is a rather good agreement between the observed
and computed velocities, and the plage contribution to the noise appe
ars to be dominant. The simulation allows to test calibration procedur
es and to study the effect on the spurious velocities of different par
ameters, such as the intensity thresholds used to determine the areas
of spots and plages, and the contrast of the active regions. In partic
ular, we find that the inclusion of intrinsic line shifts in plages ca
n change strongly both the amplitude and the shape of the simulated si
gnal, and then may be an important source of uncertainty for the simul
ation.