  The solar granulation is known for a long time to be a surface manifestation
of convection. Thanks to the current space-borne missions CoRoT and Kepler, it
is now possible to observe in disk-integrated intensity the signature of this
phenomena in a growing number of stars. The space-based photometric
measurements show that the global brightness fluctuations and the lifetime
associated with granulation obeys characteristic scaling relations. We thus aim
at providing a simple theoretical modeling to reproduce these scaling relations
and subsequently at inferring the physical properties of granulation properties
across the HR diagram.
  We develop a simple 1D theoretical model that enable us to test any
prescription concerning the time-correlation between granules. The input
parameters of the model are extracted from 3D hydrodynamical models of the
surface layers of stars, and the free parameters involved in the model are
calibrated with solar observations. Two different prescriptions for
representing the eddy time-correlation in the Fourier space are compared: a
Lorentzian and an exponential form. Finally, we compare our theoretical
prediction with a 3D radiative hydrodynamical (RHD) numerical modeling of
stellar granulation (ab-initio approach). Provided that the free parameters are
appropriately adjusted, our theoretical model satisfactorily reproduces the
shape and the amplitude of the observed solar granulation spectrum. The best
agreement is obtained with an exponential form. Furthermore, our theoretical
model results in granulation spectra that consistently agree with the these
calculated on the basis of the ab-initio approach with two 3D RHD models.
Comparison between theoretical granulation spectra calculated with the present
model and high precision photometry measurements of stellar granulation is
undertaken in a companion paper.
