  We aim to describe the oscillation power excess observed in Kepler red
giants, and to investigate empirical scaling relations governing these
parameters. From these scalings relations, we derive new physical properties of
red giant oscillations. Various different methods were compared in order to
validate the processes and to derive reliable output values. For consistency, a
single method was then used to determine scaling relations for the relevant
global asteroseismic parameters: mean mode height, mean height of the
background signal superimposed on the oscillation power excess, width of the
power excess, bolometric amplitude of the radial modes and visibility of
non-radial modes. A method for deriving oscillation amplitudes is proposed,
which relies on the complete identification of the red giant oscillation
spectrum. The comparison of the different methods has shown the important role
of the way the background is modelled. The convergence reached by the
collaborative work enables us to derive significant results concerning the
oscillation power excess. We obtain several scaling relations, and identify the
influence of the stellar mass and the evolutionary status. The effect of helium
burning on the red giant interior structure is confirmed: it yields a strong
mass-radius relation for clump stars. We find that none of the amplitude
scaling relations motivated by physical considerations predict the observed
mode amplitudes of red giant stars. In parallel, the degree-dependent mode
visibility exhibits important variations. Both effects seem related to the
significant influence of the high mode mass of non-radial mixed modes. A family
of red giants with very weak dipole modes is identified, and its properties are
analyzed.
