  The effect of metallicity on the granulation activity in stars is still
poorly understood. Available spectroscopic parameters from the updated
APOGEE-\textit{Kepler} catalog, coupled with high-precision photometric
observations from NASA's \textit{Kepler} mission spanning more than four years
of observation, make oscillating red giant stars in open clusters crucial
testbeds. We determine the role of metallicity on the stellar granulation
activity by discriminating its effect from that of different stellar properties
such as surface gravity, mass, and temperature. We analyze 60 known red giant
stars belonging to the open clusters NGC 6791, NGC 6819, and NGC 6811, spanning
a metallicity range from [Fe/H] $\simeq -0.09$ to $0.32$. The parameters
describing the granulation activity of these stars and their
$\nu_\mathrm{max}$, are studied by considering the different masses,
metallicities, and stellar evolutionary stages. We derive new scaling relations
for the granulation activity, re-calibrate existing ones, and identify the best
scaling relations from the available set of observations. We adopted the
Bayesian code DIAMONDS for the analysis of the background signal in the Fourier
spectra of the stars. We performed a Bayesian parameter estimation and model
comparison to test the different model hypotheses proposed in this work and in
the literature. Metallicity causes a statistically significant change in the
amplitude of the granulation activity, with a dependency stronger than that
induced by both stellar mass and surface gravity. We also find that the
metallicity has a significant impact on the corresponding time scales of the
phenomenon. The effect of metallicity on the time scale is stronger than that
of mass. A higher metallicity increases the amplitude of granulation and
meso-granulation signals and slows down their characteristic time scales toward
longer periods.
