  We use a new spherical accretion recipe tested on N-body simulations to
measure the observed mass accretion rate (MAR) of 129 clusters in the Cluster
Infall Regions in the Sloan Digital Sky Survey (CIRS) and in the Hectospec
Cluster Survey (HeCS). The observed clusters cover the redshift range of
$0.01<z<0.30$ and the mass range of $\sim 10^{14}-10^{15}
{h^{-1}~\rm{M_\odot}}$. Based on three-dimensional mass profiles of simulated
clusters reaching beyond the virial radius, our recipe returns MARs that agree
with MARs based on merger trees. We adopt this recipe to estimate the MAR of
real clusters based on measurements of the mass profile out to $\sim 3R_{200}$.
We use the caustic method to measure the mass profiles to these large radii. We
demonstrate the validity of our estimates by applying the same approach to a
set of mock redshift surveys of a sample of 2000 simulated clusters with a
median mass of $M_{200}= 10^{14} {h^{-1}~\rm{M_{\odot}}}$ as well as a sample
of 50 simulated clusters with a median mass of $M_{200}= 10^{15}
{h^{-1}~\rm{M_{\odot}}}$: the median MARs based on the caustic mass profiles of
the simulated clusters are unbiased and agree within $19\%$ with the median
MARs based on the real mass profile of the clusters. The MAR of the CIRS and
HeCS clusters increases with the mass and the redshift of the accreting
cluster, which is in excellent agreement with the growth of clusters in the
$\Lambda$CDM model.
