  In this paper we conduct a systematic study of the granularity of the initial
state of hot and dense QCD matter produced in ultra-relativistic heavy-ion
collisions and its influence on bulk observables like particle yields, $m_T$
spectra and elliptic flow. For our investigation we use a hybrid transport
model, based on (3+1)d hydrodynamics and a microscopic Boltzmann transport
approach. The initial conditions are generated by a non-equilibrium hadronic
transport approach and the size of their fluctuations can be adjusted by
defining a Gaussian smoothing parameter $\sigma$. The dependence of the
hydrodynamic evolution on the choices of
  $\sigma$ and $t_{start}$ is explored by means of a Gaussian emulator.
  To generate particle yields and elliptic flow that are compatible with
experimental data the initial state parameters are constrained to be $\sigma=1$
fm and $t_{\rm start}=0.5$ fm. In addition, the influence of changes in the
equation of state is studied and the results of our event-by-event calculations
are compared to a calculation with averaged initial conditions. We conclude
that even though the initial state parameters can be constrained by yields and
elliptic flow, the granularity needs to be constrained by other correlation and
fluctuation observables.
