  (Abridged) The question of how most stars in the Universe form remains open.
While star formation predominantly occurs in young massive clusters, the
current framework focuses on isolated star formation. One way to access the
bulk of protostellar activity within star-forming clusters is to trace
signposts of active star formation with emission from molecular outflows. These
outflows are bright in water emission, providing a direct observational link
between nearby and distant galaxies. We propose to utilize the knowledge of
local star formation as seen with molecular tracers to explore the nature of
star formation in the Universe. We present a large-scale statistical galactic
model of emission from galactic active star-forming regions. Our model is built
on observations of well-resolved nearby clusters. By simulating emission from
molecular outflows, which is known to scale with mass, we create a proxy that
can be used to predict the emission from clustered star formation at galactic
scales. We evaluated the impact of the most important global-star formation
parameters (i.e., initial stellar mass function (IMF), molecular cloud mass
distribution, star formation efficiency (SFE), and free-fall time efficiency)
on simulation results. We observe that for emission from the para-H2O 202 - 111
line, the IMF and molecular cloud mass distribution have a negligible impact on
the emission, both locally and globally, whereas the opposite holds for the SFE
and free-fall time efficiency. Moreover, this water transition proves to be a
low-contrast tracer of star formation. The fine-tuning of the model and
adaptation to morphologies of distant galaxies should result in realistic
predictions of observed molecular emission and make the galaxy-in-a-box model a
tool to analyze and better understand star formation throughout cosmological
times.
