  Deriving properties of cometary nuclei from coma data is of significant
importance for our understanding of cometary activity and has implications
beyond. Ground-based data represent the bulk of measurements available for
comets. Yet, to date these observations only access a comet's gas and dust coma
at rather large distances from the surface and do not directly observe its
surface. In contrast, spacecraft missions are one of the only tools that gain
direct access to surface measurements. However, such missions are limited to
roughly one per decade. We can overcome these challenges by recognising that
the coma contains information about the nucleus's properties. In particular,
the near-surface gas environment is most representative of the nucleus. It can
inform us about the composition, regionality of activity, and sources of coma
features and how they link to the topography, morphology, or other surface
properties. The inner coma data is a particularly good proxy because it has not
yet, or only marginally, been contaminated by coma chemistry or secondary gas
sources. Additionally, the simultaneous observation of the innermost coma with
the surface provides the potential to make a direct link between coma
measurements and the nucleus. If we hope to link outer coma measurements
obtained by Earth-based telescopes to the surface, we must first understand how
the inner coma measurements are linked to the surface. Numerical models that
describe the flow from the surface into the immediate surroundings are needed
to make this connection. This chapter focuses on the advances made to
understand the flow of the neutral gas coma from the surface to distances up to
a few tens of nuclei radii. We describe both simple/heuristic models and
state-of-the-art physically consistent models. Model limitations and what they
each are best suited for are discussed.
