  We examine Saturn's non-auroral (dayglow) emissions at Lyman-$\alpha$
observed by the {Cassini/UVIS} instrument from 2004 until 2016, to constrain
meridional and seasonal trends in the upper atmosphere. We separate viewing
geometry effects from trends driven by atmospheric properties, by applying a
multi-variate regression to the observed emissions. The Lyman-$\alpha$ dayglow
brightnesses depend on the incident solar flux, solar incidence angle, emission
angle, and observed latitude. The emissions across latitudes and seasons show a
strong dependence with solar incidence angle, typical of resonantly scattered
solar flux and consistent with no significant internal source. We observe a
bulge in Ly-$\alpha$ brightness that shifts with the summer season from the
southern to the northern hemisphere. We estimate atomic hydrogen optical depths
above the methane homopause level for dayside disk observations (2004-2016) by
comparing observed Lyman-$\alpha$ emissions to a radiative transfer model. We
model emissions from resonantly scattered solar flux and a smaller but
significant contribution by scattered photons from the interplanetary hydrogen
(IPH) background. During northern summer, inferred hydrogen optical depths
steeply decrease with latitude towards the winter hemisphere from a northern
hemisphere bulge, as predicted by a 2D seasonal photochemical model. The
southern hemisphere mirrors this trend during its summer. However, inferred
optical depths show substantially more temporal variation between 2004 and 2016
than predicted by the photochemical model.
