  We report a transport, thermodynamic, and spectroscopic study of the recently
identified topological semiconductor ZrTe$_5$ with a focus on elucidating the
connections between its band structure and unusual thermoelectric properties.
Using time and angle resolved photoemission spectroscopy (tr-ARPES) we observe
a small electronic band gap and temperature dependent Fermi level which
traverses from a single valence to conduction band with lowering temperature,
consistent with previous reports. This low temperature Fermi surface closely
matches that derived from quantum oscillations, suggesting it is reflective of
the bulk electronic structure. The Seebeck and low field Nernst response is
characterized by an unusually large and non-monotonic temperature evolution. We
find this can be quantitatively explained using a semiclassical model based on
the observed band character and a linear temperature shifting of the Fermi
level. Additionally, we observe a large, non-saturating enhancement of both
thermoelectric coefficients in magnetic field. We show this can be captured by
the Zeeman energy associated with a large effective $g$-factor of 25.8
consistent with that derived from Lifshitz-Kosevich analysis of the quantum
oscillations. Together these observations provide a comprehensive picture of
ZrTe$_{5}$ as a model high mobility semiconductor and potential platform for
significant magnetic field driven thermoelectricity.
