  Ground-based, high-resolution and space-based, low-resolution spectroscopy
are the two main avenues through which transiting exoplanet atmospheres are
studied. Both methods provide unique strengths and shortcomings, and combining
the two can be a powerful probe into an exoplanet's atmosphere. Within a joint
atmospheric retrieval framework, we combined JWST NIRSpec/G395H secondary
eclipse spectra and Gemini South/IGRINS pre- and post-eclipse thermal eclipse
observations of the hot Jupiter WASP-77A b. Our inferences from the IGRINS and
NIRSpec data sets are consistent with each other, and combining the two allows
us to measure the gas abundances of H$_2$O and CO as well as the vertical
thermal structure with higher precision than either data set provided
individually. We confirm WASP-77A b's subsolar metallicty
([(C+O)/H]=-0.61$^{+0.10}_{-0.09}$) and solar C/O ratio (C/O =
0.57$^{+0.06}_{-0.06}$). The two types of data are complementary, and our
abundance inferences are mostly driven by the IGRINS data while inference of
the thermal structure is driven by the NIRSpec data. Our ability to draw
inferences from the post-eclipse IGRINS data is highly sensitive to the number
of singular values removed in the detrending process, potentially due to high
and variable humidity. We also search for signatures for atmospheric dynamics
in the IGRINS data and find that propagated ephemeris error can manifest as
both an orbital eccentricity or a strong equatorial jet. Neither are detected
when using more up-to-date ephemerides. However, we find moderate evidence of
thermal inhomogeneity and measure a cooler nightside that presents itself in
the later phases after secondary eclipse.
