We baseline with current cosmological observations to forecast the power of
the Dark Energy Spectroscopic Instrument (DESI) in two ways: 1. the gain in
constraining power of parameter combinations in the standard $\mathrm{\Lambda}$ CDM
model, and 2. the reconstruction of quintessence models of dark energy. For the
former task we use a recently developed formalism to extract the leading
parameter combinations constrained by different combinations of cosmological
survey data. For the latter, we perform a non-parametric reconstruction of
quintessence using the Effective Field Theory of Dark Energy. Using mock DESI
observations of the Hubble parameter, angular diameter distance, and growth
rate, we find that DESI will provide significant improvements over current
datasets on $\mathrm{\Lambda}$ CDM and quintessence constraints. Including DESI mocks in
our $\mathrm{\Lambda}$ CDM analysis improves constraints on ${\mathrm{\Omega}}_{m}$ , ${H}_{0}$ , and
${\sigma}_{8}$ by a factor of two, where the improvement results almost entirely
from the angular diameter distance and growth of structure measurements. Our
quintessence reconstruction suggests that DESI will considerably improve
constraints on a range of quintessence properties, such as the reconstructed
potential, scalar field excursion, and the dark energy equation of state. The
angular diameter distance measurements are particularly constraining in the
presence of a non-$\mathrm{\Lambda}$ CDM signal in which the potential cannot be
accounted for by shifts in ${H}_{0}$ and ${\mathrm{\Omega}}_{m}$ .