  Evidence of disequilibrium chemistry due to vertical mixing in the
atmospheres of many T and Y-dwarfs has been inferred due to enhanced mixing
ratios of CO and reduced NH$_3$. Atmospheric models of planets and brown dwarfs
typically parameterize this vertical mixing phenomenon with the vertical eddy
diffusion coefficient, $K_{\rm zz}$. While $K_{\rm zz}$ can perhaps be
approximated in the convective regions in the atmosphere with mixing length
theory, in radiative regions the strength of vertical mixing is uncertain by
many orders of magnitude. With a new grid of self-consistent 1D model
atmospheres from $T_{\rm eff}$ of 400 - 1000 K, computed with a new
radiative-convective equilibrium python code PICASO 3.0, we aim to assess how
molecular abundances and corresponding spectra can be used as a probe of
depth-dependent $K_{\rm zz}$. At a given surface gravity, we find non-monotonic
behavior in the CO abundance as a function of $T_{\rm eff}$, as chemical
abundances are sometimes quenched in either of two potential atmospheric
convective zones, or quenched in either of two possible radiative zones. The
temperature structure and chemical quenching behavior also changes with
gravity. We compare our models with available near-infrared and M-band
spectroscopy of several T and Y-dwarfs and assess their atmospheric vertical
mixing profiles. We also compare to color-magnitude diagrams and make
predictions for JWST spectra. This work yields new constraints, and points the
way to significant future gains, in determining $K_{\rm zz}$, a fundamental
atmospheric parameter in substellar atmospheres, with significant implications
for chemistry and cloud modeling.
