Spectrophotometric redshifts for $\mathrm{z\sim1}$ galaxies and
  predictions for number densities with WFIRST and Euclid
  We investigate the accuracy of 4000\AA/Balmer-break based redshifts by
combining Hubble Space Telescope ({\it HST}) grism data with photometry. The
grism spectra are from the Probing Evolution And Reionization Spectroscopically
(PEARS) survey with {\it HST} using the G800L grism on the Advanced Camera for
Surveys (ACS). The photometric data come from a compilation by the 3D-HST
collaboration of imaging from multiple surveys (notably CANDELS and 3D-HST). We
show evidence that spectrophotometric redshifts (SPZs) typically improve the
accuracy of photometric redshifts by $\sim$17--60\%. Our SPZ method is a
template fitting based routine which accounts for correlated data between
neighboring points within grism spectra via the covariance matrix formalism and
also accounts for galaxy morphology along the dispersion direction. We show
that the robustness of the SPZ is directly related to the fidelity of the D4000
measurement. We also estimate the accuracy of continuum-based redshifts, i.e.,
for galaxies that do not contain strong emission lines, based on the grism data
alone ($\sigma^{\rm NMAD}_{\Delta z/(1+z)}{\lesssim}0.06$). Given that future
space-based observatories like WFIRST and Euclid will spend a significant
fraction of time on slitless spectroscopic observations, we estimate number
densities for objects with $\ | \mathrm{\Delta z/(1+z_{s})} \ | \leq 0.02$. We
predict $\sim$700--4400 galaxies/degree$^2$ for galaxies with D4000$>$1.1 and
$\ | \mathrm{\Delta z/(1+z_{s})} \ | \leq 0.02$ to a limiting depth of
$i_{AB}$=24 mag. This is \emph{especially} important in the absence of an
accompanying rich photometric dataset like the existing one for the CANDELS
fields, where redshift accuracy from future surveys will rely only on the
presence of a feature like the 4000\AA/Balmer breaks or the presence of
emission lines within the grism spectra.
