  Measuring precise all-flavor neutrino information from a supernova is crucial
for understanding the core-collapse process as well as neutrino properties. We
apply a chi-squared analysis for different detector setups to explore
determination of $\nu_{e}$ spectral parameters. Using a long-term
two-dimensional core-collapse simulation with three time varying spectral
parameters, we generate mock data to examine the capabilities of the current
Super-Kamiokande detector and compare the relative improvements that
gadolinium, Hyper-Kamiokande, and DUNE would have. We show that in a realistic
three spectral parameter framework, the addition of gadolinium to
Super-Kamiokande allows for a qualitative improvement in $\nu_e$ determination.
Significant improvements will be made by Hyper-Kamiokande and DUNE, allowing
for much more precise determination of $\nu_e$ spectral parameters.
