  To study the capabilities of supernova neutrino detectors, the instantaneous
spectra are often represented by a quasi-thermal distribution of the form f(E)
= E^alpha e^{-(alpha+1)E/E_{av}} where E_{av} is the average energy and alpha a
numerical parameter. Based on a spherically symmetric supernova model with full
Boltzmann neutrino transport we have, at a few representative post-bounce
times, re-converged the models with vastly increased energy resolution to test
the fit quality. For our examples, the spectra are well represented by such a
fit in the sense that the counting rates for a broad range of target nuclei,
sensitive to different parts of the spectrum, are reproduced very well.
Therefore, the mean energy and root-mean-square energy of numerical spectra
hold enough information to provide the correct alpha and to forecast the
response of multi-channel supernova neutrino detection.
