  Supernova neutrino detection in neutrino and dark matter experiments is
usually implemented as a real-time trigger system based on counting neutrino
interactions within a moving time window. The sensitivity reach of such
experiments can be improved by taking into account the time profile of the
expected signal. We propose a shape analysis of the incoming experimental data
based on a log likelihood ratio variable containing the assumed signal shape.
This approach also allows a combination of potential supernova signals in
different detectors for a further sensitivity boost. The method is tested on
the NOvA detectors to study their combined sensitivity to the core-collapse
supernova signal, and also on KamLAND, Borexino and SK-Gd as potential
detectors of presupernova neutrinos. Using the shape analysis enhances the
signal significance for supernova detection and prediction, as well as the
sensitivity reach of the experiment. It also extends the supernova prediction
time when applied to the presupernova neutrino signal detection. Enhancements
achieved with the shape analysis persist even in the case when the actual
signal doesn't match the expected signal model.
