  In order to study transient phenomena in the Universe, existing and
forthcoming imaging surveys are covering wide areas of sky repeatedly over
time, with a range of cadences, point spread functions, and depths. We describe
here a framework that allows an efficient search for different types of
time-varying astrophysical phenomena in current and future, large data
repositories. We first present a methodology to generate and store key survey
parameters that enable researchers to determine if a survey, or a combination
of surveys, allows specific time-variable astrophysical phenomena to be
discovered. To facilitate further exploration of sources in regions of
interest, we then generate a few sample metrics that capture the essential
brightness characteristics of a sky pixel at a specific wavelength. Together,
we refer to these as "annotated coadds". The techniques presented here for
WISE/NEOWISE-R data are sensitive to 10 percent brightness variations at around
12th Vega magnitude at 4.5 microns wavelength. Application of the technique to
ZTF data also enabled the detection of 0.5 mag variability at 20 AB mag in the
r-band. We demonstrate the capabilities of these metrics for different classes
of sources: high proper-motion stars, periodic variable stars, and supernovae,
and find that each metric has its advantages depending on the nature of
variability. We also present a data structure which will ease the search for
temporally varying phenomena in future surveys.
