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% brightness variations at around 12th Vega magnitude at 4.5μm wavelength. Application of the technique to Zwicky Transient Facility 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.