  Ongoing and future imaging surveys represent significant improvements in
depth, area and seeing compared to current data-sets. These improvements offer
the opportunity to discover up to three orders of magnitude more galaxy-galaxy
strong lenses than are currently known. In this work we forecast the number of
lenses discoverable in forthcoming surveys and simulate their properties. We
generate a population of statistically realistic strong lenses and simulate
observations of this population for the Dark Energy Survey (DES), Large
Synoptic Survey Telescope (LSST) and Euclid surveys. We verify our model
against the galaxy-scale lens search of the Canada-France-Hawaii Telescope
Legacy Survey (CFHTLS), predicting 250 discoverable lenses compared to 220
found by Gavazzi et al (2014). The predicted Einstein radius distribution is
also remarkably similar to that found by Sonnenfeld et al (2013). For future
surveys we find that, assuming Poisson limited lens galaxy subtraction,
searches in DES, LSST and Euclid datasets should discover 2400, 120000, and
170000 galaxy-galaxy strong lenses respectively. Finders using blue minus red
(g-i) difference imaging for lens subtraction can discover 1300 and 62000
lenses in DES and LSST. The uncertainties on the model are dominated by the
high redshift source population which typically gives fractional errors on the
discoverable lens number at the tens of percent level. We find that doubling
the signal-to-noise ratio required for a lens to be detectable, approximately
halves the number of detectable lenses in each survey, indicating the
importance of understanding the selection function and sensitivity of future
lens finders in interpreting strong lens statistics. We make our population
forecasting and simulated observation codes publicly available so that the
selection function of strong lens finders can easily be calibrated.
