  A compact device lifted over the ground surface might be used to observe
optical radiation of extensive air showers (EAS). Here we consider spatial and
temporal characteristics of Vavilov-Cherenkov radiation ("Cherenkov light")
reflected from the snow surface of Lake Baikal, as registered by the SPHERE-2
detector. We perform detailed full direct Monte Carlo simulations of EAS
development and present a dedicated highly modular code intended for detector
response simulations. Detector response properties are illustrated by example
of several model EAS events. The instrumental acceptance of the SPHERE-2
detector was calculated for a range of observation conditions. We introduce the
concept of "composite model quantities", calculated for detector responses
averaged over photoelectron count fluctuations, but retaining EAS development
fluctuations. The distortions of EAS Cherenkov light lateral distribution
function (LDF) introduced by the SPHERE-2 telescope are understood by comparing
composite model LDF with the corresponding function as would be recorded by an
ideal detector situated at the ground surface. We show that the uncertainty of
snow optical properties does not change our conclusions, and, moreover, that
the expected performance of the SPHERE experiment in the task of cosmic ray
mass composition study in the energy region $\sim$10 PeV is comparable with
other contemporary experiments. Finally, we compare the reflected Cherenkov
light method with other experimental techniques and briefly discuss its
prospects.
