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 ∼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. (T.A. Dzhatdoev) include CASA-BLANCA [16], BASJE [17], TACT [18] and the optical part of the Yakutsk array [19]. EAS fluorescent light was observed with HiRes [20] and the optical detectors of TA [21, 22] TALE [23] and PAO [15]. EAS radio emission is also studied in various experiments, such as LOPES [24], PAO [25], and LORA [26].The size of ground-based EAS detector arrays and their complexity is growing with time, and so does the difficulty of their deployment, calibration, and operation. Indeed, in order to work as an ensemble, the detectors must be distributed over a large area, sometimes hundreds [13] or thousands [15] square kilometers, and, moreover, they must be constantly power-supplied, be able to transfer information obtained with them, and kept fairly well timesynchronized.A long time ago it was pointed out that a compact device lifted over the snow-covered Earth surface is able to register reflected Cherenkov light [27]. This method is free from the above-mentioned difficulties of ground-based experiments. Moreover, a detector looking down at reflected Cherenkov light typically has a quasi-continious spatial sensitivity, i.e. it can observe light emitted from a substantial fraction of the snow-covered surface. This allows
