International Standard Atmosphere (troposphere): T(z) = T0 - L z with L = 6.5 K/km; p(z) = p0 (T/T0)^(g/(L R)); density rho = p/(R T). Oxygen partial pressure is 20.95 % of p. Water boils where its vapour pressure equals p (Clausius-Clapeyron, L_v = 2.26 MJ/kg).

Honey bees forage above about 12 C; the diurnal temperature is modelled as a cosine peaking at 15:00, so flight hours fall as the hive moves up. The bloom window shortening of about 3.8 days per 100 m is an illustrative teaching figure, not a measured local value; real bloom depends on aspect, snow melt and species.