Mathematical description of heat balance (HB) HB – defined by equation, consist of Σ(+) and Σ(-): incoming and out going heat and radiation fluxes (surface, layer…) HB equation – private form of energy saving law t=t 1 t=t 2 Σ (Qsw + Qlw+ Qshf + Qlhf) = ∆Qa-s (=0, ҂0) ∆Qa-s = срρV(T 2 – T 1) – changes of heat content of V=1 during ∆t=1
Physical meaning Radiation Balance (RB) • RB – difference between incoming (↓) and out going (↑) radiation • If RB = 0, SAT (ST) does not change! Radiation equilibrium!
Definition_1 RB = 0 : ↓ = ↑ !!! Typically for Earth as a planet on average per year Heat/Radiation Budget - ↓ ≠ ↑ Heat Content (HC) – heat enclosed in the test column of ground (snow, ice, water)
Definition_2 • Heat Storage (HS) – difference between the moment (current) heat content and a smallest (minimum) heat content during year ±∆Q Layer
Составляющие радиационного баланса подстилающей поверхности Q=(1 -α)Rs – солнечная радиация Тs 4 - излучение Земли RT - противоизлучение атмосферы Eэф = RT – εgσTs 4 эффективное излучение Rп – радиационный баланс подстилающей поверхности
Definiton_3 Reflection of solar radiation. Albedo R 1 Q R 2 α β Backscattering Albedo = (R 1+R 2)/Q
Mirror albedo Frenel formula (“mirror” surface, no backscattering) A = 0. 5[sin 2(f-r)/sin 2(f+r) + tg 2(f-r)/tg 2(f+r)] f – incidence angle; r - refraction angle, sin(f) = 1. 34 sin(r)
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