Surface Albedo and Radiative Balance of the Climate System

Surface Albedo and the Climate System

Albedo

Albedo is the ability of different surface types to reflect solar energy back into the atmosphere.

Radiation Balance

Radiation balance describes the energy flow converging in an area.

Key Threads:

• K: Solar radiation flux = S + D + K
• L: Terrestrial radiation flux = L_↑ + L_↓
• D: Sensible heat flux in the atmosphere
• H: Sensible heat flux in the soil
• C: Latent heat flux

Surface Radiative Balance

If T_s = 288 K (-15°C)

E_n = σT⁴ = 0.817 x 10^-10 Ly min^-1 K^-4 (288 K)⁴

E_n = 0.562 Ly min^-1 = 290 Kcal cm^-2 yr^-1

Since S = 1.94 Ly min^-1, the total energy intercepting the surface is:

SπR²

The total energy per unit area incident (Q₀) corresponding to 100% is:

Q₀ = SπR² / 4πR² = S / 4

Q₀ = 0.485 Ly min^-1 = 250 Kcal cm^-2 yr^-1

Ideal Gas

An ideal gas consists of particles (molecules) in random motion. The total number of molecules is large, and the volume of individual molecules is negligible compared to the gas volume. No forces act on the molecules, and collisions are elastic with negligible duration.

Boyle's Law

For a given mass of gas at constant temperature, the volume it occupies is inversely proportional to the pressure:

P ∝ 1/V

Considering two states (initial and final), if the initial pressure is P₁ and the volume is V₁ at temperature T, and in the final state P₂ = 2P₁ at the same temperature T, the volume V₂ is:

V₂ = ½V₁

Therefore, P₂V₂ = 2P₁ * ½V₁ = P₁V₁ = k, where k is a constant for a given mass of gas at a given temperature.

Gay-Lussac's Law

If pressure remains constant during heating, a gas undergoes expansion. The volume change follows the law:

V = V₀(1 + αt)

Where α is the coefficient of expansion of gases at constant pressure.

For an initial temperature of 0°C at constant pressure, the value of α for any gas is:

α = 1/273.15 °C

Substituting this value, we get:

V/V₀ = 1 + t/273.15 = (273.15 + t)/273.15 = T/T₀

That is, V/V₀ = T/T₀, where T (K) = 273.15 + t (°C) and T₀ = 273.15 K = 0°C.

Dalton's Law

In a mixture of gases, the total pressure exerted is equal to the sum of the partial pressures exerted by each gas:

P = P₁ + P₂ + ... + P_n = ΣP_i

Heat

Heat = c * m * (T_f - T_i), where Q represents heat lost or absorbed, m is the body mass, and T_f and T_i are the final and initial temperatures, respectively.

Q will be positive if T_f > T_i and negative if T_f < T_i.

• Calorie: The amount of heat needed to raise the temperature of one gram of water from 14.5°C to 15.5°C.
• Kilocalorie: The amount of heat needed to raise the temperature of one kilogram of water from 14.5°C to 15.5°C. 1 kcal = 1000 cal.
• British Thermal Unit (BTU): The amount of heat needed to raise the temperature of one pound of water from 63°F to 64°F. 1 BTU = 252 cal.

The relationship between calorie and mechanical power is the Joule: 1 cal = 4186 joules.

Specific heat is the amount of heat per unit mass and temperature, or the heat required to raise the temperature of one unit mass of a substance by one degree:

C = ΔQ / ΔT

Specific heat at constant volume (C_v) is the amount of heat needed to change the temperature while keeping the volume constant:

C_v = (dQ/dT)_v=constant

Specific heat at constant pressure (C_p) is the amount of heat needed to change the temperature while keeping the pressure constant:

C_p = (dQ/dT)_p=constant

Laws of Thermodynamics

dQ = dU + PdV

Adiabatic Process

dU = -dW. During adiabatic expansion, work is done on the environment (positive), and this work is done at the expense of internal energy. Thus, dU and dT are negative, meaning the temperature decreases during adiabatic expansion.