Earth Systems: Atmosphere, Weather, and Climate

This set covers the fundamental concepts of Earth's atmospheric systems, including gas composition, state variables, vertical structure, and moisture properties.

Permanent Gases

The group of gases in the atmosphere whose proportions remain constant by volume, primarily Nitrogen ($78.08\%$), Oxygen ($20.95\%$), and Argon ($0.93\%$).

Carbon Dioxide ($CO_2$) Concentration

A variable gas in the atmosphere measured at approximately $420\,\text{ppm}$ currently, compared to the pre-industrial level of $280\,\text{ppm}$.

Molecular Mass (MM) of dry air

The weighted average mass of atmospheric gases, which is numerically valued at $29$.

Molecular Mass of water vapour

The specific mass of water vapour, which is $18$. Since this is less than the MM of dry air, moist air is lighter than dry air at the same temperature and pressure.

State Variables

The three variables that define the state of the atmosphere: Temperature, Pressure, and Density.

Temperature ($T$)

An expression of hotness or coldness measured in Kelvin ($K$) or Celsius ($^\circ C$), where $T(K) = T(^\circ C) + 273$. The global mean at sea-level is $15^\circ C$.

Pressure ($p$)

The force exerted on a unit area due to the bombardment by molecules, measured in Pascals ($Pa$) where $1\,Pa = 1\,N\,m^{-2}$.

Standard Atmospheric Pressure

The benchmark pressure at sea level, equal to $101,325\,Pa$, $1013.25\,hPa$, or $1013.25\,mbar$.

Density ($\rho$)

Mass concentration expressed as mass per unit volume ($kg\,m^{-3}$). For dry air at $15^\circ C$ and $1013.25\,hPa$, it is $1.22\,kg\,m^{-3}$.

Equation of State (Ideal Gas Law)

The relationship governed by the formula $p = \rho R_d T$, where $p$ is pressure in $Pa$, $\rho$ is density in $kg\,m^{-3}$, and $T$ is temperature in Kelvin.

$$R_d$$

The gas constant for dry air, which has a numerical value of $287\,J\,K^{-1}\,kg^{-1}$.

Hydrostatic Pressure

Pressure exerted by air at equilibrium due to gravity, which decreases exponentially with height as air density also decreases.

Troposphere

The atmospheric layer bounded by the surface and the tropopause where air is continually stirred by weather systems; it is considered relatively unstable.

Tropopause

The boundary located approximately $10$\text{--}$11\,km$ above sea level marking the first distinctive change in the temperature gradient.

Stratosphere

The stable layer of the atmosphere above the tropopause where temperature increases with elevation.

Lapse Rate

The rate at which temperature decreases with height in the troposphere, with an average value of $6.5^\circ C\,km^{-1}$ or $0.65^\circ C$ per $100\,m$.

Latent Heat of Vaporisation ($l_v$)

The amount of energy required to convert $1\,kg$ of water into $1\,kg$ of water vapour, which is $2.47\,MJ\,kg^{-1}$ at $15^\circ C$.

Relative Humidity

The ratio of the amount of water vapour in the air to the maximum amount required for saturation at a specific temperature.

Saturation Vapour Pressure

The pressure at which water vapour is in equilibrium with its liquid state; it depends only on temperature and increases in a non-linear fashion.

Dew-point Temperature ($T_d$)

The temperature to which air must be cooled for saturation to occur, serving as a reliable measure of moisture level in the air.