Atmospheric Evaporation, Humidity Quantification, and Vapor Pressure Dynamics

Available surface energy partitions into latent heat flux, sensible heat flux, or ground conduction based on regional climate factors (temperature, precipitation, cloud cover).
Four primary controls determine net evaporation rates:
- Vapor pressure deficit (the air must be undersaturated to accept water vapor molecules).
- Water availability at the surface (overland, desert, water body, or forested area).
- Atmospheric turbulence or mixing (prevents a saturated steady-state boundary layer from forming above the surface by transporting moist air away and replacing it with drier air).
- Turbulent sensible energy fluxes and radiation fluxes for the location.

Evaporation: Phase change of water molecules into water vapor at the water surface occurring at any temperature.
Sublimation: Direct transition of molecules from solid ice (e.g., glaciers, ice sheets, freezer ice cubes) into water vapor at sub-freezing temperatures.
Boiling: Phase change from liquid water to vapor throughout the entire volume of water, occurring at a specific temperature.
Boiling Point Mechanism: Boiling occurs when saturation vapor pressure ( $e_s$ ) equals ambient atmospheric pressure.
- At sea level, standard atmospheric pressure is $101.35\,\text{kPa}$ , corresponding to a boiling point of $100\,^\circ\text{C}$ .
- Atmospheric pressure decreases as elevation increases, causing the boiling point of water to decrease linearly with altitude (e.g., in the Andes Mountains as noted by Darwin, or at Calgary airport weather station at about a 35 meters where water boils at approximately $96\,^\circ\text{C}$ ).
- Under reduced pressure (such as an artificial vacuum equivalent to $85,000\,\text{feet}$ , nearly three times the height of Mount Everest), water boils at room temperature without the addition of heat.

Absolute Humidity (Vapor Density):
- The mass of water vapor contained within a given volume of air, expressed in $\text{kg/m}^3$ or $\text{g/m}^3$ .
- Derived from the ideal gas law: vapor density equals vapor pressure ( $e$ ) divided by a gas constant multiplied by temperature ( $T$ ).
- Changes inversely with volume expansions even if the absolute number of water molecules remains unchanged.
Vapor Pressure ( $e$ ):
- The partial pressure exerted by water vapor molecules in the atmosphere, representing $0\%$ to $4\%$ of atmospheric gas by volume.
- Related to atmospheric pressure ( $p$ ) and mixing ratio ( $r$ ) using the molar mass ratio constant of water vapor to dry air ( $0.622$ ).
Mixing Ratio ( $r$ ):
- The ratio of the mass of water vapor to the mass of dry air, typically reported in $\text{g/kg}$ .
Specific Humidity ( $q$ ):
- The ratio of the mass of water vapor to the total mass of the air (including the water vapor), reported in $\text{g/kg}$ .
- Values are slightly lower than the mixing ratio because total air mass includes the moisture content; the value remains invariant under parcel volume or mass changes that do not add or remove moisture.

Dew Point Temperature ( $T_d$ ):
- The temperature to which an air parcel must be cooled at constant pressure to achieve saturation ( $100\%$ relative humidity).
- Almost always lower than the ambient air temperature ( $T$ ).
Relative Humidity ( $RH$ ):
- Quantitative measure of how close an air mass is to saturation, defined as: $RH = \left(\frac{e}{e_s}\right) \times 100\%$
- Exhibits an inverse diurnal cycle to air temperature: relative humidity reaches its minimum in the late afternoon (around 3:00 to 4:35 PM) when air temperature peaks, while absolute moisture content remains constant.
Vapor Pressure Deficit ( $VPD$ ):
- The absolute difference between the saturation vapor pressure and the actual vapor pressure at a given temperature: $VPD = e_s - e$
Dew Point Depression:
- The arithmetic difference between the ambient air temperature and the dew point temperature: $\text{Dew Point Depression} = T - T_d$
- Example: With an air temperature of $10.3\,^\circ\text{C}$ and a dew point temperature of $1.3\,^\circ\text{C}$ , the dew point depression equals $9\,^\circ\text{C}$ .

Saturation vapor pressure tables (derived from the Clausius-Clapeyron relation) provide standard values of $e_s$ as a function of temperature ( $T$ ) or $e$ as a function of $T_d$ .
Benchmark comparative calculation parameters:
- Polar Air: Air temperature $T = -2\,^\circ\text{C}$ , $RH = 100\%$ .
- Desert Air: Air temperature $T = 35\,^\circ\text{C}$ , $RH = 21\%$ .
- Specific humidity ( $q$ ) and dew point temperature ( $T_d$ ) can be determined at constant atmospheric pressure ( $p$ ) by calculating actual vapor pressure ( $e = \frac{RH \times e_s}{100}$ ) and applying standard humidity equations.