Moisture is returned directly to the atmosphere through a number of processes. The change in state from solid or liquid form to gaseous water vapor comprises the process of evaporation and sublimation. Evaporation occurs when input of energy onto an evaporating surface causes water molecules to pass from that surface to the atmosphere; this will occur when the vapor pressure of the air is below its saturation value. The rate of evaporation is governed by the state of a number of variables including water vapor, temperature, and air motion, and several formulas are available to determine the rate at which it occurs. Perhaps the oldest of these is the Dalton equation given as
where e s is the vapor pressure of the evaporating surface, e is the vapor pressure at some height above that surface, and f(u) is a function of the horizontal wind speed. Since these parameters vary widely over the Earth's surface, the rates of evaporation vary enormously.
Transpiration...
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Oliver, J.E. (1987). Evapotranspiration. In: Climatology. Encyclopedia of Earth Science. Springer, Boston, MA. https://doi.org/10.1007/0-387-30749-4_74
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