Question No. 25

Most part of the Earth’s surface is water. Why, despite this, is not the atmosphere saturated with water vapor?
Answered 28 July 2009.
Question author: BIZON.
Asked 30 May 2009.

This important question relates to the core of the physical understanding of the biotic pump of atmospheric moisture and such atmospheric phenomena as hurricanes and tornadoes (see, e.g., here). Indeed, global mean relative humidity at the surface is around 80%, i.e. surface air is not saturated with water vapor. The atmosphere continuously circulates in the horizontal as well as in the vertical dimension. Due to condensation the atmospheric air in the upper part of the atmospheric column is depauperate in water vapor compared to surface air. Mixing of the wet surface air with the dry air brought from the upper atmospheric layers by the descending air masses diminishes the relative humidity at the surface. Thus, we have to answer two questions: why there is condensation and why the atmosphere circulates.

If the Earth’s atmosphere had a uniform temperature at all heights, water vapor would be in the aerostatic equilibrium. This means that at each height the weight of the column of water vapor of unit cross-section above that height would be equal to the partial pressure of water vapor at that height. Water vapor concentration would decrease exponentially with height dropping twofold per each nine kilometers of ascent. Therefore, in such a thermally uniform atmosphere the water vapor would be unsaturated at any height except for the sea level. (Recall that saturated concentration is the maximum possible vapor concentration. If it is exceeded, the process of condensation commences.) Saturated concentration of water vapor is determined by temperature. Thus, for the atmospheric water vapor to be saturated at all heights, it is necessary that air temperature dropped with height. The dependence of saturated concentration on temperature (the Clausius-Clapeyron law) has an exponential form as well: saturated concentration diminishes twofold per each ten degrees Celsius of temperature drop. It follows that in order water vapor to be saturated at all heights in aerostatic equilibrium, it is necessary that the air temperature dropped by 10 oC per each 9 km of ascent. This gives an air temperature lapse rate of 10 oC/ 9 km or, more precisely, 1.2 oC/km.

Thus, if air temperature decreased with height not faster than by 1.2 oC/km, water vapor could remain in static equilibrium. At a critical rater of 1.2 oC/km water vapor would be static and saturated at all heights. There would be no condensation, no clouds or precipitation. The atmosphere would remain motionless. Note that this is the only possible state where water vapor is saturated in the entire atmosphere.

The observed air temperature lapse rate is 6.5 oC/km, which is six times greater than the critical value of 1.2 oC/km. Consequently, water vapor cannot be in static equilibrium in the real atmosphere: at any height water vapor pressure appears six times greater than the weight of the water vapor column above that height. In other words, the weight of saturated water vapor cannot compensate the vapor pressure. At any height there is a force in action equal to the difference between pressure and column weight of the water vapor. In the result, water vapor continuously ascends involving atmospheric air into this motion. In the upper part of the atmospheric column water vapor undergoes condensation and precipitates. These processes are in the long term compensated by surface evaporation. The atmospheric cycling of water vapor and atmospheric circulation (wind) are formed, with air ascending and descending in different places. The descending air deprived by condensation of water vapor mixes with the surface air and makes the latter drier.

The primary cause of the fact that surface air is not saturated with water vapor is that the global mean vertical lapse rate of air temperature exceeds the critical value of 1.2 oC/km. This makes water vapor condense, switches on the circulation and vertical mixing of the atmosphere, so that the lower wet air is mixed with the upper dry air. In the result, relative humidity at the surface is less than unity. Namely condensation and precipitation makes the surface air unsaturated with vapor. If the air temperature lapse rate were less than 1.2 oC/km, there were no condensation and the motionless atmosphere would be always saturated with water vapor at the planetary surface.

The following illustration might be helpful. By pressing the two rightmost buttons, it is possible to see how the the dry descending air mixes with the wet ascending air. See here for more details.

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