# Contents

## Idea

Evaporation is the conversion of a substance from the liquid or solid state into vapor. In the latter case it is often called sublimation. The vaporization of water through the stomata of living plants is often called transpiration. Over land surfaces, it is difficult to separate transpiration from vegetation and evaporation from the soil and small water surfaces, and one often speaks of evapotranspiration.

## Water and energy budget and distribution of heat

Evaporation is a main phase of the hydrological cycle, and forms a link between the water budget and the energy budget.

We can describe the water budget of a lumped system as:

$(P-E) A + Q_i - Q_0 = \frac{\mathrm{d}}{\mathrm{d} t}S$

with $P$ the rate of precipitation, $E$ the rate of evaporation, $A$ the surface area of the system, and $Q_i-Q_0$ the net inflow rate of surface and ground water, and $S$ the water volume stored in the system.

We can describe the energy budget of a lumped system as:

$R_n=L_e E + H + G$

with $R_n$ the specific flux of net incoming radiation, $L_e$ the latent heat of evaporation, $E$ (again) the rate of evaporation, $H$ the specific flux of sensible heat into the atmosphere, and $G$ the specific flux of heat into the earth. In the energy budget above certain effects are neglected, e.g. ice melt, photosynthesis…

The circulation of the planetary atmosphere is forced by the global patterns of hatent. Because the evaporation of water involves a large latent heat, evaporation redistributes large amounts of energy under nearly isothermal conditions. Air can only contain relatively small amounts of water vapor, and these can easily condense at higher levels. Therefore, air can be readily dried out, and the release of energy through condensation and precipitation is the largest single heat source for the atmosphere.

In many situations it is impossible to deal with $E$ without considering $H$. The ratio of the two is called the Bowen ratio:

$Bo=\frac{H}{L_e E}$

Near the earth’s surface the sensible heat can be expressed as \$$H=c_p T$ with $c_p$ the specific heat of the air.

## Evaporation rates and patterns

The annual average evaporation for the entire earth is of the order of 1 m, so $\bar{E}\approx 1 m/yr$. This is much, because soils, lakes, rivers appear to store much less than one m and water in atmosphere amounts to only 2-3 cm of condensed liquid/ Therefore, the turnover in the active part of hydrological cycle is fast.

A large rate of evaporation can be found in the North-Western Atlantic (> 320 cm/yr) due to the high local net radiation plus the advection of energy by Gulf Stream. As a comparison, for well-irrigated crops one demands about $1.0-1.5 l/(s \cdot ha)$, which is about 3.2-4.7 m/yr.

Over oceans, the latent heat flux $L_e E$ is on the average larger than 90% of $R_n$. Over land surfaces, it is slightly larger than 50%. For land, evaporation amounts to 60-65% of precipitation.

The rate of evaporation can be written as it mean value plus its cyclic behaviour. The major time scales are the daily and seasonal time scale. In an arid and warm climate with a pronounced dry/wet season, the seasonal cycle of $E$ is similar to the rainfall cycle. In a humid climate (or over water) $E$ follows the cycle of energy available for evaporation. Over land and small water bodies, this cyclic is similar to the cycle of solar radiation input and air temperature (summer-winter). For deep water bodies (e.g. Lake Ontario) there is storage of heat and as a consequence a time lag between the evaporation cycle and the solar radiation cycle. The daily cycle is more pronounced over land than over water. Over water, much heat can be stored below the surface. On land, the daily cycle follows the daily march of solar radiation.

• Wilfried H. Brutsaert, Evaporation into the Atmosphere: Theory, History, and Applications, Reidel, 1982.