## Ratio of lake to pan evaporation rates

 E. Linacre 3/’02

It is hard to measure the rate of evaporation from a lake Eo. It is best estimated from Penman's formula (1), or a derivative of it, if only few input data are available (2). However, a common alternative is to measure the evaporation from a pan, such as a U.S. Class-A pan illustrated in the foreground of Plate 4.1, and then multiply the measurement Ep by a factor. Ep is easily measured as the rate of fall of the level of water exposed in a pan, minus any rainfall. The factor (the ratio Ep / Eo, usually called the 'pan coefficient') is often taken as about 1.3.

That implies that there is 30% more evaporation from the small area of a pan than from a lake because of the extra heat taken in through the pan's sides. However, a comparison of Penman estimates of Eo with measured Ep shows that the factor is not a constant (3) but depends on the rate of evaporation (4). Values of the factor are indeed scattered about 1.3 if Ep is less than approximately 5 mm/day, but they are more at higher rates, e.g. around 1.7 when Ep is 12 mm/day. In other words, the extra heat through the walls of the pan increases disproportionally in high-evaporation conditions.

Incidentally, the rate of evaporation from a lake of salty water is reduced by the salt, according to its concentration. This is because the saturation vapour pressure over salt water is less than that over fresh water. The relative humidity adjacent to a water surface with the typical salinity of oceans is about 98%, but it decreases with increasing salt concentration to about 74% when the solution is saturated (assuming the salt is mainly sodium chloride). Continued evaporation of the water leaves the salt behind, so that its concentration increases and eventually there is a saturated solution and then the start of crystallisation. Then no evaporation occurs if the air's relative humidity is above 74% assuming that lake and air temperatures are similar (which is likely where the lake is shallow at its edge). Because the nighttime air is usually calm near desert lakes, with a relative humidity often in the vicinity of 74%, desert lake evaporation is almost exclusively a daytime process.

References

1.      Penman, H.L. 1948. Natural evaporation from open water, bare soil and grass. Proc. Roy. Soc. A, 193, 120-45.

2.      Linacre, E.T. 1993. Data-sparse estimation of lake evaporation using a simplified Penman equation. Agric. & Forestry Meteor., 64, 237-56.

3.      Stanhill, G.1976: The CIMO International Evaporimeter Comparisons. WMO Publ. 449 (World Meteor. Organ.) 38pp.

4.      Linacre, E.T. 1994. Estimating U.S. Class A pan evaporation from few climate data. Water International, 19, 5-14.