# Evaporation loss formulas

A while ago I created a spreadsheet to calculate evaporation loss. I found several formulas to do that, two from Kevin Rafferty and one from Engineering Toolbox. The one from Engineering Toolbox was too convoluted, and I couldn't figure out how to write it in Excel. The ones from Rafferty were fairly straightforward, but the two he published were different and yield different results.

The first is from Kevin Rafferty, P.E., Pond Heat Loss, 1986:

$$W_p=\frac{(1 + 0.225v)/0.018}{85.74 \times (T_s+460)} \times (P_w-P_a) \times 144 \times A$$

Where:

• $W_p$ = Rate of evaporation in lbm/h
• $A$ = Pond surface area in ft$^2$
• $v$ = Air velocity in ft/sec
• $P_w$ = Saturation vapor pressure of pond water in psia
• $P_a$ = Saturation pressure air dew point in psia
• $T_s$ = Surface temperature °F

The other is from Kevin Rafferty, P.E., Tonya Boyd, Aquaculture Information Package, 1998:

$$W_p=(0.097+0.38v) \times (P_w-P_a) \times A$$

Where:

• $W_p$ = Rate of evaporation (lbm/h)
• $A$ = Pond surface area (ft$^2$)
• $v$ = Air velocity (mph)
• $P_w$ = Saturation vapor pressure of pond water (psia)
• $P_a$ = Saturation pressure at the air dew point (psia)

$P_w$ is calculated by the formula

$$P_w = 6.11 \times 10^\left({7.5T_s}/{237.3 + T_s)}\right)$$

$P_a$ is calculated by the same formula except that the dew point temperature in °F is used in place of $T_s$, so the pond surface temperature is used in both main formulas, except that in the second formula it is used to calculate the pond saturation vapor pressure.

The spreadsheet file can be found here.

Does anyone have any idea which is the more accurate?

## 1 Answer

There isn't much to choose between them. They are both variants of the same general equation. They both take account of the three main variables: temperature, rate of advective removal of moisture (proportional to surface wind velocity), and difference in vapour pressure (which can be related to humidity). In countries using SI units there are several other evaporation equations along similar lines Some other equations do not take adequate account of advection (the 'v' parameter), and hence I would advise against using such equations. Strictly, the best equation, favoured by FAO, and in a slightly modified form by the American society of Civil Engineers, is the classic Penman-Monteith equation:

from https://en.wikipedia.org/wiki/Penman%E2%80%93Monteith_equation But this is a pain to calculate, so most people, including myself, put it in the 'too hard basket'. Whatever equation you decide to use on your spreadsheet, be aware of potential errors from ground conduction (underestimate of E), higher salinity (depresion of E), and boundary effects, especially in areas of high advective exposure.

• Thanks for the answer. The first formula in my question gives a result that is about 55% higher than the second, though I have an intuitive feeling that the second formula is more accurate. I wish I could figure out how to conduct an empirical experiment and actually measure evaporation. – BillDOe Oct 31 '15 at 5:28
• A 55% discrepancy is worrying! Have you checked for consistency of units? Also, it may be instructive to research the conditions under which each equation was calibrated. As a check, I suggest comparison of calculated evaporation with measured estimates from a class-A pan, as found in most met stations. Be sure to apply the correct pan coefficient. See, for example: kean.edu/~csmart/Hydrology/Lectures/Evaporation_pan.pdf – Gordon Stanger Oct 31 '15 at 7:38
• The problem with measuring actual evaporation is controlling or measuring the variables. If outdoors, the variables change throughout the day. It would be easier to do the experiment indoors where most of the variables could be controlled, or at least not change too drastically throughout the day. – BillDOe Oct 31 '15 at 18:40