# Understanding evaporation #3: potential rate

`One of a series; also see editions: #1, #2, #4`

Talk to a meteorologist about how to measure evaporation and you’ll probably be told not to bother because it can be reliably estimated from other parameters. Therein lies a simplification, an overstatement and perhaps a cop-out.

What can be “reliably” estimated from data on sunshine, temperature, humidity and wind is not the actual evapotranspiration from the landscape described last time — certainly not its day-to-day variation — rather it’s the potential rate. That’s a surprisingly ill-defined measure of the upper bound rate given ample soil moisture, called potential evapotranspiration¹.

It turns out that there are at least five common ways of estimating that, with all sorts of confusion about which is best, when and why².  Each of those is grounded deep in last century science, and each hides its own range of assumptions and empiricism.  That’s fine applied to known circumstances, but potentially dangerous when used, say, to study a changing climate.

The details are way too much for here (see Tom McMahon below), but it helps to understand the underlying basis.

### Evaporation physics

We don’t need much…  This is a phase change: liquid to gas.  That requires energy: latent heat.  Lots: about 2260 kJ/L(3).  Evaporation is everywhere an energy limited process: no heat supply — no evaporation (no exceptions!).  All of the evaporation estimation methods rely on energy accounting in one form or another.  The main energy supply is of course incident sunlight, but in some situations incoming wind may supply significant heat energy.

The atmosphere can only hold so much gaseous water.  We call the water content humidity, and the limit saturation.  If the air in contact with our evaporating surface is saturated, evaporation stops.  So for continuing evaporation (without continuing temperature increase⁴) we need a means to move the accumulating water vapour away from the evaporating surface.  That happens mainly by local convection, driven by a little extra bit of heat input on top of that required to supply the latent heat.  Wind is also important, and vapour exchange with wind depends on surface roughness.

That’s about it.  The potential evapotranspiration estimation methods all combine energy accounting and vapour accounting in one form or another, with the differences often arising as much from assumptions about the outcome (definitional differences) as from different methods of calculation. I want to highlight just one of those “definitional differences”.

### Point potential and areal potential

We’re using measured meteorological parameters, parameters that coexisted with some unknown but often low actual evapotranspiration rate. But we’re using those to estimate a different condition: the maximum rate from a wet system, potential evapotranspiration.  If you think about it there are two extreme assumptions that could be made:

1. Our new maximum rate doesn’t change the measured meteorological parameters.  So temperature and humidity don’t change as a result of our altering (generally significantly increasing) the local evapotranspiration from actual to potential.
2. Our maximum rate thoroughly alters the measured meteorological parameters to those that would coexist with the new, generally higher, potential rate across the whole landscape.

The first of those models evaporation from a small wet area in an otherwise ambient landscape.  The wet area always experiences conditions from up-wind that are pretty much as-measured, unaffected by whatever it does.  That’s called point potential evapotranspiration.  It’s close to what an evaporation pan does, so you’d expect the two to be similar, and they are (see the charts below).  It turns out that “small” in this context means up to a few hundred metres across.  Bigger than that and the assumption begins to break down, depending on how dry the surrounding landscape is. In Australia that is often very dry.

The second one models the case where the whole landscape is wet and the meteorology is allowed to adjust to suit.  That’s called areal potential evapotranspiration.  We’d expect it to be lower than point potential⁵, because of lower surface temperature and higher humidity.  (Quick question for those still paying attention: which would you choose to use in our simple model of actual evaporation in edition #2?  There are experienced practitioners who’ve never even thought about that⁶.)

### Some numbers

Here’s some plots of evaporation rates from the Australian Bureau of Meteorology’s website, to illustrate where we’ve been so far.  Click the images for the page links, and be sure to note the different colour scales (why why why?):

Pan evaporation (interpolated from sparse measurements, not calculated).

Point potential evapotranspiration (generally similar to pan evaporation)

Areal potential evapotranspiration (generally lower than point potential; often much lower)

### Notes:

1. But remember, that was a key parameter in our simple model last time.

2. The Australian Bureau of Meteorology uses three different methods (it used to be four!) in two different places on its website, without either of those referencing the other and without obvious comparative explanation.  Actually “reference evapotranspiration” (FAO) and “point potential evapotranspiration” are definitionally about equivalent, although they’re estimated very differently.

[A second order effect in potential evapotranspiration estimation is the nature of the vegetation: is it tall or short, dense or sparse. The “FAO reference evapotranspiration” removes that variation by defining a standard, short, irrigated reference crop (it’s an agricultural thing). It then positions that within similar cropland, but the estimation method (Penman-Monteith) does not allow for the extra moisture added to the atmosphere by evaporation at the potential rate (it’s assumed the parameters are measured nearby, therefore already encompass that condition). As a result the outcome is definitionally point potential; see Chiew et al 2002, below.]

3. A watched pot never boils, but that’s just about getting the thing hot.  How long does it take to boil dry? For context, vertical sunshine is good for about 1 kW/m².  There’s about 2000 peak-equivalent sunshine hours a year in the subtropics, so that’s 2000 x 1 x 3600 s/hr  ≈  7,000,000 kJ/yr of energy.  At 2260 kJ/L that’s enough to vapourise around 3000 litres.  On one square metre that would be 3000 mm of evaporation, not far above the expected annual pan evaporation rate (which would be nearer 2000 mm — less because not all the solar radiation is absorbed and some heat is lost to radiation, conduction and convection).

4. The water vapour capacity of air is strongly temperature dependent.  If the temperature is allowed to rise continuously, evaporation can also continue.

5. According to the much-cited (but theoretically bereft) Bouchet hypothesis, areal potential = (point potential + actual evapotranspiration) / 2.  It follows that for an arid site with little actual evapotranspiration, areal potential should be about half point potential.  The estimation method used to produce the BOM maps (Morton’s method) is based on Bouchet, but with additional assumptions.

6. In fact the answer isn’t obvious. The size of wet area required to fully validate the areal assumption depends on the dryness of the surrounds and potentially on windspeed and boundary layer mixing conditions. In inland Australia it may be quite large; is your modelled area small or large relative to that? Even then there are problems … it’s a very simple model.

### References:

It’s surprising how much of the quality literature on this topic is Australian; I guess we have a special interest. For the derivation of the maps, see:

• Chiew, Francis, Q. J. Wang, Fiona McConachy, Ross James, William Wright, and Graham deHoedt. “Evapotranspiration maps for Australia” In Water Challenge: Balancing the Risks: Hydrology and Water Resources Symposium 2002, p. 167. Institution of Engineers, Australia, 2002.

And for an overview of the various evaporation estimation methods I recommend Tom McMahon et al’s recent treatise (a “technical paper” of nearly 200 pages, counting the supplement):