Understanding evaporation #2: evapotranspiration

One of a series; also see editions: #1, #3, #4

Evapotranspiration is one of those ugly made-up words, intended to convey the combination of transpiration from plants and evaporation from the ground under and around them.  It’s the relevant meteorological and hydrological parameter at the catchment and landscape scale¹ — the average flux of moisture from the substrate to the atmosphere by all routes; really just another version of evaporation.

Stomata on tomato leaf

Stoma on a tomato leaf

Transpiration, of course, is the evaporation of moisture from plants via their physiology.  Plants function by photosynthesis, which is about reducing² carbon dioxide to useful organic carbon with solar energy.  They get the primary input — carbon dioxide — from the atmosphere through microscopic pores in their leaves called stomata (plural).  Most have some level of physical control over their stomata; they can open and close them.  When the pores are open the plant is able to take up CO₂ (and expire O₂), but it cannot help also losing moisture out through the same hole.  That is transpiration, an unavoidable part of terrestrial plant biology³ (just as water loss is an unavoidable part of your biology when you exhale air moistened by your lungs).

So this is already complicated even for a single plant, but there are thousands of different plants with a vast array of strategies to balance the needs of their physiology with the need to retain water.  By the time we get to that catchment or landscape scale, there’s whole ecosystems of plants interacting and competing: annual and perennial, shallow and deep rooted, soft leaved and sclerophyll, evergreen and deciduous³.  And what of that “evaporation from the ground” bit?  That must depend on how moist the surface is (what did the plant roots take?), and on how much sun and wind penetrates (what shelter from the plants?).  Doesn’t look easy…


A simple model

Fortunately this is one of those rare cases where a gross simplification of a complicated system is able to capture much of the important behavior, at least at larger scales¹.  Demonstrably so, because given rainfall, storage and an upper bound for evaporation, it is able to reproduce the other term in that hydrological equationrunoff — with skill.

To begin to build a simple model we first need to notice that what makes plants grow is not rainfall, it’s soil moisture⁵. Soil moisture rises when it rains and falls when it doesn’t, in a complex dynamic balance between the forces of meteorology, plant physiology and soil physics. In most soils most of the time, that moisture is held in place between the grains by capillary suction.  That applies across a big range of soil depths depending on the environment: less than a metre in hard country to ten or more metres on deep cracking clay soils⁶. But when it rains long and hard our soil is going to get very wet, to the point colloquially referred to as “saturated”⁷.

Gross simplification #1:  Ignore the soil itself and lump all the active soil moisture together in one big bucket holding just the water, into which rain falls and from which evapotranspiration sucks⁸.  Our bucket will have a maximum capacity representing the “saturated” soil condition, which will vary greatly depending on the soil depth and water holding capacity.

When it stops raining, the wet ground will begin evaporating and the plants will suck soil moisture and transpire.  Evapotranspiration will be high — at an upper bound rate governed mainly by the meteorological conditions, called the potential rate. As the soil dries evapotranspiration will slow, but in a highly non-linear way. Eventually as the soil dries further, a point will be reached where the plants can no longer suck water from it. That has a name in agronomy: the wilt point⁹.

Gross simplification #2:  Assume that evapotranspiration continues at the potential rate until the wilt point, when it stops. That’s right, treat it as so non-linear that it’s actually a square function: at the maximum until it’s not, then zero.  The plants transpire flat-out while ever they can and then stop when they can’t.  (Not such a dumb strategy really, when you’re competing with all those other guys.)

The wilt point is not “zero soil moisture”; it’s “plant can’t suck any more moisture out”. For simplicity we’ll call that point empty on our bucket, so the bucket volume represents the difference between the wilt point and effective saturation — what agronomists call the available water capacity.



Nearly there.  Lets say our soil moisture “bucket” is 150 mm deep (remember that’s just the water; actually 150 mm would not be a bad pick for available water capacity on Australian rangelands).  Lets also assume our bucket starts empty, after evapotranspiration has proceeded to the wilt point.  Now if it rains 100 mm — no matter how hard — assume all that happens is there’s now 100 mm in our bucket and evapotranspiration restarts.  If instead it rained 200 mm, our “bucket” will fill and then overflow — by 50 mm.  That’s runoff, or at least an “excess” which we can split between recharge to shallow groundwater and runoff on the surface; a split hydrologists call the baseflow index.



A finished model

We just described one of the most popular rainfall-runoff yield models in Australia, a really simple thing called the Australian Water Balance Model.  It happens to have three buckets instead of one — representing (usually fixed) proportions of the catchment with (usually fixed) ratios of depths — and it adds simple exponential decay storages for groundwater discharge lag (“baseflow”) and surface runoff lag … but we have the gist of it.





This simple model offers an accessible way to conceptualise the business of “evaporation from land”, how that should vary, how it might change and what that all means for a thing called drought.  More next time.


Next: edition #3



1.  “Catchment scale” means just that: an area as large as the catchment of some creek, smaller river or lake.  “Landscape scale” means something larger: an area extending to the horizon and beyond, covering the whole landscape.

2.  “Reducing” in the chemical sense — the process of energetically removing oxygen from an oxide; the opposite of oxidation.

3.  That’s right, a very large proportion of all that sucking up of moisture that plants do is just to make up the unavoidable loss associated with obtaining carbon dioxide. Plants transpire from other surfaces too, but stomata generally dominate.

4.  Leaf fall is not just for winter.  Many plants shed leaves as a drought survival strategy.  In the monsoonal tropics (including northern Australia), lots do that by default every dry season.

5.  Actually that would be sunlight and carbon dioxide as we’ve noted, but you can’t have the second of those without losing moisture to the atmosphere, so you need water from the soil … plus the “trace” elements that come with it (despite the name, even the “macro” plant nutrients — N, P and K — are usually only present in trace quantities).

6.  What we’re interested in is the depth of material accessible to plant roots, regardless of whether an agronomist would actually call all of that “soil”.  A small subset of plants (“phreatophytes”) have roots extending all the way to the perennial groundwater table. Our simple model doesn’t allow for that.

7.  Most soils away from swamps and swales are never completely saturated; there is always some air present in the pores.  Agronomy recognises a difference between “effective saturation” and a thing called field capacity, which is the maximum water content after excess water has had time to drain down.  In the real world away from deep permeable agricultural soils the difference is moot; it’s not included in out simplification.

8.  Note that our bucket has no holes in the bottom to model “deep infiltration”, which is instead handled by partitioning bucket overflow when it occurs. That is consistent with the idea that most soil moisture is held there by capillary suctions. It cannot drain out until a gross oversupply of water (“effective saturation”) overcomes the capillary effect.  (Real soils have suction effects at multiple scales: from the range of particle sizes present and from the various elements of soil structure.)

9.  The wilt point is of course vastly different for different plants, and there are different degrees and forms of “wilt”.  Many Australian plants do no visibly wilt, though they most certainly shut down transpiration under moisture stress — by closing stomata, by minimising their sun-facing leaf area, and eventually by shedding leaf area through brown-off (e.g. grasses) and leaf drop.



No one text really covers this huge scope: meteorology, plant biology, agronomy, hydrology, soil physics. For an accesible overview, I suggest:

And for the hydrological model, try: