1
Evapotranspiration (ET) Lab
February 2, 2015
Estimation of ET from Multiple Methods
Overview
This lab has two objectives:
1) Compares estimates of forest evapotranspiration from several methods.
2) Estimate the effect of forest practices (harvesting, planting density) on a stand level
water budget.
Introduction
Rainfall is partitioned onto several pathways after falling. First, it may be intercepted by
the “architecture” of whatever ecosystem it falls on. That may be the leaves, stems and
branches of a forest, or the roads and buildings of urban areas. This interception can be
between 10 and 50% of the water budget, depending of factors like the amount and intensity of
rainfall, and the type and characteristics of the vegetation. This water is generally evaporated
back to the atmosphere, but may also be stored or used. Second, rainfall may fall through the
canopy, either directly (throughfall) or via stems (stemflow). This water can either enter the
soil where it can be taken up by roots and transpired or runoff over the land surface. The
character of this partition is dependent, as before, on the amount and intensity of the rainfall,
on the infiltration capacity of the soil (which can be dramatically modified by heavy machinery
and other land cover changes) and by the amount of rainfall that has occurred prior to the
present (so-called antecedent rainfall). Any water that makes it into the soil starts to fill the
pore spaces and, if possible, percolate downwards. As water passes through the soil, plants can
use it (transpiration) or it can be returned to the atmosphere abiotically (evaporation).
The sum of the interception that is evaporated, the evaporation of throughfall, and the
transpiration of soil water is evapotranspiration, and it is generally the biggest water loss
component, often by far. The word evapotranspiration implies that it is a coupled process that
combines both biotic and abiotic mechanisms. While there are techniques to disentangle the
components, it is generally modeled as one quantity, though one that is sensitive to the
vegetation at the site where it’s estimated.
Among the most important insight about the ET process is that it requires a LOT of
energy. Remember the latent heat of vaporization? That’s the energy required to convert
liquid water at 100 deg C to vapor water at the same temperature. It takes 2.45 MJ (million
Joules, where the Joule is the SI unit of energy) to do that for 1 kg of water. For comparison,
the energy in a gallon of gasoline is about 120 MJ; that is 1 gallon of gas can evaporate only
roughly 13 gallons of water. This value (the latent heat of vaporization) is a function of
temperature, but we’ll treat it as a constant here (2.45 MJ/kg).
2
It’s also critical to remember that air has a capacity to hold water that is a function of
temperature of that air. Specifically, the es (saturation vapor pressure, measured in kPa, a
measure of pressure) is predicted by the following equation:
e s  0.6108 * exp(
17.27 * T
)
237.3  T
[1]
Where T is temperature in degrees C, and es is in units of kPa. The vapor deficit is
important, so is the slope of the saturation vapor pressure line –we use both. We compute the
slope based on the following equation:

4098 * es
(237.3  T ) 2
[2]
Where es is from the equation above, T is temperature (in Celsius) and Δ is the slope in
units of kPa per deg C. We’ll compute both equations in class to determine their values as a
function of temperature ourselves. It’s worth pointing out that the energy of radiation in (from
the sun) is lost in two main ways: latent heat export (i.e., in the energy required for the phase
conversion from liquid to vapor form) and sensible heat flow (i.e., the energy associated with a
change in air temperature). The ratio of those two pathways (latent vs. sensible heat fluxes) is
an important component of an ecosystems energy budget; it is called the Bowen Ratio.
A final item that is necessary to compute is the psychrometric constant (γ), which has a
value of 0.0667 kPa °C-1.
The other aspect of the lab is to understand the effects of stand management on ET.
Two papers are provided that describe ET processes in production stands as a function of stand
age, and in naturally regenerated stands. Differences between these imply that production
forestry may use a lot of water; that is, even though forests aren’t irrigated in North Florida,
their water use exceeds what a conserved forest would use, sometimes by a lot. Your task will
be to use those two papers to understand the magnitude of that difference, as well as better
understand the ET process.
TASK 1
ET is estimated using methods that rely on temperature alone, those that rely on radiation, and
those that consider a combination of factors (e.g., temperature, relative humidity, radiation).
We also have methods that measure the process directly, without relying on atmospheric proxy
variables. They vary in complexity, and in accuracy. Our task is to compare them.
Compute ET using three methods:
3
a) McCloud method (1955)
b) Hargreaves method (1985)
c) Penman method (1963)
McCloud Method
This is among the simplest methods for estimating ET, and is based on temperature alone. The
equation is:
ETp  K *W (T 32)
[3]
Where ETp is potential evapotranspiration (that is, what would occur if water were not limiting,
as is designed to be the case in irrigated agriculture, for which this equation was developed) in
mm per day, K is a conversion parameter (K = 0.254), W is a parameter that describes the
sensitivity of ET to temperature (W = 1.07) and T is the mean daily temperature in degrees F.
1) Compute ET using McCloud for both 2001 and 2008 data provided. Plot both vs. Julian
day (where Jan 1 = 1, Jan 2 = 2,…, Dec 31 = 365).
Hargreaves Method
The Hargreaves method is an empirical model that was developed for forage systems in
California. However, its simplicity and use of readily available data make it desirable to employ
elsewhere. It depends on solar radiation and mean air temperature data only.
ETp  0.0135 *
Rs

* (T  17.8)
[4]
Where Rs is the solar radiation reaching the Earth’s surface (measured in MJ/m2/d), λ is the
latent heat of vaporization (a constant equal to 2.45 MJ/kg) and T is mean daily temperature
(this time in degrees C). ET is computed in mm/day.
2) Compute ET using Hargreaves for both 2001 and 2008 data provided. Be careful of units!
Plot both vs. Julian day (where Jan 1 = 1, Jan 2 = 2,…, Dec 31 = 365).
Penman Method
The Penman method is the gold-standard for evapotranspiration, incorporating considerations
of the radiation at a site, and the effects of air movement. It is pretty complicated, but breaks
down into two parts, both which depend on computations made above.
ETp 


900
( Rn  G ) 
*
*U * D

   T  275
[5]
4
Where ET is the evaporation in mm/day, λ is the latent heat of vaporization (2.45 MJ/kg), Δ is
the gradient of the saturation deficit (computed in Eq. 2), γ is the psychrometric (assumed
constant at 0.0667 kPa °C-1), Rn is the net radiation in MJ/m2/d, G is the soil heat flux (which we
will neglect here), T is the temperature in °C, U is the average windspeed at 2m aloft in m/s,
and D is the saturation vapor deficit (es – ed). The saturation pressure (es in units of kPa,
computed in Eq. 1) is a direct function of temperature. The actual vapor pressure (e d, also in
units of kPa) is the saturation pressure multiplied by the relative humidity (RH, in units of %).
That is, ed = RH * es. All the data necessary to compute this has been provided. Don’t forget to
divide the right hand side of the equation by 2.45 MJ/kg at the end to get ET in mm/day.
3) Compute ET using Penman for both 2001 and 2008 data provided. Be careful of units!
Plot both vs. Julian day (where Jan 1 = 1, Jan 2 = 2,…, Dec 31 = 365).
4) How viable is the assumption that there is no soil storage of energy (that is, that G is
zero)? This can be evaluated qualitatively by looking at the changes in soil temperature
over time. Plot soil temp vs. time. If the curve is not a straight line then soil temperature
varies systematically with season.
5) Plot measured ET vs. estimated ET for each of the methods (McCloud, Hargreaves,
Penman) for 2001 and 2008; there will be 3 graphs. Fit a line to the data that is forced
through the origin (0,0), and report the slope and r2. Which model appears to
overestimate measured ET? Underestimate? Which relationship is the most noisy?
6) Plot a curve of cumulative measured ET and measured rainfall vs. time for both 2001 and
2008. What is implied by the location of the two lines? During 2001, how much of the
year was in cumulative rainfall surplus? What about 2008? Based on these two graphs,
what period of year would you predict forests to be MOST water stressed?
5
TASK 2
Three papers are attached (Gholz and Clark 2002, Powell et al. 2005, McLaughlin et al. 2013).
The first two describe two sets of measurements of evapotranspiration, while the third is a
synthesis of stand-level water use in the southeast, focusing on the impacts of forest
management on water yield. The first paper looks across a chronosequence of forest stands
from recently clear cut to rotation aged. The second measures ET from a low-density naturallyregenerated mixed pine forest in Austin Cary Memorial Forest. While the data are for a dry
period (1998 and 1999 for the first paper, 2000 through 2002 for the second) they still several
key insights in the paper about the effects of stand density management on water use. Your
task is to read all three papers and answer the following questions:
From the Gholz and Clark (2002) paper:
1) How does the Bowen Ratio change with stand age (Table 5)? What does this mean for
the temperatures in the vicinity of a clear cut vs. a mature stand?
2) What do the data in Table 7 imply about the effects of stand development on ET and
interception? What does it mean when they report a value of ET + I (evapotranspiration
+ interception) greater than precipitation?
3) Assuming ET stabilizes when leaf area has maxed out (around mid-rotation thinning),
what fraction of the rainfall is used? Compare the daily ET values in winter and summer
(from Table 6) with values in Powell et al. (2005) paper (Table 4) for a conserved forest.
4) [BONUS] Can you think of any other way to measure the hydrologic effects of stand
management (particularly clear cut harvest) other than measuring ET directly?
From the Powell et al. (2005) paper:
5) Compare the attributes between the rotation aged stand in Gholz and Clark (2002) and
the naturally regenerated stand in Powell et al. (2005). What are the major differences?
6) The paper suggests naturally regenerating stands use what fraction of annual rainfall?
What factors (beyond the authors control) might dramatically affect that percentage?
7) What is implied by Figure 5?
8) From Table 4, compute the annual ET difference between a mature production stand and
a naturally regenerated low density flatwoods (assume 180 days of summer, 180 days of
winter). What is the magnitude of additional ET (in mm/yr) expected from a watershed
converted from low-density to production pine? Where is that water coming from?
From the McLaughlin et al. (2013) paper
9) What is water yield? Why would small changes in ET from a forest stand potentially
dramatically affect water yield?
10) What is the most important stand attribute for predicting ET? How do you measure that
attribute?
11) What are the simulated effects of fire and clear-cuts? Why is the comparison of an
intensive silviculture site in 20-25 year rotations with a conserved forest not fair?
12) [BONUS] Assuming you use 150 gal/d of water, how many acres of dense pine stand
would need to be thinned to a basal area of 14 m2/ha to meet your water consumption?