Mistakes that kill your estimates Measuring evapotranspiration (ET) to understand water loss from a native or a managed ecosystem is easier than it looks, but you have to know what you’re doing. If you can’t spend the time or money on a full eddy-covariance system, you’ll have to be satisfied with making some assumptions using equations such as Penman-Monteith. Like any model, the accuracy of the output depends on the quality of the inputs, but do you know what measurements are critical for success? Plus, as your instrumentation gets more inaccurate, the errors get larger. If you’re not careful, you can end up with no idea what’s happening to the water in your system. Get the right number every time You don’t have to be a meteorologist or need incredibly expensive equipment to measure ET effectively. In this 30-minute webinar, Campbell Scientific application scientist Dr. Dirk Baker and METER research scientist Dr. Colin Campbell team up to explain: - The fundamentals of energy balance modeling to get ET - Assumptions that can simplify sensor requirements - What you must measure to get adequate ET estimates - Assumptions and common pitfalls - How accurate your equipment should be for good estimates - Causes and implications of uncertainty

2. v
EVAPOTRANSPIRATION
WHY IT’S EASIER THAN YOU THINK
Colin Campbell, PhD Dirk Baker, PhD
METER Group, Inc. Campbell Scientific, Inc.

3. ECOSYSTEM WATER LOSS
Every day during the summer months,
well-watered, closed canopies can
lose 7-10 mm of water
Knowing exactly how much water a
canopy is losing is vital
• Replenish water with irrigation
• Explore phenotype water use
• Indicator of drought
• Surrogate of biomass production
• Growth models

4. WHY IS ET SO COMPLICATED?
Two ways to get water lost from system
1. Directly – e.g., eddy covariance
Problem: Cost/maintenance
2. Indirectly – residual of energy balance
Problem: Assumptions/accuracy

5. 𝐶𝐶𝑣𝑣 =
Vapor Pressure
Air Pressure
𝐸𝐸 = 𝑔𝑔𝑣𝑣(𝐶𝐶𝑣𝑣𝑣𝑣 − 𝐶𝐶𝑣𝑣𝑣𝑣)
ASSESSING CANOPY WATER LOSS
Why not try the simple approach?
• Evaporation from a plant canopy is easily
calculated with a flux equation
We simply need to know:
1. The ability for water vapor to leave the
canopy and go into the atmosphere
2. The temperature of the leaf surface
In practice, these are very difficult
things to figure out
• Need a better solution
𝑔𝑔𝑣𝑣 =
𝑔𝑔𝑣𝑣𝑠𝑠𝑔𝑔𝑣𝑣𝑎𝑎
𝑔𝑔𝑣𝑣𝑣𝑣 + 𝑔𝑔𝑣𝑣𝑣𝑣
gv - vapor conductance
s - inside leaves in canopy
gva - related to wind
speed
gvs - unknown canopy
conductance
Problems

6. EVAPORATION AND THE
CONTINUITY EQUATION
• Basic assumption in ET – everyone knows
how mass and energy flow are connected
• If we know all other forms of energy
movement, latent heat flux is the residual
Energy Balance: 𝑅𝑅𝑛𝑛 − 𝐻𝐻 − λ𝐸𝐸 − 𝐺𝐺 = 0
𝐸𝐸 =
𝑅𝑅𝑛𝑛 − 𝐻𝐻 − 𝐺𝐺
λ
𝑅𝑅𝑎𝑎𝑎𝑎𝑎𝑎 = 𝛼𝛼𝑠𝑠 𝐹𝐹𝑝𝑝𝑆𝑆𝑝𝑝 + 𝐹𝐹𝑑𝑑𝑆𝑆𝑑𝑑 + 𝐹𝐹𝑟𝑟𝑆𝑆𝑟𝑟
+ 𝛼𝛼𝐿𝐿(𝐹𝐹𝑎𝑎𝐿𝐿𝑎𝑎 + 𝐹𝐹𝑔𝑔𝐿𝐿𝑔𝑔)
𝐿𝐿𝑜𝑜𝑜𝑜 = 𝜀𝜀𝑠𝑠𝜎𝜎𝑇𝑇𝑎𝑎
4
𝑅𝑅𝑛𝑛 = 𝑅𝑅𝑎𝑎𝑎𝑎𝑎𝑎 − 𝐿𝐿𝑜𝑜𝑜𝑜

7. BACKGROUND
• Howard Penman understood the
link between the energy balance
and evaporation
• Critical steps forward in paper but
equation did not apply everywhere
because of empiricism “f” value

8. PENMAN-MONTEITH
John Monteith understood importance of heat and
vapor conductance
• New equation removed empiricisms allowed practical solution
for broad set of locations
• If we had good values for all the variables, this would work well
Problem – many things we must estimate
𝑔𝑔𝑣𝑣 =
𝑔𝑔𝑣𝑣𝑠𝑠𝑔𝑔𝑣𝑣𝑎𝑎
𝑔𝑔𝑣𝑣𝑣𝑣 + 𝑔𝑔𝑣𝑣𝑣𝑣
gva - related to wind speed
gvs - unknown canopy
conductance
λ𝐸𝐸 =
𝑠𝑠 𝑅𝑅𝑛𝑛 − 𝐺𝐺 + 𝛾𝛾∗λ𝑔𝑔𝑣𝑣𝐷𝐷/𝑃𝑃𝑃𝑃
s + 𝛾𝛾∗
𝛾𝛾∗ =
𝑔𝑔𝐻𝐻
𝑔𝑔𝑣𝑣
𝐶𝐶𝑝𝑝
λ

9. PRACTICAL ASPECTS OF
USING PENMAN-MONTEITH
POSITIVES
• Lower cost
• Easier to maintain
• Faster to deploy
Net radiation
Soil heat flux
Canopy conductance
NEGATIVES
• Lots of assumptions
leading to inaccuracy
• Requires ongoing
canopy assessments
• Only hourly or daily
assessment

10. KEY MEASUREMENT
• If we had a complete suite of
instruments, we would have no
problem
• But typical weather stations will
only have SOME of the critical
measurements
• We are forced to make assumption

11. 𝑔𝑔𝐻𝐻𝐻𝐻 = 𝑔𝑔𝑣𝑣𝑣𝑣 = 0.2𝑢𝑢
SIMPLIFICATION TO FAO 56
General idea
• Estimate reference ET from an idealized
canopy (grass 12 cm high, well watered)
• Multiply by a ‘crop coefficient’ to adjust it
for specific need
Why does this work?
• Using a specific surface like 12 cm grass,
canopy conductance can be estimated and
a solution to turbulent transport equation
simply based on wind speed
𝑔𝑔𝑣𝑣 =
0.6(0.2𝑢𝑢)
0.6 + 0.2𝑢𝑢
mol
m2s
𝛾𝛾∗ = 6.67 ∗ 10−4 1 +
𝑢𝑢
3
𝐶𝐶−1
𝑅𝑅𝑛𝑛 = 0.77𝑅𝑅𝑠𝑠 − 4.9 ∗ 10−9
(𝑇𝑇𝑎𝑎𝑎𝑎𝑒𝑒 ∗ (0.84 − 0.14 𝑒𝑒𝑎𝑎
2)) ∗ 𝑓𝑓(𝑐𝑐)
f(c) – cloudiness function

12. PENMAN-MONTEITH
EQUATION
Parameters
Δ = slope of the saturation vapor
pressure curve
Rn = net radiation
G = soil heat flux density
γ = psychrometric constant
Cn = numerator constant
T = temperature
u2 = wind speed
es = saturation vapor pressure
ea = vapor pressure
Cd = denominator constant
𝐸𝐸𝑇𝑇𝑠𝑠𝑠𝑠 =
0.408Δ 𝑅𝑅𝑛𝑛 − 𝐺𝐺 + 𝛾𝛾
𝐶𝐶𝑛𝑛
𝑇𝑇 + 273
𝑢𝑢2 𝑒𝑒𝑠𝑠 − 𝑒𝑒𝑎𝑎
Δ + 𝛾𝛾 1 + 𝐶𝐶𝑑𝑑 + 𝑢𝑢2

13. FORMULATIONS
Two Common Formulations
• FAO 56
• ASCE Standardized Reference
METER
• FAO 56, daily calculation (ZENTRA Cloud)
Campbell Scientific
• ASCE, hourly calculation (data logger instruction)
Daily vs hourly
• Most of the time the same
• Significant variation in one or more of the measurements
FAO 56: http://www.fao.org/tempref/SD/Reserved/Agromet/PET/FAO_Irrigation_Drainage_Paper_56.pdf
ASCE: https://www.uidaho.edu/cals/kimberly-research-and-extension-center/research/water-resources/standardization

14. PENMAN-MONTEITH
EQUATION
Parameters
Δ = slope of the saturation vapor
pressure curve
Rn = net radiation
G = soil heat flux density
γ = psychrometric constant
Cn = numerator constant
T = temperature
u2 = wind speed
es = saturation vapor pressure
ea = vapor pressure
Cd = denominator constant
Measured inputs
• Incoming solar radiation
• Temperature
• Relative humidity
• Wind speed
𝐸𝐸𝑇𝑇𝑠𝑠𝑠𝑠 =
0.408Δ 𝑅𝑅𝑛𝑛 − 𝐺𝐺 + 𝛾𝛾
𝐶𝐶𝑛𝑛
𝑇𝑇 + 273
𝑢𝑢2 𝑒𝑒𝑠𝑠 − 𝑒𝑒𝑎𝑎
Δ + 𝛾𝛾 1 + 𝐶𝐶𝑑𝑑 + 𝑢𝑢2

15. P-M EQUATION
ET SENSITIVITY TO ERRORS IN INPUTS
• If wind decreases or relative
humidity increases, radiation
has larger influence
• If radiation decreases, wind
has larger influence
Rs = 900 W/m2
TA = 25 C
RH = 35%
u = 2 m/s

16. P-M EQUATION
ET SENSITIVITY TO ERRORS IN INPUTS
Rs = 900 W/m2
Rn = 500 W/m2

17. COMBINED SENSOR
UNCERTAINTY
• Seven-day period total ETo
• Site in Utah, USA
• Columns – from
measurements
• Error bars – combined
sensor uncertainty with
differing, hypothetical
sensor suites representing
high, medium and low
measurement uncertainty

18. SIMPLIFICATIONS &
IMPROVEMENTS
• P-M alternatives with fewer
measurements
• Not recommended
• Use 4-component net radiometer
• Full eddy-covariance suite

19. SITING, INSTALLATION, AND
MAINTENANCE
• Wind speed – height
• Temperature – radiation shielding
• Solar – cleaning & level
• Calibration
• Influence vs height
• Upwind conditions differing strongly from those of interest

20. SUMMARY
• Rn is the most important parameter, though largely modeled
• Simplest improvement is to measure Rn
• Siting, installation, and maintenance more important than
sensor uncertainty
• Crop coefficients – not talked about here, but can be challenging
and error-prone

21. v
QUESTIONS?