1. Potential Evapotranspiration (PET)
ATM 301 Lecture #13 (sections )
Potential and Actual Evapotranspiraton
Potential Evapotranspiration (PET)
Reference-crop Evapotranspiration (RET or ETo)
Actual Evapotranspiration (ET)

2. The Concept of Potential Evapotranspiration
Potential Evapotranspiration (PET) is a hypothetic rate at which evapotranspiration
would occur if water supply is unlimited.
Thornthwaite (1948) introduced PET as a measure of atmospheric demand for
moisture under a given weather or climate condition.
However, vegetation and other surface conditions (e.g., snow cover) can also affect
ET under a given atmospheric condition. (Why?)
Well-watered
surface
PET
Type of land cover
not defined

3. Reference-crop Evapotranspiration (ETo)
Penman (1956) introduced the reference-crop evapotranspiration (RET or ETo) to replace PET
ETo is the evapotranspiration rate over a well-watered crop land completely covered by a short
green, grass-like crop
ETo is also a hypothetic ET as the reference crop is a hypothetic surface.
Since the land surface is fixed, ETo depends only on atmospheric conditions
Another issue with the PET or ETo: the atmospheric conditions are often measured under the
smaller actual ET. The atmospheric conditions could be different if PET were occurring.
Nevertheless, PET or Eto has been widely used as a measure of the “drying power” of
a climate.

4. Annual Potential Evapotranspiration
(mm/yr Source: UNEP)

5. Annual P/PET Ratio – Aridity Index
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6. P/PET ratio has been used as an Aridity Index defining Earth’s drylands

7. P- PET for 2012 summer drought

8. Practical Definitions of PET
In practice, PET or ETo is defined by the method used to calculate it
The common methods include:
Temperature-based: uses only air temperature and day length
Radiation-based: uses net radiation and air temperature
Combination method: based on the Penman equation, uses net radiation,
air temperature, wind speed, and relative humidity
Pan evaporation: uses pan evaporation, often with modifications depending
on wind speed, temperature and humidity
See p. 294 of Dingman (2015) for more details.

9. Calculation of Reference-crop ET (ETo)
The Food and Agriculture Organization (FAO) of the UN defines the ETo as
the Penman-Monteith PET from an idealized grass crop with mean vegetation height
Zveg=0.12m, albedo a=0.23, and canopy conductance Ccan = m/s (see p.296):
where
e*(T2m) in kPa is the saturation vapor pressure with 2m air temperature T(2m) (in degC)
e* = e(17.3 T/( T))
e(2m) in kPa is the vapor pressure at 2m height
u(2m) in m/s is the 2m wind speed
K and L in MJ/(m2 day) are the surface net shortwave and longwave radiative fluxes
G in MJ/(m2 day) is the heat flux into the ground
p = air pressure in kPa

10. Example Calculation of ETo
Measurement data: T=27.2oC, u(2m)=3 m/s, RH = 80%, net solar radiation=200W/m2
net longwave radiation=95 W/m2 upward
ground heat flux=5W/m2 downward, air pressure=100kPa
Step 1: compute e*(T2m) = e(17.3 T/( T)) = e(17.3x27.2/( ))=3.62kPa
Step 2: compute the vapor pressure difference e*-e = e*x(1-RH)= 3.62x(1-0.8)=0.724 kPa
Step 3: compute net energy flux (K+L-G)= W/m2= 100W/m2 =1.00x10-4 MJ s-1m-2
=1.0x10-4x MJ s-1m-2 x(24x3600sec/day) =8.64MJ/(m2 day)
Step 4: compute
Step 5: compute
Step 6: compute
Step 7: compare ETo with radiative fluxes:
LH = w v ETo =1000kg/m3 x 2.437xMJ/kg x m/day = 8.38 MJ/day

11. Comparison of PET Estimates
Penman-Monteith Eq.
Pan Evaporation
Priestley-Taylor Eq.

12. Observed ET (E) vs. P-M Eq. Estimated ET (Eo)

13. Estimates of Actual Evapotranspiration (ET)
There are many ways to estimate the actual ET (see sec. 6.8)
1. PET-based approaches: use PET to estimate actual ET
1.1 Based on the P/PET ratio:
In hot arid regions, PET greatly exceeds precipitation  ET is water limited and ET  P
as runoff R  0
In regions with abundant precipitation in all seasons (e.g., New York), ET is limited by
available energy  ET  PET
This relation is modeled via a “Budyko-type” equation:
P/PET is an aridity index: P/PET > 1  ET is energy-limited; P/PET <1  ET is water-
limited
w (2) is a parameter which increases with watershed storage.
This equation is useful only for long-term mean ET, not suitable for short-term ET.
M. I. Budyko
Russian climatologist

14. Comparison of the P/PET-based estimates (y-axis, with w=2) vs.
water-balance-based estimates (x-axis) of annual ET over N.A.

15. Estimates of Actual Evapotranspiration (ET)
1.2 Use of soil-moisture functions:
A widely used approach for estimating ET:
where * is the effective saturation:
r is the permanent residual water content (0.05), and  is the soil porosity

16. Estimates of Actual Evapotranspiration (ET)
1.2 Use of soil-moisture functions:
Using the f() function for canopy conductance in the P-M eq., we have
Recall the P-M Eq.:
Root-zone soil moisture

17. Estimates of Actual Evapotranspiration (ET)
2. Water-balance approaches: use the regional water balance eq. to estimate ET
2.1 Land-area water balance:
ET = P + GWin – Q – GWout – S
For long-term mean, ET  P – Q
See pp for other water-balance approaches.

18. Estimates of Actual Evapotranspiration (ET)
3. Turbulent-Exchange and Energy-Balance Approaches:
3.1 Use of the Penman-Monteith Eq.: most widely used approach
Step 1: Apply it to the vegetated areas to estimate daytime transpiration
Step 2: Apply it to the un-vegetated (bare soil) area to estimate daytime and
nighttime soil evaporation
Step 3: sum up them to get the daily total ET.
3.2 Bowen-ratio Approach:
Need measurements of K, L, G, T, e and p S L SH E G Aw

19. Actual Evaporation or ET Distribution

20. Evaporation (E) vs. Precipitation (P)

21. Summary of Evapotranspiration (ET)
Evaporation process over free-water surface
Evaporation process over bare soil
Transpiration process for plants and canopy
Methods for estimating E over free-water surface
Methods for estimating E over bare soil
Methods for estimating transpiration from plants
Potential evapotranspiration and reference-crop ET
Actual ET
Key concepts: Surface energy balance, surface water balance, PET,
atmospheric conductance, leaf conductance, canopy conductance