1. ERS 482/682 Small Watershed Hydrology
Evapotranspiration
ERS 482/682
Small Watershed Hydrology
ERS 482/682 (Fall 2002)

2. water becoming water vapor consumptive use by plants
Definition
Total evaporation from all water, soil, snow, ice, vegetation, and other surfaces plus transpiration
water becoming water vapor
consumptive use by plants
ERS 482/682 (Fall 2002)

3. Processes Evaporation of precipitation intercepted by plant surfaces
Evaporation of moisture from plants through transpiration
Evaporation of moisture from soil (ground) surface
ERS 482/682 (Fall 2002)

4. How significant is evapotranspiration?
Can be as much as 90% of precipitation
Affected by changes in
Vegetation
Weather
  ET
  streamflow 
air temperature  ET
  streamflow 
ERS 482/682 (Fall 2002)

5. Evaporation Fick’s Law:
A diffusing substance moves from where its concentration is larger to where its concentration is smaller at a rate that is proportional to the spatial gradient of concentration
Figure 8.2 (Chapra 1997)
ERS 482/682 (Fall 2002)

6. Evaporation
Fick’s Law:
A diffusing substance moves from where its concentration is larger to where its concentration is smaller at a rate that is proportional to the spatial gradient of concentration
gradient (change) in concentration
indicates movement from regions of higher concentration to regions of lower concentration
will have units of substance *[L T-1]
where
Fz(X) = rate of transfer of substance X in z direction
DX = diffusivity of substance X
C(X) = concentration of X
[L2 T-1]
 units depend on substance
ERS 482/682 (Fall 2002)

7. Evaporation where E = evaporation rate
Fick’s Law:
A diffusing substance moves from where its concentration is larger to where its concentration is smaller at a rate that is proportional to the spatial gradient of concentration
where
E = evaporation rate
KE = efficiency of vertical transport of water vapor
va = wind speed
es = vapor pressure of evaporating surface
ea = vapor pressure of overlying air
[L T-1]
[L T-1 M-1]
[L T-1]
[M L-1 T-2]
[M L-1 T-2]
ERS 482/682 (Fall 2002)

8. water temperature at surface
Vapor pressure, e
Partial pressure of water vapor
saturation vapor pressure, e*: maximum vapor pressure
relative humidity
ea = Waea*
water vapor
water
es = es*
water temperature at surface
ERS 482/682 (Fall 2002)

9. Latent heat exchange, LE
Occurs whenever there is a vapor pressure difference between water and air
[E L-2 T-1]
where
w = water density
v = latent heat of vaporization
1000 kg m-3
surface water temperature (°C)
[MJ kg-1]
ERS 482/682 (Fall 2002)

10. Sensible heat exchange, H
Occurs whenever there is a temperature difference between water and air
where
B = Bowen ratio
Depends on air pressure
 constant at a particular site
ERS 482/682 (Fall 2002)

11. All expressed in units of [E L-2 T-1] except Q [E L-2]
Energy balance
Equation 7-15
where
Q = change in heat storage per unit area over time t
K = shortwave (solar) radiation input
L = longwave radiation
H = turbulent exchange of sensible heat with atmosphere
LE = turbulent exchange of latent heat with atmosphere
Aw = heat input due to water inflows and outflows
G = conductive exchange of sensible heat with ground
All expressed in units of [E L-2 T-1] except Q [E L-2]
ERS 482/682 (Fall 2002)

12. Classification of ET processes
Surface type:
Open water
Bare soil
Leaf/canopy type
Crop type
Land region
Water availability
Unlimited vs. limited
Stored energy use, Q
Water-advected energy, Aw
often assumed negligible
ERS 482/682 (Fall 2002)

13. Free-water evaporation
“Potential evaporation”
Evaporation that would occur from an open-water surface in the absence of advection and changes in heat storage
Depends only on climate/meteorology
Evaporation: net loss of water from a surface resulting from a change in the state of water from liquid to vapor and the net transfer of this vapor to the atmosphere
ERS 482/682 (Fall 2002)

14. Free-water evaporation
“Potential evaporation”
Penman equation
Standard hydrological method
recall:
ERS 482/682 (Fall 2002)

15. Free-water evaporation
“Potential evaporation”
Penman equation
Standard hydrological method
psychrometric constant
ERS 482/682 (Fall 2002)

16. Free-water evaporation
“Potential evaporation”
Penman equation
Standard hydrological method
dimensionless
Table 4-6 Dunne & Leopold (1978)
ERS 482/682 (Fall 2002)

17. Free-water evaporation
“Potential evaporation”
Pan-evaporation
Direct measurement method
where
W = precipitation during time t
V1 = storage at beginning of period t
V2 = storage at end of period t
12 in.
Class-A evaporation pan
Diameter = 1.22 m
Height = .254 m
ERS 482/682 (Fall 2002)

18. Free-water evaporation
“Potential evaporation”
Pan-evaporation
Direct measurement method
0.7 average for US
Efw = (PC)Epan
See Morel-Seytoux (1990) for pan coefficients
No adjustments necessary for annual values
ERS 482/682 (Fall 2002)

19. Bare-soil evaporation
Stages
Atmosphere-controlled stage (wet soil surface)
Evaporation rate  free-water evaporation rate
Soil-controlled stage (dry soil surface)
Evaporation rate << free-water evaporation rate
ERS 482/682 (Fall 2002)

20. Transpiration
Transpiration: evaporation of water from the vascular system of plants into the atmosphere
Figure 6.1 (Manning 1987)
ERS 482/682 (Fall 2002)

21. Transpiration Dry soils Saline soils
Figure 6.2 (Manning 1987)
Dry soils
soil capillary pressure > osmotic pressure
Saline soils
water concentrationsoil < water concentrationplant
ERS 482/682 (Fall 2002)

22. Transpiration Leaf/canopy conductance Depends on Cleaf
Number of stomata/unit area
Size of stomatal openings
Density of vegetation
Cleaf
LAI: fraction of area covered with leaves
shelter factor
Penman-Monteith model (Equation 7-56)
ERS 482/682 (Fall 2002)

23. Transpiration
Figure 3.4 (Brooks et al. 1991)
ERS 482/682 (Fall 2002)

24. Potential evapotranspiration (PET)
Rate at which evapotranspiration would occur from a large area completely and uniformly covered with growing vegetation with unlimited access to soil water and without advection or heat-storage effects
ERS 482/682 (Fall 2002)

25. Potential evapotranspiration (PET)
Thornthwaite method
where
Et = potential evapotranspiration
Ta = mean monthly air temperature
I = annual heat index
a = I – I I3
[cm mo-1]
[°C]
ERS 482/682 (Fall 2002)

26. Potential evapotranspiration (PET)
Thornthwaite method
Figures 5-4 and 5-5 (Dunne & Leopold 1978)
Index must be adjusted for # days/mo and length of day
ERS 482/682 (Fall 2002)

27. Potential evapotranspiration (PET)
Blaney-Criddle formula
where
Et = potential evapotranspiration
Ta = average air temperature
k = empirical crop factor
d = monthly fraction of annual hours of daylight
[cm mo-1]
[°C]
ERS 482/682 (Fall 2002)

28. Potential evapotranspiration (PET)
Notes
Wind speed has little or no effect
Local transport of heat can be significant
Taller and widely spaced vegetation tend to have greater heat transfer
ERS 482/682 (Fall 2002)

29. Measuring evapotranspiration
Cannot be measured directly
Transpiration
Lysimeters
Figure 6.3 (Manning 1987)
ERS 482/682 (Fall 2002)

30. Measuring evapotranspiration
Cannot be measured directly
Transpiration
Lysimeters
Tent method
Evaporation
Evaporation pans
Water budget:
ET + G = P – Q
Paired watershed studies
Figure 3.5 (Brooks et al. 1991)
ERS 482/682 (Fall 2002)