1. What Happens to Precipitation?
Hydrologic cycle
P = RO + ET + S,
Where,
P ≡ precipitation
RO ≡ runoff
ET ≡ evapotranspiration
S ≡ storage

2. Focus on Evapotranspiration
Evaporation from
Water surface
Bare soil
Transpiration
Evaporation from vegetative surfaces
Primarily through stomata
It occurs chiefly while the stomata are open for the passage of CO2 and O2 during photosynthesis.

3. Vaporization Process for
Water Surface
Bare Soil
Vegetative Surfaces
The “Heat of vaporization” is the heat required to vaporize one mass unit (one gram) of a substance at its normal boiling point. The vaporization heat of water is 540 calories per gram.

4. Evaporation from Water Surface
Evaporation – net loss of water molecules
Condensation – net gain of water molecules
Saturation – equilibrium between evaporation and condensation

5. Evaporation Rate Water vapor is a gas.
Therefore it exerts pressure in the air.
e = vapor pressure of atmosphere in mbar (millibars of mercury)
es = vapor pressure of saturated atmosphere
(es – e) = saturation vapor deficit

6. Vapor Pressure of Water
Torr – unit of pressure force per unit area, millimeters of mercury

7. Convert water vapor pressure to water vapor density for use in evaporation formula
ρ (g/m3) = 217e/T
T = degrees Kelvin

8. Evaporation Rate V (g/cm2/sec) = - (ρs- ρa)(Dv)/dv
ρs= water vapor density at surface of water
ρa = water vapor density of air
(ρs – ρa) = vapor density gradient in g/cm3
Dv = diffusion coefficient of water vapor in the air in cm2/sec
dv = thickness of wind speed dependent boundary layer in cm

9. Evaporation from Bare Soil
Stage I – wet soil surface, similar to evaporation from water surface
Stage II – evaporation rate falls below potential rate and is determined primarily by hydraulic conductivity
Stage III – liquid flux of water ceases, rate determined by vapor flux governed by soil vapor diffusivity

10. Definitions
Hydraulic conductivity or coefficient of permeability – movement of water within soil from areas of higher moisture content to lower moisture content
Flux - the rate of transfer of fluid, particles, or energy across a given surface

11. Definitions
Diffusion - the flow of energy or matter from a higher concentration to a lower concentration

12. Bare Soil E = cumulative evaporation in cm _ = 2(Θi – Θf)[Dt/π]0.5
where,
t = time in days
D = weighted mean diffusivity in cm2/day
Θi = initial profile wetness
Θf = final surface wetness

13. Evapotranspiration (EV)
Thornthwaite model of potential EV (PE)
PE = 16 (10Tm/I)a (K),
where,
Tm = monthly air temperature
I = sum of monthly heat index
∑(Tm/5)1.514
a = polynomial in I
K = adjustment in length of day for 12 hour period

14. Example of EV calculations used for watershed management in Colorado

15. Forested Watershed Actual evapotranspiration (AE)
= (1 – α)E + α(T + I),
where,
α = watershed forest coverage
E = evaporation from soil and water surfaces
T = forest transpiration (about 60% of AE)
I = forest canopy and litter interception (loss is about 10% to 30% of precipitation)

16. Average Daily ET Rates by Species
mm/day
inches/day
Location
Douglas fir
2.1
0.0821
Seattle, WA
Slash pine
3.0
0.1191
Gainesville, FL
Ponderosa pine
2.0 to 3.3 to
Alpine, AZ
White pine
3.1
Cowetta, NC
Pinyon-juniper
1.2
0.0476
Flagstaff, AZ
Spruce-fir
Frazier, CO
Aspen
1.5
0.0595
Bountiful, UT
Oak-hickory
2.6
0.1032
Yellow poplar
1.7
0.0675
East Tennessee
Annual rainfall of 45 inches is inches per day