1. Water Budget II: Evapotranspiration
P = Q + ET + G + ΔS

3. Evaporation Transfer of H2O from liquid to vapor phase
Diffusive process driven by
Saturation (vapor density) gradient ~ (rs – ra)
Aerial resistance ~ f(wind speed, temperature)
Energy to provide latent heat of vaporization (radiation)
Transpiration is plant mediated evaporation
Same result (water movement to atmosphere)
Summative process = evapotranspiration (ET)
Dominates the fate of rainfall
~ 95% in arid areas
~ 70% for all of North America

4. Evapo-Transpiration ET is the sum of Evaporation: physical process
from free water
Soil
Plant intercepted water
Lakes, wetlands, streams, oceans
Transpiration: biophysical process modulated by plants (and animals)
Controlled flow through leaf stomata
Species, temperature and moisture dependent

5. Four Requirements for ET
Energy
Water NP
Vapor Pressure Gradient
Wind TP

6. 3850 zettajoules per year
NASA

7. Energy Inputs Radiation Budget
Rtotal = Total Solar Radiation Inputs on a horizontal plane at the Earth’s Surface
Rnet = Rtotal – reflected radiation
= Rtotal * (1 – albedo)
Albedo (α) values
Snow 0.9
Hardwoods 0.2
Water 0.05
Flatwoods pine plantation 0.15
Flatwoods clear cut ____
Burn ____
Asphalt 0.05

8. Energy and Temperature
The simplest conceptualization of the ET process focuses solely on temperature.
Blaney-Criddle Method:
ET = p * (0.46*Tmean+ 8)
Where p is the mean daytime hours
Tmean is the mean daily temp (Max+Min/2)
ET (mm/day) is treated as a monthly variable

9. Vapor Deficit Drives the Process
Distance between actual conditions and saturation line
Greater distances = larger evaporative potential
Slope of this line (d) is an important term for ET models
Usually measured in mbar/°C
Graph shows mass water per mass air as a function of T

10. Wind Boundary layer saturates under quiescent conditions
Inhibits further ET UNLESS air is replaced
Turbulence at boundary layer is therefore necessary to ensure a steady supply of undersaturated air

11. Water Availability: PET vs. AET
PET (potential ET) is the expected ET if water is not limiting
Given conditions of: wind, Temperature, Humidity
AET (actual ET) is the amount that is actually abstracted (realizing that water may be limiting)
AET = a * PET
Where a is a function of soil moisture, species, climate
ET:PET is low in arid areas due to water limitation
ET ~ PET in humid areas due to energy limitation

12. Methods of Estimating ET
Since ET is the largest flux OUT of the watershed, we need good estimates
Techniques have focused mostly on predicting capacity (i.e., PET, where water is not limiting)
energy balance methods
mass transfer or aerodynamic methods
combination of energy and mass transfer (Penman equation)
pan evaporation data

13. Evaporation from a Pan Mass balance equation
Pans measure more evaporation than natural water bodies because:
1) less heat storage capacity (smaller volume)
2) heat transfer
3) wind effects
National Weather Service Class A type
Installed on a wooden platform in a grassy location
Filled with water to within 2.5 inches of the top
Evaporation rate is measured by manual readings or with an analog output evaporation gauge

14. Diurnal Water Level Variation (White, 1932)
Diel variation in water level yields ET (during the day) and net groundwater flux (at night)
Curiously, not widely used

15. Actual Diurnal Data
Nighttime slope is groundwater flow (inflow is UP, outflow is DOWN)
Assuming constant GW flow, daytime slope is ET + GW.
Specific yield (Sy)

16. What is Specific Yield?
How much water (in units of cm) drains out of a soil; also called dynamic drainable porosity

17. Energy Balance Method Assumes energy supply the limiting factor.
Consider energy balance on a small lake with no water inputs (or evaporation pan)
heat stored in system
sensible heat transfer to air Hs Rn Qe G
net radiation
energy used in evaporation
heat conducted to ground (typically neglected)

18. Energy Budget Energy in = Energy out (conservation law)
Energy In = Rtotal
Energy Out
Albedo
Latent Heat
Sensible Heat
Soil Heat Flux
If Rtotal = 800 cal/cm2/day and a = 0.25
Rnet = 800 * (1 – 0.25) = 600 cal/cm2/day

19. Energy Budget Estimates of ET
Rnet = lE + H + G
We want to know E
E = (Rnet – (H+G))/l
What are evaporative losses if:
Rtotal = 800 cal/cm2/day
Albedo = 0.2
l = 586 cal/g
H = 100 cal/cm2/d (convected heat)
G = 50 cal/cm2/d (soil heating)

20. Static Computation Rnet = lE + H + G = 800 * (1 – 0.2) = 640
E = 0.84 cm/d
Annual ET = 0.84 * 365 * 1 m/100 cm
= 3.07 m
Rtot = 800 cal/cm/d
Albedo = 0.2
l =586 cal/g
H = 100 cal/cm/d lost
G = 50 cal/cm/d lost to ground

21. Energy Budget – Bowen Ratio
b = H/lE G

22. Mass Transfer (Aerodynamic) Method
Assumes that rate of turbulent mass transfer of water vapor from evaporating surface to atmosphere is limiting factor
Mass transfer is controlled by (1) vapor gradient (es – e) and (2) wind velocity (u) which determines rate at which vapor is carried away.

23. Combination Method (Penman)
Evaporation can be estimated by aerodynamic method (Ea) when energy supply not limiting and energy method (Er) when vapor transport not limiting
 Typically both factors limiting so use combination of above methods
Weighting factors sum to 1.
 = vapor pressure deficit
g = psychrometric constant

24. Combination Method (Penman)
Penman is most accurate and commonly used method if meteorological information is available.
Need: net radiation, air temperature, humidity, wind speed
If not available use Priestley-Taylor approximation:
Based on observations that second term (advection) in Penman equation typically small in low water stress areas.
The α term is crop coefficient that assumes no “advection limitation”. Usually >1 (1.2 to 1.7), suggesting that actual ET is greater than what is predicted from radiation alone.

25. Time Scales of Variability
Controls on ET create variability at scales from seconds to centuries
Eddies change ET at the time scale of seconds
Diel cycles affect water fluxes over 24 hours
Weather patterns affect fluxes at days to weeks
Water availability
Vapor deficit
Wind and energy
Climate variability at decadal and beyond

26. High Resolution ET Observations

29. Total System ET – Ordered Process
Intercepted Water  Transpiration  Surface Water  Soil Water
Why?
Implications for:
Cloud forests
Understory vegetation in wetlands
Deep rooted arid ecosystems

30. Evapotranspiration has Multiple Components

31. Interception Interception Loss (% of rainfall)
Surface tension holds water falling on forest vegetation.
Leaf Storage
Fir 0.25”
Pines 0.10”
Hardwoods 0.05”
Litter 0.20”
SP Plantations 0.40”.
Interception Loss (% of rainfall)
Hardwoods 10-20% (less LAI)
Conifers 20-40%
Mixed slash and Cypress Florida Flatwoods 20%

32. Transpiration
Plant mediated diffusion of soil water to atmosphere
Soil-Plant-Atmosphere Continuum (SPAC)
Transpiration and productivity are tightly coupled
Transpiration is the primary leaf cooling mechanism under high radiation
Provides a pathway for nutrient uptake and matrix for chemical reactions
Worldwide, water limitations are more important than any other limitation to plant productivity
CO2
H2O
1 : 300

33. Transpiration Dominates the Evaporation Process
Trees have:
Large surface area
More turbulent air flow
Conduits to deeper moisture sources
T/ET
Hardwood ~80%
White Pine~60%
Flatwoods ~75%

34. Cover
Evaporation
Interception
Transpiration
Forest
10%
30%
60%
Meadow
25%
50% Ag
45%
15%
40%
Bare
100%

35. The SPAC (soil-plant-atmosphere continuum)
Yw (stem)
 -0.6 MPa
Yw (small
branch)
 -0.8 MPa
Yw (atmosphere)
 -95 MPa
Yw (root)
 -0.5 MPa
Yw(soil)  -0.1 MPa

36. The driving force of transpiration is the difference in water vapor concentration, or vapor pressure difference, between the internal spaces in the leaf and the atmosphere around the leaf

37. Transpiration
The physics of evaporation from stomata are the same as for open water. The only difference is the conductance term.
Conductance is a two step process
stomata to leaf surface
leaf surface to atmosphere

38. Transpiration

39. How Does Water Get to the Leaf?
Water is PULLED, not pumped. Water within the whole plant forms a continuous network of liquid columns from the film of water around soil particles to absorbing surfaces of roots to the evaporating surfaces of leaves.
It is hydraulically connected.

40. Even a perfect vacuum can only pump water to a maximum of a little over 30 feet. At this point the weight of the water inside a tube exerts a pressure equal to the weight of the atmosphere pushing down
> 100 meters
So why doesn’t the continuous column of water in trees taller than 34 feet collapse under its own weight? And how does water move UP a tall tree against the forces of gravity?

41. cell wall microfibrils of carrot
Water is held “up” by the surface tension of tiny menisci (“menisci” is the plural of meniscus) that form in the microfibrils of cell walls, and the adhesion of the water molecules to the cellulose in the microfibrils
cell wall microfibrils of carrot

42. Cohesion-Tension Theory:
(Böhm, 1893; Dixon and Joly, 1894)
The cohesive forces between water molecules keep the water column intact unless a threshold of tension is exceeded (embolism). When a water molecule evaporates from the leaf, it creates tension that “pulls” on the entire column of water, down to the soil.
To understand WHY the pipeline is vulnerable:
LOOK AT MECHANISM: COHESION – TENSION – THEORY
about 100 yrs ago – proposed independently by Boehm and by Dixon and Joly
Transpiration
Capillary forces – Tension – NEGATIVE PRESURE
Water is pulled up – cohesive forces between water molecules keep the water column together
Conduits are dead
Class: Tug-of-war – the air pulls on one end, the soil particles on the other end
Very simple mechanism and very cheap - driven by the sun
Once the pipeline is in place
plants don’t have to use energy for water transport
What makes the pipeline “vulnerable”?
It’s the MAGNITUDE of the NEGATIVE Xylem Pressure

43. ?
ET = Rain * 0.80
ET = Rain * 0.95
1,000 mm * 0.95 = 950 mm
1,000 mm * 0.80 = 800 mm
Assume Q & ΔS = 0
G = P - ET
G = 50 mm
G = 200 mm
4x more groundwater recharge from open stands than from highly stocked plantations.
NRCS is currently paying for growing more open stands, mainly for wildlife.

45. Controls on Stand Water Use
More leaves per area = more water use
Foresters don’t measure LAI
Proxies for LAI

46. A Fair Comparison Pine stands are clear-cut every 20-25 years (low ET)
Compare water yield (Rain – ET) over entire rotation

47. Ecosystem Service – Water Yield
Forest management may yield “new” water
Win-win for other forest services
Who pays and how much?

48. Trading Environmental Priorities?
Water for Carbon
Water for Energy
Jackson et al (Science)

49. Surface Water Evaporation
Air Temp
Air relative humidity
Water temp
Wind
Radiation
Water Quality
Actual surface water evaporation ~ pan evaporation * 0.7

50. Soil Water Evaporation
Stage 1. For soils saturated to the surface, the evaporation rate is similar to surface water evaporation.
Stage 2. As the surface dries out, evaporation slows to a rate dependent on the capillary conductivity of the soil.
Stage 3. Once pore spaces dry, water loss occurs in the form of vapor diffusion. Vapor diffusion requires more energy input than capillary conduction and is much, much, slower.
Note that for soils under a forest canopy, Rnet, vapor pressure deficit, and turbulent transport (wind) are lower than for exposed soils.

51. Soil water loss with different cover
Forest Soil

52. Rooting Depth Effects
Surface
2 months later

53. Next Time…
Streamflow