Water Budget II: Evapotranspiration

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. 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 • In Florida, ~ a is unity for the summer, 0.75 otherwise • ET:PET is low in arid areas due to water limitation • ET ~ PET in humid areas due to energy limitation

11. A Simple Catchment Water Balance • Consider the net effects of the various water balance components (esp. ET) • ET controlled by water availability and atmospheric demand • The “Budyko” Curve • Dry conditions: when PET:P → ∞, AET:P → 1 and Q:P → 0 • Wet conditions: when PET:P → 0 AET → PET

12. Theory vs. Real Data – Budyko curves across the world’s catchments AET:P PET:P

13. 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

14. 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

15. Evaporation from a Pan • 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 • 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

16. 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

17. Actual Diurnal Data

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

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

20. 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

21. l

22. Energy Budget • 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)

23. Static Computation • Rnet = lE + H + G = 800 * (1 – 0.2) = 640 • 640 = (586*E) + 100 + 50 • 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

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

25. 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.

26. 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

27. 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.

28. 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

29. High Resolution ET Observations

32. 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

33. Evapotranspiration has Multiple Components

34. Interception • 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%

35. CO2 H2O 1 : 300 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

36. 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%

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

39. 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

40. 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

41. Transpiration

42. 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.

43. 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? > 100 meters 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

44. 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

45. 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.

46. ? 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.

48. Trading Environmental Priorities? • Water for Carbon • Water for Energy Jackson et al. 2005 (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.