Water Budget II: Evapotranspiration

P = Q + ET + G + ΔS

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

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

Four Requirements for ET

Vapor Pressure Gradient

Energy

Water

Wind

NP

TP

NASA

3850 zettajoules per year

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

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

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

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

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

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

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

)(

0

12

12

HHPE

EPHH

IS

p

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

0.50

0.51

0:00 12:00 0:00 12:00 0:00

h (cm/hr)

S

Wate

r L

evel

ET = Sy(S + 24 x h)

Exfiltration = Sy(24 x h)

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)

Wate

r L

evel

(m

)W

ate

r L

evel

(m

)

0.585

0.595

0.605

0.615

0:00 12:00 0:00 12:00 0:00 12:00

0.76

0.77

0.78

0.79

0.80

0:00 12:00 0:00 12:00 0:00 12:00

h

h

s

s

ET/Sy

ET/Sy

What is Specific Yield?

• How much water (in units of cm) drains out of a soil; also called dynamic drainable porosity

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)

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

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)

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

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

Energy Budget – Bowen Ratio

b = H/lE

G

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.

)100

1(0027.0)(

ln

102.0)(

))()((

22

uuB

zz

uuB

zeeuBE

o

s

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

ar EEEg

g

g

23.237

4098

T

es

CPa 0/8.66g

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.

rEEg

a

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

High Resolution ET Observations

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

Evapotranspiration has Multiple Components

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%

Transpiration • Plant mediated diffusion of soil water to

atmosphere

– Soil-Plant-Atmosphere Continuum (SPAC)

CO2 H2O

1 : 300

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

Transpiration Dominates the Evaporation Process

•Large surface area

•More turbulent air flow

•Conduits to deeper moisture sources

Hardwood ~80%

White Pine~60%

Flatwoods ~75%

T/ET

Trees have:

Cover Evaporation Interception Transpiration

Forest 10% 30% 60%

Meadow 25% 25% 50%

Ag 45% 15% 40%

Bare 100%

Ywsoil) -0.1 MPa Yw (root) -0.5 MPa

Yw (stem) -0.6 MPa

Yw (small branch) -0.8 MPa

Yw (atmosphere) -95 MPa

The SPAC (soil-plant-atmosphere continuum)

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

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

Transpiration

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.

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?

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

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.

ET = Rain * 0.80 ET = Rain * 0.95

1,000 mm * 0.80 = 800 mm 1,000 mm * 0.95 = 950 mm

Assume Q & ΔS = 0

G = 200 mm G = 50 mm

4x more groundwater recharge from open stands than from highly stocked plantations.

?

G = P - ET

NRCS is currently paying for growing more open stands, mainly for wildlife.

Controls on Stand Water Use

• More leaves per area = more water use

• Foresters don’t measure LAI

• Proxies for LAI

A Fair Comparison

• Pine stands are clear-cut every 20-25 years (low ET)

• Compare water yield (Rain – ET) over entire rotation

Ecosystem Service – Water Yield

• Forest management may yield “new” water

• Win-win for other forest services

• Who pays and how much?

Trading Environmental

Priorities?

• Water for Carbon

• Water for Energy

Jackson et al. 2005 (Science)

Surface Water Evaporation

•Air Temp

•Air relative humidity

•Water temp

•Wind

•Radiation

•Water Quality

Actual surface water evaporation ~ pan evaporation * 0.7

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.

Soil water loss with different cover

Surface

2 months later

Rooting Depth Effects

Next Time…

• Streamflow