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Water Budget II:

Evapotranspiration

P = Q + ET + G + ΔS


Evaporation

• Transfer of H 2 O from liquid to vapor phase

– Diffusive process driven by

• Saturation (vapor density) gradient ~ (r s – r a )

• 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


• ET is the sum of

Evapo-Transpiration

– 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

TP

Energy

Water

Vapor Pressure Gradient

NP

Wind


NASA

3850 zettajoules per year


• Radiation Budget

Energy Inputs

– R total = Total Solar Radiation Inputs on a horizontal plane at

the Earth’s Surface

– R net = R total – reflected radiation

= R total * (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*T mean + 8)

– Where p is the mean daytime hours

– T mean 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

• Mass balance equation

S

I 0

• 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

H


2

E


p

H

• Pans measure more

evaporation than natural

water bodies because:

1

P ( H

– 1) less heat storage capacity

(smaller volume)

– 2) heat transfer

– 3) wind effects

P E

2


H

1

)


Water Level

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

0.51

h (cm/hr)

S

ET = S y (S + 24 x h)

Exfiltration = S y (24 x h)

0.50

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


Water Level (m)

Water Level (m)

Actual Diurnal Data

0.615

0.605

0.595

0.585

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

0.80

0.79

0.78

0.77

0.76

h

ET/S

s

y

h s

ET/S y

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

• Nighttime slope

is groundwater

flow (inflow is

UP, outflow is

DOWN)

• Assuming

constant GW

flow, daytime

slope is ET + GW.

• Specific yield (S y )


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.

sensible heat

transfer to air

net

radiation

energy used in

evaporation

H s R n Q e

heat stored

in system

G

heat conducted to ground

(typically neglected)

• Consider energy balance on a small lake with no

water inputs (or evaporation pan)


Energy Budget

• Energy in = Energy out (conservation law)

– Energy In = R total

– Energy Out

• Albedo

• Latent Heat

• Sensible Heat

• Soil Heat Flux

• If R total = 800 cal/cm 2 /day and a = 0.25

• R net = 800 * (1 – 0.25) = 600 cal/cm 2 /day


Energy Budget Estimates of ET

• R net = lE + H + G

– We want to know E

• E = (R net – (H+G))/l

• What are evaporative losses if:

– R total = 800 cal/cm 2 /day

– Albedo = 0.2

– l = 586 cal/g

– H = 100 cal/cm 2 /d (convected heat)

– G = 50 cal/cm 2 /d (soil heating)


Static Computation

• R net = 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

R tot = 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


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 (e s – e)

and (2) wind velocity (u)

which determines rate at

which vapor is carried away.

E

B(

u)


B(

u)

B(

u)(

e

s

0.102u


ln

z



e(

z))

2

z

o




2

u

0.0027(1 )

100


Combination Method (Penman)

• Evaporation can be estimated by aerodynamic method (E a ) when energy

supply not limiting and energy method (E r ) when vapor transport not

limiting

• Typically both factors limiting so use combination of above methods

E


g

E r E a

g

g

• Weighting factors sum to 1.

= vapor pressure deficit

g = psychrometric constant


4098

e s

2

237.3 T

g 66.8Pa /

0 C


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:

E


a g

• 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.

E r


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”

Interception Loss (% of rainfall)

• Hardwoods 0.05”

•Hardwoods 10-20% (less LAI)

• Litter 0.20”

•Conifers 20-40%

• SP Plantations 0.40”.

•Mixed slash and Cypress Florida Flatwoods 20%


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

CO 2

H 2 O

1 : 300


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%


Cover Evaporation Interception Transpiration

Forest 10% 30% 60%

Meadow 25% 25% 50%

Ag 45% 15% 40%

Bare 100%


The SPAC (soil-plant-atmosphere continuum)

Y w (atmosphere)

-95 MPa

Y w (small

branch)

-0.8 MPa

Y w (stem)

-0.6 MPa

Y w soil) -0.1 MPa

Y w (root)

-0.5 MPa


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

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


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

G = 200 mm

Assume Q & ΔS = 0

G = P - ET

G = 50 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.


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, R net , vapor pressure

deficit, and turbulent transport (wind) are lower than for

exposed soils.


Soil water loss with different cover


Rooting Depth Effects

Surface

2 months later


• Streamflow

Next Time…

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