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
Spatial Variation in P - ET
• Controls streamflow (mm/yr)
Beck et al. (2015)
Globally
(P – ET in mm/yr)
Beck et al. (2015)
Four Requirements for ET
Energy
Water
NP
Vapor Pressure Gradient
Wind
TP
3850 zettajoules per year
NASA
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
Budyko Revisited
• Budyko Curve shows annual catchment hydrology
– Can neglect G and ΔS, focus on ET (P ~ ET + Q)
– Aridity index on the x-axis (potential ET:rain)
– Evaporative index on the y axis (actual ET:rain)
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
H 2  H1  P  E
 E p  P  ( H 2  H1 )
•
•
•
•
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
• Pans measure more
evaporation than natural
water bodies because:
– 1) less heat storage capacity
(smaller volume)
– 2) heat transfer
– 3) wind effects
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
Water Level
0.51
h (cm/hr)
S
ET = Sy(S + 24 x h)
Exfiltration = S y(24 x h)
0.50
0:00
12:00
0:00
12:00
0:00
Actual Diurnal Data
Water Level (m)
0.615
s
ET/Sy
0.595
0.585
0:00
0.80
Water Level (m)
h
0.605
12:00
0:00
12:00
0:00
12:00
0.79
h
s
ET/Sy
0.78
0.77
0.76
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 (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 (Budyko).
sensible heat
transfer to air
Hs
net
radiation
Rn
energy used in
evaporation
Qe
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 = 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)
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 R = 800 cal/cm/d
tot
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 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.
E  B (u )(es  e( z ))
B (u ) 
0.102u
ln z 2 
  z o 
2
u
B (u )  0.0027(1 
)
100
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

g
E
Er 
Ea
 g
 g
• Weighting factors sum to 1.
4098es
 = vapor pressure deficit

g = psychrometric constant
g  66.8Pa / 0 C
237.3  T 2
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
Er
 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.
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
Eddy Correlation Measures
• Moving air is combination of multiple scales of eddies
(turbulent gyres)
• Measure gas concentrations (water vapor, CO2, CH4) in
up-welling vs. down-welling air is ecosystem fluxes
(correlation between concentration and flow direction)
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
CO2
H2O
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)
Yw (atmosphere)
 -95 MPa
Yw (small
branch)
 -0.8 MPa
Yw (stem)
 -0.6 MPa
Ywsoil)  -0.1 MPa
Yw (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
G = 200 mm
1,000 mm * 0.95 = 950 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
–
–
–
–
Basal area
Age
Height
Site Index
A Fair Comparison
• Pine stands are
clear-cut every 2025 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
Rooting Depth Effects
Surface
2 months later
Next Time…
• Streamflow