Download ERS 482/682 Small Watershed Hydroloy

Evapotranspiration
ERS 482/682
Small Watershed Hydrology
ERS 482/682 (Fall 2002)
Lecture 10 - 1
Definition
Total evaporation from all water, soil, snow,
ice, vegetation, and other surfaces plus
transpiration
consumptive use by plants
water becoming water vapor
ERS 482/682 (Fall 2002)
Lecture 10 - 2
Processes
• Evaporation of precipitation intercepted by
plant surfaces
• Evaporation of moisture from plants
through transpiration
• Evaporation of moisture from soil (ground)
surface
ERS 482/682 (Fall 2002)
Lecture 10 - 3
How significant is
evapotranspiration?
• Can be as much as 90% of precipitation
• Affected by changes in
– Vegetation   ET   streamflow 
– Weather
air temperature  ET   streamflow 
ERS 482/682 (Fall 2002)
Lecture 10 - 4
Evaporation
Fick’s Law:
A diffusing substance moves from where
its concentration is larger to where its
concentration is smaller at a rate
that is proportional to the spatial
gradient of concentration
Figure 8.2 (Chapra 1997)
ERS 482/682 (Fall 2002)
Lecture 10 - 5
Evaporation
Fick’s Law:
A diffusing substance moves from where
its concentration is larger to where its
concentration is smaller at a rate
that is proportional to the spatial
gradient of concentration
indicates movement
dC  X 
from regions of higher Fz ( X )   DX
dz
concentration to regions
of lower concentration
gradient (change) in
concentration
will have units of
substance *[L T-1]
where
Fz(X) = rate of transfer of substance X in z direction
DX = diffusivity of substance X [L2 T-1]
C(X) = concentration of X  units depend on substance
ERS 482/682 (Fall 2002)
Lecture 10 - 6
Evaporation
Fick’s Law:
A diffusing substance moves from where
its concentration is larger to where its
concentration is smaller at a rate
that is proportional to the spatial
gradient of concentration
E  K E va es  ea 
where
E = evaporation rate [L T-1]
KE = efficiency of vertical transport of water vapor [L T-1 M-1]
va = wind speed [L T-1]
es = vapor pressure of evaporating surface [M L-1 T-2]
[M L-1 T-2]
ea = vapor pressure of overlying air
ERS 482/682 (Fall 2002)
Lecture 10 - 7
Vapor pressure, e
Partial pressure of water vapor
saturation vapor pressure, e*: maximum vapor pressure
relative humidity
water vapor
water
 17.3Ta 

e  0.611exp
 Ta  237.3 
*
a
ea = Waea*
es = e s *
 17.3Ts  water temperature

e  0.611exp
at surface
 Ts  237.3 
*
s
ERS 482/682 (Fall 2002)
Lecture 10 - 8
Latent heat exchange, LE
• Occurs whenever there is a vapor pressure
difference between water and air
LE   wv E
[E L-2 T-1]
where
1000 kg m-3
w = water density
v = latent heat of vaporization
v  2.50  2.36 103 T
[MJ kg-1]
surface water temperature (°C)
ERS 482/682 (Fall 2002)
Lecture 10 - 9
Sensible heat exchange, H
• Occurs whenever there is a temperature
difference between water and air
H
B
 H  B  LE
LE
where
B = Bowen ratio
Depends on air pressure
 constant at a particular site
ERS 482/682 (Fall 2002)
Lecture 10 - 10
Energy balance
Equation 7-15
where
Q
K
L
H
LE
Aw
G
Q
 K  L  G  H  Aw  LE
t
= change in heat storage per unit area over time t
= shortwave (solar) radiation input
= longwave radiation
= turbulent exchange of sensible heat with atmosphere
= turbulent exchange of latent heat with atmosphere
= heat input due to water inflows and outflows
= conductive exchange of sensible heat with ground
All expressed in units of [E L-2 T-1]
except Q [E L-2]
ERS 482/682 (Fall 2002)
Lecture 10 - 11
Classification of ET processes
• Surface type:
–
–
–
–
–
Open water
Bare soil
Leaf/canopy type
Crop type
Land region
• Water availability
– Unlimited vs. limited
• Stored energy use, Q
• Water-advected energy, Aw
ERS 482/682 (Fall 2002)
often assumed negligible
Lecture 10 - 12
Free-water evaporation
“Potential evaporation”
Evaporation that would occur from an openwater surface in the absence of advection
and changes in heat storage
Depends only on climate/meteorology
Evaporation: net loss of water from a surface resulting from a
change in the state of water from liquid to vapor and the net
transfer of this vapor to the atmosphere
ERS 482/682 (Fall 2002)
Lecture 10 - 13
Free-water evaporation
“Potential evaporation”
• Penman equation
– Standard hydrological method
0
0
0
Q
K LH
E
 K  L  G  H  Aw  LE
 wv
t
recall: LE   wv E
ERS 482/682 (Fall 2002)
Lecture 10 - 14
Free-water evaporation
“Potential evaporation”
• Penman equation
– Standard hydrological method
*
*
e

e
K LH   s a
E
Ts  Ta
 wv
ca P
psychrometric constant  
0.622v
  0.066 kPa K -1
ERS 482/682 (Fall 2002)
H  E
E
 
Lecture 10 - 15
Free-water evaporation
“Potential evaporation”
• Penman equation
– Standard hydrological method

H E
H  E

Table 4-6 Dunne & Leopold (1978)
E
E

 
1
dimensionless
ERS 482/682 (Fall 2002)

Lecture 10 - 16
Free-water evaporation
“Potential evaporation”
• Pan-evaporation
– Direct measurement method
E pan  W  V2  V1 
where
W = precipitation during time t
V1 = storage at beginning of period t
V2 = storage at end of period t
12 in.
Class-A evaporation pan
Diameter = 1.22 m
Height = .254 m
ERS 482/682 (Fall 2002)
Lecture 10 - 17
Free-water evaporation
“Potential evaporation”
• Pan-evaporation
– Direct measurement method
E pan  W  V2  V1 
0.7 average for US
Efw = (PC)Epan
See Morel-Seytoux (1990) for pan coefficients
No adjustments necessary for annual values
ERS 482/682 (Fall 2002)
Lecture 10 - 18
Bare-soil evaporation
• Stages
– Atmosphere-controlled stage (wet soil surface)
• Evaporation rate  free-water evaporation rate
– Soil-controlled stage (dry soil surface)
• Evaporation rate << free-water evaporation rate
ERS 482/682 (Fall 2002)
Lecture 10 - 19
Transpiration
Transpiration:
evaporation of water
from the
vascular system of
plants into the
atmosphere
ERS 482/682 (Fall 2002)
Figure 6.1 (Manning 1987)
Lecture 10 - 20
Transpiration
Figure 6.2 (Manning 1987)
• Dry soils
soil capillary pressure > osmotic pressure
• Saline soils
water concentrationsoil < water concentrationplant
ERS 482/682 (Fall 2002)
Lecture 10 - 21
Transpiration
• Leaf/canopy conductance
– Depends on
• Number of stomata/unit area
Cleaf
• Size of stomatal openings
• Density of vegetation
LAI: fraction of area
covered with leaves
Ccan  f s  LAI  Cleaf
shelter factor
Penman-Monteith model (Equation 7-56)
ERS 482/682 (Fall 2002)
Lecture 10 - 22
Transpiration
Figure 3.4 (Brooks et al. 1991)
ERS 482/682 (Fall 2002)
Lecture 10 - 23
Potential evapotranspiration (PET)
Rate at which evapotranspiration would occur
from a large area completely and uniformly
covered with growing vegetation with
unlimited access to soil water and without
advection or heat-storage effects
ERS 482/682 (Fall 2002)
Lecture 10 - 24
Potential evapotranspiration (PET)
• Thornthwaite method
10Ta 
Et  1.6 
 I 
where
Et
Ta
I
a
a
= potential evapotranspiration [cm mo-1]
1.5
12 T
 ai 
= mean monthly air temperature [°C]
 
i 1  5 
= annual heat index
= 0.49 + 0.0179I – 0.000077I2 + 0.000000675I3
ERS 482/682 (Fall 2002)
Lecture 10 - 25
Potential evapotranspiration (PET)
• Thornthwaite method
Figures 5-4 and 5-5 (Dunne & Leopold 1978)
Index must be adjusted for #
days/mo and length of day
ERS 482/682 (Fall 2002)
Lecture 10 - 26
Potential evapotranspiration (PET)
• Blaney-Criddle formula
Et  0.142Ta  1.095Ta  17.8kd
where
Et
Ta
k
d
= potential evapotranspiration [cm mo-1]
[°C]
= average air temperature
= empirical crop factor
= monthly fraction of annual hours of daylight
ERS 482/682 (Fall 2002)
Lecture 10 - 27
Potential evapotranspiration (PET)
• Notes
– Wind speed has little or no effect
– Local transport of heat can be significant
– Taller and widely spaced vegetation tend to
have greater heat transfer
ERS 482/682 (Fall 2002)
Lecture 10 - 28
Measuring evapotranspiration
• Cannot be measured directly
• Transpiration
– Lysimeters
Figure 6.3 (Manning 1987)
ERS 482/682 (Fall 2002)
Lecture 10 - 29
Measuring evapotranspiration
• Cannot be measured directly
• Transpiration
– Lysimeters
– Tent method
• Evaporation
Figure 3.5 (Brooks et al. 1991)
– Evaporation pans
• Water budget:
ET + G = P – Q
• Paired watershed studies
ERS 482/682 (Fall 2002)
Lecture 10 - 30