Download - Lecture 10 - 1 ERS 482/682 (Fall 2002) Evapotranspiration ERS 482/682 Small Watershed Hydrology
ERS 482/682 (Fall 2002) Lecture 10 - 2
Definition
Total evaporation from all water, soil, snow, ice, vegetation, and other
surfaces plus transpiration
water becoming water vaporwater becoming water vapor
consumptive use by consumptive use by plantsplants
ERS 482/682 (Fall 2002) Lecture 10 - 3
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 - 4
How significant is evapotranspiration?
• Can be as much as 90% of precipitation• Affected by changes in
– Vegetation– Weather
ETET streamflowstreamflow
air temperature air temperature ETET streamflowstreamflow
ERS 482/682 (Fall 2002) Lecture 10 - 5
Fick’s Law:A diffusing substance moves from where
its concentration is larger to where itsconcentration is smaller at a ratethat is proportional to the spatial
gradient of concentration
Evaporation
Figure 8.2 (Chapra 1997)
ERS 482/682 (Fall 2002) Lecture 10 - 6
Fick’s Law:A diffusing substance moves from where
its concentration is larger to where itsconcentration is smaller at a ratethat is proportional to the spatial
gradient of concentration
Evaporation
dz
XdCDXF Xz )(
where Fz(X) = rate of transfer of substance X in z direction DX = diffusivity of substance X C(X) = concentration of X
[L[L22 T T-1-1]]
units depend on substanceunits depend on substance
will have units ofwill have units ofsubstance *[L Tsubstance *[L T-1-1]]
indicates movementindicates movementfrom regions of higherfrom regions of higher
concentration to regionsconcentration to regionsof lower concentrationof lower concentration
gradient (change) ingradient (change) inconcentrationconcentration
ERS 482/682 (Fall 2002) Lecture 10 - 7
Fick’s Law:A diffusing substance moves from where
its concentration is larger to where itsconcentration is smaller at a ratethat is proportional to the spatial
gradient of concentration
Evaporation
asaE eevKE where E = evaporation rate KE = efficiency of vertical transport of water vapor va = wind speed es = vapor pressure of evaporating surface ea = vapor pressure of overlying air
[L T[L T-1-1]]
[L T[L T-1-1 M M-1-1]]
[L T[L T-1-1]][M L[M L-1-1 T T-2-2]]
[M L[M L-1-1 T T-2-2]]
ERS 482/682 (Fall 2002) Lecture 10 - 8
Vapor pressure, e
Partial pressure of water vapor
saturation vapor pressure, e*: maximum vapor pressure
waterwater vapor
eess = e = ess**
3.237
3.17exp611.0*
s
ss T
Te water temperaturewater temperature
at surface at surface
eeaa = W = Waaeeaa**
3.237
3.17exp611.0*
a
aa T
Terelative humidityrelative humidity
ERS 482/682 (Fall 2002) Lecture 10 - 9
Latent heat exchange, LE
• Occurs whenever there is a vapor pressure difference between water and air
ELE vwwhere w = water density v = latent heat of vaporization
Tv31036.250.2
[E L[E L-2-2 T T-1-1]]
[MJ kg[MJ kg-1-1]]
1000 kg m1000 kg m-3-3
surface water temperature (surface water temperature (°C)°C)
ERS 482/682 (Fall 2002) Lecture 10 - 10
Sensible heat exchange, H
• Occurs whenever there is a temperature difference between water and air
LEBHLEH
B
where B = Bowen ratio
Depends on air pressure constant at a particular site
ERS 482/682 (Fall 2002) Lecture 10 - 11
Energy balanceEquation 7-15
All expressed in units of [E LAll expressed in units of [E L-2-2 T T-1-1]]except except Q Q [E L[E L-2-2]]
where Q = change in heat storage per unit area over time t K = shortwave (solar) radiation input L = longwave radiation H = turbulent exchange of sensible heat with atmosphere LE = turbulent exchange of latent heat with atmosphere Aw = heat input due to water inflows and outflows G = conductive exchange of sensible heat with ground
LEAHGLKtQ
w
ERS 482/682 (Fall 2002) Lecture 10 - 12
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
often assumed negligibleoften assumed negligible
ERS 482/682 (Fall 2002) Lecture 10 - 13
Free-water evaporation
Evaporation that would occur from an open-water surface in the absence of
advection and changes in heat storage
Depends only on climate/meteorology
“Potential evaporation”
Evaporation: net loss of water from a surface resulting from achange 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 - 14
Free-water evaporation
• Penman equation– Standard hydrological method
LEAHGLKtQ
w 0 0 0
vw
HLKE
ELE vwrecall:
“Potential evaporation”
ERS 482/682 (Fall 2002) Lecture 10 - 15
Free-water evaporation
• Penman equation– Standard hydrological method
as
as
TT
ee
**
v
a Pc
622.0psychrometric constantpsychrometric constant
1-K kPa 066.0
EH
Evw
HLKE
“Potential evaporation”
ERS 482/682 (Fall 2002) Lecture 10 - 16
Free-water evaporation
• Penman equation– Standard hydrological method
EH
E1
EH
E
dimensionless
Table 4-6 Dunne & Leopold (1978)
“Potential evaporation”
ERS 482/682 (Fall 2002) Lecture 10 - 17
Free-water evaporation
• Pan-evaporation– Direct measurement method
12 VVWEpan where W = precipitation during time t V1 = storage at beginning of period t V2 = storage at end of period t
Class-A evaporation panDiameter = 1.22 m
Height = .254 m
“Potential evaporation”
12 in.
ERS 482/682 (Fall 2002) Lecture 10 - 18
Free-water evaporation
• Pan-evaporation– Direct measurement method
12 VVWEpan
Efw = (PC)Epan
See Morel-Seytoux (1990) for pan coefficientsNo adjustments necessary for annual values
“Potential evaporation”
0.7 average for US
ERS 482/682 (Fall 2002) Lecture 10 - 19
Bare-soil evaporation
• Stages– Atmosphere-controlled stage (wet soil wet soil
surface)surface)• Evaporation rate free-water evaporation rate
– Soil-controlled stage (dry soil surfacedry soil surface)• Evaporation rate << free-water evaporation rate
ERS 482/682 (Fall 2002) Lecture 10 - 20
Transpiration
Transpiration: evaporation of water from the
vascular system of plants into the atmosphere
Figure 6.1 (Manning 1987)
ERS 482/682 (Fall 2002) Lecture 10 - 21
Transpiration
• Dry soilssoil capillary pressure > osmotic pressure
• Saline soilswater concentrationsoil < water concentrationplant
Figure 6.2 (Manning 1987)
ERS 482/682 (Fall 2002) Lecture 10 - 22
Transpiration
• Leaf/canopy conductance– Depends on
• Number of stomata/unit area• Size of stomatal openings• Density of vegetation
Cleaf
LAI: fraction of area covered with leaves
leafcan CLAIfC s
shelter factorshelter factor
Penman-Monteith model (Equation 7-56)
ERS 482/682 (Fall 2002) Lecture 10 - 24
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 - 25
Potential evapotranspiration (PET)
• Thornthwaite methoda
at I
TE
10
6.1
where Et = potential evapotranspiration Ta = mean monthly air temperature I = annual heat index a = 0.49 + 0.0179I – 0.000077I2 + 0.000000675I3
[cm mo[cm mo-1-1]]
[°C][°C]5.1
12
1 5
i
aiT
ERS 482/682 (Fall 2002) Lecture 10 - 26
Potential evapotranspiration (PET)
• Thornthwaite method
Figures 5-4 and 5-5 (Dunne & Leopold 1978)
Index must be adjusted for Index must be adjusted for # days/mo and length of # days/mo and length of
dayday
ERS 482/682 (Fall 2002) Lecture 10 - 27
Potential evapotranspiration (PET)
• Blaney-Criddle formula
kdTTE aat 8.17095.1142.0
where Et = potential evapotranspiration Ta = average air temperature k = empirical crop factor d = monthly fraction of annual hours of daylight
[cm mo[cm mo-1-1]][°C][°C]
ERS 482/682 (Fall 2002) Lecture 10 - 28
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 - 29
Measuring evapotranspiration
• Cannot be measured directly• Transpiration
– Lysimeters
Figure 6.3 (Manning 1987)