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Evaporation
• Slides prepared by Daene C. McKinney and Venkatesh Merwade
• Reading: Applied Hydrology Sections 4.1 and 4.2
Evaporation
• Terminology– Evaporation – process by which liquid
water passes directly to the vapor phase– Transpiration - process by which liquid
water passes from liquid to vapor through plant metabolism
– Sublimation - process by which water passes directly from the solid phase to the vapor phase
Factors Influencing Evaporation
• Energy supply for vaporization (latent heat)– Solar radiation
• Transport of vapor away from evaporative surface– Wind velocity over surface– Specific humidity gradient above
surface
• Vegetated surfaces– Supply of moisture to the surface– Evapotranspiration (ET)
• Potential Evapotranspiration (PET) – moisture supply is not limited
nR
E
Net radiation
Evaporation
Air Flowu
Evaporation from a Water Surface
• Simplest form of evaporation– From free liquid of permanently saturated
surface
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
h
Area, A
CS
w
a
AEm wv
dtdh
E
nRsH
Sensibleheat to air
Net radiationVapor flow rate
Heat conductedto ground
G
Methods of Estimating Evaporation
• Energy Balance Method
• Aerodynamic method
• Combined method
Energy Method
• CV contains liquid and vapor phase water• Continuity - Liquid phase
CS
wCV
wv ddt
dm dAV
0
dt
dhAw No flow of liquid No flow of liquid
water through CSwater through CS
AEm wv
Edt
dh hw
a
vm
dt
dhE
nRsH
G
Energy Method
• Continuity - Vapor phase
CS
avw qAE dAV
0Steady flow of airSteady flow of air
over waterover water
AEw
CS
avCV
avv qdqdt
dm dAV
CS
avw
qA
E dAV
1
CS
avv qm dAV
hw
a
vm
dt
dhE
nRsH
G
CSu
CVu
dgzVe
dgzVedt
d
dt
dW
dt
dH
AV
)2/(
)2/(
2
2
Energy Method• Energy Eq.
0
hw
a
vm
dtdh
E
nRsH
G
.,0;0 consthV
CV
wu dedt
d
dt
dH
GHRdt
dHsn
GHR sn
Energy Method• Energy Eq. for Water in CV
Assume:Assume:1. Constant temp of water in CV1. Constant temp of water in CV2. Change of heat is change in internal energy of water 2. Change of heat is change in internal energy of water evaporatedevaporated
hw
a
vm
dtdh
E
nRsH
G
vvmldt
dH
GHRdt
dHsn
GHRml snvv AEm w
GHRAl
E snwv
1
RecallRecall::
wv
nr l
RE
Neglecting sensible and Neglecting sensible and ground heat fluxesground heat fluxes
Transport Processes
• Sun is the major source of energy in hydrologic cycle
• Energy transport takes place through:– Conduction– Convection– Radiation
EnergyEnergy
Energy & Mass
Energy & Mass
Energy & Mass
Mass
LandOcean
Energy & Mass
Sun
Flux• The rate of flow of extensive property per unit area
of surface through which it passes is called the flux.
area
flowrateFlux
A
A
dtdE /
2VA
QV
A
Vm
A
Qm
Volumetric flux
Mass flux
Momentum flux
Energy flux
Mass flux = density x volumetric flux
Momentum flux = mass flux x velocity
Conduction• Heat is transferred as
molecules with higher temperature collide with lower temperature molecules
• Results from random molecular motion in substances
• Eg. Heating of earth’s land surface
Conduction of mass, momentum and energy
• Flux is proportional to the gradient of a potential
dz
du
dz
dCDfm
dz
dTkfh
Momentum flux (laminar flow)
Newton’s law of viscosity
Mass flux Fick’s law of diffusion
Energy flux Fourier’s law of heat conduction
is dynamic viscosity, D is diffusion coefficient, and k is heat conductivity. Dynamic viscosity () is related to kinematic viscosity () as =
The direction of transport of extensive properties is transverse to the direction of flow.
Convection
• Energy transfer through the action of turbulent eddies or mass movement of fluids with different velocities.
• Turbulence – mechanism causing greater rate of exchange of mass, energy, and momentum than molecular exchanges
• Unlike conduction, convection requires flowing fluid• Eg. Convection causes vertical air circulation in which
warm air rises and cool air sinks, resulting in vertical transport and mixing of atmospheric properties
Convection of mass, momentum and energy
dz
duKmturb
dz
dCKf wm
dz
dTKCf hph
Momentum flux (turbulent flow)
Km is momentum diffusivity or eddy viscosity
Mass flux
Energy flux Kh is heat diffusivity
Kw is mass diffusivity
• Km is 4-6 orders of magnitude greater than turb is the dominant momentum transfer in
surface water flow and air flow.
The direction of transport of extensive properties is transverse to the direction of flow.
Velocity Profile
• Determining momentum transfer requires knowing velocity profile
• Flow of air over land or water – log velocity profile
/0* u Shear velocity
Von Karman constant Roughness heightk
)ln()(0
*
z
z
k
uzu
0Wall shear stress
0z
zk
u
dz
du 1* Velocity gradient
Wind as a Factor in Evaporation
• Wind has a major effect on evaporation, E– Wind removes vapor-laden air by convection – This Keeps boundary layer thin – Maintains a high rate of water transfer from
liquid to vapor phase– Wind is also turbulent
• Convective diffusion is several orders of magnitude larger than molecular diffusion
Aerodynamic Method
• Include transport of vapor away from water surface as function of: – Humidity gradient above
surface– Wind speed across surface
• Upward vapor flux
• Upward momentum flux
nR
E
Net radiation
Evaporation
Air Flow
12
21
zz
qqK
dz
dqKm
vvwa
vwa
12
12
zz
uuK
dz
duK mama
12
21
uuK
qqKm
m
vvw
Aerodynamic Method
• Log-velocity profile
• Momentum flux
nR
E
Net radiation
Evaporation
Air Flow
12
21
uuK
qqKm
m
vvw
oZ
Z
ku
uln
1
*
2
12
12
ln
ZZ
uuka
212
122
ln21
ZZK
uuqqkKm
m
vvaw
Thornthwaite-Holzman Equation
u
Z
Aerodynamic Method
• Often only available at 1 elevation
• Simplifying
nR
E
Net radiation
Evaporation
Air Flow
212
122
ln21
ZZK
uuqqkKm
m
vvaw
uqv and
22
22
ln
622.0
o
aasa
ZZP
ueekm
AEm w
aasa eeBE
22
22
ln
622.0
ow
a
ZZP
ukB
2 @ pressure vapor Zea
Combined Method
• Evaporation is calculated by– Aerodynamic method
• Energy supply is not limiting
– Energy method• Vapor transport is not limiting
• Normally, both are limiting, so use a combination method
ar EEE
wv
nr l
REE
aasa eeBEE
wv
hp
Kl
pKC
622.0
2)3.237(
4098
T
e
dT
de ss
rEE
3.1
Priestly & Taylor
Example
– Elev = 2 m, – Press = 101.3 kPa, – Wind speed = 3 m/s, – Net Radiation = 200 W/m2, – Air Temp = 25 degC, – Rel. Humidity = 40%,
• Use Combo Method to find Evaporation
kJ/kg 244110)25*36.22500(
237010501.23
6
x
Txlv
mm/day10.7997*102441
2003
xl
RE
wv
nr
Example (Cont.)
– Elev = 2 m, – Press = 101.3 kPa, – Wind speed = 3 m/s, – Net Radiation = 200 W/m2, – Air Temp = 25 degC, – Rel. Humidity = 40%,
• Use Combo Method to find Evaporation
mm/day45.7
)day1/s86400(*)m1/mm1000(*126731671054.4 11
xEa
sm/Pa1054.4
1032ln997*3.101
3*19.1*4.0*622.0
ln
622.0 1124
2
22
22
x
xZZP
ukB
ow
a
Pa3167ase
Pa12673167*4.0* asha eRe
Example (Cont.)
– Elev = 2 m, – Press = 101.3 kPa, – Wind speed = 3 m/s, – Net Radiation = 200 W/m2, – Air Temp = 25 degC, – Rel. Humidity = 40%,
Pa/degC1.67102441*622.0
103.101*1005
622.0 3
3
x
x
Kl
pKC
wv
hp
• Use Combo Method to find Evaporation
Pa/degC7.188)253.237(
3167*40982
738.0
mm/day2.745.7*262.010.7*738.0
ar EEE
262.0
Example
– Net Radiation = 200 W/m2,
– Air Temp = 25 degC,
• Use Priestly-Taylor Method to find Evaporation rate for a water body
rEE
3.1 Priestly & Taylor
mm/day10.7rE 738.0
mm/day80.610.7*738.0*3.1 E
Evapotranspiration
• Evapotranspiration– Combination of evaporation from soil surface and
transpiration from vegetation– Governing factors
• Energy supply and vapor transport• Supply of moisture at evaporative surfaces
– Reference crop• 8-15 cm of healthy growing green grass with abundant water
– Combo Method works well if B is calibrated to local conditions
Potential Evapotranspiration
• Multiply reference crop ET by a Crop Coefficient and a Soil Coefficient
rcs ETkkET
3.10.2
t;Coefficien Crop
c
c
k
k
10
t;Coefficien Soil
s
s
k
k
ET Actual ET
ET Crop Reference rET
http://www.ext.colostate.edu/pubs/crops/04707.html
CORN
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100 120 140 160
Time Since Planting (Days)
Cro
p C
oef
fici
ent,
kc
Resources on the web
• Evaporation maps from NWS climate prediction center– http://www.cpc.ncep.noaa.gov/soilmst/e.shtml
• Climate maps from NCDC– http://www.nndc.noaa.gov/cgi-bin/climaps/climaps.pl
• Evapotranspiration variability in the US– http://geochange.er.usgs.gov/sw/changes/natural/et/
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