Groundwater and Aquifers Groundwater Hydraulics Daene C. McKinney.
Evaporation Slides prepared by Daene C. McKinney Reading: Applied Hydrology Sections 4.1 and 4.2...
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Transcript of Evaporation Slides prepared by Daene C. McKinney Reading: Applied Hydrology Sections 4.1 and 4.2...
Evaporation
• Slides prepared by Daene C. McKinney
• Reading: Applied Hydrology Sections 4.1 and 4.2
• Quotation for today (from Socrates) "There is only one good, that is knowledge; there is only one evil, that is ignorance."Contributed by Matt Harold.
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
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/