Transcript Document 7462002

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
Rn
u
Net radiation
Air Flow
E
Evaporation
Evaporation from a Water
Surface
• Simplest form of evaporation
– From free liquid of permanently saturated
surface
Evaporation from a Pan
Sensible
heat to air
Net radiation
m
 v   w AE
Rn
Hs
Vapor flow rate
a
•
•
•
•
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
CS
E
w
dh
dt
Area, A
G
Heat conducted
to ground
h
Methods of Estimating Evaporation
• Energy Balance Method
• Aerodynamic method
• Combined method
Energy Method
• CV contains liquid and vapor phase water
• Continuity - Liquid phase
Hs
Rn
d
 m v    w d    wV  dA
dt CV
CS
m
v
a
dh
E
dt
w
G
h
dh dh
 w A
 E
dt dt
m
 v   w AE
0
No flow of liquid
water through CS
Energy Method
• Continuity - Vapor phase
m v 
Hs
Rn
d
 qv  a d   qv  aV  dA
dt CV
CS
0
m
v
m v   qv  aV  dA
a
E
dh
dt
w
CS
  w AE
h
Steady flow of air
over water
 w AE   qv  aV  dA
CS
G
E
1
 qv  aV  dA
 w A CS
Energy Method
• Energy Eq.
0
Hs
Rn
dh
dt
w
CS
 0;
m
v
V  0, h  const.
dH d
  eu  w d
dt dt CV
a
E
dH dW d

  (eu  V 2 / 2  gz) d
dt
dt
dt CV
 
  (eu  V 2 / 2  gz) V  dA
 Rn  H s  G
h
dH
 Rn  H s  G
dt
G
Hs
Rn
Energy Method
• Energy Eq. for Water in CV
a
E
dh
dt
dH
 Rn  H s  G
dt
dH
 lv m v
dt
E
1
lv  w A
w
G
Assume:
1. Constant temp of water in CV
2. Change of heat is change in internal energy of water evaporated
lv m
 v  Rn  H s  G
m
v
Recall:
Rn  H s  G 
m
   w AE
Neglecting sensible and ground heat
fluxes
R
Er  n
lv  w
h
Transport Processes
• Sun is the major
source of energy
in hydrologic
cycle
• Energy transport
takes place
through:
– Conduction
– Convection
– Radiation
Sun
Energy
Energy & Mass
Energy & Mass
Ocean
Energy & Mass
Energy
Energy & Mass
Mass
Land
Flux
• The rate of flow of extensive property per unit
area of surface through which it passes is
called the flux. Flux  flowrate
area
Q
A
Volumetric flux
q
Mass flux
m 
Momentum flux
m V QV

 V 2 Momentum flux = mass flux x velocity
A
A
Energy flux
Q
A
dE / dt 
A
Mass flux = density x volumetric flux
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
Momentum flux
(laminar flow)
 
Mass flux
f m  D
Energy flux
f h  k
du
dz
Newton’s law of viscosity
dC
dz
dT
dz
Fick’s law of diffusion
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 (n) as  =  n
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
Momentum flux
(turbulent flow)
 turb  K m
Mass flux
f m   K w
Energy flux
f h  C p K h
du
dz
dC
dz
dT
dz
Km is momentum diffusivity or eddy viscosity
Kw is mass diffusivity
Kh is heat diffusivity
• Km is 4-6 orders of magnitude greater than
n.
 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
u*
z
u( z) 
ln( )
k
z0
u*   0 / 
Shear velocity
 0 Wall shear stress
du u * 1
Velocity gradient

dz
k z
3
Elevation (z)
k Von Karman constant
z 0 Roughness height
4
u( z) 
u*
z
ln( )
k
z0
2
1
0
0
1
2
Velocity (u)
3
4
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
Rn
Net radiation
Air Flow
E
Evaporation
• Upward vapor flux
qv1  qv2
dqv
m    a K w
 a K w
dz
z2  z1
• Upward momentum flux
du
u2  u1
  a K m  a K m
dz
z2  z1

K w qv1  qv2
m  
K m u 2  u1 

Aerodynamic Method

K w qv1  qv2
m  
K m u 2  u1 
Rn

Air Flow
• Log-velocity profile
Evaporation
u
• Momentum flux
 k u  u  
  a  2 1 
 lnZ 2 Z1 
E
Z
u 1  Z 
 ln 
u * k  Z o 
Net radiation
2
m 


K w k 2  a qv1  qv2 u 2  u1 
K m lnZ 2 Z1 2
Thornthwaite-Holzman Equation
Aerodynamic Method
m 


K w k 2  a qv1  qv2 u 2  u1 
Net radiation
K m lnZ 2 Z1 2
Air Flow
qv and u
• Often only available at 1
elevation
• Simplifying
m 
Rn
0.622k 2  a eas  ea u 2
PlnZ 2 Z o 2
m
   w AE
ea  vapor pressure @ Z 2
E
Evaporation
Ea  Beas  ea 
B
0.622k 2  a u 2
P w lnZ 2 Z o 2
Combined Method
• Evaporation is calculated by
– Aerodynamic method
• Energy supply is not limiting
E  Er 
– Energy method
• Vapor transport is not limiting
Rn
lv  w
E  Ea  Beas  ea 
• Normally, both are limiting, so use a combination
method
E


Er 
Ea
 
 
C p Kh p
des
4098es



2
0.622lv K w
dT (237.3  T )
Priestly & Taylor
E  1.3

Er
 
Example
• Use Combo Method to find Evaporation
–
–
–
–
–
–
Elev = 2 m,
Press = 101.3 kPa,
Wind speed = 3 m/s,
Net Radiation = 200 W/m2,
Air Temp = 25 degC,
Rel. Humidity = 40%,
lv  2.501x106  2370T
 (2500  2.36 * 25) x103  2441 kJ/kg
Er 
Rn
lv  w

200
3
2441x10 * 997
 7.10 mm/day
Example (Cont.)
• Use Combo Method to find Evaporation
–
–
–
–
–
–
Elev = 2 m,
Press = 101.3 kPa,
Wind speed = 3 m/s,
Net Radiation = 200 W/m2,
Air Temp = 25 degC,
Rel. Humidity = 40%,
B
0.622k 2  a u 2
P w lnZ 2 Z o 2

eas  3167 Pa
ea  Rh * eas  0.4 * 3167  1267 Pa
0.622 * 0.4 2 *1.19 * 3

101.3 * 997 ln 2 3x10 4
2
 4.54 x1011 m/Pa  s
Ea  4.54x1011 3167  1267 * (1000 mm / 1 m) * (86400s / 1day)
 7.45 mm/day
Example (Cont.)
• Use Combo Method to find Evaporation
–
–
–
–
–
–
C p Kh p
1005*101.3x103
Elev = 2 m,


0.622lv K w 0.622 * 2441x103
Press = 101.3 kPa,
Wind speed = 3 m/s,
4098* 3167
Net Radiation = 200 W/m2,  
 188.7 Pa/degC
2
(237.3  25)
Air Temp = 25 degC,
Rel. Humidity = 40%,

 0.738
 
E

 
 67.1 Pa/degC
 0.262


Er 
Ea  0.738 * 7.10  0.262 * 7.45  7.2 mm/day
 
 
Example
• Use Priestly-Taylor Method to find
Evaporation rate for a water body
– Net Radiation = 200 W/m2,
– Air Temp = 25 degC,
Er  7.10 mm/day
E  1.3

Er
 

 0.738
 
E  1.3 * 0.738* 7.10  6.80 mm/day
Priestly & Taylor
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
ET  k s kc ETr
ET  Actual ET
ETr  Reference Crop ET
0.2  k c  1.3
k s  Soil Coefficient;
0  ks  1
0.9
0.8
Crop Coefficient, kc
k c  Crop Coefficient;
CORN
1
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
20
40
60
80
100
Time Since Planting (Days)
http://www.ext.colostate.edu/pubs/crops/04707.html
120
140
160
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/