EVAPORATION
• Definition: Process by which water is changed from the
liquid or solid state into the gaseous state through the
transfer of heat energy (ASCE, 1949).
• It occurs when some water molecules attain sufficient
kinetic energy to break through the water surface and
escape into the atmosphere (~ 600 cal needed to
evaporate 1 gram of water).
• Depends on the supply of heat energy and the vapor
pressure gradient (which, in turn, depends on water and
air temperatures, wind, atmospheric pressure, solar
radiation, etc).
TRANSPIRATION (T)
• Transpiration is the evaporation occurring
through plant leaves (stomatal openings).
• Transpiration is affected by plant physiology
and environmental factors, such as:
- Type of vegetation
- Stage and growth of plants
- Soil conditions (type and moisture)
- Climate and weather
EVAPOTRANSPIRATION (ET)
• Combined “loss” of water vapor from within the leaves of
plants (“transpiration”) and evaporation of liquid water
from water surfaces, bare soil and vegetative surfaces.
• Globally, about 62% of the precipitation that falls on the
continent is evapotranspired (~72,000 km3/yr); 92% of
which from land surfaces evapotranspiration and 3%
from open water evaporation (source: Dingman,
“Physical Hydrology”).
• Approximately 70% of the mean annual rainfall in the
U.S. is returned to the atmosphere as evaporation or
transpiration.
EVAPOTRANSPIRATION (ET)
• In practice, the terms E and ET are often used to
mean the same thing - the evaporation from the
land surface.
• Therefore, you must use the context to
determine what the term evaporation means in a
specific case (i.e., is it just from an open water
surface or the entire land surface?).
POTENTIAL EVAPORATION (PE)
• is the climate controlled evaporation from
an open water surface with unlimited
supply (and no thermal capacity).
POTENTIAL
EVAPOTRANSPIRATION (PET)
• is the ET that would occur from a well
vegetated surface when moisture supply is
not limiting (often calculated as the PE).
• Actual evapotranspiration (AET; ET)
drops below its potential level as the soil
dries.
DESIGN
• Evaporation must be considered in the design of
large water storage reservoirs, large-scale water
resources planning and water supply studies.
• For flood flow studies, urban drainage design
applications it may be neglected.
• Example: during typical storm periods with
intensities of 0.5 in/hr, evaporation is on the
order of 0.01 in/hr.
METHODS FOR ESTIMATING
EVAPORATION
• Water budget methods
• Energy budget methods
• Mass transfer techniques (e.g., Meyer,
Thornthwaile-Holzman)
• Combination of energy budget and mass
transfer methods (e.g.,Penman)
Energy budget method
Total solar
radiation - Rt
Net energy advected
(net energy content
of incoming and
outcoming water -
Ee
Reflected solar
radiation - Rr
Energy used for
evaporation
(latent heat)- Ee
Sensible heat loss
from the water
body to the
atmosphere - Hn
Net long-wave radiation
exchange between the
atmospere and the water
body- R1
Energy stored - Es
R1 includes long-wave (LW) radiation from the atmosphere, reflected LW radiation, LW radiation emitted by water
Energy budget method
 g  cal 
Es 
   E a  R t    R r  E e  H n  R1 
2
 cm - day 
Ee
Rt
Rr
Ee
Hn
R1
Es
R1 includes long-wave (LW) radiation from the atmosphere, reflected LW radiation, LW radiation emitted by water
Energy budget method
• Amount of evaporation - E
 mm 
Ee
E
  10
Hv
 day 
 g  cal 
Hv
 596  0 . 52 T - latent heat of vaporizat ion
3 
 cm 
T  C  - temperatu re of the water surface
Energy budget method
Characteristics:
• most accurate method (evaporation is a function of the
energy state of the water system)
• difficult to evaluate all terms
• energy balance equation has to be simplified
• empirical formulas are used (although radiation
measurements are preferable)
Water budget method
S
t
  P  Q  Q r  Q s   Q 0  Q d  E 

E 
Precipitation - P
Evaporation- E
Inflow- Q
Surface runoff - Qr
Subsurface
runoff - Qs
Outflow- Q0
Subsurface seepage losses- Qd
Water budget method
• Units:
 ac - ft 
E

month


• Depth of evaporation:
 in  12 E
E 

 day  nA p
*
 mm  12 ( 25 . 4 ) E
E 

nA p
 day 
*
n – number of days
Ap – area of the pond [ac]
Water budget method
Characteristics:
- Simple
- Difficult to estimate Qd and Qs
- Unreliable, accuracy will increase as Δt
increases
• Example on water balance model
Mass transfer methods - definitions
 17 . 3T 
e s [ mb ]  6 . 11 exp 
;
 T  237 . 3 
e s mm Hg  
Rh 
e s [ mb ]
;
Table 14.1
1 . 36
e
es
e – actual vapor pressure (difference in the atmospheric pressure with
and without the vapor)
es – saturated vapor pressure (partial pressure of water vapor in
saturated air)
T [ºC] – air temperature
Rh – relative humidity
• Evaporation is a diffusive process (moves from
where its concentration is larger to where its
concentration is smaller at a rate that is
proportional to the gradient of concentration):
E = b0 (es0 – ea)
es0 – vapore pressure of the evaporating surface;
saturation vapor pressure at the water surface
temperature Ts
- ea – vapor pressure of overlying air at the same
height
- b0 – empirical coefficient that has to be
calibrated
• E = b0 (es0 – ea)
• Studies showed that
b0 = function (air turbulence)=fn(v)
• E = b1 fn(v)(es – ea)
• Meyer’s formula:
E = 0.5 (1 + 0.1 v30)(es – ea)
v30 - wind speed [mi/h] at 30 ft height;
es; ea [in Hg]
E [in/day]
• b0 = f(v, es, ea, Ta, Tw)
• Thornthwaite-Holzman equation (no calibration)
b0 = f(v,T,k);
k – Von Karman constant (0.41)
833 k ( e1  e 2 )( v 2  v1 )
2
E 
2
 z2 
 T  459 . 4 
ln 

 z1 
• Example
Combination approach – Penman equation
• Combine mass-transfer and energy-balance equations
to derive an evaporation equation that does not
require water surface temperature data.
(14  24 )
Hw 
  E n    E ao
 
Hw
 mm 

 - evaporatio n
 day 
En
 mm 

 - net radiation
 day 
E ao
 mm 

 - mass transfer
 day 
Hw 
Penman equation:
(14  14 )
 
e0  e
*
a
T0  T

1
  E n    E ao
 
25 , 083
1 . 36 T  237 . 3 
2
 17 . 3T 
exp 

 T  237 . 3 
Δ [mm Hg/ºC] – slope of the saturation vapor pressure curve at mean temperature
T0 [ºC] – temperature of the water surface
T [ºC] – temperature of the air
e0 [mm Hg] - vapor pressure of the water surface
ea* [mm Hg] - saturated vapor pressure at temperature T
Penman equation:
Hw 
  E n    E ao
 
• En [mm/day] – net radiation
 g - cal 
• Start with energy equation: R n 
  RI  R B
2
 cm  day 
Rn – net radiation
RI – amount of energy absorbed (shortwave)
RB – net outward flow of longwave radiation
Penman equation:
Hw 
  E n    E ao
 
Rn  RI  RB
n 

R I  R A 1  r  a  b 
D

RI [g-cal/cm2-day] – amount of energy absorbed (shortwave)
RA [g-cal/cm2-day] – total possible radiation for the period of estimation;
it is function of latitude and season; Table 14-3.
r – reflection coef. (0.05-0.12)
a,b – empirical coef. (a=0.2; b=0.5)
n/D – fraction of possible sunshine (from climatic atlas)
Rn  RI  RB

R B   T  273  0 . 47  0 . 077
4
  1 . 1777  10
7

n 

e  0 .2  0 .8 
D



cal


2
4
cm

C
day


• Rn[g-cal/cm2-day] – net radiation
• RI [g-cal/cm2-day] – amount of energy absorbed (shortwave)
• RB [g-cal/cm2-day] – net outward flow of longwave radiation
• e [mm Hg] – actual vapor pressure
• T [ºC] – air temperature
• n/D – fraction of possible sunshine (from climatic atlas)
Penman equation:
 mm 
Rn
En 
  10
Hv
 day 

Hw 
  E n    E ao
 
net radiation
 g - cal 
Rn 
  net radiation
2
 cm  day 
 g - cal 
Hv
 596  0 . 52 T - latent heat of vaporizat ion
3 
 cm 
Penman equation:
Hw 
  E n    E ao
 
 g - cal 
Rn 

2
 cm  day 
 mm 
Rn
En 
  10
Hv
 day 
 g - cal 
Hv
 596  0 . 52 T
3 
 cm 
• En – net radiation
• Rn – net radiation
•Hv –latent heat of vaporization
Penman equation:
 
c p pa
Hw 
  E n    E ao
 
(14 - 11)
0 . 62 H v
c p  specific
heat of air at constant
p a  atmospheri
pressure
c pressure
 g - cal 
Hv
 596  0 . 52 T - latent heat of vaporizat ion
3 
 cm 
  0.485
(typical value)
H w (E ) 
Penman equation:
E ao
 mm 

 - mass transfer
 day 
  E n    E ao
(based on diffusivit
E a 0  0 . 35 e s  e 0 . 2  0 . 55 V
e s mm Hg  - saturated
 
y law)

vapor pressure at air temper ature T a
e mm Hg  - actual vapor pressure at air temper ature T a
V [m/sec] - wind spead at 2 m height
Penman equation:
 mm    E n    E ao
Hw

 
 day 
- evaporatio n
E acre - ft  - total evaporatio n
 mm 
1
1
E acre - ft   H w 

  n days   Area acres  
12 25 . 4
 day 
example
Measuring evaporation
Irrigated lysimeter
PE = Rainfall + Irrigation - Percolation
Atmometer
U.S. Weather Bureau Class A Pan
4 ft
Wooden
support
10 in
6 in
Galvanized
steel
Evaporation pan
S
t
  P  Q  Q r  Q s   Q 0  Q d  E 
P  Ep 
Surface runoff - Qr
S
t

Ep  P 
S
t
Evaporation - E Precipitation - P
Inflow- Q
Subsurface
runoff - Qs
Outflow- Q
Subsurface seepage losses- Qd
Evaporation Pan
• Historical records of daily pan evaporation
are available from the National Climatic
Data Center (NCDC) for U.S. Weather
Buruau Class A Land pans.
Evaporation Pan
• We are not really interested in what
evaporates from a pan; instead we want to
know the regional evaporation from land
surface or the evaporation from a nearby
lake. Unfortunately, pan evaporation is
often a poor indicator of these variables
(due in part to pan boundary effects and
limited heat storage).
Evaporation Pan
• Evaporation from an open water surface (E) is
usually estimated from the pan evaporation (Ep)
as:
E = K Ep
where K is the pan coefficient (regional coef,
usually around ~0.7). Similar expressions are
also used in practice to estimate potential
evapotranspiration from pan data.
Pan coefficient
FIGURE 2. Source:
Farnsworth,
Richard K., Edwin
S. Thompson, and
Eugene L. Peck.
After Map 4: Pan
Coefficients.
In NOAA Technical
Report NWS 33,
Evaporation Atlas
for the Contiguous
48 United States,
NWS, NOAA, 1982.
evapotranspiration from satellite data
• When a surface evaporates, it looses energy and
cools itself. It is that cooling that can be observed from
space. Satellites can map the infrared heat radiated
from Earth, thus enabling to distinguish the cool
surfaces from the warm surfaces.
winter
summer