Environmental Engineering Reference
In-Depth Information
6.3.16.1 Use of Penman (1948) Equation
The Penman (1948) equation can be used to calculate net
radiation Q n for a soil-atmosphere heat budget. Net radiation
can be written in terms of a flux designated as millimeters
per day:
Table 6.5 Albedo Coefficients for Water and Various
Earth Materials
Surface
Conditions
Albedo, α 4
Clouds
Low overcast, 100m thick
0.40
Q n =
( 1
r) R c
Low overcast, 200m thick
0.50
0 . 092 u ai v 0 . 5 0 . 10
σ s T a 0 . 56
Low overcast, 500m thick
0.70
0 . 90 n
N
+
Smooth, solar angle 60 o
Liquid water
0.05
Smooth, solar angle 30 o
0.10
(6.35)
where:
Smooth, solar angle 10 o
0.35
Smooth, solar angle 5 o
0.60
Q n =
net radiation budget, mm/day,
Wavy, solar angle 60 o
0.10
r
=
reflection coefficient (unitless),
Solid water
Fresh snow, low density
0.85
air temperature, C,
T a
=
Fresh snow, high density
0.65
R c =
short-wave radiation equal
to R a ( 0 . 18
+
0 . 55
Old snow, clean
0.55
n/N), mm/day,
Old snow, dirty
0.45
solar radiation, MJ/m 2 /day,
R a
=
Glacier ice, clean
0.35
Stefan-Boltzmann constant, W/m 2 / K 4 ,
σ s
=
Glacier ice, dirty
0.25
u air
v
=
vapor pressure in the air above ground surface,
kPa, and
Sand
Dry, light; high sun
0.35
Dry, light; low sun
0.60
n/N
=
sunshine ratio (i.e., actual/possible hours of bright
sunshine).
Gray, wet
0.10
Gray, dry
0.20
White, wet
0.25
Net radiation values calculated using the Penman (1948)
equation have been found to be greater than measured net
radiation values.
White, dry
0.35
Soil
Organic, dark
0.10
Clay
0.20
Sandy, light
0.30
6.3.16.2 FAO56-Penman-Monteith Method
The International Commission for Irrigation and Drainage
and the Food and Agriculture Organization of the United
Nations have recommended that the Penman-Monteith
(FAO56-PM) method be used for the calculation of
PE. Allen et al. (1998) outlined a procedure for the
determination of net radiation R a required for the FAO-56
method. Net radiation was calculated as follows:
Grass
Typical fields
0.20
Dead, wet
0.20
Dead, dry
0.30
Tundra
0.15
Crops
Cereals
0.25
Cotton, potato, tomato
0.20
Sugar cane
0.15
Trees
Rain forest
0.15
Eucalyptus
0.20
R n =
R ns
R nl
(6.36)
Redpineforest
0.10
Mixed hardwoods in leaf
0.18
where:
net radiation, J/m 2 /d,
R n =
Source : Data from Lee (1980).
incoming net short-wave radiation, J/m 2 /d, and
R ns =
outgoing net long-wave radiation, J/m 2 /d.
R nl
=
The albedo coefficient is a measure of how strongly a
material reflects a light source such as the sun. Albedo (or
whiteness) is defined as a dimensionless ratio of the total
reflected radiation to incident radiation. The average albedo
for the earth's surface is about 0.30.
The outgoing net long-wave radiation R nl is proportional
to the absolute temperature of the surface raised to the fourth
power and can be expressed as follows:
The incoming net short-wave radiation R ns is a result of
the difference between incoming and reflected solar radia-
tion and can be written as follows:
R ns =
R s
α 4 R s
(6.37)
where:
0 . 092 u ai v 0 . 5 0 . 10
σ s T aK 0 . 56
0 . 90 n
N
α 4 =
albedo
or
canopy
reflection
coefficient
(see
R nl =
+
Table 6.5 for typical values of α 4 ) and
total incoming solar radiation, J/m 2 /d.
(6.38)
R s
=
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