Download long wave radiation at sea surface

LONG WAVE RADIATION AT SEA SURFACE
The long wave radiation is the radiation emitted by the ocean
surface at wavelengths greater than those of the visible light
(at about 800 nanometres (nm)) but shorter than those of
microwaves (at about 800,000 nm). Infrared radiation is
associated with heat energy and not with visible light.
We will consider the NET long wave (LWnet) radiation at
sea surface which represents the difference between the
upward infrared radiation emitted by the ocean surface
(LWs) and downward infrared radiation from the
atmosphere (LWa):
LWnet = LWs - LWa
(1)
Net LW radiation at sea surface comes out as a result of many
complex processes
LW irradiance of clear sky
LW irradiance
of sea surface
reflected
atm. LW
LW irradiance
of clouds
LWa
sea surface
LWnet=???
The ocean surface irradiance consists of the emitted LW
radiation from the sea surface and reflected atmospheric LW
irradiance:
LWs = LWs0 + LLWa
(2)
where LWs0 is LW irradiance of ocean surface
L is surface long wave albedo
Thus, the net LW radiation at sea surface can be expressed as:
LWnet = LWs0 - (1-L)LWa
(3)
Two industrial workers
go for a lunch:
They take (besides the meals) each cup of tea simultaneously.
• The first worker puts sugar into the cup immediately and starts to eat the
main dish.
• The second worker first starts to eat and puts the sugar into the cup just
before the drinking.
They start to drink their tea
simultaneously
Whose tea will be hotter at
the moment of drinking?
Upward long wave irradiance from sea surface
This is the major component of longwave exitance!!!! For this
part the physics is a simple blackbody radiation
LWs0 = Ts4
(4)
where
 is the Stefan-Boltzmann constant (5.6710-8Wm-2K-4)
Ts is the sea surface !!!skin!!! temperature in degrees Kelvin
 is the emissivity of the sea surface
Emissivity of the sea surface  in a general case depends on
the sea state and optical properties of the sea water. For the
fresh water  = 0.92 and varies from 0.89 to 0.98 for different
conditions.
Sea surface skin temperature Ts is not equivalent to SST,
measured at ships by buckets or engine intakes, it is the
temperature of very thin (several to several hundreds ) surface
skin layer, namely skin temperature. Longwave absorption and
emission both take place in just about the top 0.5 mm of water,
depending on wavelength.
Back to the skin temperature issue - later
Downward amospheric long wave irradiance
Downwelling longwave radiation (longwave irradiance)
originates from the emission by atmospheric gases (mainly
water vapor, carbon dioxide and ozone), aerosols and clouds.
Long-wave albedo is also poorly known and depends on the sea
state and cloud conditions. Downwelling LW is the smallest, but
the most uncertain term in the net LW radiation (longwave
exitance).
Determining surface net long wave radiation
LW irradiance of clear sky
LW irradiance
of clouds
emission of gases
(water vapor, CO2,
ozone) and aerosols
LWa
reflected
atm. LW
sea surface
Measurements
Modelling - RTMs
Parameterization
Measurements of LW radiation:
The pyrgeometer is of a similar
construction to the pyranometer, but
the single dome is made from silicon or
similar material transparent to the
longwave band, coated on the inside
with an interference filter to block
shortwave radiation. The longwave
irradiance passing through the dome,
which we wish to determine, is only
one component of the thermal balance
of the thermopile. The remaining
components come from various parts
of the instrument. To isolate the
geophysical
component,
the
manufacturers provide the correction
equations.
More detailed description of pyrgeometer
The PIR, or pyrgeometer, is sensitive to wavelengths in the range from 3000 to 50000 nm, which covers the
span of temperatures (or thermal radiation) expected from the earth and atmosphere. The pyrgeometer works
on the same principle as the pyranometer in that radiant energy is converted to heat energy which, in turn, is
measured by a thermopile. However, protecting the sensor from the environment (e. g., solar radiation) is
difficult. To do this, the dome is made of silicon, which is nearly opaque to solar wavelengths. The dome is
also coated with a grayish interference filter that does not transmit wavelengths shorter than 3000 nm, but
sharply increases to 50% transmission at 4000 nm. From 4000 to 50000 nm its transmittance slowly falls to
about 30-40%. The detector senses a net signal from a number of sources which includes emissions from
targets in its field of view, emission from the case of the instrument, and emission from the dome. To
resurrect the true environmental thermal infrared irradiance, temperatures of the detector, case, and dome are
monitored with thermistors. Because the case is shielded from the sun, its temperature represents the air
temperature and therefore is a proxy for the degree of thermal emission by the atmosphere. The dome,
however, is not protected from solar heating. Therefore, the difference between the thermal emissions of the
case and dome represents an erroneous signal that must be removed. (As mentioned before, shading the
dome would make this error negligible.) An empirical calibration equation accounts for all of these effects and
converts the three measured temperatures to a true environmental thermal infrared irradiance in watts per
square meter.
Requirements for calibration facilities
Calibrating facilities for infrared instruments are more complicated and therefore less common than those for
solar radiation, and require careful technique. Field intercomparisons if several instruments are available are
desirable. The use of on-site atmospheric soundings in clear-sky conditions can provide an absolute
reference for longwave irradiance. The calculation of the downwelling longwave flux under a cloud requires
knowledge of both cloud base height and emissivity. Cloud base height may be measured with active systems
such as a MicroPulse lidar (Spinhirne, 1993) or a cloud profiling radar, although an infrared radiometer (such
as the pyrgeometer) would still be needed to estimate cloud emissivity.
Modelling of the long wave
radiation (RTMs)
The radiative transfer equation (RTE)
states that the energy radiated by a parcel
of material in a particular frequency
range and particular direction (denoted by
an increment of solid angle around the
direction) is the sum of energy transmitted
through the parcel and the energy
emitted from within the parcel, in that
frequency interval and direction.
Structure of a simple RTM
TN
TN-1
Dv,N+1
layer N
v,N
layer n
v,n
layer 1
v,1
Uv,N-1
Dv,N
Uv,n
Tn
Tn-1
Dv,n+1
Uv,n-1
Dv,n
Uv,1
T1
T0
RTE evaluates the effect of changes in
temperature, humidity, cloud, aerosols,
and chemical composition. Calculation of
LW radiation should include all the major
absorption bands of CO2, H2O, and O3, as
well the weaker bands of CO2, N2O and
CH4.
optical
thickness
Uv,N
Dv,2
Uv,0
Dv,1
Atmospheric column consists of N
plane parallel layers, n=1,2,…,N.
Temperatures Tn, n=0,1,….,N are
denoted at layer edges. The mean
optical thickness of the nth layer at a
particular frequency  is n.
At frequency  and beam angle  the upward IR irradiance U,n and the downward IR
irradiance D,n at the edges of the layer n are:
U ,n  U ,n 1e
 ,n / 
D ,n  D ,n 1e
 ,n / 
 E ,n 
(5.6)
 E ,n 
where  = cos. In (5,6): the first terms are the transmitted IR irradiances given by
Lambert’s law, and the second terms are the IR irradiances emitted in the layer:
  ,n
d '
E ,n   B ,n ( ') exp[ ( ,n   ' ) /  ]

0
  ,n
E ,n 
 B ,n ( ') exp[  ' /  ]
0
d '
(7,8)

where B,n is the Planck function at frequency  and temperature Tn. Boundary
conditions:
D , N 1  0, U ,0   B ,0   D ,1
(9,10)
 is the albedo, =1- is the emissivity of the ocean surface.
Equation (9): no downward IR flux at the top of the atmosphere.
Equation (10): the upflux at the ocean surface is given by the sum of emission from
the ocean plus the reflection of the downward flux.
For the frequency range [a,b] the total upward Un and downward Dn IR fluxes result from
integrating U,n and U,n overall frequencies in [a,b] and beam angles:
n
b
U n   d  U ,n cos d
0
a
0
b
Dn   d  D ,n cos d

9,10
a
Problems:
Numerical solution of (5)-(12) is difficult and expensive due to:
 The spectral complexity of the atmospheric constituents
 Vertical inhomogeneity of the chemical composition of the
atmosphere
There is a lack of measurements of basic parameters in the
atmospheric column
Short summary:
Most exact are the Line-By-Line Radiative Transfer Models (LBLRTM) which
compute transfer of each constituent for each emission and absorption
spectral line at many levels throughout the profile. Their computational
burden is therefore large, which makes them unsuitable for routine use in
numerical models.
Over the years therefore, many broadband RTM's have been developed,
increasing in accuracy and efficiency with improved parameterizations and
increased computer power. Such models are widely applied in climate
modelling, and in flux retrieval from direct and remotely sensed atmospheric
variables.
The computation of LW flux with the best high spectral resolution codes
under clear conditions is at an advanced state.
For cloudy sky conditions, however, RTM's are not well validated. The
calculation of the downwelling longwave flux under a cloud requires
knowledge of both cloud base height and emissivity.
Parameterization of LW radiation:
LWnet = LWs0 - (1-L)LWa
What do we measure?
SST
Ta, q, C (Cn, Cl)
1. No problem to parameterize the LWs0 , if we have SST and
the emissivity of the sea surface:
LWs0 = Ts4
However, you have to remember that is Ts4 a skin temperature
and is not equal to the bulk SST (LATER!)
2. LW albedo is more poorly known that a SW albedo. Some very tentative
estimates give values in the range of 0.04-0.05 (e.g. Clark et al. 1974). Since
 the value [1-LW albedo] is close (at least of the same
order as) to the emmissivity of sea surface []
 the accuracy of L and  is approximately the same
there is an approach to establish an effective emissivity and to re-write the
equation for the net LW as follows:
LWnet = Ts4  - (1-L)LWa
LWnet = (Ts4  - LWa)
(13)
where  is an effective emissivity and should not be understood as an
emissivity of the sea surface (typical mistake). From (2), (4), (13):
 =(LWs0 - LWa)/ (Ts4  - LWa)
Important:
   = LWs0 / Ts4 
(14)
3. Parameterization of downwelling atmospheric LW radiation
LWnet =  (Ts4 - LWa )
The simplest approach is to measure downwelling LW radiation
and to compare it with different combinations of surface
parameters:
Tair, q, Cn, Cl
However, this approach results in very uncertain
dependencies due to very different optical properties of clear
sky and cloudy atmosphere. Air temperature blackbody
radiation shows significant differences for clear skies and
cloudy skies.
Guest (1998) –
2 months of direct LW measurements in Weddell Sea:
Cloudy conditions
Clear sky
Processes are quite different
under clear skies and clouds
! separate analysis should be performed for
atmospheric LW under clear sky and clouds
1. Downwelling long wave radiation under clear skies
Since information about atmospheric gases and aerosols is generally
unavailable in routine observational practice, major efforts of researchers
were concentrated on studying relationships between the clear sky
downwelling atmospheric LW on
 Surface humidity
 Surface air temperature
Theoretically, from a physical view point, surface humidity should have a
closer link with surface humidity.
Bignami et al. (1995) using results from direct
observations in seven cruises in Mediterranean
Sea, found close relationship between surface
water vapor pressure and the ratio between
atmospheric downwelling LW and air temperature
blackbody radiation:
where
LWa = Ta4(a+be)
a=0.684, b=0.0056, =0.75
However, in practice much better relationships are observed for surface air
temperature. Reasons:
 more easily available (more observations)
 measurements are more accurate
Swinbank (1963) from Indian Ocean and lake observations:
LWa = Ta4(a+bTa)
or
ln(LWa / Ta4) =a+ln(Ta)
where
(14a)
(14b)
a=-15.75, =0.75
Guest (1998) tested many formulations of clear sky
atmospheric LW.
 No evidence of a better approximation for humidity than
for air temperature.
Guest (1998) results (for your files):
Malevsky et al (1992) from a very big data set collected in
different World Ocean regions (incl. tropics and mid-latitudes)
found the following relationship between the downwelling
atmospheric LW and humidity (water vapor pressure):
LWa = Ta4(0.60+0.049e)
(16)
Similar dependency for air temperature was:
LWa = 1.026Ta210-5 –0.541
(17)
There has been found considerably lesser scatter for (17) than for
(16) and a smaller RMS error. INTERESTING: equation (17) looks
physically less reasonable than those which include Ta4.
However, analysis of empirical data shows that formula (17)
works well in most conditions.
Thus, now we assume the following form of parameterization of
the net LW radiation:
Effective emissivity of sea
surface (accounts for the LW
albedo and skin effect)  !!!
Sea surface !skin! temperature
blackbody radiation. Since we
do not have normally “skin”
estimate, we account for the
bulk effect in 
LWnet =  [ Ts4 - ( LWa0  F(c) )]
Atmospheric
skies:
downwelling
LW
under
clear
Parameterized as a function of either
surface humidity or surface temperature
Relationships with temperature give better
results!
?
Function of cloud cover –
Should account for the
effect of clouds
2. Downwelling long wave radiation under clouds – the cloud
modification of LWa.
What should be parameterized from a theoretical view point is
a cloud temperature blackbody radiation: Tcl4
Lind and Katsaros (1982):
LWc(2) = n(2)(2) Tcl(2)4 + [1-n(2)] LWc(3)
LWc(1) = n(1)(1) Tcl(1)4 + [1-n(1)] LWc(2)
LWc(tot) = (1-(0)) LWc(1) +
+ LWa(sky) +(0)T0(1)4

n

is fractional cloud cover of the
subscribed cloud layer
Tcl is cloud base temperature of the
subscribed cloud layer

is effective emittance of the
subscribed cloud layer
(0) is emittance of layer from the surface
to lowest cloud base
Tcl is equivalent radiative temperature of
the lower layer
We DO NOT know (measure)
We come actually to another RTM!
The only available parameter is the
total fractional cloud cover and
sometimes is the fractional cover of
the low-level cloudiness.
LWa
LWa + LWcl
Typical approach: to make
measurements under the known
cloud conditions and to compare
clear sky atmospheric LW with that
measured under the cloudy sky.
Parameterization of
F(n)
Bignami et al. (1995):
F(n) = 1+0.1762c2 (Mediterranean Sea)
Clark et al. (1974):
F(n) = 1-0.69c2
(Pacific Ocean)
Efimova (1962):
F(n) = 1-0.80c
This effect has to be parameterized
(land data)
Typical expression is
for the total cloud cover
1ac
Malevsky et al. (1992) from his collection of field measurements
for the total cloud cover found:
LWcl+a = 0.928Ta210-5 –0.397
(18)
He assumed that
LWcl+a = LWa (1+ktnt2)
(19)
Coefficient kt can be derived from (19) under nt=1:
kt = (LWcl+a + LWa) / (LWa)
where:
(20)
LWa = 1.026Ta210-5 –0.541)
Not surprisingly, in this formulation kt becomes dependent on
the air temperature, since both LWcl+a and LWa are the
functions of air temperature.
Computation of the kt from a simple RTM:
kt = (1/LWa) [cla Tcl4 +
+LWa(0)(4h/Ta)-1]
cl – emissivity of the cloud base
cl – temperature of the cloud base
LWa(0) – irradiance below the cloud layer
cl – surface temperature
 - temperature gradient in the undercloud layer
h – cloud layer height
Thus, for the total cloud cover only:
LWa = [LWa0  F(c)]=(1.026Ta210-5-0.541)(1+ktnt2)
kt = (-0.098Ta210-5 + 0.144) / (1.026Ta210-5-0.541)
Malevsky et al. (1992) first considered the effect of cloudiness for three
different layers (low cloudiness, mid-level cloudiness and upper layer
cloudiness).
For upper layer:
For mid-level:
For lower layer:
LWclu+a = 0.995Ta210-5 –0.496
LWclm+a = 0.932Ta210-5 –0.401
LWcll+a = 0.921Ta210-5 –0.385
(21)
(22)
(23)
For the cloud coefficients:
For upper layer:
For mid-level:
For lower layer:
ku = (LWclu+a+LWa)/(LWa)
km = (LWclm+a+LWa)/(LWa)
kl = (LWcll+a+LWa)/(LWa)
(24)
(25)
(26)
However, normally we have observations only for the fractional cloud cover
of total and low-layer cloudiness. Thus, this 3-layer formulation has been
simplified for the consideration of the total and low-layer cloudiness:
LWa = (1.026Ta210-5-0.541)(1+klnl2)(1+ku+m(nt2-nl2) (27)
ku+m is the coeeficient accounting for the total effect of the mid and
upper layer cloudiness, which can be derived from the coefficients for the
total and low-level cloudiness:
kl = (LWcll+a+LWa)/(LWa)
ku+m = (ktnt2 - klnl2) / [(1+ktnt2)(nt2–nl2)]
(28)
(29)
Now we can finally derive the parameterization of the net long-wave radiation
at ocean surface in a general form:
LWnet =  [Ts4 - (LWa0  F(c))]
Summary:
 History is very long
 The number of parameterizations approaches several tens
 Formulations are similar
 Differences are large
Brunt (1932)
LW=Ts4(0.39-0.05ez1/2)(1-0.8nd), =0.98, d=1
Berliand and Berliand (1952)
LW=Ts4(0.39-0.05ez1/2)(1-0.8nd)+4Ta3(Ts-Ta), =0.98, d=1
Anderson (1952)
LW=[Ts4-Ta4(0.74+0.0049ez)](1-0.8 nd), =0.98, d=1
Efimova (1961)
LW=Ta4(0.254-0.00495ez)(1-cnd)+4Ta3(Ts-Ta), =0.96, d=1
Swinbank (1963)
LW=[Ts4-9.3610-6Ta6](1-0.8 nd), =0.98, d=1
Clark et al. (1974)
LW=Ts4(0.39-0.05ez1/2)(1-cnd)+4Ta3(Ts-Ta), =0.98, d=2
Bunker (1976)
LW=0.022[Ta4(11.7-0.23ez)(1-0.68nd)+4Ta3(Ts-Ta), =0.96, d=1
Hastenrath and Lamb (1978)
LW=Ts4(0.39-0.056q1/2)(1-0.53nd)+4Ta3(Ts-Ta), =0.98, d=2
Malevsky et al. (1992b)
LW=(Ts4-(1.026Ta210-5-0.541)(1+cnd)), =0.91, d=2
Bignami et al. (1995)
LW=Ts4-[Ta4 (0.653+0.00535 ez)(1+0.1762nd)), =0.98, d=2
Josey et al. (2001)
LW=Ts4-(1-L)[Ta +an2 +bn +c +0.84(D+4.01)]4 , =0.98, a, b, c,
D = empirical coefficients, L = 0.045
North Atlantic SW balance: 20S-70N
Variations in short-wave radiation
and long-wave radiation due to the
parameterizations
Malevsky et al. (1992)
LW radiation, 10**14 W
Clark et al. (1974)
Efimova (1961)
Reed (1977)
Lind et al. (1984)
Malevsky et al. (1992)
-80
SW radiation, 10**14 W
(North Atlnatic SW and LW
radiation budget)
-60
Bignami et al. (1995)
50
Dobson and Smith (1988)
-100
-120
-140
40
30
-160
20
1
2
3
4
5
6
7
month
8
9
10
11
12
-180
1
2
3
4
5
6
7
month
8
9
10
11
12
Summary of LW radiation parameterizations:
 Under clear sky and small cloudiness the accuracy is
normally better than 15 W/m2
 Higher uncertainties occur under the moderate and high
cloud cover
 Uncertainties in the tropics are typically higher than in
mid and high latitudes and are primarily associated with
atmospheric clear sky IR irraidance
 “Hot issues” of all parameterizations are “skin
temperature” and representation of the multi-layer
cloudiness of different types by fractional [total] cloud
cover
Recommendations:
 Do not hesitate to use “old” parameterizations
 Try to avoid the use of parameterizations based on water
vapor pressure and humidity
 Do not use Bignami et al. (1995) except for Mediterranean
sea
 Be careful with the choice of emissivity value. Always
remember – it is effective emissivity and not the
emissivity of surface
Radiation balance of the ocean
RB = SW(1-) - LWnet
(30)
At the ocean surface:
Incoming
radiation
defcit
surplus
LW
SW
Outgoing radiation
At the top of atmosphere
Winter
Spring
Summer
Fall
SW
LW
RB
Variations of SW and LW radiation due to different parameterizations
short-wave radiation, W/m*m
350
300
mean variance
max variance
250
200
150
100
50
0
-20
-10
0
10
20
30
40
50
60
70
LATITUDE
long-wave radiation, W/m*m
100
90
mean variance
80
max variance
70
60
50
40
30
20
10
-20
-10
0
10
20
30
LATITUDE
40
50
60
70
/helios/u2/gulev/handout/
longwave1.f – collection of LW radiation F77 codes




RIZL – Malevsky et al. (1992) scheme
RLWISI – Efimova (1961) as modified by Isemer et al (1989)
RLW_CLA – Clark et al. (1974)
RLW_BIG – Bignami et al. (1995)
Try to compare Malevsky, Efimova, Bignami and Clark schemes:
For Ts = 12C:
 Clear sky, dependence on temperature, humidity
 Cloud cover octa=4, dependence on temperature
 Tair = 15C, dependence on cloud cover (in octas)
/helios/u2/gulev/handout/
swm_test.f – program to compute instantaneous values of SW radiation,
using Malevsky et al. (1992) and Dobson and Simth (1988) schemes.
Compilation: f77 –o swm_test swm_test.f radiation.f
Results:
sw.res
swr_test.f – program to compute daily values of SW radiation, using Reed
(1977) scheme.
Compilation: f77 –o swr_test swr_test.f radiation1.f
Results:
swr.res
lw_test.f – program to compute values of LW radiation, using Malevsky et al.
(1992), Clark et al. (1974), Bignami et al. (1995) and Emivova (1962)
schemes.
Compilation: f77 –o lw_test lw_test.f longwave1.f
Results:
lw.res
READING
Angström, A.K., 1925: On the variation of the atmospheric radiation. Gerlands. Beitr. Geophys., 4, 21-145.
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session at the 20th General Assembly of the International Union of Geodesy and Geophysics, IAPSO, Wien, August 1991.
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