1. PARAMETERIZATION OF SHORT WAVE RADIATION AT SEA SURFACE
Massive measurements of SW radiation at sea are not available,
because merchant ships are not equipped with pyranometers (and
pyrgeometers) to measure the incoming shortwave radiation.
Instead, the insolation has to be estimated from the information
about ship's position and the cloud cover visually estimated by
the ship officer. Such an estimate is considered to be relatively
crude, however, it represents the state of the art of our knowledge
about SW radiation at sea surface.

2. SW radiation at
sea surface is
determined by:
Solar altitude
Molecular
diffusion
Gas absorption
Water vapor
absorption
Aerosol
Measurements
Modelling
Parameterization

3. Two examples of in-situ daily time series of SW radiation
Broken clouds
Nearly clear
sky conditions
At which time scales do we need to parameterize SW?

4. SST,°C Ta,°C q, g/kg C (Cn, Cl), octa
What do we really measure at sea surface?
SST,°C Ta,°C q, g/kg C (Cn, Cl), octa
The short-wave radiation flux (SW) at sea surface can be parameterized (i.e. expressed in terms of the parameters measured in-situ) as:
Qsw = Qt TF (1)
where
Qt =S0 cos h (2)
Qt is SW radiation at the top of the atmosphere,
S0 is solar constant,
h is solar altitude,
TF is the transmission factor of the atmosphere, it has
to be parameterized in terms of cloud cover and
thermodynamic parameters of the atmosphere.

5. Two approaches to parameterize the SW radiation
One-step parameterizations: transmission factor depends on cloudiness and the atmospheric temperature/humidity variables
Two-step parameterizations: atmospheric transmission is separated into SW modification under clear sky and modifications by clouds
In which units the cloud cover is measured?
Octa (1-8) (ii) Tens of % (1-10)
Be concerned about the units used!
Octa ~ 4
PR ~ 5
Octa ~ 7
PR ~ 8.75

6. One-step parameterizations
What should be parameterized, is the atmospheric transmission factor:
TF = Qsw / Qt = Qsw / (S0 cos h) (3)
Linear models (Lumb 1964, Lind et al. 1984):
TF = ai + bi (cos h) (4)
where
i is the cloud category
a, b, are the empirical
coefficients derived
from observations

7. Values of numerical coefficients:
Lind et al. (1984)
Lumb (1964)
Octa
categories a b  1
0.517
0.317
0.117
0.480
0.359
0.136 2
0.474
0.381
0.138
0.383
0.443
0.154 3
0.421
0.413
0.148
0.363
0.420
0.150 4
0.380
0.468
0.151
0.308
0.453
0.166 5
0.350
0.457
0.156
0.250
0.366
0.137 6
0.304
0.438
0.158
0.181
0.321
0.157 7
0.230
0.384
0.221
0.256
0.153 8
0.106
0.285
0.124
0.206
0.116 9
0.134
0.295
0.130
0.076
0.186
0.086

8. Direct measurements at OWS J (Dobson and Smith 1988) (1958-1961)
Regressions of transmission factors
for the three OCTA categories
Transmission factor grows
with solar altitude
The highest slope is
observed for moderate
cloud cover
Higher scatter occurs
under small solar
declinations and high

9. Summary of one-step parameterizations:
The accuracy of this approach is low because it requires
consideration of the radiation transfer in the whole
atmospheric column
Most of parameters are usually poorly determined because of
a very complicated and uncertain dependence of the transmission
factor on the cloud cover
Better implementation requires poorly and seldom observed
meteorological parameters (cloud types, weather code)
Recommendations:
Not necessarily bad, if you have information on cloud types (later)
Try to avoid the use of 1-step parameterizations developed
for the land conditions (Budyko, Berliand) over sea
If you use 1-step parameterizations, opt for Dobson and Smith
(1988) nonlinear scheme, as calibrated at Sable Island

10. Two-step parameterizations
To avoid very large uncertainty, associated with the dependence of the
transmission factor on the surface parameters, it is more helpful to
parse the transmission factor into two terms:
One represents the modification of short-wave radiation under clear
sky conditions (astronomy, temperature, humidity, and aerosols are
the main agents of these modification).
The other is the cloud modification of clear sky radiation.
In this case, general formula for the SW radiation becomes:
Qsw = Q0 F(n, T, q, h) (4)
Q0 is clear sky solar radiation at sea surface, which is a function of
the astronomy and of the transmission for the clear sky atmosphere
F(n, T, q, h) is the empirical function of the fractional cloud cover n,
air temperature T, surface humidity q, and solar altitude h
What should be parameterized? Q and F(n, T, q, h)

11. 1. Clear sky surface SW radiation
In most schemes, it is parameterized through the purely astronomical characteristics
(latitude and solar altitude) and empirical coefficients which account for the atmospheric
air transparency under clear skies (e.g. Seckel and Beaudry 1973):
For monthly values (daily round for 15th day of the month): Smithsonian formula
Q0 = A0+A1cos+B1sin+A2cos2+B2sin2 (5)
 = (t-21)(360/365), t is time of the year in days, L is the longitude
Lat: 20S – 40N
A0= cosL
A1= cos(L+90)
B1= sinL
A2= sin2(L-45)
B2= cos2(L-5)
Lat: 40N – 60N
A0= L-0.018L2
A1= L+0.043L2
B1= L-0.017L2
A2= L+0.011L2
B2= L-0.034L2
For hourly clear sky radiation Lumb’s (1964) formula can be used:
Q0 = 1353 (sin h) [ (sin h)] (6)
Be careful!!! – always account to whether you work with monthly or hourly estimates

12. There are parameterizations which directly include surface atmospheric parameters into the clear sky radiation formula. Malevsky et al. (1992) suggested for Q0 :
Q0=c(sin h)d (7)
where, c and d are empirical coefficients, which depend on the atmospheric transmission P.

13. The Bouguer low (Beer or Lambert low):
What is the atmospheric transmission (or transparency) P?
The Bouguer low (Beer or Lambert low):
where I is the radiation intensity (on the TOA), Io is the incident
radiation intensity, τ is optical thickness (or the Bourguer’s thickness)
of the atmosphere, ho is solar altitude.
The coefficient of transparency
(or the optical mass number):
In this parameterization atmospheric transmission represents
the Bougeer’s transmission for the optical mass number 2
(i.e. h=30) and is defined as P2. To be parameterized, it was
estimated from the measurements in different regions.

14. P2 = (S30/S0)1/2 Estimation of P2:
Why P2 (and not e.g. P4)?
For most regions estimates according to P2 = (S30/S0)1/2 were performed under h=30º. A simple determination of Pxx constant under a different optical mass number and the further projection of
the results to h=30º leads to the errors associated with the Forbes effect.
Forbes effect is the effect of changing atmospheric transmission with solar altitude. E.g. with the increasing h the optical mass number also increases. Thus, to adjust Pxx, defined under a different
from 2 optical mass number, you need to derive a new dependence of Pxx on the atmospheric conditions.
P2 = (S30/S0)1/2
where S30 is the measured solar radiation
under h=30, S0 is the solar constant
P2 is the empirical function of atmospheric
water vapor (or surface temperature, if
humidity measurements are not present).
winter
summer

15. General formula: P2=0.790-0.003Ta
North Atlantic
P2= e e2
P2= Ta
Pacific and Indian
P2= e e2
P2= Ta
General formula: P2= Ta
Under clear skies:
Q0=c(sin h)d where c=f(P2), d=f(P2)
P2 = f (Ta, e)

16. 2. Cloud reduction factor
WHAT IS THE CLOUD REDUCTION?
It is a compromise between the complexity of the radiation
transfer in the cloudy atmosphere and the availability of data
to describe this complexity.
It is obvious that a universal parameterization of the cloud
modification of radiation should be based on the consideration
of cloud types and heights (e.g. Dobson and Smith 1988).
However, the only reliable parameter in marine meteorological
data is still the amount of clouds. Similarly, in the models (and
reanalyses) we can more rely on the [total] cloud cover rather
then on the other cloud characteristics.

17. Reed formula is designed for daily and monthly estimates ONLY
Reed (1977): 40 months of direct measurements at three coastal stations (Swan Island, Caribbean; cape Hatteras; Astoria)
SW=Q0(1-0.62n h), (8)
n is !!! fractional !!! cloud cover, n10 = 1.25 octa
h is noon solar altitude,
Q0 is clear sky insolation on sea surface
Reed formula is designed for
daily and monthly estimates ONLY
For the radiation under clear skies
Lumb (1964) formula
Q0 = 1353 (sin h) [ (sin h)]
Smithsonian
formula

18. EVALUATION OF REED (1977) FORMULA
Gilman and Garrett (1994): The
Reed formula should only be used
for 0.3<n<1 and for n < 0.3 it is
assumed: SW=Q0

19. Malevsky et al. (1992) suggested formulae for the use of the low and total cloud cover as available from the VOS reports. It is based on the data from research cruises in the tropics and mid latitudes (more than measurements).
For total cloud cover and mean ocean conditions:
SW=Q0(1+0.19nt-0.71nt), (9)
nt is !!! fractional !!! total cloud cover
Formula (9) gives just a general dependency and should not be used for practical computations. Original dependencies of cloud reduction factor on could cover (both total and two-level) and solar altitude are tabulated (e.g. Niekamp 1992, codes will be supplied).
Malevsky parameterization is designed for hourly estimates!!!

20. Malevsky scheme accounts for the secondary reflection of radiation from the cloud margins under low declinations and small cloud cover by assuming the possibility for the cloud “reduction” coefficients to be greater than 1.

21. Summary of two-step parameterizations:
Most of them are developed from continuous instrumental
measurements undertaken in mid latitudes. However, the
tropical cloudiness is characterized by very different
transmission characteristics.
The atmospheric radiation community generally avoids the
use of these parameterizations arguing that the optical
thickness in (8, 9) is implicitly constant. In a formal RTM
(Radiative Transfer Model) the perturbation to surface
insolation is induced by overcast clouds (n =1 in (8,9)) over
a dark ocean.
For similar reasons, remote sensing of the cloud cover
and of the cloud optical depth from satellites are equally
challenging problems.
Nevertheless, expressions such as (8,9) will continue to be
used in practical applications.

22. Comparisons of the parameterizations with in-situ measurements
Dobson and Smith
RMS error
Malevsky - total
Malevsky – total + low
Under high cloud cover
the accuracy of all
parameterizations
becomes considerably
smaller compared to
the clear sky conditions
or moderate cloud
cover
correlation

23. State of the Sun disk under different cloud forms
The largest uncertainty is observed under the overcast conditions
For the further improvement of
parameterization we need to analyze
the dependency of atmospheric
transmission on the cloud types
and the state of the Sun disk.
Different cloud types
State of the Sun disk under different cloud forms
360 W/m2
8 octa - Ns
620 W/m2
8 octa - Nm ☼1 ☼2 ☼0
☼cloudy

24. Different cloud types

25. MORE – Meridional oceanic
radiative experiment (2004 – 2010)
IFM-GEOMAR / IORAS,
A. Macke / S. Gulev

26. 1. log-function in clear sky conditions instead of linear bi ai
Dependence of the atmospheric
transmission on the Sin (solar altitude)
OCTA 1 2 3 4 5 6 7 8 bi
0,15
0,13
0,17
0,14
0,12 ai
0,81
0,80
0,78
0,76
0,74
0,71
0,67
0,60
0,31

27. 2. Different cloud categories under 6-8 octa№
Category
Atm. transmission 1
Ns(7/0_2_X)
T=0,14 x sinh +0,11 2
Sc(Cu) (4_0_0)
T=0,33 x sinh +0,17 3
AsAc(0_7_X)
T=0,34 x sinh +0,19 4
Sc(no_Cu) (5_0_0_Sun1/0)
T=0,31 x sinh +0,22 5
Sc(no_Cu) (5_0_0_Sun_П)
T=0,25 x sinh +0,11
General (fit-for-all) formula:
Atmospheric transmission factor
strongly depends on the cloud
types, especially under high solar altitude (20-60% variance)

28. 3. Parameterization for the eastern North Atlantic
tropics and subtropics
SAIL
Dust Sea
Daily
47 W/m2
6 W/m2
Hourly
52 W/m2
30 W/m2

29. Advanced parameterization
1-2
3-4
5-6
7-8
Clear skies
y = 0,15*ln(x)+0,81 +
Cloud category
East-subtropical Atlantic №
Category
Atm. transmission 1
Ns(7/0_2_X)
T=0,14 x sinh +0,11 2
Sc(Cu) (4_0_0)
T=0,33 x sinh +0,17 3
AsAc(0_7_X)
T=0,34 x sinh +0,19 4
Sc(no_Cu) (5_0_0_Sun1/0)
T=0,31 x sinh +0,22 5
Sc(no_Cu) (5_0_0_Sun_П)
T=0,25 x sinh +0,11

30. Qsw=Qsw (1-A) A=Qsw / Qsw i r Albedo at sea surface
Not the whole amount of incoming short wave irradiance is absorbed by the water. Part of it is reflected by the water surface.
Qsw=Qsw (1-A)
A=Qsw / Qsw
Theoretically albedo has to be estimated from the Fresnel law for the pure mirror reflection: i r
Three reasons not to use directly Fresnel law:
Variable transparency of sea water
Sea surface roughness
Impact of the diffused SW radiation

31. Measurements and parameterizations
The broadband albedo can be measured with a pair of pyranometers, one
facing upward and the other downward, but the latter must be mounted on
a boom so that it does not “see” the platform. This presents obvious
difficulties for ships on the open ocean. More frequent measurements are
done on the platforms.
Payne (1972) made comprehensive
measurements from a platform in
Buzzards Bay, MA (41°N),
expressing the results in terms
of only two parameters, solar
altitude and atmospheric
transmittance. The latter is the
ratio of solar irradiance actually
measured at the surface to such
an incident at the top of the
atmosphere, which can be
simply calculated from the solar
constant, date, time and location
(Paltridge and Platt 1976).

32. Physics of albedo:
Solar transmittance is affected by absorption or scattering from atmospheric constituents, mainly water vapor, ozone, aerosols and clouds. Thus, Payne’s (1972) parameterization actually relates to the varying ratio of diffuse to direct shortwave radiation. The Fresnel laws predict that reflectivity at a water surface increases toward glancing angles of incidence.
For high solar altitude and clear skies the albedo is small, but any increases in the diffuse component due to cloudiness will reduce the average angle of incidence and increase the albedo. For low solar altitude, the addition of cloudiness has the opposite effect.
Katsaros et al. (1985) confirmed Payne’s albedo (experiments GATE at 7°N and JASIN at 60°N)
– their Figure 1 provides an excellent illustration of the effects of diffuse radiation, solar altitude and surface roughness on surface albedo.

33. Implicitly accounts for diffusive SW radiation
Girdiuk et al. (1985): dependence of albedo on cloudiness:
Implicitly accounts for diffusive SW radiation
17630 open ocean observations onboard research ships, including 1120 observations under clear skies.

34. Girdiuk et al. albedo
Comparison
of Payne’s albedo with Girdiuk’s
albedo:
Payne is always higher under higher solar altitudes

35. /meolkerg/gulev6s/problems/
radiation.f – collection of SW radiation F77 codes
RSWM – Malevsky scheme for monthly means
RSW – Malevsky scheme for individual values
RSWD – Dobson and Smith scheme
radiation1.f – another collection of SW radiation F77 codes
(German comments!!!!)
RSWISI – Reed’s scheme for monthly means
Try to compare Malevsky, Dobson and Reed’s schemes:
Clear sky, dependence on solar altitude
Cloud cover octa=4, dependence on solar altitude
h=10, h=30, h=60, dependence on cloud cover (in octas)

36. READING
Liou, K.N., 2002: An introduction to atmospheric radiation. Academic Press, 583 pp.
Dobson, F., and S. D. Smith,1988: Bulk model of solar radiation at sea. Q.J.R. Meterol. Soc.,
114,
Gulev, S.K., 1995: Long-term variability of sea-air heat transfer in the North Atlantic Ocean.
Int.J.Climatol., 15,
Katsaros, K. B., L. A. Mcmurdie, R. J. Lind, and J. E. DeVault (1985), Albedo of a Water
Surface, Spectral Variation, Effects of Atmospheric Transmittance, Sun Angle and Wind
Speed, J. Geophys. Res., 90(C4), 7313–7321.
Lumb, F.E., 1964: The influence of cloud on hourly amount of total solar radiation at the sea
surface. Quart. J. Roy. Meteor. Soc., 90,
Niekamp, K., 1992: Untersuchung zur Gute der Parametrizierung von Malevsky-Malevich zur
Bestimmung der solaren Einsrahlung an der Oceanoberflache. Diploma MSc, Institut fuer
Meereskunde, Kiel, 108 pp.
Payne, R.E., 1972: Albedo at the sea surface. J.Atmos.Sci., 29,
Reed, R.K., 1977: On estimating insolation over the ocean. J. Phys. Oceanogr., 7,
Seckel, G.R., and F.H.Beaudry, 1973: The radiation from sun and sky over the Pacific Ocean
(Abstratct) Trans. Am. Geophys. Union, 54, 1114.