PARAMETERIZATION OF SHORT WAVE

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 have to be estimated from
information on the ship's position and the cloud
information visually estimated by the ship
officer. Such an estimate has to be considered
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
• Aerosols
• diffusion

Measurements
Modelling
Parameterization
3
What do we really measure at sea surface?
SST,C Ta,C q, g/kg C (Cn, Cl),
okta
The short-wave radiation flux (SW) at sea surface
may 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 the SW
radiation at the top of the atmosphere, S0 is
the solar constant, h is solar altitude,
TF is the transmission factor of the
atmosphere and has to be parameterized in
terms of the cloud cover and
thermodynamic parameters of the atmosphere.
4
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
5
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 the
observations
6
Values of numerical coefficients
Lind et al. (1984) Lind et al. (1984) Lind et al. (1984) Lumb (1964) Lumb (1964) Lumb (1964)
Octa categories a b ? 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 0.148 0.221 0.256 0.153
8 0.106 0.285 0.124 0.124 0.206 0.116
9 0.134 0.295 0.130 0.076 0.186 0.086
7
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
• cloud cover

8
Nonlinear models Experimental analysis of
atmospheric transmission factor (Paltridge and
Platt 1976, Dobson and Smith 1988) TF F
exp(-D0 /(cos h))? Cexp(-Di /(cos h))Ei
(1-C) F is the fraction of the incoming
clear-sky radiation not absorbed by
atmospheric constituents D0 is the clear sky
direct-beam optical density i is the cloud
category Di is the optical density of the
direct-beam radiation through clouds Ei is the
transmission factor for diffusive radiation
through clouds (1-C) is the factor which
allows for clear sky radiation through the
fraction of clear sky not covered by cloud
9
Analysis of experimental measuments with
pyranometer at OWS P during 14 years (1959-1975)
(Dobson and Smith 1988) F0.87, D00.084
10

• 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
• very complicated and uncertain dependency of
  the transmission
• factor on the surface parameters available
  from marine data
• Better implementation requires poorly and seldom
  observed
• meteorological parameters (cloud types,
  weather code)

• Recommendations
• Try to avoid the usage of one-step
  parameterizations
• Never (!!) try to use them in atmospheric
  models, even if your
• model radiation block (RTM) is not well
  working
• If you, nevertheless, decide to use them, use
  Dobson and Smith
• (1988) nonlinear scheme, as calibrated at
  Sable Island

11
Two-step parameterizations

• To avoid very large uncertainty, associated with
  the dependency 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 the
  clear sky radiation.
• In this case, the 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? Q0
  and F(n, T, q, h)

12
1. Clear sky surface 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)
  
• Smithsonian formula
• Q0 A0A1cos?B1sin?A2cos2?B2sin2? (5)
• ? (t-21)(360/365),
• t is time of the year in days,
• L is the longtitude

Lat 20S 40N A0-15.82326.87cosL A19.63192.44
cos(L90) B1-3.27108.70sinL A2-0.647.80sin2(L-
45) B2-0.5014.42cos2(L-5)
Lat 40N 60N A0342.61-1.97L-0.018L2 A152.08-5.
86L0.043L2 B1-4.802.46L-0.017L2 A21.08-0.47L0
.011L2 B2-38.792.43L-0.034L2
13
Smithsonian formula is derived for monthly mean
values! For hourly clear sky radiation estimates
Lumbs (1964) formula can be used Q0 1353
(sin h) 0.610.20 (sin h) Be careful!!!
always account to whether you work
with monthly or hourly estimates
14
However, there are a few parameterisations which
directly include surface atmospheric parameters
into the clear sky radiation formula. Malevsky et
al. (1992) suggested to use for Q0 the
parameterization Q0c(sin h)d where, c and d
are empirical coefficients, which depend on
atmospheric transmission P.
15
What is the atmospheric transmission P? In this
parameterization it represents the Bugers
transmission for the optical mass number 2 (i.e.
h30?) and is defined as P2. To be parameterized,
it was estimated from the measurements in
different regions as P2 (S30/S0)1/2
S30 is the measured solar radiation under h30?
S0 is the solar constant P2 is the
empirical function of atmospheric water vapor
(or surface temperature, if humidity
measurements are not present).
16
P2
Pacific and Indian P20.797-0.0032e0.000034e2 P2
0.785-0.0018Ta
North Atlantic P20.829-0.0078e0.000115e2 P20.79
9-0.0037Ta
General formula P20.790-0.003Ta
17
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
  parameterisation of the cloud
• modification of radiation should be based
  on the consideration
• of cloud types and heights (e.g. Dobson and
  Smith 1988).
• Against that it is often considered that the
  only reliable
• parameter in the marine meteorological
  data is the amount
• of cloud cover.

18
Reed (1977) 40 month of direct measurements at
three coastal stations (Swan Island, Carribean
cape Hatteras Astoria) SWQ0(1-0.62n0.0019h),
(6) n is !!! fractional
!!! cloud cover, n10 1.25 okta h is noon
solar altitude, Q0 is clear sky insolation on
sea surface
Reed formula is performed for monthly
estimates ONLY
Gilman and Garrett (1994) The Reed formula
should only be used for 0.3ltnlt1 and for n lt 0.3
it it assumed SWQ0
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 19000 measurements). For
total cloud cover and mean ocean
conditions SWQ0(10.19nt-0.71nt), (7) nt
is !!! fractional !!! total cloud cover
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.
Formula (7) 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). Malevsky parameterization is used for
hourly estimates
20
Summary of two-step parameterizations

• Most of them are developed from continuous
  instrumental
• measurements undertaken in mid latitudes.
  However the
• tropical cloudiness is characterised by
  very different
• transmission characteristics.
• The atmospheric radiation community
  generally avoids the use
• (optical thickness) in (6, 7) is
  implicitly constant. In a formal
• radiative transfer model (RTM) the
  perturbation to surface
• insolation induced by overcast cloud (n
  1 in (6,7)) over
  
  
• a dark ocean.
• For similar reasons, remote sensing of cloud
  cover n and
• cloud optical depth with satellite data
  are equally challenging
• problems.
• Nevertheless, expressions such as (6,7) will
  continue to be
• useful for some applications, since they
  allow changes in the
• surface insolation.

21
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)
AQsw? / Qsw
Theoretically albedo has to be estimated from the
Frenel law for the pure mirror reflection

• Three reasons not to use directly Frenel law
• Variable transparency of sea water
• Sea surface roughness
• Impact of the diffused SW radiation

WHAT TO DO?
22
Measurements and parameterizations The broadband
albedo can be measured with a pair of
pyranometers, one facing upward and the other
downward, but as with upwelling longwave 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
(41N), 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).
23
Solar transmittance is affected by absorption or
scattering from atmospheric constituents, mainly
water vapor, ozone, aerosols and clouds. Thus,
Paynes (1972) parameterization actually relates
to the varying ratio of diffuse to direct
shortwave radiation. The Frenel laws predict (and
common observation confirms) 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.
24
Katsaros et al. (1985) confirmed Paynes albedo
results during GATE at 7N and JASIN at 60N
(both during summer), and their Figure 1 provides
an excellent illustration of the effects of
diffuse radiation, solar altitude and surface
roughness on surface albedo.
25
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.
26
Comparison of Paynes albedo with Girdiuks
albedo Payne is always higher under higher
solar altitudes
27
MORE Meridional oceanic radiative
experiment IFM-GEOMAR / IORAS, A. Macke / S.
Gulev Try to become part of MORE
Contact Prof. Andreas Macke 600-4057,
amacke_at_ifm-geomar.de
28

• /helios/u2/gulev/handout/
• 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 Reeds scheme for monthly means
• Try to compare Malevsky, Dobson and Reeds
  schemes
• Clear sky, dependence on solar altitude
• Cloud cover octa4, dependence on solar altitude
• h10, h30, h60, dependence on cloud cover (in
  oktas)

29
READING Dobson, F., and S. D. Smith,1988 Bulk
model of solar radiation at sea.
Q.J.R.Meterol.Soc., 114,165-182. Girdiuk, G.V.,
T.V.Kirillova, and S.P.Malevsky, 1985 Cloudiness
influence on the oceanic albedo. Meterol.
Hydrol., 12, 63-69. Gulev, S.K., 1995 Long-term
variability of sea-air heat transfer in the North
Atlantic Ocean. Int.J.Climatol., 15,
825-852. 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,
43-56. Malevsky, S.P., G.V.Girdiuk, and B.Egorov,
1992b Radiation balance of the ocean
surface. Hydrometeoizdat, Leningrad, 148
pp. 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,
959-970. Reed, R.K., 1977 On estimating
insolation over the ocean. J.Phys.Oceanogr.
7, 482-485. 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.