PARAMETERIZATION OF SHORT WAVERADIATION 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.

SW radiation at sea surface is determined by:

Solar altitude Molecular diffusion Gas absorption Water vapor absorption Aerosols diffusion

ozon ozon

water vapor water vapor

clouds

top of the atmosphere

ocean surface

clear sky cloud sky

diffusion in space (7%)

ozon absorption (3% )

100%

water vapor absorption (10%)

reflection byclouds (45%)

cloud absorption (10%)

8 0 % 2 5 %

Measurements Modelling Parameterization

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.

What do we really measure at sea surface? SST,°C Ta,°C q, g/kg C (Cn, Cl), okta

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

One-step parameterizations

0 1 2 3 4 5 6 7 8 9 10octa m odel categories

0 . 0

0 . 1

0 . 2

0 . 3

0 . 4

0 . 5

0 . 6a,

b -

co

effi

cien

tsLum b (1964)

Lind et al. (1984)

a - coefficient

b - coefficient

RMS error

Lind et al. (1984)

Lumb (1964)

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 coefficientsderived from the observations

Values of numerical coefficients:

Lind et al. (1984) 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

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

Nonlinear models:

Experimental analysis of atmospheric transmission factor (Paltridge and Platt 1976, Dobson and Smith 1988):

TF = F exp(-D0 /(cos h)) {C[exp(-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

Analysis of experimental measuments with pyranometerat OWS P during 14 years (1959-1975) (Dobson and Smith 1988)

F=0.87, D0=0.084

S=cos h

Clear sky radiation which falls on this area (1-C) is further attenuated by clouds over area C

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

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 atmosphereF(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)

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 = A0+A1cos+B1sin+A2cos2+B2sin2 (5)

= (t-21)(360/365), t is time of the year in days, L is the longtitude

Lat: 20S – 40N

A0=-15.82+326.87cosLA1=9.63+192.44cos(L+90)B1=-3.27+108.70sinLA2=-0.64+7.80sin2(L-45)B2=-0.50+14.42cos2(L-5)

Lat: 40N – 60N

A0=342.61-1.97L-0.018L2

A1=52.08-5.86L+0.043L2

B1=-4.80+2.46L-0.017L2

A2=1.08-0.47L+0.011L2

B2=-38.79+2.43L-0.034L2

Smithsonian formula is derived for monthly mean values!

For hourly clear sky radiation estimates Lumb’s (1964) formula can be used:

Q0 = 1353 (sin h) [0.61+0.20 (sin h)]

Be careful!!! –

always account to whether you work with monthly or hourly estimates

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:

Q0=c(sin h)d

where, c and d are empirical coefficients, which depend on atmospheric transmission P.

0 . 6 0 . 7 0 . 8 0 . 9atm ospheric transm ission

0 . 8

1 . 0

1 . 2

1 . 4

C, D

- c

oef

fici

ents

What is the atmospheric transmission P?

In this parameterization it represents the Buger’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 as:

P2 = (S30/S0)1/2

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). 0 10 20 30 40 50 60

latitude

0.70

0.72

0.74

0.76

0.78

0.80

0.82

P2

- va

lue

-100 -80 -60 -40 -20 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280

-100 -80 -60 -40 -20 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280

-80

-60

-40

-20

0

20

40

60

80

-80

-60

-40

-20

0

20

40

60

80

-160 -140 -120 -100 -80

-160 -140 -120 -100 -80

North AtlanticP2=0.829-0.0078e+0.000115e2

P2=0.799-0.0037Ta

Pacific and IndianP2=0.797-0.0032e+0.000034e2

P2=0.785-0.0018Ta

General formula: P2=0.790-0.003Ta

P2:

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.

Reed (1977): 40 month of direct measurements at three coastal stations (Swan Island, Carribean; cape Hatteras; Astoria)

SW=Q0(1-0.62n+0.0019h), (6)

n is !!! fractional !!! cloud cover, n10 = 1.25 oktah is noon solar altitude, Q0 is clear sky insolation on sea surface

Gilman and Garrett (1994): The Reed formula should only be used for 0.3<n<1 and for n < 0.3 it it assumed:

SW=Q0

Reed formula is performed for

monthly estimates ONLY

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:

SW=Q0(1+0.19nt-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

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.

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 Frenel law for the pure mirror reflection:

)(

)(

)(sin

)(sin

2

12

2

2

2

ritg

ritg

ri

riA

i

rThree reasons not to use directly Frenel law:

Variable transparency of sea waterSea surface roughnessImpact of the diffused SW radiation

WHAT TO DO?

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 (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).

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 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.

Katsaros et al. (1985) confirmed Payne’s albedo results during GATE at 7°N and JASIN at 60°N (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.

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.

Girdiuk et al. albedo

Comparison of Payne’s albedo with Girdiuk’s albedo:

Payne is always higher under higher solar altitudes

MORE – Meridional oceanic radiative experimentIFM-GEOMAR / IORAS, A. Macke / S. Gulev

Try to become part of MOREContact: Prof. Andreas Macke: 600-4057, amacke@ifm-geomar.de

/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 – Reed’s scheme for monthly means Try to compare Malevsky, Dobson and Reed’s schemes:

1. Clear sky, dependence on solar altitude2. Cloud cover octa=4, dependence on solar altitude3. h=10, h=30, h=60, dependence on cloud cover (in oktas)

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.