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PARAMETERIZATION OF SHORT WAVE RADIATION AT SEA SURFACE

PARAMETERIZATION OF SHORT WAVE RADIATION AT SEA SURFACE.

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PARAMETERIZATION OF SHORT WAVE RADIATION AT SEA SURFACE

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  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) Qtis the SW radiation at the top of the atmosphere, S0is the solar constant, h is solar altitude, TFis 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:

  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)) {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

  9. S=cos h Clear sky radiation which falls on this area (1-C) is further attenuated by clouds over area C Analysis of experimental measuments with pyranometer at OWS P during 14 years (1959-1975) (Dobson and Smith 1988) F=0.87, D0=0.084

  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? Q0andF(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 = 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+326.87cosL • A1=9.63+192.44cos(L+90) • B1=-3.27+108.70sinL • A2=-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

  13. 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

  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 Q0the parameterization: Q0=c(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 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 S30is the measured solar radiation under h=30 S0is the solar constant P2is the empirical function of atmospheric water vapor (or surface temperature, if humidity measurements are not present).

  16. P2: • Pacific and Indian • P2=0.797-0.0032e+0.000034e2 • P2=0.785-0.0018Ta • North Atlantic • P2=0.829-0.0078e+0.000115e2 • P2=0.799-0.0037Ta General formula:P2=0.790-0.003Ta

  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) SW=Q0(1-0.62n+0.0019h), (6) nis !!! fractional !!! cloud cover, n10 = 1.25 okta h is noon solar altitude, Q0is 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 0.3<n<1 and for n < 0.3 it it 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 19000 measurements). For total cloud cover and mean ocean conditions: SW=Q0(1+0.19nt-0.71nt), (7) ntis !!! 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. 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 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 broadbandalbedo 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).

  23. Solar transmittanceis 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.

  24. 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.

  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. Girdiuk et al. albedo Comparison of Payne’s albedo with Girdiuk’s 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@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 – 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 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.

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