PARAMETERIZATION OF SHORT WAVE RADIATION AT SEA SURFACE

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 • diffusion 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. 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) Qtis SW radiation at the top of the atmosphere, S0is solar constant, h is solar altitude, TFis 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 iis the cloud category a, b,are the empirical coefficients derived from observations

7. Values of numerical coefficients:

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 • cloud cover

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? Q0andF(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, Lis the longitude • 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 For hourly clear sky radiation Lumb’s (1964) formula can be used: Q0= 1353 (sin h) [0.61+0.20 (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. What is the atmospheric transmission (or transparency) P? The Bouguer low (Beer or Lambert low): where Iis 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. 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. Forbeseffect 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 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). winter summer

15. P2: • North Atlantic • P2=0.829-0.0078e+0.000115e2 • P2=0.799-0.0037Ta • Pacific and Indian • P2=0.797-0.0032e+0.000034e2 • P2=0.785-0.0018Ta General formula:P2=0.790-0.003Ta Under clear skies: Q0=c(sin h)d wherec=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 (1977):40 months of direct measurements at three coastal stations (Swan Island, Caribbean; cape Hatteras; Astoria) SW=Q0(1-0.62n+0.0019h), (8) nis !!! fractional !!! cloud cover, n10 = 1.25 octa h is noon solar altitude, Q0is clear sky insolation on sea surface Reed formula is designed for daily and monthly estimates ONLY For the radiation under clear skies Smithsonian formula Lumb (1964) formula Q0= 1353 (sin h) [0.61+0.20 (sin h)]

18. EVALUATION OF REED (1977) FORMULA Gilman and Garrett (1994):The Reed formula should only be used for0.3<n<1and forn < 0.3it 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 19000 measurements). For total cloud cover and mean ocean conditions: SW=Q0(1+0.19nt-0.71nt), (9) ntis !!! 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. 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 8 octa - Ns 360 W/m2 8 octa - Nm 620 W/m2 ☼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 Dependence of the atmospheric transmission on the Sin (solar altitude)

27. 2. Different cloud categories under 6-8 octa 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

29. y = 0,15*ln(x)+0,81 Advanced parameterization 1-2 3-4 5-6 7-8 Clear skies + Cloud category East-subtropical Atlantic

30. 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: • 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 broadbandalbedo 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 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 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. 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., 114,165-182. Gulev, S.K., 1995: Long-term variability of sea-air heat transfer in the North Atlantic Ocean. Int.J.Climatol., 15, 825-852. 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, 43-56. 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.