Algorithm to estimate daily Photo-synthetically Available Radiation at the Ocean surface (OTSK14)
A. Algorithm Outline(1) Algorithm name: daily Photo-synthetically Available Radiation at the Ocean surface(2) Product Code: PAR(3) PI names: A2GRF003 Robert Frouin
B. Theoretical Description
1.1 Algorithm Description (revised for version 2.2 –includes diurnal variability of clouds and modified parameterizationof surface albedo)
The algorithm estimates daily (i.e., 24-hour averaged) Photosynthetically Active Radiation (PAR) reaching the oceansurface from GLI data. PAR is defined as the quantum energy flux from the Sun in the spectral range 400-700 nm. It is2

expressed in Einstein/m /day.
The PAR model uses plane-parallel theory and assumes that the effects of clouds and clear atmosphere can bede-coupled. The planetary atmosphere is therefore modeled as a clear sky atmosphere positioned above a cloud layer.
This approach was shown to be valid by Dedieu et al. (1987) and Frouin and Chertock (1992). The great strength ofsuch a de-coupled model is its simplicity. It is unnecessary to distinguish between clear and cloudy regions within apixel, and this dismisses the need for often-arbitrary assumptions about cloudiness distribution.
Under solar incidence θs, the incoming solar flux at the top of the atmosphere, E0 cos(θs) is diminished by a factor
TdTg/(1-SaA) by the time it enters the cloud/surface layer. In this expression, Td is the clear sky diffuse transmittance, Tg
is the gaseous transmittance, Sa is the spherical albedo, and A is the cloud/surface layer albedo. As the flux, E0cos(θs)TdTg/(1-SaA), passes through the cloud/surface layer, it is further reduced by a factor A. The solar flux reaching
the ocean surface is then given by
E = Eclear(1 – A)(1 – As)-1(1-SaA)-1(1)where As is the albedo of the ocean surface and Eclear = E0cos(θs)Td Tg is the solar flux that would reach the surface if
the cloud/surface layer were non reflecting and non-absorbing. In clear sky conditions, A reduces to As.
In order to compute E, A is expressed as a function of the radiance measured by GLI in the PAR spectral range. The
algorithm works pixel by pixel and proceeds as follows.
First, for each pixel not contaminated by glitter the GLI radiance Li* in band i (i = 1, 2,…, 6), where 1 is 0.412 µm, 2 is20.443µm, 3 is 0.490 µm, 4 is 0.519 µm, 5 is 0.544 µm, and 6 is 0.679 µm, expressed in mW/cm /µm/sr, is transformed
into reflectance, Ri*:2

Ri* = πLi*/[E0i(d0/d) cos(θs*)](2)

where Eoi is the extra-terrestrial solar irradiance in band i, θs* is the sun zenith angle at the GLI observation time, andd0/d is the ratio of mean and actual Earth-Sun distance. The glint areas are not selected because they would beinterpreted as cloudy in the PAR algorithm.
Second, Ri * is corrected for gaseous absorption, essentially due to ozone:
Ri’ = Ri*/Tgi

(3)

with

GLI Algorithm Description

3.2.2-1

Tgi = exp[-koiUo/cos(θs*)](4)

where koi is the ozone absorption coefficient in band i and Uo the ozone amount.
Third, the reflectance of the cloud/surface layer, Ri, is obtained from Ri’ following Tanré et al. (1979) and assuming
isotropy of the cloud/surface layer system. That is:
Ri = (Ri’ – Rai)[Tdi(θs*)Tdi(θv) + Sai(Ri’ – Rai)]

-1

(5)

where θv is the viewing zenith angle and Rai is the intrinsic atmospheric reflectance in band i (corresponds to photons
that have not interacted with the cloud/surface layer). The assumption of isotropy is made because no information on
pixel composition is available.
In Eq. (5), Ra is modeled using the quasi single-scattering approximation:
Ra = (τmolPmol + ωaerτaerPaer)[4cos(θs*)cos(θv)]

-1

(6)

where τmol and τaer are the optical thicknesses of molecules and aerosols, Pmol and Paer are their respective phasefunctions, and ωaer is the single scattering albedo of aerosols. Subscript i has been dropped for clarity. The diffuse
transmittance Td and spherical albedo Sa are computed using analytical formulas developed by Tanré et al. (1979):
Td(θ) = exp[-(τmol +τaer)/cos(θ)]exp[(0.52τmol + 0.83τaer)/cos(θ)](7)

Sa = (0.92τmol + 0.33τaer)exp[-(τmol + τaer)](8)

where τmol is the optical thickness of molecules, τaer that of aerosols, and θ is either θs* or θv.
The optical thickness of aerosols in band i, τaeri, is obtained from the optical thickness in band 18 centered at 0.866 µm,

τaer8, and the Angström coefficient, α :τaeri = τaer18(λ18/λi)α(9)where λi and λ18 are equivalent wavelengths in GLI bands i and 18, respectively. A monthly climatology may be usedfor τaer and α, since aerosol properties cannot be determined when the pixel is cloudy. This procedure is also justified
because, in general, aerosol effects on E are secondary compared to cloud or θs effects.
To estimate ωaer and Paer, the two closest of 12 aerosol models, k and l, that verify α(l)< α< α(k) are selected, and adistance daer = [α(l) – α]/[α(l) – α(k)] is computed. Using this distance, ωaer and Paer are obtained as follows:ωaer = daerωaer(k) + (1 – daer) ωaer(l)(10)

Paer = daerPaer(k) + (1 – daer)Paer(l)(11)

where ωaer(l) and ωaer(k) are the single scattering albedos of aerosol models l and k, and Paer(l) and Paer(k) theirrespective phase functions.
Next, an estimate of daily PAR, <E>day, is obtained by integrating Eq. (1) over the length of the day:
-1-1

<E>day = <E0>∫day{cos(θs)<Tg><Td>[1 – <A>] [1 – <As>] [1 – <Sa><A>] } dt

(12)

with
<Tg> = exp[-<ko>Uo/cos(θs)]exp[-<kv>Uv /cos(θs)](13)<Td> = ∑i(TdiEoi)/∑iE0i(14)<Sa> = ∑i(SaiEoi)/∑iE0i(15)GLI Algorithm Description

3.2.2-2

-1<As> = <Tdir><Td> [0.05/(1.1[cos(θs)]

1.4-1+ 0.15] + 0.08<Tdif><Td>(16)<Tdir> = ∑iTdiriEoi/∑iE0i(17)<Tdif> =<Td> - <Tdir>(18)

Tdiri = exp[-(τmoli + τaeri)/cos(θs)](19)<A> = F(t*)<R(t*)>A’/A’(t*)(20)<R> = ∑iRi(t*)/∑iE0i(21)

where t* is the GLI observation time, Tdiri is the direct component of Tdi in band i, A’ is a climatological albedo, and <>symbolizes average value over the PAR range. Note that because of saturation at low radiance in some of the GLI
spectral bands, the algorithm only takes into account, for each pixel, the spectral bands that do not saturate. It ispossible, as an option, however, to use only the band centered at 0.544 µm (does not saturate over clouds) to estimate
cloud effects on PAR. In the code, this option is activated when the flag “flag544” is on.
In Eq. (12), absorption by water vapor in the PAR spectral range, occurring weakly between 690 and 700 nm, isincluded. The ozone and water vapor absorption coefficients <ko> and <kv> in Eq. (13) are taken from Frouin et al.
(1989). Surface albedo is parameterized as a function of sun zenith angle and fractions of direct and diffuse incomingsunlight. The formula of Briegleb and Ramanathan (1982), developed for the total spectrum, is adapted to the PAR
range via a simple multiplication factor (1.13). This parameterization, which takes into account Fresnel reflection anddiffuse under-light, is sufficient since the influence of <As> on surface PAR is small. In some cases, however, theretrieved <A> might be less than <As>. When this happens, <A> is fixed to <As>.
Even though the cloud/surface layer is assumed to be isotropic in the correction of clear atmosphere effects (Eq. 5),R(t*) is corrected by the angular factor F(t*) (Eq. 20). Analytical formulas proposed by Zege (1991) for non-absorbing,
optically thick scattering layers are applied.
Diurnal changes in the cloud/surface layer are taken into account by introducing the factor A’/A’(t*) in Eq. (20). A
regional diurnal albedo climatology (Standfuss et al. (2001) (see also Viollier et al., 2001) is used. This climatology(monthly, 2.5 degree resolution, 16 local times from 05:30 to 20:30) was obtained from 5 years of ERBS scanner data(1985-1990). Note that using Eq. (12) the algorithm yields a daily PAR estimate for each instantaneous GLI pixel.
22Finally, the individual daily PAR estimates, obtained in units of mW/cm /µm, are converted into units of Einstein/m /day.
22The factor required to convert units of mW/cm /µm to units of Einstein/m /day is equal to 1.193 to an inaccuracy of afew percent regardless of meteorological conditions (Kirk, 1994, pp. 4-8.). In middle and high latitudes, several daily
estimates may be obtained over the same target during the same day, increasing product accuracy.
Test results of the PAR code, version 2.2 are displayed in Figures 1 and 2 for input radiance of 10 and 20
2mW/cm /µm/sr, respectively. Flag554 is equal to zero (i.e., all the wavelengths are taken into account in thecomputations). Differences between the results of version 2.2 (diurnal variability of clouds included) and version 2.0(diurnal variability of clouds neglected) are displayed in Figures 3 and 4, respectively.

GLI Algorithm Description

3.2.2-3

Figure 1. PAR as a function of Julian Day and latitude for input radiance of 10mW/cm2/µm/sr. Units are Einstein/m2/day.

2Figure 2. Same as Figure 1, but for input radiance of 20 mW/cm /µm/sr. Units are2Einstein/m /day.

GLI Algorithm Description

3.2.2-4

Figure 3. Difference between PAR from Version 2.2 and PAR from Version 2.0 for
22

input radiance of 10 and 20 mW/cm /µm/sr. Units are Einstein/m /day.

2Figure 4. Same as Figure 3, but for input radiance of 20 mW/cm /µm/sr. Units are
2Einstein/m /day.

GLI Algorithm Description

3.2.2-5

C. References
1. Briegleb, B. P., and V. Ramanathan, 1982: Spectral and diurnal variations in in clear sky planetary albedo. J.
Climate Appl. Meteor., 21, 1168-1171.
2. Dedieu, G. P.-Y. Deschamps, and Y. H. Kerr, 1987: Satellite estimation of solar irradiance at the surface of the earth
and of surface albedo using a physical model applied to Meteosat data. J. Climate Appl. Meteor., 26, 79-87.
3. Frouin, R., D. W. Lingner, K. Baker, C. Gautier, and R. Smith, 1989: A simple analytical formula to compute clear
sky total and photosynthetically available solar irradiance at the ocean surface. J. Geophys. Res., 94, 9731-9742.
4. Frouin, R., and B. Chertock, 1992: A technique for global monitoring of net solar irradiance at the ocean surface.
Part I: Model. J. Appl. Meteor., 31, 1056-1066.
nd

5. Kirk, J. T. O., 1994: Light and photosynthesis in aquatic ecosystems, 2edition, Cambridge University Press, 509

pp..
6. Standfuss, C., M. Viollier, R. S. Kandel, and P. Duvel, 2001: Regional diurnal albedo climatology and diurnal time
extrapolation of reflected solar flux observations, Application to the ScaRaB record. J. Climate, 14, 1129-1146.
7. Tanré, D., M. Herman, P.-Y. Deschamps, and A. De Leffe, 1979: Atmospheric modeling for space measurementsof ground reflectances, including bi-directional properties. Appl. Optics, 18, 3587-3594.
8. Viollier, M., C. Standfuss, and F. Parol, 2002: Monthly means of reflected solar flux from POLDER (ADEOS-1) andcomparison with ERBE, ScaRaB, and CERES. Geophys. Res. Lett., 2001GL014255.
9. Young, D. F., P. Minnis, D. R. Doelling, G. G. Gibson, and T. Wong, 1998: Temporal interpolation methods for theclouds and Earth’s Radiant Energy System (CERES experiment. J. Appl. Meteor., 37, 572-590.
10. Zege, E. P.,

A. P. Ivanov, and I. L. Katsev, 1991:Image transfer through a scattering medium. Springer-Verlag,

New York, 349 pp.

GLI Algorithm Description

3.2.2-6