3.2.1 OTSK1A
3.2.1-1 Atmospheric Correction for Ocean Color
A. Algorithm Outline(1)

Algorithm name: Atmospheric Correction for Ocean Color(2)

Product Code: NWLR

(3)

PI names: G-0065 Hajime Fukushima(4)

Overview of algorithm (Status: Operational level)
This algorithm is an extension of the OCTS atmospheric correction algorithm (Fukushima et al., 1998).
It treated the multiple scattering among the aerosol particles and gas molecules, as well as the effects ofvariable ozone concentration, surface pressure, surface wind speed, and water vapor amount. The
atmospheric correction with iterative procedure was developed to avoid the black pixel assumption. Due tosaturation problems of the GLI nominal band16 (749nm) and band18 (865nm), alternative bands(band13:678nm and band19:865nm) were used. The water reflectance at near infrared bands are
estimated by in-water model for chlorophyll a (chl) and inorganic suspended matter (ism) concentrations aswell as absorption coefficient of colored dissolved organic matter (cdom). These values are estimated byusing a neural network-based in-water algorithm.

B. Theoretical Description(1)

Methodology and Logic flow
1-1 Radiative transfer model
The satellite-observed reflectance, ρT, is modeled as follows.

ρT (λ ) = ρ M (λ ) + ρ A(λ ) + ρ MA (λ ) + T (λ )ρ G (λ ) + t(λ )ρ WC (λ ) + t(λ )ρ W (λ )(1)where λ is wavelength, ρM is reflectance due to gas molecules, ρA is aerosol reflectance, ρMA is reflectancedue to the interaction between molecules and aerosol particles, ρG is the reflectance resulting from thespecular reflection by the direct sun light, ρWC is the reflectance resulting from the whitecap, ρW isreflectance of the ocean, T is the direct transmittance of the atmosphere, and τ is the diffuse transmittanceof the atmosphere.
The ρG term in the above equation is generally ignored because ocean-color sensors are equipped witha provision for tilting the scan plane away from the specular image of the sun.

The purpose of

atmospheric correction is to retrieve ρW from above equation with ρM which is calculated based on the
lookup tables and ρA+ρMA and t which are estimated by the satellite data.
1-2 Aerosol models
Since the water reflectance, ρW, can be discarded in the NIR (710~865nm) bands, we obtain the aerosol
reflectance for these bands including the interaction part as follows,ρ A(λ ) + ρ MA (λ ) = ρ T (λ ) − ρ M (λ )(2)We need to estimate ρA+ρMA for band 1 to 12 and 14 but it is not straight forward since the spectral
relation of ρA+ρMA over the whole visible and near IR region is dependent on θ0, θ, the satellite zenith angle,
and ∆φ, the relative azimuth angle between the sun and the satellite, in addition to the type and optical
thickness of aerosol. Similar to the method proposed by Gordon and Wang (1994), we introduce thetables that store the relation between the aerosol reflectance ρA+ρMA and aerosol optical thickness, τA, foreach band and use them to determine the magnitude of ρA+ρMA in the shorter wavelengths bands based

GLI Algorithm Description

3.2.1-1

on the estimated spectral ratio of ε between two NIR bands. Since the relation between ρA+ρMA and τA is
dependent on aerosol type, GLI algorithm has the following nine candidate aerosol models:-

Tropospheric aerosol with R.H. of 70% (Model 1)-

Oceanic1600 aerosol with R.H. of 70% (Model 2)-

Oceanic800 aerosol with R.H. of 70% (Model 3)-

Oceanic400 aerosol with R.H. of 70% (Model 4)-

Oceanic200 aerosol with R.H. of 60 and 73% (Models 5 and 6)-

Oceanic100 aerosol with R.H. of 70% (Model 7)-

Oceanic50 aerosol with R.H. of 70 and 83% (Model 8 and 9)
The definition of these models are based on Shettle and Fenn (1979). The “Oceanic1600 type” consistsof 99.9375% (one 1600th) of tropospheric and 0.0625% of oceanic aerosols, in terms of number ofparticles. RH means the assumed relative humidity. Other models through Model 9 are defined similarly.
1-3 Lookup tables
The following lookup tables were prepared beforehand to speed up processing of atmospheric correction.
- ρM table that gives ρM(λ) for the given θ0, θ, and ∆φ.
- “ρA+ρMA → τA” table that contains coefficients a0, a1, a2, a3 and a4 in the equation,

τ A (λ ) = a0 + a1 X (λ ) + a 2 X (λ )2 + a3 X (λ )3 + a 4 X (λ )4X (λ ) = ρ A (λ ) + ρ MA (λ )(3)for all (θ0, θ, ∆φ), aerosol types and atmospheric correction bands such as 678nm (ch13), 749nm (ch16),
865nm (ch18) and 865nm (ch19, denoted as 865A band).
- “τA --> ρA+ρMA” table that contains coefficients a0, a1, a2, a3 and a4 in the equation,

ρ A (λ ) + ρ MA (λ ) = a0 + a1τ A (λ ) + a 2τ A (λ )2 + a3τ A (λ )3 + a4τ A (λ )4(4)

for all (θ0, θ, ∆φ), aerosol types and channels except atmospheric correction bands..
- ωA table that has the single scattering albedo of all the aerosol models.
- KEXT table that contains the values of extinction coefficients for all aerosol models.
- PA table that retains aerosol scattering phase functions for all the aerosol models.
The entries for these tables were all generated by rstar5b code developed by T. Nakajima and his group.

GLI Algorithm Description

3.2.1-2

1-4 Saturation problem at 749nm and 865nm bands
It has been predicted that 749nm and 865nm bands will be saturated even in the fair-sky oceans. Somenumerical simulations on atmospheric correction have been conducted in order to investigate alternative
atmospheric correction bands. The analysis revealed that 678nm (ch13) and 865nm (ch19) bands could
be used as the alternative bands. Therefore two band pairs, i.e. 749nm and 865nm band pair and 678nm
and 865nm (ch19, "865A") band pair, are alternatively used as the atmospheric correction bands. Pixelwise-procedure of GLI atmospheric correction algorithm with the alternative bands will be described in thenext section.
1-5 Pixel-wise procedure
The pixel-wise procedure for the atmospheric correction is described as follows. In what follows, ε’(M)means the estimated value of the spectral ratio of ωAτAPA between 749 and 865nm bands for an assumed
aerosol model M, while ε(M) is the theoretically derived value of ωAKEXTPA ratio for a model M. And 865A
means 865nm (ch19).
An annotated flow diagram of the entire atmospheric correction algorithm is presented in Fig.1.
(a) Convert total radiance, LT, into total reflectance, ρT.
(b) Calculate white cap reflectance, ρWC.
(c) Calculate air molecules scattering reflectance, ρM, by using lookup tables.
(d) Subtract ρM and ρWC from ρT(λ).
(e) When measured radiance at 749nm band, Lt(749), is less than 0.9 mW/cm2/µm/sr and Lt(865) is less2

than 0.6 mW/cm /µm/sr, estimate τA at 749nm and 865nm bands for each candidate aerosol model(M)in reference to the aerosol lookup tables. Then proceed to step (i).
2(f) When Lt(749) is in the range of 0.9 - 1.2 mW/cm /µm/sr estimate τA at 678nm and 749nm band foreach candidate aerosol model(M) in reference to the aerosol lookup tables, and convert τA(M, 678) toτA'(M, 749) by using Kext lookup tables. Then τA(M, 749) and τA'(M, 749) are composed as follows:τA(M, 749) = ratio1*τA(M, 749) + (1-ratio1)* τA'(M, 749)

(5)

ratio1=-30.0+(240.0+(-233.0+74.0741*Lt(749))*Lt(749))*Lt(749)(6)2(g) When Lt(865) is in the range of 0.6 - 0.8 mW/cm /µm/sr, estimate τA at 865nm and 865A bands foreach candidate aerosol model(M) in reference to the aerosol lookup tables, and convert τA(M, 865A) toτA'(M, 865) by using Kext lookup tables.

Then τA(M, 865) and τA'(M, 865) are composed as follows:τA(M, 865) = ratio2*τA(M, 865) + (1-ratio2)* τA'(M, 865)

(7)

ratio2=-30.0+(360.0+(-525.0+250.000*Lt(865))*Lt(865))*Lt(865)(8)2(h) When Lt(749) and Lt(865) are over 1.2 and 0.8 mW/cm /µm/sr, respectively, estimate τA at 678nm and
865A bands for each candidate aerosol model(M) in reference to the aerosol lookup tables.

Then

convert τA(M, 678) and τA(M, 865A) to τA(M, 749) and τA(M, 865) by using Kext lookup tables, respectively.
(i) Calculate ε’ value for 9 aerosol models at 749nm and 865nm bands.

ε ′(M, 749, 865) ==ρ AS (749)ρ AS (865)ω A (M, 749)τ A (M, 749)PA (M, 749)
ω A (M,85)τ A (M, 865)PA (M, 865)

(9)(i) Calculate ε’ave and select a pair of aerosol models A and B, such that ε(A) < ε'ave and ε(B) > ε'ave, by theiteration scheme. Define interpolation ratio r as ( ('ave-((A) )/( ( (B)-('(A) ).

GLI Algorithm Description

3.2.1-3

(j) For models A and B, obtain (A(( M) for band 1 to 12 and 14 by
K (λ , M )τ A (λ , M ) = ext
τ (865, M )K ext (865, M ) A(10)Derive ρA(λ)+ρMA(λ) for the models A and B in use of the aerosol lookup tables.
(k) Obtain final ρA(λ)+ρMA(λ) by interpolating the ρA+ρMA values for the models A and B.
(l) Calculate water-leaving reflectance, ρw.
(m) Convert ρW into normalized water-leaving radiance, nLW.

GLI Algorithm Description

3.2.1-4

Fig.1 An annotated flow diagram of the pixel-wise GLI atmospheric correction

GLI Algorithm Description

3.2.1-5

1-6 Atmospheric correction with iteration (new OTSK1)
Due to saturation problems of the GLI nominal band16 (749nm) and band18 (865nm) even in non-cloudy ocean
areas, GLI band13 (678nm) and band19 (865nm), were used for atmospheric correction. An iteration scheme isneeded since these bands may be influenced by upward radiance from the sea. These near-infrared (NIR) waterleaving radiances should be corrected before atmospheric correction by using specific in-water model.
We developed an iterative procedure that corrects atmospheric effect with iteration to avoid the black pixel
assumption (Siegel et al., 2000). As shown in Figure 3-1, the water reflectance at near infrared bands are firstestimated by using in-water model assuming initial values for chlorophyll a (chl) and inorganic suspended matter(ism) concentrations as well as absorption coefficient of colored dissolved organic matter (cdom).

First

atmospheric correction is executed, and new chl, ism and cdom are estimated by using neural network in-wateralgorithm. After the first atmospheric correction, the new water-leaving reflectance is estimated from obtained chl,and the second stage atmospheric correction is conducted. This process is repeated until chl, ism and cdom
estimates converge.

1-6-1 In-water model at near infrared region
The in-water model for NIR water-leaving radiance is defined as follows[ ρ w (λ )]N = 0.533πR(λ ) /Q ,(11)

by Lee et al. (1994) where λ is wavelength, and Q = 4.5 (Morel

Initial values ofchl, ism, cdom

and Gentili, 1991). [ ρ w (λ )]N is normalized water- reflectance(Gordon, 1997) given by[ ρ w (λ )]N = ρ w (λ ) / t 0 ,NIR ρw model
NIR ρw correction(12)

where t0 is the transmittance between sun and ocean surface.
R is the reflectance just below surface and is defined by

Atmospheric correction

Joseph (1950) as

R(λ ) =

1 + 2bb (λ ) / a(λ ) − 1
1 + 2bb (λ ) / a(λ ) + 1

neural network
in-water algorithm(13)

New chl, ism, cdom, and ρw in VIS

where a and bb is absorption and backward scattering
Converged?

coefficient, respectively. a(λ) and bb(λ) are defined by

Outputa ( λ ) = a w ( λ ) + a c ( λ ,chl ) + a s ( λ ,ism ) + a y ( λ ) , (14)andbb (λ ) = bbw (λ ) + bbc (λ ,chl) + 2.7 ⋅ bbs (λ ,ism) \(15)

where subscript w, c, s, y represents water, chlorophyll-a,

Figure 3-1 A simplified flow diagram of the
pixel-wise GLI atmospheric correction with
iteration. In the diagram, NIR and VIS stand forthe near-infrared and visible bands, respectively.

inorganic suspended matter and yellow substance (cdom) respectively. Absorption coefficient values are given
as follows.

a w (678) = 0.42829 , a w (865) = 4.6416(16)

by Pope and Fry (1997)

a c (λ ) = a cs (λ ) ⋅chl

(17)

where chl is chlorophyll a concentration in mg/m3

a cs (678) = 0.01968, a cs (865) = 0
GLI Algorithm Description

by Kishino (personal ٛ comm.)

3.2.1-6(18)

a y (λ ) = a y (440) ⋅ exp{−0.014 ⋅ (λ − 440)}

by Bricaud et al. (1981)(19) λ −4.32
bbw (λ ) = 0.5× 0.00288 ⋅  550 by Morel (1974)(20)

bbc (λ ) = 0.081⋅ bc (λ )by Oishi et al. (2002)(21)

 λ −0.2933
bc (λ ) = 0.27.chl 0.698 .
 550 by Kishino (personal ٛ comm..)(22)

bbs (λ ) = bs (λ ) ⋅ 0.01478

by Babin and Doerffer (1996)(23)

 λ −0.812
bs (λ ) = 0.125 ⋅ism ⋅  550 by Kronfeld (1988)(24)

The back scattering coefficients are given as follows:

1-6-2 Neural network-based in-water algorithm
A neural network is used for the iteration process to derive estimates of the chlorophyll-a concentration (chl),inorganic suspended solid concentration (ism) and absorption coefficient of colored dissolved organic matter(cdom) at 440nm (Tanaka et al., 1998). The inputs for the neural net are the normalized water-leaving radiances
at 412, 443, 460, 520, and 545 nm bands. These bands are chosen because they have high saturation radiances.

Figure 3-2 Neural network-based in-water algorithm
1-6-3 Alternative bands
Due to saturation problems of the GLI nominal band16 (749nm) and band18 (865nm) even in non-cloudy ocean
areas, GLI band13 (678nm) and band19 (865nm), were used for atmospheric correction. An iteration scheme isneeded since these bands may be influenced by upward radiance from the sea. These near-infrared (NIR) waterleaving radiance should be corrected before atmospheric correction by using specific in-water model.

GLI Algorithm Description

3.2.1-7

(2)Physical and Mathematical aspects of the algorithm
This algorithm is originated from the Ocean Color Atmospheric Correction algorithm. An extension fromthe OCTS algorithm is being made to improve the processing accuracies by taking use of many additionaland new GLI bands. The OCTS algorithm, in turn, was initially developed based on an atmosphericcorrection method used to handle SeaWiFS data (Gordon and Wang, 1994), in taking the following effects
into consideration:• Polarized Rayleigh scattering (including the multiple scattering)• Aerosol scattering• Scattering among aerosol particles and gas molecules• Reflection of sky light from sea surface• Absorption effect by ozone• Transmittance along the path sun-to-sea surface-to-satellite• Sun glint
Corrections of the light components due to Rayleigh scattering and aerosol scattering etc. are made byusing lookup tables prepared beforehand. In addition to the atmospheric pressure, ozone concentration,wind speed etc., the atmospheric correction requires also other kinds of analysis data made available byMeteorological Agency.
When applying to GLI, the following effects will be newly taken into account:• Influence of white cap• Absorbing effect of water vapor• Absorbing effects of carbon dioxide gas and others

C. References
1.

Research Report: On the development of a retrieval algorithm for ADEOS-II/GLI ocean color data –Chapter 3: An Algorithm for GLI Ocean Color Atmospheric Correction, FY1996.

2.

Research Report: Advanced Earth Observing Satellite (ADEOS) OCTS Data Processing Algorithm
Description Ver.2.0 (NASDA) – Chapter 8.6: OCTS Type Algorithm.

3.

Babin M. and R. Doerffer (1996), Specifications for case II coastal water reference model., Algorithm
Theoretical Basis Document for MERIS (ATBD 2.12), ESA-ESTEC, pp.61-73.

4.

Bricaud, A.,A. Morel and L. Prieur(1981), Absorption by dissolved organic matter of the sea (yellow
substance) in the UV and visible domains, Limnol. Oceanogr., Vol.26, No.1, pp.43-53.

5.

Ding, K. Y., & Gordon, H. R. (1994). Atmospheric correction of ocean color sensors: Effects of the earth's
curvature. Applied Optics, 33 (30), 7096-7106.

6.

Fukushima, H. A. Higurashi, Y. Mitomi, T. Nakajima, T. Noguchi, T. Tanaka, and M. Toratani (1998):
Correction of atmospheric effect on ADEOS/OCTS ocean color data: Algorithm description and evaluationof its performance, J. Oceanography, 54, 417-430.

7.

Fukushima, H. and M. Toratani (1997): Asian dust aerosol: optical effect on satellite ocean color signal
and a scheme of its correction. J. Geophys. Res., 102(D14), 17,119-17,130

8.

Gordon, H.R.(1997),Atmospheric correction of ocean color imagery in the Earth Observation System era,
J. Geophys. Res., 102 (D14), 17,081-17,106.

9.

Gordon, H.R., and M. Wang.(1994), Retrieval of water-leaving radiance and aerosol optical thickness
over the oceans with SeaWiFS: a preliminary algorithm, Appl. Opt., 33 (3), 443-452.

10.

Joseph, J. (1950), Untersuchungen über ober- und unterlichtmessungen im Meere und über ihren

GLI Algorithm Description

3.2.1-8zusammenhang mit durchsichtigkeitsmessungen, Deut. Hydorograph. Z., Vol.3, pp.324-335.
11. Kronfeld, U. (1988),Die optishen eignenschatten der ozea nischen shwebstoffe und ihre bedentung fur
fernerkundung von phytoplankton., GKSS Forschungszentrum, D-2054 Geesthacht, Germany, p.153.
12. Lee, Z., K. Carder, S. Hawes, R. Steward, T. Peacock and C. Davis (1944), Model for the interpretation of
hyperspectral remote-sensing reflectance, Applied Optics, Vol.33, pp.5721-5732.
13. Morel A. and B. Gentili (1991), Diffuse reflectance of oceanic waters: its dependence on sun angle asinfluenced by the molecular scattering contribution, Applied optics, 30, 4427-4438.
14. Morel, A. (1974), Optical properties of pure water and pure sea water, chapter 1 in Optical Aspects of
Oceanography, edited by N. G. Jerrov and E.S. Nielsen, Academic Press, New York, 1-24.
15. Nakajima, T., M. Tanaka, M. Yamamoto, M. Shiobara, K. Arao, and Y. Nakanishi (1989), Aerosol opticalcharacteristics in the yellow sand events observed in May, 1982 at Nagasaki - part II models, J. Meteor.
Soc. Japan, 67, 279-291.
16. Oishi, T., Y. Takahashi, A. Tanaka, M. Kishino, and A. Tsuchiya (2002), Relation between the backwordas well as total scattering coefficients and the volume scattering functions by cultured phytoplankton. J.
School Mar. Sci. Technol. Tokai Univ., Vol.53, pp.1-15 (in Japanese with English abstract).
17. Pope, R. M. and E. S. Fry (1997), Absorption spectrum (380-700) of pure water, II: Integrating cavity
measurement, Applied Optics, Vol.36, pp.8710-8723.
18. Shettle, E.P., and R. W. Fenn. (1979), Models for the aerosols of the lower atmosphere and the effects ofhumidity variations on their optical properties, AFGL-TR-79-0214, 675, 94pp,.
19. Siegel D. A., M. Wang, S. Maritorena, and W. Robinson (2000): Atmospheric correction of satellite ocean
color imagery: the black pixel assumption, Appl. Opt., 30, 21, 3582-3591.
20. Tanaka, A., T. Oishi, M. Kishino, and R. Doerffer (1998), “Application of the neural network to OCTS
data”, Proc. Ocean Optics XIV, S. G. Ackleson and J. Campbell (eds.), Office of Naval Research,
Washington, D.C..

GLI Algorithm Description

3.2.1-9

3.2.1-2

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 (OTSK14)(2)

Product Code: PAR(3)

PI names: G-0035 Robert Frouin(4)

Overview of algorithm (Status: Operational level)
The algorithm estimates daily (i.e., 24-hour averaged) Photo-synthetically Active Radiation (PAR) reaching
the ocean surface.

B. Theoretical Description
PAR is defined as the quantum energy flux from the Sun in the spectral range 400-700 nm. It is expressed in
Einstein/m2/day.
The PAR model uses plane-parallel theory and assumes that the effects of clouds and clear atmosphere canbe de-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 of such a de-coupled model is its simplicity. It is unnecessary to distinguish between clear andcloudy regions within a pixel, 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, E0cos(θs) is diminished by afactor 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 thesurface 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 0.412µm, 2 is 0.443µm, 3 is 0.490 µm, 4 is 0.519 µm, 5 is 0.544 µm, and 6 is 0.679 µm, expressed in mW/cm2/µm/sr, istransformed into reflectance, Ri*:
Ri* = πLi*/[E0i(d0/d)2cos(θs*)](2)

where Eoi is the extra-terrestrial solar irradiance in band i, θs* is the sun zenith angle at the GLI observation time,and d0/d is the ratio of mean and actual Earth-Sun distance. The glint areas are not selected because they would
be interpreted as cloudy in the PAR algorithm.
Second, Ri * is corrected for gaseous absorption, essentially due to ozone:
Ri’ = Ri*/Tgi(3)

Tgi = exp[-kiU/cos(θs*)]

(4)

with
where ki is the ozone absorption coefficient in band i and U the ozone amount.
Third, the reflectance of the cloud/surface layer, Ri, is obtained from Ri’ following Tanré et al. (1979) andassuming isotropy of the cloud/surface layer system. That is:
Ri = (Ri’ – Rai)[Tdi(θs*)Tdi(θv) + Sai(Ri’ – Rai)]-1

GLI Algorithm Description

3.2.1-10(5)

where θv is the viewing zenith angle and Rai is the intrinsic atmospheric reflectance in band i (corresponds tophotons 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 θ is either θ s* or θ v.
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/ λ i) α(9)where λ i and λ 18 are equivalent wavelengths in GLI bands i and 18, respectively. A monthly climatology may be
used for 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 θ s effects.
To estimate ωaer and Paer, the two closest of 12 aerosol models, k and l, that verify α (l)< α < α (k) areselected, and a distance 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:<E>day = <E0>∫{cos(θ s)<Tg><Td>[1 – <A>]
[1 – <As>]-1[1 – <Sa><A>]-1} dt(12)<Tg> = exp[-<k>U/cos(θ s)](13)<Td> = ∑i(TdiEoi)/∑iE0i(14)<Sa> = ∑i(SaiEoi)/∑iE0i

(15)

with

<As> = <Tdir><Td>-1 [0.05/(1.1[cos(θ s)]1.4 + 0.15]+ 0.08<Tdif><Td>

-1

(16)

<Tdir> = ∑iTdiriEoi/∑iE0i(17)<Tdif> =<Td> - <Tdir>(18)

Tdiri = exp[-(τmoli + τaeri)/cos(θ s)](19)<A> = F<R(t*)>(20)<R> = ∑iRi(t*)/∑iE0i(21)

where t* is the GLI observation time, Tdiri is the direct component of Tdi in band i, and <> symbolizes averagevalue over the PAR range. Note that because of saturation at low radiance in some of the GLI spectral bands, thealgorithm only takes into account, for each pixel, the spectral bands that do not saturate. It is possible, as an
option, however, to use only the band centered at 0.679 µm (does not saturate over clouds) to estimate cloud
effects on PAR. In the code, this option is activated when the flag “flag679” is on.

GLI Algorithm Description

3.2.1-11

In Eq. (12), absorption by water vapor in the PAR spectral range, occurring weakly between 690 and 700 nm,
is neglected. The ozone absorption coefficient <k> in Eq. (13) is taken from Frouin et al. (1989). Surface albedo isparameterized as a function of sun zenith angle and fractions of direct and diffuse incoming sunlight, according to
Briegleb and Ramanathan (1982). This parameterization, which takes into account Fresnel reflection and diffuse
under-light, is sufficient since the influence of <As> on surface PAR is small.
Even though the cloud/surface layer is assumed to be isotropic in the correction of clear atmosphere effects(Eq. 5), and therefore A ≈ R, the dependence of A on sun zenith angle is taken into account via the angular factor,
F (Eq. 20). Instead of using for F angular models determined statistically (e.g., Young et al., 1998), analyticalformulas proposed by Zege (1991) for non-absorbing, optically thick scattering layers are applied. The available
angular models are fairly similar for partly cloudy, mostly cloudy, and overcast conditions, and they compare
reasonably well with Zege’s (1991) formulas.
The cloud/surface layer, however, is assumed to be stable during the day and to correspond to the GLI
observation. This assumption is crude, and PAR accuracy will be degraded in regions where clouds exhibit strong
diurnal variability. Still, useful daily PAR estimates would be obtained by averaging in space and time. Note thatusing Eq. (12) the algorithm yields a daily PAR estimate for each instantaneous GLI pixel.
Finally, the individual daily PAR estimates, obtained in units of mW/cm2/µm, are converted into units ofEinstein/m2/day. The factor required to convert units of mW/cm2/µm to units of Einstein/m2/day is equal to 1.193 to
an inaccuracy of a few percent regardless of meteorological conditions (Kirk, 1994, pp. 4-8.). In middle and highlatitudes, several daily estimates may be obtained over the same target during the same day, increasing productaccuracy.
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 surfaceof 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 tocompute 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

5.

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

surface. Part I: Model. J. Appl. Meteor., 31, 1056-1066.
Press, 509 pp.
6.

Tanré, D., M. Herman, P.-Y. Deschamps, and A. De Leffe, 1979: Atmospheric modeling for spacemeasurements of ground reflectances, including bi-directional properties. Appl. Optics, 18, 3587-3594.

7.

Young, D. F., P. Minnis, D. R. Doelling, G. G. Gibson, and T. Wong, 1998: Temporal interpolation
methods for the clouds and Earth’s Radiant Energy System (CERES experiment. J. Appl. Meteor., 37,
572-590.

8.

Zege, E. P., A. P. Ivanov, and I. L. Katsev, 1991:Image transfer through a scattering medium. SpringerVerlag, New York, 349 pp.

GLI Algorithm Description

3.2.1-12