Spectral Albedo Integration Algorithm for POLDER-2 1/5 Spectral Albedo Integration Algorithm for POLDER-2 Aim of the algorithm : Derivation of the shortwave albedo/reflectance as a function of the spectral albedos/reflectances at 443 nm, 670 nm and 865 nm. Date of the document : October 1996 ; revised October 2002 Author : J. C. Buriez Laboratoire d'optique Atmosphérique UMR CNRS, Université des Sciences et Technologies de Lille, 59655 Villeneuve d'ascq Cedex (France) e-mail : buriez@univ-lille1.fr Content : 1. INTRODUCTION 2. ALGORITHM DESCRIPTION 3. DETERMINATION OF COEFFICIENTS 4. OUTPUT PARAMETERS 5. REFERENCES Development of the POLDER Earth radiation budget, water vapor, and clouds algorithms results from a joint effort of Laboratoire d Optique Atmosphérique (LOA), Laboratoire des Sciences du Climat et de l Environnement (LSCE) and Laboratoire de Météorologie dynamique (LMD). It has been supported by CNES (Centre National d Etudes Spatiales), CNRS (Centre National de la Recherche Scientifique) and Région Nord-Pas de Calais.
Spectral Albedo Integration Algorithm for POLDER-2 2/5 1. INTRODUCTION This algorithm has been shortly described in Buriez et al. (1997). The shortwave albedo A SW is derived as a function of the spectral albedos A 443, A 670 and A 865. In the same way, the shortwave bidirectional reflectances are derived from the spectral bidirectional reflectances R 443, R 670 and R 865. The values of albedo/reflectance at 443 nm, 670 nm and 865 nm are considered as representative of the spectral intervals 0.2-0.55 µm, 0.55 0.7 µm and 0.7-4 µm respectively. Concerning the gaseous absorption, the first two intervals are affected by ozone, while the last interval is affected by water vapor. The solar ozone absorption is estimated from the ozone content measured by the Total Ozone Mapping Spectrometer (TOMS). The solar water vapor absorption is estimated from the ratio of the POLDER reflectances at 910 nm and 865 nm. In this document, we start with the description of the algorithm, followed by a discussion about some coefficients used in this algorithm. We conclude with the list of the output parameters. 2. ALGORITHM DESCRIPTION Consider a given superpixel (generally composed of 3 x 3 pixels) observed by POLDER in a viewing geometry represented by (µ s,µ v,φ), where µ s is the cosine of solar zenith angle, µ v the cosine of viewing zenith angle and φ the relative azimuth angle. 2.1. Shortwave reflectances The corrected spectral reflectances issued from the Gaseous Absorption Correction Algorithm for POLDER-2 are averaged over the superpixel. Let be R 443 (µ s,µ v,φ), R 670 (µ s,µ v,φ), R 865 (µ s,µ v,φ) and R 910 (µ s,µ v,φ) these mean reflectances at 443, 670, 865 and 910 nm respectively. Except for the gaseous absorption, the first three reflectances are assumed to be representative of the spectral intervals 0.2-0.55 µm, 0.55 0.7 µm and 0.7-4 µm respectively. The shortwave reflectance is thus expressed as Rsw(µ s,µ v,φ) = C 1 T 1 (mu 03 ) R 443 (µ s,µ v,φ) + C 2 T 2 (mu 03 ) R 670 (µ s,µ v,φ) + C 3 T 3 (R 910 (µ s,µ v,φ)/r 865 (µ s,µ v,φ)) R 865 (µ s,µ v,φ) + C 4 + C 5 /µ s (1) where C 1,, C 5 are constants, the two last terms in Equ.(1) are only adjustment terms, and the transmission functions T 1, T 2 and T 3 are defined as follows : T 1 and T 2 represent the ozone transmission weighted by the solar incident irradiance in the interval 0.2-0.55 µm and 0.55-0.7 µm respectively. They depend on the product m U 03, where m is the air mass factor (m = 1/µ s +1/µ v ) and U 03 the vertical column of ozone derived from TOMS observations. Practically, T 1 (mu 03 ) and T 2 (mu 03 ) are approximated by means of Padé approximants (Baker, 1965).
Spectral Albedo Integration Algorithm for POLDER-2 3/5 The function T 3 represents the water vapor transmission weighted by the solar incident irradiance in the interval 0.7-4 µm ; it is assumed to be directly related to the observed R 910 /R 865 ratio by T 3 (R 910 (µ s,µ v,φ)/r 865 (µ s,µ v,φ)) = A + B R 910 (µ s,µ v,φ)/r 865 (µ s,µ v,φ) (2) where A and B are constants fitted from radiative transfer simulations. 2.2. Shortwave albedos Let be A 443 (µ s, µ v, φ), A 670 (µ s, µ v, φ) and A 865 (µ s, µ v, φ) the bidirectional values of albedo, that is the albedo values derived in a given viewing direction at 443, 670 and 865 nm respectively. These values are issued from the Spectral Albedo and Cloud Optical Thickness Algorithm for POLDER-2. The shortwave bidirectional albedo is expressed as A SW (µ s,µ v,φ) = C 1 T 1 (MU 03 ) A 443 (µ s,µ v,φ)) + C 2 T 2 (MU 03 ) A 670 (µ s,µ v,φ) + C 3 T 4 (R 910 (µ s,µ v,φ)/r 865 (µ s,µ v,φ)) A 865 (µ s,µ v,φ) + C 4 + C 5 /µ s (3) where M is the equivalent air-mass factor given by M = 1/µ s + η (4) where η is a diffusivity factor to take into account the effect of integration over viewing angles. We choice η = 1.66 as usually used in infrared transmission calculations (e.g., Goody and Yung, 1989). The transmission function T 4 that replaces T 3 is now defined by T 4 (R 910 (µ s,µ v,φ)/r 865 (µ s,µ v,φ)) = A + B [R 910 (µ s,µ v,φ)/r 865 (µ s,µ v,φ)] ζ(µs,µv) (5) with ζ(µs,µv) = β M, (6) m where β is a constant derived from transmission calculations. The shortwave albedo A SW (µ s ) is then deduced by a weighted averaging of the different values of A SW (µ s, µ v, φ). The weighting function is a function of the scattering angle and depends on the observed cloudiness. It is the same as in the Spectral Albedo and Cloud Optical Thickness Algorithm for POLDER-2. In the same way, we calculate the clear-sky estimate of the shortwave albedo from the modeled clear-sky albedos used in the calculation of cloud optical thickness (see Spectral Albedo and Cloud Optical Thickness Algorithm for POLDER-2) [A model (τ c =0)] SW = C 1 T 1 (MU 03 ) [A model (τ c =0)] 443 + C 2 T 2 (MU 03 ) [A model (τ c =0)] 670 + C 3 T 5 (MU ECMWF ) [A model (τ c =0)] 865 + C 4 + C 5 /µ s (7)
Spectral Albedo Integration Algorithm for POLDER-2 4/5 where T 5, that replaces T 4, is a function of the product M U ECMWF, where U ECMWF is the total vertical column of water vapor derived from ECMWF (European Centre for Medium-Range Weather Forecasts) analysis. Practically this water vapor transmission function T 5 (MU ECMWF ) is a Padé approximant. 3. DETERMINATION OF COEFFICIENTS The coefficients C 1,, C 5 used in Equ. (1), (3) and (7) can be determined either theoretically or empirically. The second approach (empirical) is certainly highly preferable. The constants may be determined by using a least squares method to minimize the r.m.s. difference between the POLDER shortwave reflectances given by Equ. (1) and the true shortwave reflectances simultaneously measured by an ERB (Earth Radiation Budget) scanner. Before the launch of ADEOS 1 in 1996, a comparison between POLDER and ScaRaB (Scanner for Radiation Budget) was scheduled. Unfortunately, during the period ADEOS 1-POLDER was working (November 1996 - June 1997), there was neither ScaRaB nor any ERB scanner in flight. Consequently, the constants C 1,, C 5 used for ADEOS 1-POLDER were determined from simulations. To do that, we used the radiative transfer code GAME (Global Atmospheric ModEl). This allows accurate treatment of scattering by aerosols, clouds and molecules. Multiple scattering effects are treated using the Discrete Ordinates Method (Stamnes et al., 1988). Absorption is calculated from a line by line code (Dubuisson et al., 1996). The simulations were performed for various values of µ s (from 0.2 to 1) and for two very different standard atmospheres : the tropical atmosphere and the subartic winter atmosphere (McClatchey, 1972). In addition to the sea-surface with a reflectivity of 6 %, two land surface models were considered : vegetation and sand. The calculations were performed for clear-sky situations with standard aerosol models (WMO, 1986) and for overcast situations corresponding to two cloud altitudes and various cloud optical thicknesses. However, at this time, only liquid water cloud droplets with an effective radius of 10 µm were considered. This is consistent with the cloud optical thickness retrieval method previously used for ADEOS 1- POLDER (Buriez et al., 1997). From these simulations, the values of C 1,, C 5 were derived by a least squares method. We found a r.m.s. difference between the approximate and the exact shortwave reflected fluxes of 10 Wm -2, but no significant bias for any atmosphere model. In the future, we wish to take advantage of spatiotemporal coincidences between the satellites ADEOS 2 and TERRA. From the comparison between the POLDER reflectances and the CERES (Clouds and Earth s Energy System) shortwave reflectances, we hope to derive new coefficients C 1,, C 5 and thus to improve the determination of the shortwave albedo. 4. OUTPUT PARAMETERS Two nondirectional parameters issued from this algorithm are delivered in the ERB, WV & clouds products : the shortwave albedo, A SW, derived from the 443, 670 and 865 nm albedos, the clear-sky estimate of the shortwave albedo derived from the modeled clear-sky albedos, [A model (τ c =0)] SW, that is independent of POLDER measurements.
Spectral Albedo Integration Algorithm for POLDER-2 5/5 In addition, two parameters are delivered for each viewing direction (i = 1, 14) : the bidirectional shortwave reflectance, R SW (i), the bidirectional shortwave albedo, A SW (i). 5. REFERENCES Baker, G. A., 1965 : The theory and application of the Padé approximant method. Advances in Theoretical Physics, Vol. 1 (Ed. K. A. Brueckner). Academic Press, New York, 1-58. Buriez, J. C., C. Vanbauce, F. Parol, P. Goloub, M. Herman, B. Bonnel, Y. Fouquart, P. Couvert and G. Seze, 1997: Cloud detection and derivation of cloud properties from POLDER. Int. J. Remote Sensing, 18, 2785-2813. Dubuisson, P., J. C. Buriez and Y. Fouquart, 1996: High spectral resolution solar radiative transfer in absorbing and scattering media: Application to the satellite simulation. J. Quant. Spectrosc. Radiat. Transfer, 55, 103-126. Goody, R. M. and Y. L. Yung, 1989: Atmospheric Radiation: Theoretical Basis, Oxford University Press, NY, 519 pp. McClatchey, R. A., R., W., Fenn, J. E. A. Selby, F. E. Voltz and J. S. Garing, 1972: Optical properties of the atmosphere. AFCRL-72-0497, 108 pp. Stamnes, K., S.-C. Tsay, W. Wiscombe, and K. Jayaweera, 1988: Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media, Appl. Opt., 27, 2502-2509. WMO, 1986: A preliminary cloudness standard atmosphere for radiation computation, World Meteorological Organization, Report no 24, WCP-112, 53 pp.