Retrieval of Chlorophyll-a Concentration via Linear Combination of ADEOS-II Global Imager Data

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1 Journal of Oceanography, Vol. 62, pp. 331 to 337, 2006 Retrieval of Chlorophyll-a Concentration via Linear Combination of ADEOS-II Global Imager Data ROBERT FROUIN 1 *, PIERRE-YVES DESCHAMPS 2, LYDWINE GROSS-COLZY 1, HIROSHI MURAKAMI 3 and TAKASHI Y. NAKAJIMA 4 1 Scripps Institution of Oceanography, University of California San Diego, 8810 La Jolla Shores Drive, La Jolla, CA 92037, U.S.A. 2 Laboratoire d Optique Atmosphérique, Université des Sciences de Lille, Villeneuve d Ascq, France 3 Earth Observation Research Center, Japan Aerospace Exploration Agency, Harumi, Chuo-ku, Tokyo , Japan 4 Department of Network and Computer Engineering, Tokai University, Tomiyaga, Shibuya-ku, Tokyo , Japan (Received 17 September 2005; in revised form 17 December 2005; accepted 19 December 2005) Top-of-atmosphere reflectance measured above the ocean in the visible and near infrared, after correction for molecular scattering, may be linearly combined to retrieve surface chlorophyll-a abundance directly, without explicit correction for aerosol scattering and absorption. The coefficients of the linear combination minimize the perturbing effects, which are modeled by a polynomial, and they do not depend on geometry. The technique has been developed for Global Imager (GLI) spectral bands centered at 443, 565, 667, and 866 nm, but it is applicable to other sets of spectral bands. Theoretical performance is evaluated from radiation-transfer simulations for a wide range of geophysical and angular conditions. Using a polynomial with exponents of 2, 1, and 0 to determine the coefficients, the residual influence of the atmosphere on the linear combination is within ±0.001 in most cases, allowing chlorophyll-a abundance to be retrieved with a root-mean-squared (RMS) error of 8.4% in the range mgm 3. Application of the method to simulated GLI imagery shows that estimated and actual chlorophyll-a abundance are in agreement, with an average RMS difference of 32.1% and an average bias of 2.2% (slightly lower estimated values). The advantage of the method resides in its simplicity, flexibility, and rapidity of execution. Knowledge of aerosol amount and type is avoided. There is no need for look-up tables of aerosol optical properties. Accuracy is adequate, but depends on the polynomial representation of the perturbing effects and on the bio-optical model selected to relate the linear combination to chlorophyll-a abundance. The sensitivity of the linear combination to chlorophyll-a abundance can be optimized, and the method can be extended to the retrieval of other bio-optical variables. Keywords: Ocean color, remote sensing, aerosols, atmospheric correction, chlorophyll. 1. Introduction Standard algorithms to estimate phytoplankton chlorophyll concentration from space (e.g., Gordon, 1978, 1997; Viollier et al., 1980; Gordon and Wang, 1994; Fukushima et al., 1998; Antoine and Morel, 1999; Gao et al., 2000) aim at correcting accurately for atmosphere and surface effects. The procedure consists of estimating the aerosol radiance in the red and near infrared where the * Corresponding author. RFrouin@UCSD.edu Copyright The Oceanographic Society of Japan/TERRAPUB/Springer ocean can be considered black (i.e., totally absorbing), and extrapolating the estimated radiance to shorter wavelengths. The retrieved water-leaving radiance is then related to chlorophyll concentration using a bio-optical model. This approach has been successful, and it is employed in the operational processing of data from major satellite ocean-color missions. Other, more recent algorithms (André and Morel, 1991; Land and Haigh, 1996; Fraser et al., 1997; Gordon et al., 1997; Zhao and Nakajima, 1997; Chomko and Gordon, 1998) attempt to determine aerosol properties and pigment concentration simultaneously, in a single step. Through systematic vari- 331

2 ation of candidate aerosol models, aerosol optical thickness, chlorophyll concentration, and in some algorithms phytoplankton scattering, a best fit to the spectral top-ofatmosphere radiance (visible and near infrared) is obtained. The advantage of the single-step approach is its ability to handle both weakly and strongly absorbing aerosols (Gordon et al., 1997). The drawback is that convergence may not be achieved immediately in some cases, making it difficult to apply the algorithms to large amounts of satellite data. The two types of algorithms are fairly complicated. They require, in particular, large look-up tables of aerosol optical properties or aerosol radiance. These tables are called internally as the atmospheric correction (standard procedure or non-linear optimization) is effected. It may be possible, however, to linearly combine the topof-atmosphere radiance in selected spectral bands, so that the atmosphere and surface effects are substantially reduced. This simple altâ native requires appropriate modeling or decomposition of the perturbing effects and sufficient sensitivity of the linear combination to chlorophyll concentration, as explained below. First we describe the approach and the procedure to determine the coefficients of a suitable linear combination, and we evaluate the impact of residual atmospheric effects on the retrieval of chlorophyll concentration. Next we apply the algorithm to simulated Global Imager (GLI) imagery and follow with an analysis of the resulting chlorophyll concentration errors. Finally we debate the advantages and drawbacks of the algorithm and conclude with a discussion of improvements and potential developments. 2. Methodology Instead of using radiance, L, we use reflectance, R, defined as R = πl/f 0 cosθ 0, where F 0 is the extraterrestrial solar irradiance and θ 0 is the solar zenith angle. Neglecting the influence of direct sun glitter, whitecaps, and gaseous absorption, the remaining top-of-atmosphere reflectance R*(λ) at wavelength λ can be expressed as R*(λ) = R m (λ) + R a (λ) + R ma (λ) + t m (λ)t a (λ)r w (λ), (1) where R m (λ) and R a (λ) are the pure molecule- and aerosol-scattering contributions, respectively, R ma (λ) is the effect of molecule-aerosol interaction, R w (λ) is the water-body reflectance (just above the surface), and t m (λ) and t a (λ) are diffuse transmittances due to molecules and aerosols, respectively, along the path sun-to-surface and surface-to-sensor. The terms R m (λ) and R a (λ) include the contribution of photons directly transmitted to the surface, reflected by the surface, and diffusely transmitted to the sensor, and of photons diffusely transmitted to the surface, reflected by the surface, and directly transmitted to the sensor. The molecular variables R m (λ) and t m (λ) can be computed precisely from atmospheric pressure. One can therefore subtract R m (λ) from R*(λ) and remove the effect of t m (λ) on the last term of Eq. (1), the term of interest, to form R c (λ) = [R*(λ) R m (λ)]/t m (λ) = [R a (λ) + R ma (λ)]/t m (λ) + t a (λ)r w (λ) = R (λ) + t a (λ)r w (λ). (2) In this expression, the effect of aerosols is essentially confined to R (λ). The transmittance t a (λ) is usually close to 1 (Tanré et al., 1979; Gordon, 1997). Linearly combining the corrected reflectance R c in spectral bands centered at λ i yields the following index I = Σ i [a i R c (λ i )] = Σ i [a i R (λ i )] + Σ i [a i t a (λ i )R w (λ i )]. (3) To eliminate most of the atmospheric influence on I, one has to find coefficients a i that fulfill Σ i [a i R (λ i )] = 0. (4) For this, we approximate R (λ i ) by a polynomial, i.e., ( ) [ ] ( ) i j j i R λ Σ b λ, 5 where is not necessarily an integer. Indeed, accuracy depends on the selected polynomial, but, in general, a satisfactory representation can be obtained with only a few terms. Specification of the polynomial, however, must take account of the spectral bands (number, characteristics) as well as sensitivity to chlorophyll concentration (see below). Substituting R by its polynomial expression, Eq. (4) becomes Σi{ aiσj[ bj λ i ]} = 0. ( 6) This equation can be rearranged to read Σ { b Σ [ a λ ]} = 0. ( 7) j j i i i To satisfy Eq. (7), it is sufficient to have, for each [ ] = 0. () 8 Σ i a i λ i This system of linear equations has an infinite number of solutions, which offers a lot of flexibility, but we are only interested in solutions (i.e., in coefficients a i ) that keep the second term on the right-hand side of Eq. (3), hence 332 R. Frouin et al.

3 Index I GSD Theory Fig. 1. Residual influence of the atmosphere on the index I for varied geophysical and angular conditions (see text for details). the index I, sensitive to chlorophyll concentration. Note that the coefficients b j, which vary with geometry and geophysical conditions (i.e., are different for each pixel), do not need to be known. A suitable solution is obtained with [λ i ] = [443, 565, 667, 866] (in nm) and [ ] = [ 2, 1, 0], yielding [a i ] = [1, , , ]. The selected [λ i ] are among those of the Global Imager (GLI) (Nakajima et al., 1997, 1998), an instrument onboard the ADEOS-II satellite, which was launched in December 2002 and provided data until October Thus, the index I is expressed explicitly as I = R c (443) 5.020R c (565) R c (667) 1.743R c (866). (9) C, mgm -3 Fig. 2. Sensitivity of index I to chlorophyll concentration. Solid circles: simulations with the bio-optical model of Morel and Maritorena (2001) (no atmospheric effects). Open circles: GSD data. Estimated C, mgm r 2 = Error (rms) = 8.4% Actual C, mgm -3 Fig. 3. Estimated versus actual chlorophyll concentration C for the cases of Fig. 1 with C randomly selected in the range mgm 3. The scatter around the 1:1 line is due to residual atmospheric effects in the index I. Figure 1 displays this solution I as a function of view zenith angle. One thousand cases are plotted, and they correspond to view and sun zenith angles varying between 0 to 60 degrees, aerosol optical thickness at 550 nm between 0.05 and 0.3, and varied mixtures of continental and maritime aerosols. The radiation-transfer code of Vermote et al. (1997), which properly takes moleculeaerosol interaction and surface-atmosphere coupling into account, is used to simulate R (λ i ). The Σ i [a i R (λ i )] values are small in magnitude, generally within ±0.001, except at large view angles where they may reach The larger values are also associated with large sun zenith angle and large aerosol optical thickness (not shown here). Compared with individual R (λ i ) values, the linear combination is typically one to two orders of magnitude smaller. While substantially reducing the aerosol and other perturbing effects, the linear combination remains sensitive to chlorophyll concentration. This is illustrated in Fig. 2 (solid circles), which shows Σ i [a i R w (λ i )], i.e., the second term on the right-hand side of Eq. (3) with t a (λ i ) = 1, as a function of chlorophyll-a concentration, C. The model of Morel and Maritorena (2001) is used to Retrieval of Chlorophyll-a Concentration from GLI Data 333

4 Fig. 4. GLI simulated reflectance imagery corrected for molecular scattering and sun glint effects. simulate R w (λ i ). The dependence is practically linear with the logarithm of C in the range mgm 3. The resulting error in the retrieval of C when using the index I (Eq. (3)) is given in Fig. 3. For each case considered, C was randomly selected in the range mgm 3. The agreement between estimated and actual (prescribed) C values is very good, with a root-mean-squared (RMS) error of 8.4% and a negligible bias. The variability around the 1:1 line is due not only to Σ i [a i R (λ i )], which is not exactly equal to zero, but also to t a (λ i ), which is unknown. 3. Application to Simulated GLI Data The algorithm is applied to GLI synthetic imagery, generated by the GLI Project Office using the radiationtransfer code of Nakajima and Tanaka (1988). A wide range of atmospheric conditions are represented in the data set, with aerosol optical thickness at 500 nm varying between 0.05 and 0.6, Angström coefficient in the visible between 0.1 to 1.5, and wind speed between 2 to 8 ms 1. Total ozone amount is fixed at 348 Dobson units, and surface air pressure at 1013 hpa. The water reflectance is computed from concentrations of chlorophyll-a (0.01 to 80 mgm 3 ) and other varying components, including colored dissolved organic matter and inorganic suspended matter, using a bio-optical model developed by the University of Tokai (Tanaka et al., 1998, 2004). The sun and view zenith angles and the relative azimuth angle vary within the range degrees, 0-50 degrees, and degrees, respectively. For the four spectral bands considered, Fig. 4 displays the GLI reflectance corrected for whitecaps, direct sun glitter, and molecular effects (see Eq. (2)). The radiation-transfer code of Vermote et al. (1997) is used to make the corrections. Pixels for which the glitter contribution to the GLI reflectance at 866 nm is above 0.02, located on the bottom right of the images, are masked in black. Japan, located on the left side of the images, and clouds are also masked in black. The corrected reflectance field is patchy, due mostly to aerosol variability. East of Hokkaido, some ocean features are apparent at 565 and 667 nm, but not at 443 nm, suggesting productive Case II waters. Values are generally higher in the top left portion of the image, i.e., north of Hokkaido and south of Sakhalin, because of larger aerosol optical thickness and aerosols of smaller size (Angström coefficient above 1). From the corrected reflectance imagery of Fig. 4, the index I (see Eq. (3)) is formed and related to the actual chlorophyll-a concentration C. Unlike the corrected reflectance, the index does not exhibit any apparent correlation with aerosol characteristics (Fig. 5, lower left), indicating that atmospheric correction is achieved effectively. The average relation between the index I and the 334 R. Frouin et al.

5 Fig. 5. Index I and estimated C from GLI simulated imagery, actual C, and fractional C error. actual C, displayed in Fig. 2 (open circles), is different from the one obtained using the bio-optical model of Morel and Maritorena (2001) and assuming no atmosphere (Fig. 2, solid circles). The discrepancy is due to the different bio-optical model used to compute water reflectance (Tanaka et al., 2004 versus Morel and Maritorena, 2001) and to the different radiation transfer code used to generate the GLI data and to correct molecular and sun glint effects in the simulated imagery (Nakajima and Tanaka, 1988 versus Vermote et al., 1997). Applying the I-C relation (i.e., Fig. 2, open circles) to the synthetic data yields the estimated C image displayed in Fig. 5, upper left. This image closely resembles the actual C image (Fig. 5, upper right). The chlorophylla features are retrieved satisfactorily, except in two small areas, one just South of Sakhalin and the other North of Hokkaido, where C is underestimated. C is also underestimated in the productive waters east of Hokkaido. In general, estimated and actual values agree well in the entire range of chlorophyll-a concentration (Fig. 6), with an average rms error of 32.1% and a bias of 2.2% (slightly lower estimated values). Most of the errors are within ±20% (Fig. 7), but the histogram of errors is shifted toward negative values, yielding the negative bias mentioned above. The relative errors tend to be large (>40%) west and north of Japan (Fig. 5, lower right), where aero- Estimated C, mgm Ave. RMS Error = 32.1% Ave. Bias = -2.2% Actual C, mgm -3 Fig. 6. Estimated versus actual chlorophyll concentration C for the GLI simulated imagery. sol optical thickness and Angström coefficient are also large. Estimated and actual C values are distributed in a similar way (Fig. 8), but the estimated C field contains significantly more values below 0.2 mgm 3, and fewer Retrieval of Chlorophyll-a Concentration from GLI Data 335

6 Nornalized Frequency Distribution Normalized C Error Fig. 7. Normalized frequency distribution of fractional error in chlorophyll concentration C estimated from simulated GLI imagery. Fig. 8. Estimated and actual chlorophyll concentration C distribution (cumulative) for the simulated GLI imagery. values between 0.2 and 0.5 mgm 3 (the curves for estimated and actual values get very close above 0.5 mgm 3 ). 4. Discussion and Conclusion The index I proposed above, formed by linearly combining satellite reflectance corrected for molecular scattering and sun glint effects, allows one to substantially reduce the influence of aerosols on the satellite imagery. One advantage of the index, compared with other techniques, is that no look-up tables of geometry dependent aerosol optical properties need to be called for, therefore created. Knowledge of aerosol amount and type is avoided. Moreover, the coefficients of the linear combination are independent of sun and view angles. Another advantage is the rapid execution of the algorithm. In current techniques, it is time consuming to find the proper aerosol model or iterate and minimize the difference between simulations and measurements. The accuracy of the retrievals, however, depends on the bio-optical model used to relate the index to chlorophyll concentration (varies depending on the biological province). This is generally the case with techniques (e.g., Gordon et al., 1997; Zhao and Nakajima, 1997; Chomko and Gordon, 1998) that attempt to retrieve chlorophyll concentration directly, without estimating water reflectance in a first step. In our case, however, it is easy to change the bio-optical model (no look-up tables have to be re-computed). The modeling of R, the spectral bands selected, and the sensitivity of the index to chlorophyll concentration can be optimized. The polynomial of Eq. (5), for example, can be selected to describe complex aerosols (e.g., dust and pollution particles) better. A judicious way to improve the modeling of R is would be to perform a principal component analysis (e.g., Jolliffe, 1986) of an ensemble of R spectra. This would lead to R (λ i ) Σ j [b j e ij ], where e ij are the coordinates of the principal components underlying the R spectra ensemble, expressed in the [λ i ] base. In this approach, the only a priori choice is the spectral bands, i.e., the [λ i ] base. Using all the principal components would allow one to reproduce the entire variability of R. Equation (7) would become Σ i [a i e ij ] = 0. This equation can be solved with a constraint on the a i coefficients, so that the index I remains sensitive to chlorophyll concentration. Since the relation between water reflectance and chlorophyll concentration is nonlinear, the a i coefficients could be made dependent on the chlorophyll level. Then a simple iterative procedure would allow more accurate estimates in the entire range of concentrations expected. Other variations and developments can be envisioned. Water reflectance and other bio-optical variables could be estimated instead of chlorophyll concentration. The a i coefficients could also be constrained to make the index less sensitive to noise in the satellite signal and to backscattering coefficient, i.e., phytoplankton type. These various possibilities and extensions of the algorithm are currently under investigation. Acknowledgements This work was supported by the Japan Aerospace Exploration Agency (under contract 03/JAXA/AEO No ), by the National Aeronautics and Space Admin- 336 R. Frouin et al.

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