Algorithm Theoretical Basis Document (ATBD)

4 Design of the Procedure 4 Enhancement of the retrieval 6 Special feature: cut off reflectance 7 The bio-optical model 8 Pure water 8 Absorption by phytoplankton pigments 9 Absorption by yellow substance 9 Scattering and Absorption by total suspended matter in Finnish lakes 9 Ranges 10 Values and Ranges as defined in the simulation runs 10 Environmental Conditions 11 Calculation of the minimum irradiance attenuation coefficient k_min and the signal depth z90 11 References 12 MERIS Lake Algorithm for BEAM ATBD water Page 4 of 12 Copyright © 2007 GKSS GmbH Abstract The paper describes the lake water algorithm, which is a further development of the BEAM processor of the Medium Resolution Imaging Spectrometer (MERIS). The version described here is adapted to the bio-optical data, which were provided for the lakes in Finland. All data were provided by the Finnish partners of the project. In contrast to the algorithm developed for coastal waters, the lake algorithm derives directly the concentrations of (1) phytoplankton chlorophyll , of (2) total suspended dry weight and (3) the absorption of dissolved organic matter (gelbstoff) at 443 nm (MERIS band 2).The inherent optical properties (IOP) are not determined in this first version because of the type of optical data provided. The algorithm is based on a neural network (NN), which relates the bidirectional water leaving radiance reflectances with these concentration variables. The network is trained with simulated reflectances. The bio-optical model used for the simulations is based on a data set collected in different lakes in Finland . Two NN's are trained with simulated reflectances: 1. invNN to emulate the inverse model (reflectances, geometry) concentrations, and 2. forwNN to emulate the forward model (concentrations, geometry) reflectances. The invNN is used to obtain an estimate of the concentrations which is used as a first guess to start a minimization procedure, which uses the forwNN iteratively to minimize the difference between the calculated reflectances and the measured ones. The procedure is fast as it takes advantage of the Jacobian which is a byproduct of the NN calculation. Design of the Procedure The NN transforms the directional water leaving radiance reflectances measured in eight spectral bands (outcome of the atmospheric correction procedure) and the three angles pixel by pixel with high efficiency into the three components, i.e. (1) chlorophyll concentration (from its relationship between absorption and concentration), (2) the dry weight of the total suspended matter, which is related to its scattering and absorption properties, and (3) the absorption of gelbstoff. The directional water leaving radiance reflectance RLw(θv,φv) associated with the water leaving radiance Lw(θ,φ) and the downwelling irradiance above the sea surface Ed is defined to be: RLw(θv,φv) =Lw(θv,φv)/Ed(θs) where θv and φv are the zenith and azimuth observation angles respectively. Ed depends on the solar zenith angle, θs, for the pixel under examination. For convenience we will denote the wavelength dependency in the following chapters only where necessary. Since simultaneous measurements of concentrations and water leaving radiance reflectance spectra are rare and, thus, do not cover the data space with sufficient density, the construction MERIS Lake Algorithm for BEAM ATBD water Page 5 of 12 Copyright © 2007 GKSS GmbH of the NN is based on a large table (50K entries) of simulated data generated by our forward model which was built from the HYDROLIGHT radiative transfer code (Mobley 1994) plus a bio-optical model relating scattering and absorption coefficients to concentrations. This bio-optical model is based on a data set of measurements of inherent optical properties and describes the variability of the three major components of lake waters, i.e. scattering by all particles and the absorption after bleaching, absorption by phytoplankton pigments and absorption by humic organic matter (gelbstoff). For given concentrations / IOPs of water constituents the forward model calculates the angular distribution of water leaving radiance in eight visible MERIS bands. These angular distributions are sampled in the appropriate angle ranges to derive the entries of the training / test tables for building the NN: three concentrations, three angles and eight water leaving radiance reflectances. The concentrations of the water constituents are randomly sampled from an exponential distribution in order to disentangle small concentration differences in regions of small concentrations. In order to get roughly constant relative concentration errors the logarithm of the concentrations was used as NN output. To avoid extrapolation from the training set the NN has to learn the variability of the inherent optical properties (IOP) of the water constituents as well as the errors in reflectances caused by the instrument and the atmospheric correction. Thus, the natural variability of the IOPs was built into the forward model by sampling the parameters describing the spectral dependence of the IOPs from their measured distributions Two NN's are trained (Schiller, 2000) with this table: (1) invNN to emulate the inverse model from reflectances r and geometry information , and (2) forwNN to emulate the forward model ) ( 1 r c − = F g g ) (c r F g = deriving reflectances from concentrations c and geometry information r g . In the MERIS ground segment (Schiller and Doerffer, 1999, Doerffer & Schiller, 2007) the two NN's are combined to give a new NN (s. Fig. 1), which first uses the invNN part to obtain an estimate of the concentrations . These together with the geometry information c g are fed into the forwNN. If not only the measurement of the reflectances but also the model is perfect the idendity should hold. Therefore the reflectances returned by the forwNN are compared with the measured ones. Large deviations signal a violation of the necessary condition for a successful inversion; corresponding pixels are then flagged (Doerffer and Schiller, 2000)). )) ( 1 ( r r − = F F g g ' r MERIS Lake Algorithm for BEAM ATBD water Page 6 of 12 Copyright © 2007 GKSS GmbH Fig. 1 A combination of NN's is used in the MERIS ground segment for the retrieval of water constituent concentrations c from remotely sensed reflectances and geometry information . The c obtained from the invNN emulating the inverse model is used together with the geometry information as input to the forwNN which calculates the corresponding reflectances which are compared with the measured ones to give a quality measure of the retrieval. r g g ' r q Enhancement of the retrieval The advanced algorithm (Schiller and Doerffer, 2005) is depicted in fig. 2. Now after the comparison of the reflectances returned by the forwNN with the measured ones, optimization steps are inserted. The aim is to improve the agreement of C with r by iteratively adjusting the estimate of c . ' r