3.1. Selection of MERIS Data
Table 1. Notation and Nomenclature for Optical Parameters and Implementation in the Optical Modela
|a, ak||total absorption, absorption for one of the individual optical components, CHL, TSM, and CDOM (m−1)|
| ||specific absorption coefficients for any of the single optical components (for CHL, m2 mg−1; for TSM, m2 g−1; for CDOM, m−1)|
|b, bk||total scattering, scattering for one of the individual the optical components (m−1)|
| ||specific scattering coefficients for any of the single optical components (for TSM, m2 g−1)|
|bb||total backscattering (m−1)|
|Ck, Cm||concentration of a single optical substance (for CHL, mg m−3; for TSM, g m−3; for CDOM absorption normalized by CDOM absorption at 440 nm). m distinguishes modeled concentrations|
| ||downwelling incident irradiance on a horizontal plane above the water surface (W m−2 nm−1)|
|f′||a reflectance model factor|
|i||counts intervals between consecutive bands|
|k||a single optical substance such as chlorophyll, total suspended matter, or colored dissolved organic matter|
| ||water-leaving radiance (the upwelling radiance measured above the water surface in the sensor viewing direction; W m−2 nm−1 sr−1)|
| ||number of spectral band used in the fit|
| ||a factor that relates radiance below the water surface to irradiance below the water surface|
| , ||natural logarithms of total a and total b (m−1).|
| ||wavelength dependent exponential term in the specific absorption model|
| ||wavelength dependent exponential term in the specific scattering model|
| ||solar zenith angle (deg)|
| ||sensor view zenith angle (deg)|
| ||wavelength of light (nm)|
| ||remote sensing reflectance (sr−1)|
| ||difference in remote sensing reflectance in consecutive bands (sr−1)|
| ||water-leaving reflectance from a plane above the water surface, normalized surface reflectance|
| ||estimated uncertainty in |
| ||relative sensor-Sun azimuth angle (deg)|
 The definition of remote sensing reflectance (ρrs) in equation (1) also implies that the contribution of electromagnetic radiance from the substances in the atmosphere (such as aerosols) have been removed from the total signal registered by the satellite sensor, but the standard ESA atmospheric correction [Moore et al., 1999; Moore and Aiken, 2000] is under investigation. High backscatter and absorption in both atmosphere (by aerosols from land such as dust and soot) and water (by extreme concentrations of optically active substances) can confuse the atmospheric correction software [Guanter et al., 2010], which can result in selection of an erroneous aerosol model [Moore et al., 1999; Zagolski et al., 2007]. This misinterpretation of aerosol type causes underestimation of reflectance in the shorter wavelengths of the L2 data, where signals are already low because of high absorption by chlorophyll a (CHL), TSM, and colored dissolved organic matter (CDOM).
 Specifically for lakes, it has been attempted to revert to (not atmospherically corrected) Level 1b top of atmosphere (TOA) radiance data to correct for stray light from nearby vegetated land [Vidot and Santer, 2005] and make a customized atmospheric correction using VISAT/BEAM Java plug-ins [Hommersom et al., 2010; Brockmann Consult, ESA BEAM wiki, http://www.brockmann-consult.de/beam-wiki/, accessed 20 June 2011]. Because of its specific inherent optical properties, this was less successful for Markermeer (see also Binding et al.  for Lake of the Woods).
 Instead, the 30 MERIS full-resolution L2 images for 2006 were processed using HYDROPT [Van der Woerd and Pasterkamp, 2008], which uses band differences in its χ2 fitting of measured and modeled reflectances to make it less sensitive to remaining biases from the applied aerosol model. Band 1, comprising reflectance at detector averaged center wavelength of 413 nm (bandwidth 10 nm), was excluded from the processing because of occasional occurrence of negative reflectances in this band [Zibordi et al., 2006; Zagolski et al., 2007] due to overcorrection for atmospheric effects. All water pixels were processed: the suite of additional MERIS product confidence flags was only used for a posteriori quality checking. This approach successfully compensates for some problems in atmospheric correction, which made careful use of the L2 data feasible [Van der Wal et al., 2010].
3.2. Optical Modeling
 In theory, the water-leaving reflectances ( ) at wavelength (λ) from the L2 data sets can be related to the inherent optical properties (IOPs) total absorption coefficient (a in m−1) and total backscatter coefficient (bb in m−1) through a factor f′:
This f′ factor varies with Sun zenith angle and with IOPs [Morel and Gentili, 1991]. represents reflection and refraction effects at the air-sea interface [Morel and Gentili, 1996]. Q relates upwelling radiance to upwelling irradiance just beneath the air-sea interface [Ruddick et al., 2006].
 Specific inherent optical properties (SIOPs) relate absorption and scattering to concentrations of individual optically active substances. SIOPs are defined as normalized absorption (a*) or scattering (b*) per unit concentration of mass, m2 (mg CHL)−1 or m2 (g TSM)−1, respectively, and for CDOM absorption normalized at 440 nm. For the eight Markermeer SIOP sets of June 1999 [Pasterkamp, 2001], water samples had been filtered to measure first TSM, and after extraction in ethanol, chlorophyll a (and phaeopigment) concentrations. Radiance had been measured on site with a PR-650 field spectroradiometer (Photo Research, Chatsworth, CA, USA). Spectra of absorption (a) and beam attenuation (c) had been measured using a Philips PU8800 UV/VIS double-beam laboratory spectrophotometer. The TSM (seston) absorption spectrum was derived from the measured optical density on the filter. The absorption spectrum of tripton (the inorganic part of TSM) on the filter was obtained after bleaching of the pigments from the filter using hot ethanol. The phytoplankton absorption spectrum was derived by subtracting the tripton spectrum from the TSM spectrum. The absorption of the dissolved humic substances (CDOM) in the filtrate and the beam attenuation of the water sample were determined from optical density measurements in a cuvette. The scattering coefficient (b) was estimated by subtraction of the absorption coefficients from the beam attenuation coefficient [Rijkeboer et al., 1998].
 The resulting mean specific absorption and scattering coefficients of Markermeer are given in Table 2. Careful study of these otherwise robust results reveals an absorption signal in at 665 nm that could indicate a problem with TSM bleaching. In this paper, TSM is broadly defined as indicating total suspended matter, which is usually present in the form of flocs, small clay particles bound with organic material into delicate aggregates that can also contain fine silt [Van Duin, 1992; Vijverberg et al., 2011].
Table 2. For Wavelengths Corresponding to the Medium Resolution Imaging Spectrometer (MERIS) Bands, the Absorption and Scattering of Pure Water, the Absorption per Unit Concentration for Chlorophyll a, Absorption and Scattering per Unit Concentration for Suspended Particular Matter, and Absorption of Colored Dissolved Organic Mattera
|Pure Water (m−1)||CHL (m2 mg−1)||TSM (m2 g−1)||CDOMb (m−1)||Pure Water (m−1)||TSM (m2 g−1)|
 Actual implementation in HYDROPT is based on a look-up table (LUT) describing the relationship of remote sensing reflectances (ρrs) with a range of inherent optical properties and other environmental conditions as calculated by the forward radiative transfer model Hydrolight [Mobley and Sundman, 2001]. To populate the LUT, Hydrolight was parameterized with the properties of three independent components: (1) pure water characterized by the pure water absorption, scattering and phase function, (2) absorption (alias chlorophyll in Hydrolight) with user defined total absorption, and (3) particle scattering (alias minerals) with total scattering assuming the Petzold average particle phase function. Other Hydrolight settings were an idealized sky model and uniform background sky, no bioluminescence, no fluorescence or Raman scattering, a wind speed of 5 m s−1, and an optically infinitely deep water column (for these turbid waters). Thus the LUT stored modeled reflectances (ρrs) at MERIS band centers (modeled spectra) for every possible combination of a physically realistic set of IOPs (total a and b) and angles (solar zenith angle θ0, vertical nadir angle θv and azimuth angle ).
 The inversion comprises a spectral matching algorithm; the HYDROPT algorithm searches the modeled spectrum that best matches a spectrum for each measured pixel [Van der Woerd and Pasterkamp, 2008]. This was implemented as a χ2 merit function based on the squared difference in remote sensing reflectance in the consecutive bands:
Δρrs,i is the difference in observed remote sensing reflectance between consecutive bands. Δρrs(λi, Cm, θ0, θv, ) is the difference in modeled remote sensing reflectance between consecutive bands (for wavelength interval λi, a set of modeled concentrations Cm, and modeled viewing and solar geometries θ0, θv, and ). σi is the estimated uncertainty in Δρrs,i. N is the number of spectral bands for the fit.
 As previously explained, the LUT contains the link to the total IOPs; the decomposition into concentrations (C) of single substance optical components (k) was realized as follows:
Presuming that both α and β equal 1 results in the linear SIOP definition:
To complete the inversion, the derivatives of the natural logarithmic value of the remote sensing reflectance ∂ln(ρrs) and the derivatives of the concentrations (Ck) were expressed as a function of natural logarithms of total a and b, x1 = ln(a) and x2 = ln(b):
Thus, the inverse model estimates the concentrations of, among others TSM from MERIS water-leaving radiance reflectance data at 6 optical wavelength intervals (Table 2). Subsequently, the retrieved TSM data were compared against independent in situ measurements.
3.3. In Situ TSM Data for Intercomparison
 Independent gravimetric in situ measurements of TSM (sampling depth 1 m below water surface) were obtained from the Rijkswaterstaat monitoring stations that were visited several (9–12) times per year (Figure 1). These in situ concentrations, and HYDROPT TSM concentrations from the full-resolution (FR) images were plotted for Markermeer midden (MM), the station farthest (about 10 km) from the shore (and therefore least influenced by radiation from land). True matchups of remote sensing and in situ samples during unclouded conditions at overpass are rare [Eleveld et al., 2008]. Comparison of the two data sets was performed when the time difference was two days maximally, which should be perceived as verification rather than as formal validation [Mélin et al., 2007]. To increase material for comparison, additional MERIS reduced resolution (RR) data were processed to TSM concentrations when they matched in situ monitoring data plus or minus one day difference. For RR images matching the FR images, TSMRR and TSMFFR are highly correlated (TSMRR = 0.98TSMFR + 1.69; r2 = 0.95, F = 477.30, n = 27, p ≪ 0.0001).