A new Retrieval of Sun-induced Chlorophyll Fluorescence in Water from Ocean Colour Measurements applied on OLCI L-1b and L-2

The retrieval of sun-induced chlorophyll fluorescence is greatly beneficial to studies of 1 marine phytoplankton biomass, physiology, and composition and is required for user applications 2 and services. Customarily phytoplankton chlorophyll fluorescence is determined from satellite 3 measurements through a fluorescence line-height algorithm using three bands around 680 nm. We 4 propose here a modified retrieval, making use of all available bands in the relevant wavelength 5 range with the goal to improve the effectiveness of the algorithm in optically complex waters. 6 For the Ocean and Land Colour Instrument (OLCI) we quantify a Fluorescence Peak Height from 7 fitting a Gaussian function and related terms into the top-of-atmosphere reflectance bands between 8 650 and 750 nm. This algorithm retrieves, what we call Fluorescence Peak Height from fitting 9 a Gaussian function upon other terms to top-of-atmosphere reflectance bands between 650 and 10 750 nm. This approach is applicable to Level-1 and Level-2 data. We find a good correlation of the 11 retrieved fluorescence product to global in-situ chlorophyll measurements, as well as a consistent 12 relation between chlorophyll concentration and fluorescence from radiative transfer modelling and 13 OLCI/in-situ comparison. The algorithm is applicable to complex waters without needing an 14 atmospheric correction and vicarious calibration and features an inherent correction of small spectral 15 shifts, as required for OLCI measurements. 16

As of now, the most established fluorescence product, which is operationally available is the Fluorescence Line Height (FLH) ([12-14]). There, a baseline is first formed by a linear interpolation of two baseline bands, and then subtracted from the radiance of the fluorescence band to obtain the FLH. The equation reads: where λ F , λ L , λ R are the center wavelengths of the fluorescence band and the two baseline bands. L F , L L , L R are the radiances of the fluorescence band and the two baseline bands. For MERIS, the common band combination is λ F = 681 nm, λ L = 665 nm, λ R = 709 nm. For MODIS, it is λ F = 678 nm, λ L = 667 nm, λ R = 748 nm. For MODIS, the standard algorithm returns the normalized Fluorescence Line Height (nFLH) in mWcm −2 µm −1 sr −1 , which is based on the normalized water-leaving radiance (L N w ). Here, normalization implies the application of a Bidirectional Reflectance Distribution Function (BRDF) correction. The relation between L N w and ρ w is the following [15]: Where θ S , θ V and φ are the sun zenith angle, the viewing zenith angle and the azimuth angle 46 respectively. While ρ w (θ S , θ V , φ) can have different values for each combination of angles, ρ N w is The aim of this paper is the introduction of a new fluorescence algorithm (OC-Fluo), that makes 118 use of OLCI's enhanced spectral capabilities in order to allow the retrieval of fluorescence even in 119 optically complex waters. The physical principles are presented as well as the technical implementation.  The physical basis of the presented algorithm is the Lambert-Beer law, which describes extinction of electromagnetic radiation by matter.
Here, I 0 is incoming and I is outgoing intensity. σ i is the attenuation cross section of the attenuating species i in the material sample; n i is the number density of the attenuating species i in the material sample; L is the path length of the beam of light through the material sample. The equation can also be written as In atmospheric remote sensing it is common to use the DOAS (Differential Optical Absorption to the logarithm of I/I 0 . Since each atmospheric trace gas has it's unique spectral finger print it is unique spectral shape. The IOPs of the major water constituents as they are implemented in the 155 RTM MOMO ([31], see also Section 3.4) are shown in figure 1: Chlorophyll fluorescence, which is an 156 elastic process and can be modelled by a Gaussian curved source of radiation in radiative transfer, 157 chlorophyll absorption, described by a measured absorption spectrum, detritus and CDOM absorption, 158 both represented by an exponential decay with different slopes and scattering on particles is assumed 159 as an spectrally inverse function. For the Fluorescence retrieval we use a simplified version of eq. 4, 160 because the light path of the photons throughout the complete wavelength range of interest is similar. 161 We either use radiance (~I) or reflectance (~I/I 0 ). This is done under the assumption that the spectral 162 features, which are extracted by the retrieval, are induced only by the water body. Figure 1. Optical properties of water constituents considered in the retrieval. Note, that this is only an example magnitude of the different properties.

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The nomenclature we are using here for the retrieval follows the conventions given in Rodgers

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• x expresses the state vector, which includes the parameters to be retrieved.

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• y expresses the measurement vector, which includes the measurements.

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• F mod is the forward model, which describes y as a function of x 168 F mod (λ, x) = y(λ) The measured radiance or reflectance (the equation only expresses radiance for clarity) is described as: which is a function of 4 unknown (state) parameters:

Technical Description
Given the definitions above, the measurement vector y is given by OLCI data band 8-12 and the 185 state x is defined by the factor for fluorescence (FPH), absorption (APD), a slope (S) and an offset (O).

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However, including λ A , λ F , w F , w A (see equation 6) as additional parameters, makes the problem 196 non-linear. A non-linear inversion problem can be solved in defining it locally linear, but then a 197 number of iterations has to be performed, with an iteratively changing K, which is also different for The approach could also be expanded to an optimal estimation approach, which includes apriori knowledge about the state. Here measurement and apriori knowledge are weighted by their particular covariance matrices.
where S e is the measurement covariance matrix, S a the apriori covariance matrix and x a the apriori 200 state. The approach we are presenting her is the simplest special case of the possibilities above and most 201 promising at this stage for OLCI measurements, but in future, when having either more knowlegde 202 about fluorescene in water (apriori knowledge) or with hyperspectral measurements (more possible 203 retrieval parameters) the above mentioned equation could be of value.

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L-FPH is the amplitude of the Gaussian function, which is related to the fluorescence peak 205 (centered at 682.5 nm) that is fitted to Level-1 radiance (L TOA ). It is therefore a measure of the 206 fluorescence signal in the TOA radiance spectrum without any normalization. L-FPH is given in 207 units of mWm −2 sr −1 nm −1 . ρ w -FPH is the amplitude of the Gaussian function, which is related to the 208 fluorescence peak (centered at 682.5 nm) that is fitted to Level-2 water-leaving reflectance (ρ w ). It is 209 therefore a measure of the fluorescence signal in the water-leaving reflectance which is normalized by 210 irradiance. Operational OLCI Level-2 products are defined as the directional water surface reflectance, 211 ρ w -FPH is dimensionless. The OLCI Level-2 products include the corrections to the water reflectance 212 value with the Sun at zenith, the mean Earth-Sun distance, and non-attenuating atmosphere. They do 213 not include the BRDF corrections for viewing geometry, water optical properties, and the sky radiance The spectral distribution of the solar irradiance is known and the seasonally corrected In-band 217 solar irradiance (F 0 (λ)) is delivered with Level-1 OLCI data. In order to compensate for spectral 218 structures introduced by F 0 that could interfere with optical properties of chlorophyll, the preprocessing 219 for the retrieval of L-FPH includes a rectification with a normalised F 0 (λ). In practice L TOA are divided 220 by F 0 (λ) and multiplied by F 0 in band 682 nm.

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OLCI consists of five optical cameras, of which each exhibits a variation of the relative spectral response of the bands across the field of view, called a smile effect. This variation is further different for each module [33]. The camera to camera variations in the central spectral wavelength as well as additional small variations in each detector array are visible as stripes across swath. Those variations, up to 1.5 nm are hardly visible when looking at the whole spectral range, but they can be important when spectrally narrow features are measured with spectrally narrow channels. Accordingly the stripes can be visible in the results from algorithms assuming measurements at nominal wavelength as it is the case for the presented algorithm. Level-1 data is delivered including the central wavelength for each pixel. Operationally Level-2 data is smile corrected assuming a linear relationship between Rayleigh corrected reflectances in neighbouring bands [29]. With this assumption the water reflectances are corrected to the values as if they were measured at nominal wavelengths. We developed and implemented a smile correction for Level-1b data for band Oa08 -Oa12. The internal OC-Fluo smile correction is based on the relationship between neighbouring bands defined by Eq. 6, therefore it begins technically with the application of the retrieval (equation 13) on Level-1b data ( y sh ) measured at λ sh (the subscript sh denotes the shifted measures).
With the resulting state x sh . Assuming that the forward modelled spectrum based on x sh represents 223 the slope from measured to nominal wavelength, the change in radiance units can be calculated from 224 the shift in wavelength through F mod : This ∆L TOA is then added to the measured L * TOA .
L TOA,corr (λ) is now input to the retrieval. As an example for the effectiveness of this smile 226 correction, Figure 3 shows a detail of the Barents Sea scene (Figure 7), which is also used for evaluation 227 (see Section 3) with L-FPH, which was smile corrected by our retrieval and ρ w -FPH, where the boundary 228 of two cameras is still visible despite of the Level-2 smile correction.

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As it is a common practice for the evaluation of remote sensing products, the main part is 259 performed through the comparison to in-situ measurements of the same quantity. In this case the   in FPH for a chlorophyll concentration roughly lower than 1 mg/m 3 , we define the sensitivity range of 287 the algorithm above this limit, which is white in Figure 6.

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Additionally, L-FPH and ρ w -FPH are correlated to chlorophyll from the two standard operational  As an example of extreme complex water, we examine the Rio de la Plata Estuary. The South

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Atlantic Ocean near the Rio de la Plata Estuary is a highly dynamic and complex region that 316 encompasses both Case 1 and Case 2 water types. The head of the estuary is characterized by a 317 well-developed turbidity front. High turbidity constrains photosynthesis. Immediately offshore the 318 turbidity front, water becomes less turbid and phytoplankton peaks [40]. Figure 9 shows the L-FPH water-leaving radiances, including BRDF correction, as described in [41] and both our OLCI products 339 still include BRDF effects (see Section 1). Also, MODIS nFLH characterizes the line-height of the 340 measured spectrum at 678 nm and OLCI FPH characterizes a peak height of a peak centered at  Finally L-FPH and ρ w -FPH are compared to the input chlorophyll from RTM simulations.

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Radiative transfer simulations of synthetic L TOA and ρ w spectra were performed for the development 351 and evaluation of the OC-Fluo algorithm. As described before, the emitted fluorescence quantum in 352 nature depends on many factors, like the quantum yield, the chlorophyll concentration, illumination, 353 etc., which are not known, or at least not accurately known. A synthetic approach, like the one 354 described here is the only way to control all influences on the fluorescence signal. In the RTM 355 fluorescence is a strictly increasing function of the chlorophyll concentration. In case the mathematical 356 function is able to capture the fluorescence peak from OLCI spectrally convoluted reflectances the 357 retrieved FPH should be a strictly increasing function to input chlorophyll.

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The simulations are performed using the vector version of MOMO ([42], [43]). Here a horizontal homogeneous atmosphere and ocean consisting of layers with vertical uniform optical properties are assumed. The upward and downward directed light field is calculated at all inter-layer boundaries and for all solar positions. The azimuthal dependence of the light field is internally expressed as Fourier series and reconstructed at equidistant distributed azimuth angles. For this set of simulations a water body was implemented with 20 layers of 1m thickness and is assumed to be homogeneous with an equal distribution of constituents (phytoplankton and CDOM) in each layer. We apply a bio-optical model, where chlorophyll concentration governs as well chlorophyll absorption coupled to chlorophyll fluorescence with a quantum yield of 0.03, as CDOM absorption and scattering ([44]). The chlorophyll-a extinction coefficient and the corresponding single scattering albedo control the amplitude and spectral signature of phytoplankton. A normalized chlorophyll-a absorption spectrum is scaled at 440 nm in order to calculate the absorption spectrum a ph (λ) for different phytoplankton amounts. The single scattering albedo ω 0 at 440 nm is set to 0.68 to calculate spectral phytoplankton  L TOA is a direct model output, namely the upward radiance (L↑) at the uppermost atmospheric layer. The ρ w is not a direct model output, but is derived from up-and downward radiances (L↑, L↓) and irradiances (E↑, E↓) just above water surface: where the water-leaving radiance L w is calculated from and L black is L↑ from only the ocean surface. This is realised in the model, by implementing a very thin 368 water body with a black surface below.

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L TOA and ρ w are convoluted using the spectral response functions of OLCI. ρ w is shown in Figure   370 11 in 1 nm resolution and in OCLI's spectral resolution within the spectral domain of the OLCI bands 371 Oa8 to Oa12. The MERIS band setting, which is a subset of OLCIS bands is included. Figure 11. Hyperspectral (green) ρ w from RTM and its convolution to OLCI (blue) spectral resolution for θ S =48 • , θ V =34 • , φ V =90 • and chlorophyll concentrations given in table 2, while the lowest spectrum is the one with the lowest chlorophyll concentration. Band Oa09 from OLCI which is additional to MERIS bands is shown in magenta. to investigate the reasons for the similarity of OLCI and MERIS results, we illustrate the extracted 378 spectral components. The division into the spectral components is shown in Figure 13 for OLCI 379 and for only MERIS bands applied to a ρ w -spectrum with low and with high chlorophyll. For low chlorophyll concentrations the spectral model seems to reproduce the simulated spectrum perfectly 381 as well for MERIS as for the OLCI band setting. For higher concentrations the additional band Oa9 382 pulls the reproduced spectrum a bit down, which leads to a slightly lower FPH. The fact that the 383 reproduced spectrum is slightly off the measured bands indicates that for extremely high chlorophyll 384 concentrations the model could be adjusted to a spectrally even more complex behaviour. Figure 14 Figure 13. Components found by the retrieval of ρ w -FPH applied to a ρ w -spectrum with low (left panels) and with high (right panels) chlorophyll for MERIS (upper panel) and for OLCI (lower panel) band setting.

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shows L-FPH retrieved from OLCI measurements over L-FPH retrieved from MERIS measurements 386 and the same for ρ w -FPH. The correlation is very high and shows that the algorithm could be directly 387 transferred to MERIS data. Finally the results of the RTM exercise, which are shown in Figure 12 are 388 overlaid with the results from the in-situ comparison in Section 3.1 (see Figure 15). Absolute values 389 and slope of the FPH -chlorophyll comparison are very consistent. We presented an algorithm that derives the Fluorescence Peak Height (L-FPH and ρ w -FPH) from 392 spectral radiance satellite data. The algorithm is based on a simple physical model of the spectral 393 absorption and emission in water. The algorithm is applicable on Level-1 data, and therefore, does