Estimating chlorophyll-a absorption with the Total Algae Peak Integration Retrieval TAPIR considering chlorophyll-a fluorescence from hyperspectral top of the atmosphere signals in optically complex waters

The Total Algae Peak Integration Retrieval TAPIR relates the chlorophyll-a absorption 1 coefficient at 440 nm (a440) to the reflectance peak near 683 nm induced by chlorophyll-a properties. 2 The two-step retrieval provides both the hyperspectral quantification of the phytoplankton 3 fluorescence and scattering and the estimation of a440 from reflectance signals. Integrating the 4 peak, the Total Algae Peak (TAP) accounts for the variance in the peak’s magnitude, shape, and 5 central peak wavelength. TAPIR is a solely optical approach estimating a440 and supports the 6 application of retrieval-independent individual regional bio-optical models afterwards to retrieve 7 the chlorophyll-a concentration. Simulations reveal the major sensitivity on the considered model 8 chlorophyll-a absorption spectrum and its single scattering albedo. Additional water and atmosphere 9 constituents have a low impact. An uncertainty assessment reveals uncertainties of less than 30 % for 10 TAPIR a440 greater than 0.8 m−1 and less than 38 % for lower a440. In optically complex waters, first 11 validation efforts promise the applicability of TAPIR for high chlorophyll-a concentration estimations 12 in the presence of additional water constituents. The technique is generic and considers external 13 conditions (sun zenith angle, number of measurement bands, surface or satellite measurements, and 14 radiometric quantity). TAPIR applies to all kind of waters including optically complex waters, arctic 15 to tropical regions, and inland, coastal, and open ocean waters. Among other hyperspectral satellite 16 sensors, the Environmental Mapping and Analysis Program (EnMAP) provides sufficient sampling 17 bands for the application of TAPIR. 18


Introduction
The space-borne observation of natural waters is mainly limited by three factors: Firstly, strong water absorption restricts passive remote sensing to the visible spectrum (VIS) mostly preventing the application of available measurement bands in the near infrared or beyond.
Secondly, the top of the atmosphere (TOA) measurement is the sum of the water-leaving radiation Thirdly, apart from the atmospheric influence, retrieving a particular water constituent can become ambiguous due to various possible optically active constituent (OAC) compositions for a specific TOA signal.The inherent optical properties (IOPs) of the OACs in the water define the resulting water-leaving radiation.In optically complex waters (e.g. at coasts or lakes), Reinart et al. and Zheng et al. [1,2] exemplary reported the superposition of the effects of the IOPs of a wide range of OACs (e.g.phytoplankton, coloured dissolved organic matter (cdom), inorganic particles).
The blue-green ratios and the polynomial Ocean Colour algorithms (e.g.OC4, OC3, OC4Me) for a wide range of space sensors [10][11][12] retrieve chl-a in case-1 waters which contain only phytoplankton [13].In optically complex waters (case-2), Huot et al. and Gower [14,15] recently demonstrated the complicating impact of mainly cdom on chl-a retrievals due to high cdom absorption at the required bands for the blue-green ratio.
Jerlov and Doerffer and Fischer [16,17] investigated the spectral absorption from cdom in the visible spectrum from in situ measurements and satellite retrievals, respectively.The absorption of cdom exponentially decreases from 400 nm to 800 nm [18] whereas phytoplankton exhibits the pigment related optical feature of the fluorescence near 683 nm [19][20][21][22].The amount of chl-a and the photosynthetic activity scale the fluorescence [23].Therefore, in coastal or inland waters with a contribution of cdom, chl-a retrievals benefit from an accurate estimation of the fluorescence [14,15].Physically, fluorescence is the process of light emission transforming the energy of a released electron of a relaxed chlorophyll-a molecule which was excited by solar radiation.Although, this phenomenon can occur for both living and deceased phytoplankton cells, this study focuses on animated cells.Besides photosynthesis and heat dissipation, fluorescence is one of the major competitive fates of the absorbed VIS light [24].Therefore, fluorescence does not only indicate an amount of chl-a but also the "living activity" of phytoplankton although Xing et al. [25] report less than 5 % of the total absorbed light is used for the fluorescence process.
In spite of a rather small fluorescence efficiency, which is the ratio between the number of emitted fluorescent photons and the absorbed photons available for the fluorescence process, of 0.1 % to 1.0 % [19,20,22,26,27], space-borne sensors are able to observe the emitted fluorescence in reflectance spectra [e.g.[28][29][30].
In the last three decades, the sun-induced fluorescence in waters was investigated theoretically [e.g.19,20] and in situ [31][32][33].Using multispectral measurements from space with, for instance, the Moderate resolution Imaging Spectrometer (MODIS) onboard Aqua and Terra and the Medium Resolution Imaging Spectroradiometer (MERIS) onboard the Environmental Satellite (Envisat), fluorescence can be obtained with fluorescence line height algorithms (FLH) [34][35][36][37].The Ocean and Land Colour Imager (OLCI) onboard Sentinel-3A launched in February 2016 also provides bands for the FLH algorithm.
The FLH estimates the fluorescence magnitude by the difference of measurements at a signal wavelength (e.g.681.25 nm for OLCI) and a baseline generated from two additional bands [20].
Unfortunately, the FLH becomes ambiguous for increasing chl-a due to the increased absorption at the local chlorophyll-a absorption maximum near 670 nm.Schalles and Gilerson et al. [21,27], exemplary, report the shift of the peak towards longer wavelength from 680 nm to 705 nm for 0 mg m −3 to 30 mg m −3 (redshift).Therefore, FLH algorithms based on a constant single signal wavelength only apply for case-1 waters with low to medium chl-a.
In order to account for the redshift and the changing shape of the effective peak (see fig. 1 and section 2.1) due to chlorophyll-a reabsorption on the peak's blue edge, the increasing water absorption on the peak's red edge [38], and the chlorophyll-a fluorescence, hyperspectral simulations promise improved fluorescence and phytoplankton properties estimations with hyperspectral sensors [27].For instance, the Hyperspectral Imager (HSI) onboard EnMAP provides 65 bands with a full width at half-maximum (FWHM) from 6 nm to 9 nm within the visible range from 420 nm to 800 nm [39].The comparison of high resolved simulations and the theoretical EnMAP measurements shows a sufficient reproduction of the peak near 683 nm (fig.2).
In order to exploit the presumably available hyperspectral TOA measurements and estimate the phytoplankton amount, the Total Algae Peak Integration Retrieval (TAPIR) is introduced.Section 2 demonstrates the peak's variability and quantify phytoplankton with a spectral integration of the Total Algae Peak (TAP) within the fluorescence emission range from 670 nm to 750 nm.TAPIR is based on the correlation of a440 and the corresponding TAP.
The application of TAPIR for TOA or surface measurements supports a direct estimation of chl-a with an arbitrary bio-optical model adjusted for regional conditions.
Radiative transfer simulations (section 3.1) are used to investigate the sensitivity and uncertainty for various conditions in the water and the atmosphere in section 3.2 and section 3.3.In section 4.2, early validation efforts are performed using in situ measurements described in section 4.1.Furthermore, the findings are discussed in section 5 and the conclusions are presented in section 6.

Rationale
The phytoplankton and water VIS absorption coefficients, and the fluorescent emission mainly control the magnitude, shape, and location of the effective fluorescence peak.
Section 3.1 introduces radiative transfer simulations which are used for the analysis of the peak and the development of our algorithm.Phytoplankton absorbs light within the total visible spectrum with two local absorption maxima near 440 nm and 670 nm.Modelling the phytoplankton absorption for the simulations, a normalized absorption spectrum is scaled with the 440 nm coefficient supporting bio-optical models which usually use chlorophyll-a absorption coefficients near 440 nm for chl-a retrievals [e.g.4].Thus, this study referes to the 440 nm chlorophyll-a absorption coefficient (a440) for changes in the simulated phytoplankton amount.
For increasing a440, the simulated reflectance increases within the fluorescent interval from 660 nm to 750 nm (fig.1a) due to increased available energy for the emission of fluorescence and the proportionally increased modelled phytoplankton scattering (section 3.1) which additionally increases the reflectance spectrum outside and within the fluorescence spectrum.Additionally, the local reflectance maximum R(λ P ) at the maximum peak wavelength λ P shifts towards longer wavelengths (fig. 1b).Therefore, using more bands than a constant single signal channel (e.g.λ P = 681.25 nm for the OLCI FLH), the redshift can be considered properly and the estimation of optical phytoplankton properties is enhanced.
The peak is expected to occur within the fluorescent interval from 680 nm to 710 nm on top of the generally decreasing reflectance slope (fig.1a).On the one hand, phytoplankton emits light near 683 nm due to the fluorescence process [23] and, on the other hand, the total absorption spectrum,  which mainly combines water and phytoplankton absorption in the visible, exhibits a local minimum from 675 nm to 685 nm.In comparison to the sourrounding spectrum, the absorption minimum facilitates the transition of upwelling light which appears as peak in the reflectance spectrum.For increasing a440, the part of the water absorption becomes less important and the effective peak appears to be shifted towards longer wavelengths (fig. 1b).There are constant peak wavelengths of 680 nm due to a hardly detectable or unapparent peak for low a440 (e.g.R(λ; a440 = 0.1 m −1 ) in fig.1a) and the maximum at 680 nm of the decreasing reflectance within this spectral range.
Figure 1c reveals the relative shape of the effective peak for increasing a440.The peak enlarges with increasing a440 due to increased phytoplankton scattering and fluorescence but its slope narrows due to i) phytoplankton reabsorption near 670 nm and ii) water absorption.
i).The local chlorophyll-a absorption maximum spectrally expands for higher a440 and reabsorbs emitted fluorescence and scattered radiation.Therefore, the maximum of the peak appears to be shifted towards longer wavelengths and the slope of the peak's left (blue) edge raises.
ii).The peak becomes spectrally broad due to high phytoplankton scattering and fluorescence induced by high a440 and extends to the longer wavelengths beyond 690 nm where the water absorption rapidly increases.The emitted light from the fluorescence process and the phytoplankton scattering is reabsorbed from water absorption and the peak's right (red) edge becomes steeper.
These two spectral mechanisms are independent and their impact is nonuniform resulting in different peak shapes for increasing a440.
In conclusion, the peak near 683 nm describes both the phytoplankton fluorescence and the phytoplankton scattering.For an increasing phytoplankton absorption constraining the fluorescence and scattering, the peak exhibits i) an increasing magnitude, ii) a shift towards longer wavelengths, iii) an increasing spectral width, and iv) a squeezed slope.Therefore, in this study, the estimation of the chlorophyll-a properties account for magnitude, shape and spectral position of the peak by a spectral integration.Correlating the Total Algae Peak TAP in section 2.2 from simulated reflectance spectra and the corresponding absorption coefficient a440, the Total Algae Peak Integration Retrieval TAPIR is developed.

Total Algae Peak (TAP)
In order to obtain the chlorophyll-a properties expressed by TAP, only reflectance residuals shown as shaded areas in fig. 2 are used.Therefore, teh reflectance is reduced by a spectrum dependent constant R(λ 1 ) located at the local reflectance minimum λ 1 within 665 nm to 678 nm (eq.( 1)) accounting for the local phytoplankton absorption maximum near 670 nm.The lower integration limit λ 1 hardly spectrally shifts for increasing a440.
In contrast to FLH retrievals using a spectrally falling baseline, a baseline is computed without slope (eqs.( 1) and ( 2)).The slope of the FLH baseline highly depends on the peak's shape and the surrounding spectrum which can lead to a strong over-or underestimation of fluorescence.However, the TAP is not solely correlated to the fluorescence but also the phytoplankton scattering.The TAP baseline indicated with LW in fig. 2 is only dependent on one free parameter λ 1 and the baseline's spectral length highly varies.Thus, TAP accounts for the changing spectral shape of the peak for different a440.
Additionally, using an interpolation on given simulated wavelengths or sensor bands, i) the accuracy of λ 2 and also TAP is increased, and ii) the number sensor of channels becomes less important.
Section 3 presents the optical model of the Total Algae Peak Integration Retrieval TAPIR which solely depends on optical properties: TAPIR links the combined fluorescence and phytoplankton scattering estimation expressed with TAP retrieved from radiometric signals to a phytoplankton IOP.The coefficients are dependent on the sensor or model (e.g.MOMO simulations or EnMAP) retrieved reflectance peak areas (TAPs).The TAPs vary with the phytoplankton amount and a series of variables in the water and the atmosphere.Table 1 lists a selection that is used in this study.
The technique enables us to retrieve a440 from space-borne, air-borne or in situ reflectance measurements.TAPIR is a fast regional independent algorithm to retrieve the chl-a proxy a440 in optically complex waters.Applying regional bio-optical models for chl-a and a440 from literature [e.g 4,6,40] afterwards, a region specific chlorophyll-a concentration can be obtained.

Radiative transfer simulation
The Matrix Operator Model MOMO is an advanced radiative transfer code for multiple applications in coupled atmosphere-water-systems [41][42][43].It includes an arbitrary selection of the number of layers, the viewing and sun geometry, the atmospheric conditions, and the state of the water body parameterised by the IOPs from water constituents.measurements in China [44] and laboratory measurements [45].In order to investigate the sensitivity of TAPIR, the normalized chlorophyll-a absorption spectrum (a ph ), the aerosol-optical thickness (aot), a spectrally invariant "white" scattering coefficient (b) in the water, the fluorescence quantum yield ε, the single scattering albedo ω 0 of phytoplankton at 440 nm, the salinity s, the standard atmosphere atm after [46], and the water surface temperature T s are varied.
In MOMO, the extinction coefficient and the corresponding single scattering albedo control the spectral impact of phytoplankton.The reference ω 0 at 440 nm is set to 0.68 to calculate the spectral phytoplankton scattering coefficient depending on the absorption spectrum.Therefore, in MOMO, the magnitude of the chlorophyll-a scattering coefficient b440 scales with a440 • ω 0 (1 − ω 0 ) −1 .Increasing a440 increases the spectral absorption scaling the normalized absorption spectrum a ph and increases the spectrally decreasing phytoplankton scattering.
MOMO models the emitted phytoplankton fluorescence near 683 nm [19] with an exiciation energy based on photosynthetically active radiation (PAR) from 395 nm to 685 nm, the fluorescence efficiency and the phytoplankton absorption.The additional light from the fluorescence process is attached to the radiation during the radiative transfer simulation.
The nadir TOA reflectance R = L u /E d is calculated from simulated upwelling radiance L u and downwelling irradiance E d for a sun-zenith angle of 50 • without any atmospheric corrections.R(a440) are reference spectra defined for section 3 with reference parameters highlighted in table 1.

Sensitivity analysis
Using the MOMO simulations, retrieved reference TOA TAPs are linked with corresponding a440 (solid lines in fig. 3) and the variations of TAP (dashed lines) due to varied parameters p (table 1).
According to eq. ( 4), a power function expresses the TAPs of the TOA reflectance R = L u /E d with a power function: The reference TAPIR function f ref increases linearly with increasing a440 up to 0.2 sr −1 nm in fig. 3 and for low a440 it is non-linear or zero.In order to estimate the sensitivity of TAPIR, fig. 4 shows the deviations of f ref with the variation of the parameters.The Jacobians J p = J ij (p) are calculated for TAPIR functions f i with varied parameters p j with eq. ( 6).
∆p for parameter a ph is computed with the maximum absorption at 670 nm from the normalized absorption spectra (fig.5a).Demonstrating the impact of reduced bands, a change in the measurement location, and the standard atmospheres, ∆p = 1 applies for EnMAP, BOA, and atm.The Jacobians are non-zero for i = j and the absolute Jacobians generally increase with increasing a440.TAPIR is more sensitive to all of the considered parameters for higher a440.
The sensitivity analysis is grouped in four parts accounting for i) water conditions, ii) atmosphere conditions, iii) phytoplankton parameterisation, and iv) external conditions.
i).In this study, the water conditions vary with the considered parameters cdom, the white scatterer b, surface temperature T and salinity s (figs.3a to 3d).In contrast to the blue-green ratio proxy estimating chl-a, the spectral range of the fluorescence is nearly invariant to cdom absorption and, therefore, a negligible dependence on the TAPs is expected.
The in-water parameters have a minor impact on TAPIR due to Jacobians less than two orders of magnitude than the reference TAPs (figs.4a to 4d).
The TAPs are slightly sensitive to cdom with Jacobians less than three orders of magnitude.
However, the impact of cdom is less than the influence of the scatterer b. "White" scatterers (e.g.sediments) brightens the total visible reflectance spectrum and, therefore, slightly enlarge the peak due to a higher available fluorescence excitation energy and increased total scattering.Salinity and surface temperature are negligible.
Therefore, TAPIR is applicable for all kind of waters including case-1 and case-2, coastal and inland waters, and regions with high or low sea surface temperature.
ii).Figures 3e and 3f display the impact of varying standard atmosphere conditions atm and aerosol optical thickness aot.A change in the atmospheric vertical temperature and pressure distribution results in a low sensitivity on the atmosphere structure with Jacobians below 10 −5 (fig.4e).
In fig.4f, an increasing aot diminishes the TAPs linearly with increasing a440 due to less available light for the fluorescence process and absorption of the upwelling signal in the atmosphere.
Unfortunately, the sensitivity on aot ranges in the same magnitude of the reference TAPIR function and, therefore, aot must be considered in the retrieval.1).The solid lines link the TAPs computed from reference simulations from which the TAPIR function in eq. ( 5) is calculated.
iii).MOMO parameterises phytoplankton using a given normalised phytoplankton absorption spectrum scaled with the spectral extinction coefficients and the corresponding single scattering albedo (section 3.1).Figure 5 illustrates variations of chlorophyll-a absorption spectra a ph (λ) normalized at 440 nm and the corresponding single scattering albedo ω 0 for constant values of 0.68, 0.75 and 0.82 at 440 nm.In this study, varying ω 0 solely changes the ratio of phytoplankton scattering and absorption.
The current absorption coefficient remains equal whereas the phytoplankton scattering coefficient increases or decreases, respectively.Thus, an increasing ω 0 induces an increased extinction coefficient.
The spectra NechadMIN and NechadMax are averaged from normalized HydroLight absorption spectra [8] for the ranges from 0.2 m −1 to 0.3 m −1 for a ph (670 nm) and 0.7 m −1 to 0.8 m −1 , respectively.
They vary in magnitude and width of the local absorption maximum at 670 nm and the spectral shape (e.g in the blue visible range in fig.5a).
TAPIR is strongly sensitive to the underlying absorption spectrum (figs.3g, 4g and 5a).The lower the absorption spectrum beyond 550 nm the faster rises the slope of the TAPIR function with increasing a440 due to an increased scattering (fig.5b).Accounting for the fluorescence efficiency ε, figs.3j and 4j reveal a strong impact on the retrieved TAPs mainly depending on the competitive impact of the effective fluorescence peak shifting towards shorter wavelength for increasing ε and an increasing redshift for increasing a440.
Therefore, the major TAPIR sensitivity originates from the phytoplankton's IOPs and bio-physical condition whereas phytoplankton scattering is the main impacting factor.Table 2. List of variables x and their σ x used in the uncertainty calculation in eq. ( 9).Exemplaryly, the table presents the summands of eq. ( 9) (m −1 ) 2 for a440 of 2.0 m −1 and 6.5 m −1 .σ TAP depends on a440.The variables c 0 and c 1 exhibit the units [sr −1 nm m] and [dl], respectively.
In conclusion, TAPIR is mainly sensitive to a440 and the phytoplankton optical properties   10) (sr −1 nm) 2 per parameter for a440 of 2.0 m −1 and 6.5 m −1 .σ atm is set to 1 because the parameter atm contains vertical atmospheric profiles.The values of p re f and p var for parameter a ph are the 670 nm coefficients of the normalised absorption spectra "Doerffer" and "NechadMIN".The parameters λ 1 and λ 2 depend on the selected reflectance spectrum and vary with a440.The deviation is estimated by small variations of ±1 nm and assume a σ λ of 1 nm.

Uncertainty Assessment
TAPIR supports the estimation of the phytoplankton amount proxy a440.Thus, the reference TOA TAPIR function from eq. ( 4) is inverted to f −1 and an uncertainty propagation for a440 is conducted.
Assuming uncorrelated variables, eq. ( 9) computes the uncertainty σ a .The deviation of f −1 depends on i = 3 variables x: The fitting coefficients c 0 and c 1 and the TAP per a440.
Equation ( 9) is determined ∂ x f −1 (x) analytically.Fitting the simulated TOA TAPs to the input a440 in section 3.2, the coefficients c 0 and c 1 are empirically retrieved and simultaneously the standard deviations σ c 0 and σ c 1 are obtained and listed in table 2.
The uncertainty σ a additionally depends on the accuracy of the TAP computation with eq. ( 3).
The TAP deviates with varied parameters from table 1 and the selection of the integration limits λ 1 and λ 2 .The parameters SZA, number of measurement bands (e.g.EnMAP), and the measurement location (e.g. at the surface (BOA)) are excluded because they can be considered previously to the TAPIR function development.The TAP uncertainty σ TAP for j parameters p is computed with eq. ( 10) .
The summands of eq. ( 10) ∂ p j TAP are numerically estimated.Therefore, the difference between TAP(p j,re f ) and TAP(p j,var ) is calculated to retrieve ∆TAP(p j ).The values of the reference and variation of the parameters, p re f and p var , are listed in table 3. The reference value for cdom is dependent on a440 with g(a440) in section 3.1 and for a ph we extract the 670 nm absorption coefficient from the normalised spectra "Doerffer" and "NechadMIN" (fig.5a).The deviation ∆p j is the difference between parameter p j,re f and its variation p j,var .We set ∆p atm to 1 because the parameter atm contains vertical profiles.We conservatively choose parameter dependent uncertainties σ x from literature or assume reasonable values.

Preprints
Figure 6a illustrates the σ 2 TAP summands (black lines) from eq. ( 10) which exponentially increase with increasing a440.The final σ 2 TAP (thick grey line) mainly consists of the variation of ω 0 .The "spikes" near 2.0 m −1 appear due to the logarithmic presentation and a local minimum close to zero.Using different p j,var , they shift or disappear.
Analogous, fig.6b shows the σ 2 a summands (black lines) from eq. ( 9) and the final squared uncertainty for a440 (grey) which mainly consists of the variation of TAP.Therefore, the accuracy of a440 primarily depends on the parameterisation of phytoplankton.
Generally, σ 2 a increases exponentially with increasing a440 and ranges from approximately 10 −3 m −2 to 10 1 m −2 .Unfortunately, σ a is rather large and ranges in the magnitude of a440.Exemplary, an uncertainty σ a of 0.55 m −1 and 1.68 m −1 for a440 of 2.00 m −1 and 6.50 m −1 is retrieved.The uncertainty is less than 30 % of a440 for absorption coefficients greater than 0.8 m −1 and less than 38 % for the entire a440 range from 0.1 m −1 to 10.0 m −1 .For BOA and EnMAP applications, the a440 uncertainty ranges from 17 % to 20 % and 25 % to 40 %, respectively.

Measurement dataset
For first validation efforts in section 4. Unfortunately, the a ph (λ) and R RS have not been measured simultaneously for InW and NoS and a440 is computed from the available measured chl-a.Fortunately, some different measurement stations in the North Sea provide matching a440 and chl-a measurements [8] and an empirical bio-optical model a440 = (0.040±0.004) * chl-a (0.850±0.108) could be developed.

Validation assessment
In fig.7 in situ measurements of the North Sea (NoS) and Indonesian Waters (InW) are compared with the retrieved TAPIR function at the surface (eq.( 7)) for preliminary validation efforts.Unfortunately, the measurements only provide re-calculated a440 (see section 4.1) up to 1 m −1 .However, the calculated TAPs from measured hyperspectral reflectance spectra are closely located to the retrieved TAPIR BOA function (black solid line in fig.7a).
In fig.7a, there are 55 of 92 and 25 of 48 zero TAPs of InW (grey squares) and NoS (black triangles), respectively, within a440 from 0.0 m −1 to 0.4 m −1 , due to an unapparent peak in the reflectance spectra.Chl-a and additionally provided measurements of total suspended matter (TSM) range within 0.8 mg m −3 to 50 mg m −3 and 0 g m −3 to 200 g m −3 , respectively.
The zero TAPs occur for TSM and chl-a measurements within 0 g m −3 to 50 g m −3 and 0.8 mg m −3 to 10 mg m −3 , respectively.A combination of low chl-a (<10 mg m −3 ) and the occurrence of non-phytoplankton TSM may result in an unapparent peak.However, there are measurements of similar conditions with an apparent peak and non-zero TAP.
12 TAP(InW) are remarkably raised compared to TAPs expected from sthe TAPIR BOA function (black line).Increased scattering for high amounts of TSM (>70 g m −3 ) and chlorophyll-a (>17 mg m −3 ) can be assumed to raise the peak and the corresponding TAP.However, as outlined in section 3.2 and section 3.3, the phytoplankton parameterisation in the simulations mainly impacts the TAPIR.A raised portion of non-phytoplankton TSM, a tight packaging of phytoplankton chloroplasts, and the cell walls itself can cause an increased scattering which may increase the magnitude of the peak.Therefore, an empirical TAPIR function (eq.( 11)) based on the TAPs in the Indonesian Waters (dashed black line in fig.7a) is developed.The slope of the function is raised compared to the BOA function.

TAPIR InW
BOA : TAP(a440) = 0.023 * a440 1.1463  (11)   Applying the ocean colour algorithm OC4 [12] in fig.7b, the retrieved OC4 chl-a match up with the measured chl-a for less than 10 mg m −3 which borders the upper definition limit.The OC4 chl-a remains stable near 10 mg m −3 for measured chl-a beyond 10 mg m −3 due to the presence of additional OACs.
The chl-a retrieved from TAPIR (triangles and squares with error bars in fig.7c) is blurrier than the OC4 chl-a for chl-a measurements below 10 mg m −3 but still exhibits a good estimation.For larger chl-a, TAPIR overestimates chl-a with the current TAPIR BOA from eq. ( 7) but in contrast to OC4, TAPIR is able to reproduce higher chl-a according to the 1:1 line.The maximum a440 for this data set is less than 1 m −1 and section 3.3 shows higher uncertainties for absorption coefficients below 0.8 m −1 .However, TAPIR reproduces sufficient chl-a estimations for the North Sea (grey squares in fig.7c).
Applying the empirical TAPIR InW BOA function (eq.(11) and dashed line in fig.7a), the retrieved TAPIR chl-a (bullets with dashed error bars) in fig.7c closely approach the 1:1 line.
The deviation from measured chl-a may occur due to the following issues.The TAPIR function in eq. ( 7) is developed with the reference parameters for the surface.Applying a different phytoplankton parameterisation (e.g. a ph =NechadMIN) or additional features considering scattering by non-phytoplankton matter, may improve the chl-a accuracy with TAPIR.Increasing the parameters of the TAPIR BOA function slightly in order to "simulate" increased scattering according to fig. 3, the chl-a estimations for InW approach the 1:1 line.
In order to assign the retrieved TAPs to a440 in fig.7a, it was necessary to convert the measured chl-a to a440 applying a bio-optical model which likely adds additional uncertainties.
However, we highly recommend TAPIR for usage in optically complex waters due to the ability to retrieve low and high chl-a in the presence of additional OACs.

Discussion
In an algae cell, the processes photosynthesis, dissipation, and fluorescence antagonistically consume the energy of absorbed photons.Nevertheless, fluorescence can also occur in deceased phytoplankton but the aquatic community mainly focuses on living cells.Thus, measuring the fluorescence, the amount of chlorophyll-a and the living activity can be estimated.The estimation and interpretation of fluorescence remain still complex because an increase in fluorescence occurs either due to more chl-a or the reduction of one or both of the other processes.Among others, the fluorescence process depends on the algae type, physiology, health, and environmental conditions.
The study focuses on an increase of fluorescence due to an increase of chl-a and a440, respectively.
However, the peak near 683 nm does not solely occur due to fluorescence but is mainly induced by phytoplankton scattering.Therefore, in contrast to FLH retrievals claiming results of pure fluorescence, investigating the reflectance peak within the fluorescence range from 670 nm to 700 nm, both the fluorescence and the algae scattering is obtained.Phytoplankton absorption influences and scales both properties.
Section 3 demonstrates the applicability of TAPIR which is influenced by various parameters (see table 1).TAPIR provides advantages by "catching" the total effective peak with its variable magnitude, location, and shape.
In contrast to FLH, TAPIR exhibits a monotonically increasing slope with increasing a440 and chl-a, respectively, obviating ambiguous a440 and assimilates to the natural behaviour of the effective peak by avoiding constant measurement bands.Of course, TAPIR requires a minimum number of bands for a proper integration whereas EnMAP specifications promise sufficient results.The minimum number has to be investigated for a pre-defined acceptance uncertainty.
Providing specific TAPIR functions for several external conditions (number of bands, SZA, TOA/BOA), we can use these globally in inland and coastal waters and open oceans due to the insensitivity to salinity, temperature, and pressure.
Considering the atmospheric parameters atm and aot, the simulated TAPs and the TAPIR sensitivity promise a neglection of the vertical temperature and pressure distribution in the atmosphere.However, the impact of strongly absorbing gases in the visible could have been underestimated.Therefore, water vapour, ozone, and oxygen should be considered sensitively in future studies.Unfortunately, the impact of aot ranges in similar magnitudes of the phytoplankton properties and may not be neglected.
Nevertheless, future studies may reveal a constant linear relation (fig.4f) which can support a simple correction of the TOA signals required for TAPIR.For BOA applications, aot is less important.
In the water, only the upper 3 m to 5 m can be described because the water absorption in the red visible spectrum is rather strong and the radiometric signal maximum depth is limited.However, in optically complex waters with a contribution of cdom, the penetration depth is limited to a few meters even in the blue spectrum.
Sediments and cdom hardly influence TAPIR and it is applicable to optically complex waters.
TAPIR mainly depends on the phytoplankton IOPs producing the highest uncertainties and largest sensitivities.Further investigations of phytoplankton type specific measurements accounting for chlorophyll-a absorption spectra, scattering spectra, the phase function, and the efficiency factor support the parameterisation of phytoplankton in optical models.This might be an opportunity for retrievals based on TAPIR to obtain phytoplankton types or the fluorescence exclusively.
On the one hand, the fluorescence depends on the phytoplankton condition and properties and on the other hand on the available fluorescence excitation energy from the ambient light field.The presence of aquatic and atmospheric constituents change the amount of light available for the absorption which directly changes the amount of available excitation energy for fluorescence.The magnitude of reduction depends on the parameter whereas the selection of the fluorescence efficiency ε can mainly control the magnitude, shape, and location of the effective fluorescence peak.Assuming ideal conditions (clear atmosphere, little water constituents) and a low ε (maybe due to the physiological condition of algae), the fluorescence can be smaller than expected.Therefore, it is important to consider the sensitivity and uncertainty of all parameters on the reflectance of the entire visible spectrum although they may have little impact on the fluorescent spectrum around 683 nm.A retrieval considering the redshift, which increases with decreasing ε but increasing a440, might be able to obtain reference values of ε.
Quantifying the fluorescence and also phytoplankton scattering with TAP, the selection of the lower integration limit λ 1 depends on the available signal bands near 670 nm.λ 1 constrains the integration and can influence the final TAP due to the definition of the "reflectance constant" R(λ 1 ), which reduces the total reflectance, and the upper integration limit λ 2 .The impact of λ 1 has to be considered but, usually, most of the sensors (e.g.EnMAP) have a less radiometric resolution than MOMO which limits the choice of λ 1 to 1 or 2 possible bands.Therefore, developing sensor specific TAPIR functions from simulations relativises the relation between TAP and a440 among each other.
Accounting for sensors with fewer bands than EnMAP (e.g.Hyperion or OLCI with 10 and 5 bands within 660 nm to 750 nm, respectively), the peak could be estimated with a fitting function.
Unfortunately, the absorption properties of phytoplankton and water highly influence the peak's shape which complicates the application of a unique function (e.g.Gauß).However, it is necessary to study the change of sensitivities and uncertainties of the TAPs for all parameters, which might highly differ, for a function describing the fluorescence peak.
The uncertainties retrieved in this study are within 25 % to 38 % of the phytoplankton absorption a440 and are dependent on a440 itself.Considering different parameter values and parameter uncertainties σ p , they likely change.The assumption of the σ p particularly influences the final a440 uncertainty σ a440 .Nevertheless, a first validation assessment reveals sufficient results for TAPIR retrieved a440 and chl-a, respectively.

Conclusions
This study indroduces the Total Algae Peak Integration Retrieval TAPIR which links the phytoplankton induced reflectance peak near 683 nm with chlorophyll-a absorption at 440 nm (a440).
Firstly, the peak loacted near 683nm induced by chlorophyll-a fluorescence and phytoplankton scattering is quantified with an integration (TAP).Secondly, a TAPIR function is developed for top of the atmosphere (TOA) simulated data depending on a440.Afterwards, the inverse of the function provides the possiblity to retrieve a440 from reflectance data.Therefore, TAPIR and its functions support relation to phytoplankton absorption, scattering, fluorescence, and the concentration.
Sensitivity studies on various atmospheric and aquatic parameters reveal a major dependence on the parameterisation of phytoplankton (IOPs and fluorescence efficiency factor), some aerosol influence, and little impact on water constituents.The simulations for EnMAP specific conditions are promising for an accurate fluorescence and chl-a retrieval and studies can benefit from a high spatial resolution (30 m).

Preprints
(www.preprints.org)| NOT PEER-REVIEWED | Posted: 14 February 2018 doi:10.20944/preprints201802.0097.v1Besides the Hyperspectral Imager for the Coastal Ocean (HICO) mounted on the International Space Station (ISS) and the Compact High Resolution Imaging Spectrometer (CHRIS) onboard the satellite Project for On-Board Autonomy 1 (PROBA-1), the Earth Observing satellite 1 (EO-1) carried the hyperspectral sensor Hyperion with 220 bands in the VIS and near infra-red (NIR) from November 2000 to January 2017.Recently, the Sentinel-5 Precursor (S5p) carrying the Tropospheric Monitoring Instrument (TROPOMI) was launched in October 2017.The Hyperspectral Precursor and Application Mission (PRISMA), the Environmental Mapping and Analysis Program (EnMAP), the Hyperspectral Infrared Imager (HyspIRI), and the Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) launching in 2018, 2020, 2022, and 2022, respectively, are promising future space missions for the application of advanced fluorescence and phytoplankton algorithms.

Figure 1 .
Figure 1.Details of simulated TOA reflectance R = L u /E d for increasing absorption coefficients a440 (indicated by symbols) within 660 nm to 750 nm.a) Effective fluorescence peak, b) shift of the maximum reflectance R(λ P ) towards longer wavelengths (redshift), and c) shape and amplitude of the fluorescence peak relative to the signal wavelength λ P and the local maximum R(λ P ).The symbols in panels a), b) and c) correspond to the legend in panel b).

Figure 2 .
Figure 2. The TAP for two simulated TOA reflectance spectra.The spectral width of the baselines highly differs but λ 1 hardly deviates from 678 nm.

Figure 3 .
Figure 3. Retrieved TAPs over a440 and their variants due to adjusted simulation parameters (table1).The solid lines link the TAPs computed from reference simulations from which the TAPIR function in eq.(5) is calculated.

Figure 4 .
Figure 4. Jacobians of the reference TAPIR function f ref (eqs.(5) and (6)) calculated from simulations with the reference parameters emphesised in table 1 per a440.Note the different ordinate scales and magnitudes which represent the sensitivity.

Figure 5 .
Figure 5. Variation of a) the phytoplankton absorption spectrum (normalised to a ph (440 nm)) and b) the corresponding single scattering albedo for ω 0 (440 nm)=0.68(reference) and 0.82 (grey).The black solid lines illustrate the reference spectra and the dashed lines the variations collected from HydroLight simulations by [8].

(
single scattering albedo, the underlying absorption spectrum, and the efficiency), which suggests the opportunity of distinguishing different phytoplankton types.The application of various phytoplankton type dependent absorption spectra may result in variants in TAPIR due to slightly shifted absorption maxima and intensities.Unfortunately, the aot influence cannot be neglected due similar magnitudes of the TAPIR function and the corresponding Jacobians and must be considered with an atmospheric correction.Preprints (www.preprints.org)| NOT PEER-REVIEWED | Posted: 14 February 2018 doi:10.20944/preprints201802.0097.v1

Figure 6 .
Figure 6.Summands of eq.(10) (black lines with markers indicating the parameter) and σ 2 TAP (grey line) in panel a).Panel b) shows the summands of eq.(9) (black) and the final σ 2 a (grey).The squared uncertainties relate to the values listed in tables 2 and 3.

2 ,
datasets collected by Nechad et al. [8] are used.They provide hyperspectral in situ measurements at the North Sea (NoS) and in Indonesian waters (InW) among other locations.Besides various IOPs and apparent optical properties (AOPs), each set contains spectral phytoplankton absorption coefficients a ph (λ) and irradiance reflectance converted to remote sensing reflectance R RS .

PreprintsFigure 7 .
Figure 7. TAPs of surface measurements at the North Sea (NoS) and in Indonesian waters (InW) collected from [8] and the functions TAPIR BOA and TAPIR InW BOA (eqs.(7) and (11)) in a).Panels b) and c) show the performance of the OC4 and the TAPIR retrievals.The vertical bars in panel c) represent calculated uncertainties for BOA applications.The circle markers with the thin dashed bars show chl-a estimated from the empirical TAPIR InW BOA function (dashed line in panel a) and eq.(11)) with a raised slope based on the TAPs from InW in a).

Table 1
summarizes the parameters used in the simulations from 390 nm to 790 nm (λ) for chlorophyll-a absorption coefficients at 440 nm from 0.1 m −1 to 10.0 m −1 referring to high a440 Preprints (www.preprints.org)| NOT PEER-REVIEWED | Posted:
• C

Table 3 .
(10) of parameters used in the uncertainty estimation in eq.(10).The deviation's denominator ∆p is computed with p var and p re f and use a reasonable conservative σ p from literature (column "ref.") or assume it.Table1lists their units.Exemplary, the table presents the summands of eq. (