Based on HYDROLIGHT simulations of more than 2000 reflectance spectra from datasets typical of coastal waters with highly variable optically active constituents as well as on intercomparisons with field measurements, the magnitude of chlorophyll fluorescence was analyzed and parameterized as a function of phytoplankton, CDOM, and suspended inorganic matter concentrations. Using the parameterizations developed, we show that variations in the fluorescence component of water leaving radiance in coastal waters are due more to the variability of attenuation in the water than to the variability of the fluorescence quantum yield, which we estimate to be relatively stable at around 1%. Finally, the ranges of water conditions where fluorescence plays a significant role in the reflectance NIR peak and where it is effectively undetectable are also determined.
©2007 Optical Society of America
There is a growing consensus on the need for the improvement of remotely sensed sun-induced chlorophyll fluorescence measurements for ocean color interpretation. An increasing number of applications become viable if chlorophyll fluorescence and its contribution to the NIR spectral peak near 700 nm can be measured accurately and appropriately. These include the retrieval of chlorophyll concentration [Chl] and quantum yield using current and more recently developed algorithms [1,2], detection and characterization of harmful algae blooms [3,4], improvement of [Chl] retrieval using the NIR peak [5–7], and analysis of photosynthetic processes .
The magnitude of sun-induced chlorophyll fluorescence is now routinely retrieved by satellite observations in the open ocean using Fluorescence Line Height (FLH) algorithms [1,4] which are broadly based on the estimation of excess reflectance at the fluorescence peak above the baseline connecting the reflectances at the wings of the fluorescence peak. In the open ocean, FLH determined in this manner usually correlates well with the actual fluorescence amplitude, with minor corrections needed depending on the choice of spectral observation bands. Unfortunately, this retrieval is much more complicated in coastal waters where chlorophyll fluorescence overlaps with a strong NIR elastic scattering peak. The overlap occurs because the confluence of strongly decreasing algal absorption and increasing water absorption, coupled in a density dependent manner with scattering by phytoplankton cell structures, is located in the same spectral region as the fluorescence emission [5, 9–11]. In addition, accurate retrievals in coastal waters are further limited because of the absence of robust atmospheric correction schemes. However, with recent advances in this area [12–14], reflectances from coastal waters can be retrieved more accurately. At the same time, multispectral reflectance data are also becoming more readily available from aircraft and satellite sensors with higher spectral resolution.
If fluorescence measurements are to be trusted in coastal waters, a more detailed analysis of the remote sensing reflectance spectra is needed to reassess existing fluorescence algorithms in order to identify sources of errors. In particular, it is important to understand their limits in coastal waters in the context of optically active constituents, including variations in specific absorption of chlorophyll and accessory pigments, CDOM absorption, and scattering and absorption by nonalgal particles (NAP). While expressions for the estimation of fluorescence magnitude are well known [2,15], there are no simple relationships that can be used to relate fluorescence magnitudes to other water constituents in coastal waters. This is one of the main reasons why the fluorescence spectral region is usually avoided in the retrieval algorithms . However, if it were possible to obtain relationships which can properly connect fluorescence height to other parameters, fluorescence could then be included in the retrieval algorithms by expanding their use into the NIR.
To address these issues, this paper reconsiders the relationships between fluorescence magnitude and [Chl] in the presence of the other water constituents, some of which were previously studied [9, 17–19]. Through extensive simulations using the HYDROLIGHT radiative transfer program [20,21] special high resolution datasets appropriate to variable coastal waters were prepared and used to reexamine existing relationships between fluorescence and water parameters, to compare them with the results of our field measurements in Chesapeake Bay as well as with field data of other authors. As part of this approach we examine the impacts of spectrally interfering effects including self absorption, CDOM and NAP absorption as well as variations in quantum yield on observed fluorescence. The results are then used to determine the range of water conditions where fluorescence plays a significant role in the NIR peak’s magnitude and position, and conditions where the impacts are almost undetectable.
2. Methodology of field measurements
The spectral features of chlorophyll a fluorescence are well known  with a peak centered at approximately 685 nm. These features are usually approximated by a Gaussian shape with a full width at half maximum (FWHM) of 25 nm . This description is commonly included in simulation models  and in the algorithms for fluorescence retrieval . At the same time, it is also known  that fluorescence overlaps with major changes in the chlorophyll absorption spectrum. For example, the in vivo chlorophyll a specific absorption coefficients decrease from 0.0203 m2/mg at 674 nm, to 0.0076 at 686 m, to 0.0008 at 700 nm . Several approaches were used to disentangle the overlapping spectral features of chlorophyll fluorescence and the elastic NIR peak. These include long pass and band pass filter methods [9, 23], polarization discrimination [10,11] and comparison of measured total reflectance with the simulated elastic reflectance based on retrieved inherent optical properties (IOP) . It was shown in the laboratory tests and in the field that fluorescence can contribute from about 4%  to 30% [11, 23] to the magnitude of the reflectance peak in the NIR, thereby affecting retrieval algorithms considerably. In our methodology, we used an approach similar to  to estimate fluorescence reflectance components, however, instead of using retrieved IOPs, we utilized measured spectra from our WET Labs sensor package (see more detailed description below).
In-situ measurements were carried out at 42 stations over the Maryland coast of the Chesapeake Bay and adjacent rivers and harbors during July 11–20, 2005. The upwelling water radiance Lu(λ) was collected using a fiber optic probe placed just beneath the water surface and connected to USB2000 Ocean Optics spectrometer. Another probe with a cosine collector connected to a similar spectrometer was used to collect downwelling irradiance Ed(λ). Both spectrometers had undergone absolute radiometric calibration before the cruise. (See  for descriptions of the study area, paired upwelling and downwelling measurements, and laboratory procedures for water analysis). Remote sensing reflectance below the surface rrs (λ) was obtained from normalization of the upwelling radiance, Lu(λ), to the downwelling irradiance, Ed(0+) multiplied by air-water transmission which was assumed to be 0.96:
The Lu(λ) values were also measured in parallel using a GER spectroradiometer with a fiber optic probe and were normalized to the downwelling irradiance Ed(λ) measured by the same probe from a Spectralon plate. The data from both measurement sets were checked and found to show very similar reflectance spectra.
Water samples were also collected at each station. From these [Chl] concentrations were obtained using filtration through glass fiber filters (Whatman GFC) within several hours of sample collection, freezing of filters for at least 24 h, extraction with grinding in 90% buffered acetone, and spectrometric determination with a Genesis 2 spectroradiometer (Spectronics Corp.) and the trichromatic equation for total chlorophyll a . CDOM was estimated from absorption measurement of the sample filtrate and total suspended solids (TSS) concentrations were determined gravimetrically with tared, pre-ashed glass fiber filters.
Water IOP parameters at sample sites were measured using a ship-deployed profiling package assembled by WET Labs (Philomath, Oregon). This package consisted of three instruments: an AC-S recording total absorption (a) and total attenuation (c) at 82 wavelengths almost equally spaced between 400 nm and 750 nm giving an average spectral resolution of 4 nm, an ECO-scattering meter with one of the channels measuring the fluorescence signal of chlorophyll, and a CTD to obtain temperature, salinity and pressure data. The AC-S instrument was properly calibrated using optically pure water as a reference (Barnstead NANOpure) before and after the cruise in order to track and compensate for any drift. The AC-S data were corrected for temperature, salinity and scattering according to the manufacturer recommendations. A data logger was used to power all the instruments, acquire data, coordinate different timing schemes and transmit the data up through a single cable to the processing computer. The depth of the WET Labs profiler package was raised and lowered either manually or by automatic winch in order to sample depth profiles. The range of parameters measured in the field was [Chl]=9.1-354.2 mg/m3, total absorption at 400 nm 1.41-10.8 m-1, concentrations of total suspended solids TSS 7-64.8 g/m3 demonstrating a wide variability of conditions.
3. Synthetic datasets and relationships for the bio-optical model
To analyze the relationships of fluorescence with other water parameters a four-component bio-optical model was used to generate the IOPs of the water body [25,26]. This model provided inputs for HYDROLIGHT program which was then used to generate a series of reflectance spectra datasets. The constituents included: the water itself, yellow substance (CDOM), nonalgal particulates - mineral and detritus (NAP) and chlorophyll containing particles (phytoplankton). We use the subscripts “w”, “y”, “nap” and “chl” to identify these four components in the text below. Our simulations closely followed assumptions used in the simulations of the of IOCCG database  but with several significant differences. First, for accurate fluorescence evaluation and retrieval, datasets were simulated from 400 to 800 nm with 1 nm resolution instead of 10 nm. Secondly, concentrations of CDOM and NAP were assumed to be random and not related to [Chl] as necessary for case 2 water conditions. The main model relationships are explained below.
The total spectral absorption coefficient a(λ) is given as
where the water absorption spectrum aw(λ) was obtained from Pope and Fry .
The chlorophyll absorption for case 2 (coastal) waters was considered proportional to [Chl] as is often assumed  and given by:
where a * chl(λ) a is the specific chlorophyll absorption spectrum, m2/mg. The choice of the specific chlorophyll absorption spectra is critical to the corresponding reflectance spectra and fluorescence magnitudes and is discussed below in more detail.
where a * nap(400) a is the specific absorption of nonalgal particulates at 400 nm, m2/(g) and Cnap is a concentration, g/m3.
CDOM absorption was obtained from the relationship:
where ay(400) a is the absorption of CDOM at 400 nm, m-1.
Ranges of parameters for the datasets were taken as:
a * nap=0.02-0.1m2/g, Sy=0.01-0.02, Snap=0.007-0.015.
The total scattering coefficient was simulated as a sum of three components:
where b * nap(550) is a specific scattering of non algal particles at 550 nm, m2/g.
The ranges of parameters for scattering were:
γ 2=0.5-2 b * nap(550)=0.5-1 m2/g.
To model the scattering of phytoplankton, both Mie calculations and field measurements indicate that the scattering spectrum of algae cells can be calculated as the difference between their attenuation and absorption [31, 32],
while the attenuation spectrum itself can be modeled as a power law function :
where p=0.1-0.5 and γ 1=0.1-1.6.
In our simulations, the backscattering coefficient was taken to be the sum of the contributing components
where bbw(λ) is obtained according to  and b̃bchl, b̃bnap are backscattering ratios for chlorophyllous and nonalgal particles assumed to be independent of wavelength [30, 34]; typical values were used b̃bchl=0.01 and b̃bnap=0.02 (assuming a strong mineral component in NAP) together with the predefined Fournier-Forand phase function.
The bio-optical model for the simulation of IOP spectra described above uses 3 main parameters as inputs: the concentration of phytoplankton [Chl], the concentration of nonalgal particles Cnap, and the absorption of CDOM at 400 nm ay(400). To generate HYDROLIGHT datasets, values of all constituents were randomly varied within the prescribed ranges identified for each dataset. Simulations were divided into 2 datasets, each representative of different ranges of nonalgal particle content.
Dataset 1: 500 runs were executed with randomly chosen values: [Chl]=1-100 mg/m3, Cnap=0-1 g/m3 and ay(400)=0-5 m-1. With a wide variety of specific chlorophyll absorption spectra available [35–38] in our case the set of specific absorptions was taken from Ciotti et al.  as a sum of specific absorptions of microplankton and picoplankton with different weighting factors, Sf, where Sf=[0.1,0.2,0.3,0.4,0.5].
These spectra are shown in Fig. 1. They assume similar spectral shape and relatively low specific absorption amplitudes which are typical for waters with [Chl]>1-5 mg/m3  (achl(675)=0.01-0.016). Higher values 0.5<Sf<1 correspond to the specific absorption spectra more typical for open ocean waters with lower [Chl] and were not considered in this study.
Dataset 2 follows dataset 1, but with nonalgal particle concentrations in the range Cnap=1-100 g/m3.
Datasets of reflectances were calculated both with and without fluorescence and assuming a fluorescence quantum yield of η0=1%. All reflectances were simulated for the sun zenith angle θi=30° and for nadir observation. The solar input was simulated using the Gregg and Carder model with a cloud-free sky [20,21] and the default wind speed was 5 m/s. Since the final fluorescence signal is completely linear with the value of η0, it can be scaled accordingly as needed. Finally, the water body was assumed homogeneous with a maximum integration depth specified as z max=5/c(685) (where c(685) is the attenuation at 685 nm) to account for the deepest layer which can contribute to the fluorescence detected at the surface .
4. Relationships between fluorescence amplitude and concentrations of chlorophyll and other water constituents - simulations and measurements
4.1 Basic features of the relationship
The amplitude of the fluorescence peak in the water leaving radiance at 685 nm can be derived following Huot, et al.  as:
where Q * a is a reabsorption coefficient in the algae cells, Ed(λ,0) is the downwelling irradiance just below the surface, η is the fluorescence quantum yield, K(λ) is the attenuation coefficient in the fluorescence excitation zone, Kf is the attenuation coefficient in the fluorescence emission zone, Cf is a coefficient which depends on the assumed fluorescence shape and which also takes into account propagation of the fluorescence through the air-water interface. The integral in (12) clearly shows the modification of photosynthetically available radiation (PAR) due to absorption and scattering in the water.
According to Babin et al.  Q * a=0.3-0.6 for [Chl]>1 mg/m3. To take reabsorption into account in HYDROLIGHT simulations and make it consistent with (12), we assumed a value of Q * a=0.5. Since Q * a value is not included directly in the HYDROLIGHT program we scaled the fluorescence quantum yield as η=η 0/Q * a (i.e. by a factor of 2).
In algae dominated waters, the amplitude of fluorescence component in water leaving radiance in radiance units (Wm-2sr-1µm-1) for vertical illumination and detection is determined by [Chl], absorption of water aw(λ) and specific absorption of algae a * chl(λ). In fact, it is useful for parameterization purposes to use a the simplified version  of expression (12) with attenuation terms in the integral replaced by the sums of average absorption values in the excitation and emission zones
Here, awsum=aexw+aemw, a * Chlsum=a * exChl+a * emChl, aexw is the average absorption of water in the excitation wavelength region 400–700 nm, aemw is the average absorption of water in the emission wavelength region around 685 nm and a * exChl and a * emchl are algae specific absorptions in the excitation and emission zones with all other parameters included in the proportionality coefficient. Summing the absorptions is required since the downwelling light is attenuated by absorption in the excitation band while upwelling fluorescence is similarly attenuated in the emission band.
The coefficient in the expression (13) implicitly includes specific chlorophyll absorption in the excitation zone a * exChl and will change proportionally to its value. This coefficient was chosen  to be consistent with the relationship Fl=0.15[Chl] which is obtained from field measurements for very clear waters with low [Chl] where the only attenuation factor is water absorption. In waters with higher [Chl] attenuation by phytoplankton absorption should be taken into account by adding the awsum/(awsum+a * Chlsum[Chl] term. Estimation of awsum and a * Chlsum in the excitation and emission zones, results in the following parameterized formula for the fluorescence amplitude suitable for open ocean 
Here, the fluorescence amplitude at 685 nm is expressed in radiance units (Wm-2sr-1µm-1), the coefficient 0.2 in the denominator has units of m3/mg (a * chlsum/awsum) as needed to make the denominator non-dimensional and coefficient 0.15 has units of radiance per [Chl] (Wm-2sr-1µm-1)* (m3/mg).
With increasing [Chl] concentrations, saturation occurs because of stronger light absorption in both excitation and fluorescence emission zones. For non-nadir illumination angles, the absorption in both emission and excitation bands needs to be multiplied by µi=1/cosϑi, and µv=1/cosϑv respectively, where ϑi and ϑv are the related illumination and viewing angles. Since absorption of water in the excitation band is small in comparison with the emission band, variations due to illumination angle in the range 0–30° are noticeable only for high [Chl]. Coefficients in (14) are based on case 1 waters assumptions, in particular high specific chlorophyll absorption. With increasing [Chl] these values become lower  and coefficients should be changed, so Eq. (14) will be less and less accurate.
Since Eq. (14) is based on experimental data it is useful to estimate fluorescence quantum yield in this expression. Remote sensing reflectances above water were simulated (independently of datasets 1 and 2) using HYDROLIGHT and standard case 1 water assumptions with and without fluorescence and ϑi=30°. The subtraction of these two spectra at 685 nm defined the simulated fluorescence amplitude. When a fluorescence quantum yield of η=1% is used in the simulations, the amplitude of the simulated fluorescence (at 685 nm) agrees very well with the amplitude obtained from Eq. (14) for [Chl]=1-15 mg/m3 (Fig. 2). This very good agreement provides a very strong constraint on the quantum efficiency and motivates us to explore this question further for case 2 waters.
We should note that in order to obtain the simulated fluorescence value in radiance units (Wm-2sr-1nm-1) compatible with Eq. (14), we multiplied here and throughout the paper the fluorescence amplitude obtained as an equivalent remote sensing reflectance by the irradiance at 685 nm (Ed=1.1 Wm-2 nm-1), which is calculated in HYDROLIGHT for clear sky conditions just above the surface and ϑi=30°.
The simple model (13–14) described above does not correspond to case 2 waters. In coastal waters, with the presence of CDOM and mineral particles, attenuation is not limited to the absorption by phytoplankton, as in the open ocean, but should also include absorption of CDOM and NAP as well as NAP backscattering. So the relationship between Fl and [Chl] should take into account these attenuation components. Thus, if these components are now included in the development of Eq. (13) as additional attenuation mechanisms we get
where awsum≈0.5 m-1  and aCDOMsum, anapsum and bbnapsum are respectively the sums of CDOM, NAP absorptions and backscattering of nonalgal particles in the excitation and emission spectral regions. Since CDOM, NAP absorptions and backscattering decrease rapidly with wavelength (Eqs (4), (5) and (7)) they can be generally neglected in the emission band as a first approximation. In addition, for the low NAP case, the impact of backscattering can be also considered substantially smaller than that of absorption.
All terms on the right side of Eq. (16) can be calculated from the relationships in Section 3 for the given input parameters [Chl], ay(400) and Cnap which also provide the IOPs needed for the simulations. The fluorescence amplitudes can be taken from reflectance simulations (with and without fluorescence), thus establishing proportionality coefficient for (16). Unfortunately this approach does not provide an absolute proportionality constant because of the unknown fluorescence quantum yield. Recourse to field measurements is needed to address this question.
4.2 Determination of Quantum Efficiency Parameter Regime
Unlike case 1, waters in coastal waters field data are generally sparse, and simultaneous measurements of water leaving reflectance, water IOPs and chlorophyll concentrations are not readily available. Therefore, it is much harder to relate the model to measurements. However, a significant increase in experimental validation would result if we can connect the quantum yield directly to the water leaving reflectance properties without complementary measurements of IOPs, since there are more measurements of this type available in case 2 waters. In this section, we show how quantum yield can be related to features in the reflectance spectra, which result in strong constraints on the fluorescence quantum yield.
Thus, while generally, it is assumed that the fluorescence quantum yield can vary widely, in a range of 0.3% to 10% [17, 19, 40], we will show below, that the observed variability is usually much less. If this were not the case, it would lead to appearance of reflectance features in the NIR, which are not, in fact observed in the field.
As discussed in the introduction, the NIR peak in the reflectance spectra is a sum of the overlapping spectra of fluorescence and elastic reflectance. The elastic reflectance spectrum itself is a result of the confluence of the decreasing algal absorption and increasing absorption of water which creates a local minimum on the total absorption spectrum that therefore corresponds to the maximum on the reflectance spectrum. As shown in Fig. 3 for low [Chl]<6 mg/m3, the fluorescence component is a dominant part of the NIR peak and the maximum of the reflectance is close to the position of the fluorescence maximum at 685 nm. With an increase in [Chl], the elastic peak becomes stronger and shifts to the red, causing the combined fluorescence/elastic reflectance peak to shift in the same direction. For high [Chl]>60-70 mg/m3 elastic part of the peak is dominant and significantly less dependent on the fluorescence component. In fact, it was found in  that the shift of the total NIR peak from 685 nm is clearly related to [Chl] as shown in Fig. 4.
These data are complemented by our Chesapeake Bay field measurements results of which encompass a broader range of conditions. For Chesapeake Bay data the upper boundary is similar to results obtained in  which were approximated by us in Fig. 4 (solid line). The lower boundary for Chesapeake data was also approximated (dashed line) for [Chl]<100 mg/m3. (The older data  were measured in a hypereutrophic oxbow lake with spring diatom and summer and fall cyanobacteria blooms.)
These results, in fact, impose significant limitations on the fluorescence amplitude values which can be assumed in modeling. If the fluorescence is too dominant for a given [Chl] level, the shifts in the NIR reflectance peak from the fluorescence peak at 685 nm will be much less than those observed in the field, while if the fluorescence is much less, deviations would be larger than observed in the field. This is borne out by comparison with the results of simulations in Fig. 5, where shifts of the reflectance peak in the NIR (similar to the one shown in Fig. 4) were simulated for reflectances from dataset 1 with an absorption shape corresponding to Sf=0.5 (see Fig. 1) and three fluorescence quantum yield values η=0, 1 and 2 %. These results are then compared with the field data from Fig. 4.
In general, the spectral shifts obtained from our field data fall between the boundary conditions (dash curves in Fig. 5) and are consistent with the shifts observed from our HYDROLIGHT simulation for η=1%. For other specific chlorophyll absorption shapes Sf<0.5 (Fig. 1), the results were similar or corresponded to slightly lower quantum efficiency. Based on these results, we assume η=1% in the following analysis. This value is the same as for case 1 waters as suggested by Babin et al.  and also follows from our previous case I results in Section 4.1.
Further analysis of Fig. 5 shows that for [Chl]>60-70 mg/m3 fluorescence does not significantly affect the NIR peak (blue, green and red points corresponding to η=0, 1 and 2% are very close to each other).
4.3 Refinement of relations between fluorescence amplitude and concentrations of water constituents from simulated datasets
Using our simulations, which generated reflectance spectra with and without fluorescence and using the fluorescence quantum yield value determined above, we calculated fluorescence amplitudes at 685 nm for our datasets and extended the original expression in Eq. (14) in accordance with the approach followed to derive expression (16). Applying η=1% to the datasets 1 (Cnap<1 g/m3) and 2 (Cnap=1-100 g/m3), we found the best LSQ fit for the relation
where the term x2*ay(400) accounts for the effect of CDOM and the term x3*Cnap for the effect of nonalgal particles.
For dataset 1, we find that the effect of nonalgal particles is negligible and the relation takes the form
In this expression the coefficient in the numerator is reduced from 0.15 in (14) to 0.0375, and the coefficient 0.2 at [Chl] in the denominator is reduced to 0.032, which is due to the lower specific chlorophyll absorption in coastal waters for high [Chl] compared with the specific absorption model for open ocean waters . Lower specific chlorophyll absorptions mean smaller PAR which results in the smaller coefficient in the numerator and smaller a * Chlsum values in (16). This relationship is illustrated in Fig. 6(a) which shows that in the low NAP case, expression (18a) can be successfully used to quantify fluorescence amplitude with a correlation coefficient R2=0.938 where the fluorescence is explicitly connected to the CDOM absorption and [Chl]. In addition, we found that the variability of specific chlorophyll absorptions (Fig. 1) does not significantly affect the correlation.
Taking into account the concentration of nonalgal particles and using dataset 2 we arrive at Eq. (18b).
We note that the correlation is somewhat lower (R2=0.81) for the high NAP case if expression (18b) is used to calculate fluorescence (Fig. 6(b)). However, this reflects not only the variability of the specific scattering of non-algal particles b * nap(550) and scattering spectra slope γ 2 (see description in Section 3 for details) but also the changes in the fluorescence spatial distribution in the presence of a highly scattering medium. Our simulations showed that this correlation significantly improves if Cnap is limited to 10 g/m3 but even for the whole range of Cnap=1-100 g/m3, we consider this expression to be a good first approximation of the fluorescence amplitude for waters where both CDOM and nonalgal particles contribute to the attenuation of light.
Thus, the relationships (18a,b) estimate fluorescence amplitude as a function of [Chl], absorption of CDOM ay(400) and concentration of nonalgal particles Cnap. If all three of these parameters are known, estimation of fluorescence amplitude Fl is straightforward. However, it is not likely that the field data in many cases will be sufficiently accurate for point by point comparison of Fl due to the inherent measurement inaccuracies as well as the complexity of coastal waters. But the model can be also used in a statistical way to define a confidence region in the Fl - [Chl] plane where we can expect the bulk of the measurements to occur and where the boundaries of these regions are formed by taking appropriate limits, as follows.
4.3.1 Low NAP concentration with varying CDOM absorption
From Eq. (18a) we find that for the average CDOM absorption in dataset 1 ay(400)=2.5 m-1 in the absence of nonalgal particles Fl is given by:
in the absence of CDOM, ay(400)=0 which establishes the higher boundary for Fl as
and for maximum CDOM, ay(400)=5 m-1 which establishes the lower Fl boundary as
4.3.2 High NAP concentration
From dataset 2 with Cnap=1-100 g/m3 we find the lower Fl boundary which occurs when both ay(400) and Cnap are near their maximum and is given by:
The value 4.0 in the denominator is higher than the value which can be calculated from the full expression (18b) directly. This reflects the errors in (18b) for high Cnap.
The complete set of expressions (19a-d) together with expression (14) can be utilized to determine realistic bounds of Fl over case 1 and case 2 waters.
4.4 Comparison and assessment of models for fluorescence values
4.4.1 Models derived from radiative transfer simulations
Relationships (19a-d) for coastal waters together with relationship (14) for the open ocean waters are shown in Fig. 7. As discussed earlier, the assumptions for the open ocean become less accurate with increasing [Chl], so the curve 1 in Fig. 7 only applies to conditions where [Chl]<20 mg/m3.
The main conclusion from Fig. 7 is that the fluorescence amplitude is usually lower in case 2 waters than in the open ocean because of the smaller specific chlorophyll absorption values, attenuation of light in the excitation and emission spectral zones by absorption of CDOM and/or NAPs and NAP backscattering, thus making detection of fluorescence much more challenging. As there is no exact boundary between case 1 and case 2 waters, the zone between curves 1 and 3 will correspond to conditions close to case 1 waters, but with higher CDOM values, as well as to the waters with higher specific chlorophyll absorptions which can be modeled with the values of Sf>0.5 in (11) which are more typical for open ocean waters. Finally, we should comment that at very high [Chl], the curves in Fig. 7 have some saturation levels which depend on concentrations of CDOM and nonalgal particles but these conditions correspond to very strong algae blooms which should be considered separately and are beyond the scope of this paper.
4.4.2 Comparison with field measurements
To test the above simulation results on field data, we modeled the total below surface reflectance spectrum for each station as a sum of two components. The first component was the elastic reflectance spectrum as calculated from measured attenuation and absorption spectra using the WET Labs AC-S instrument, and the second was a fluorescence reflectance component. These are derived as shown below using Eq (20).
Here, rfl mod is the fluorescence amplitude in remote sensing reflectance below the surface, and Φ(λ) is the fluorescence spectral distribution, which was considered Gaussian with a peak at 685 nm and 25 nm FWHM and Q is the bidirectional factor with a value of Q=4.5. bm(λ) and am(λ) are the field determined scattering, and absorption spectra. The scattering is not obtained directly but is deduced from bm(λ)=[cm(λ)-am(λ)], where cm(λ) is the measured attenuation coefficient.
This total reflectance has two free parameters b̃bmod and rfl mod. We retrieved the fluorescence component rfl mod by fitting modeled reflectance into the measured below surface reflectance spectrum with values of b̃bmod and rfl mod determined with LSQ approach. In practice, model parameters were found based on constrained LSQ minimization with the boundaries for b̃bmod taken as 0.005 to 0.4 and rfl mod taken to vary from 0 to 0.1 which includes almost all realistically possible variations of these parameters. To compare fluorescence amplitudes with our previous simulation results from datasets 1 and 2, we assumed that the fluorescence amplitude is given n by Flfield=0.53rfl mod Ed, where Ed=1.1 Wm-2 nm-1 is the downwelling irradiance in the fluorescence zone, (the same value as was used in the simulation analysis) and where the 0.53 factor accounts for the reflectance ratio at the water - air interface .
Out of 42 stations for which both reflectance and WET Labs data were available, the fluorescence was retrieved for 28 stations. For other stations, attenuation spectra could not be measured completely because of saturation in some parts of the spectra or because there was an obvious mismatch between simulated and measured spectra, probably due to the local changes in the water composition at the sites where reflectance and WET Labs data were acquired.
Typical total measured and modeled reflectance spectra, modeled elastic spectra and retrieved fluorescence spectra are shown in Figs. 8(a) and 8(b) for 2 stations. These stations had significant differences in [Chl], but other parameters were more uniform. Total suspended solids (TSS) were 8.1 and 13.2 g/m3, ay (400) was about 0.55 m-1 and 1.0 m-1, and [Chl] was 16.6 mg/m3 and 42.6 mg/m3 respectively. In both cases, the fluorescence was a significant part of the NIR peak. However, for [Chl]=46.6 mg/m3, a larger proportion of the peak was due to elastic reflectance and absorption changes, and the cumulative NIR peak location was at a significantly longer wavelength than the fluorescence peak. It is important to remember that TSS includes the mass of both algal and nonalgal particles, and is not a clear indicator of the nonalgal particle concentration Cnap.
Our field data were complemented by other fluorescence amplitude values retrieved from results of field campaigns by Roesler and Perry . We considered two of their data sets which are identified as “Coastal Environment” and “Estuarine Environment”. The first set was acquired in the Gulf of Maine and along the Oregon coast with [Chl]=0.5-2.8 mg/m3. Their reflectance spectra, when analyzed, clearly corresponded to low CDOM concentrations. Both locations were close to the open ocean. The second dataset was acquired in Puget Sound, Washington with reflectances corresponding to higher CDOM effects and with features more typical of case 2 waters. In that paper, fluorescence amplitudes were presented in irradiance reflectance units. Therefore, to compare them with our fluorescence data in radiance units above the water, we multiplied their values by 0.53 Ed/Q, using Q=4.0 as a reasonable estimate .
The relationships between fluorescence magnitude and [Chl] from all sets of field measurements are shown in Fig. 9 and compared with Eqs. (19) for datasets 1 and 2. These expressions, we recall, are designed to illustrate the “average” and extreme water conditions regarding NAP scattering and CDOM observed in our simulation studies.
It can be seen that within our Chesapeake Bay data, most of the points are inside or very close to the boundaries determined from our simulations, confirming that the data can be represented using a much smaller range in quantum yield. Sporadic higher or lower values might be attributable to either higher variability in the absorption spectra compared to values in data sets 1 and 2, or variations in fluorescence quantum yield. As expected, the “Coastal Environment” data  were very close to the fluorescence — [Chl] dependence for case 1 waters, while the “Estuarine Environment” data  fall mostly between the case 1 water curve and our estimated case 2 waters with low NAPs and low CDOM. It is obvious that some deviations from the models exist.
In classifying the Chesapeake water conditions, statistics cs on ay(400) and TSS concentrations for the Chesapeake Bay stations for which fluorescence was retrieved is shown in Fig. 10. TSS values are not directly related to the concentrations of nonalgal particles, but since contribution of nonalgal particles to attenuation is relatively small (18b), this statistics once again makes reasonable grouping of Fl values around curve of expression (19a) in Fig. 9 which corresponds to the moderate values of ay(400) and TSS.
Taking into account the wide range of conditions at our Chesapeake bay stations, with [Chl]=9.1-235 mg/m3, ay (400)=0.55-5.6 m-1, TSS concentrations 7-64.8 g/m3, salinity 1.8-12 ‰, clear sky to hazy and cloudy conditions, data added from three other locations and water conditions  and rough assumptions for the Q parameter and fluorescence quantum yield, we believe the resultant consistency between our datasets and the η=1% regime should be considered excellent. We stress again that all fluorescence amplitude values are presented in radiance units and were calculated from the reflectance measurements and simulations by multiplication using Ed=1.1 Wm-2 nm-1. For conditions other than clear sky, this factor should be chosen appropriately.
Our results clearly show that in coastal waters, the high variability observed in fluorescence amplitude for fixed [Chl] values, which are often attributed to high quantum yield variability, should be attributed instead mostly to effects of strong absorption by phytoplankton and CDOM and scattering by NAPs. Together, these can change fluorescence amplitude for [Chl]=1-50 mg/m3 by a factor of 3–10. Smaller values of specific chlorophyll absorption  also contribute significantly to the lower fluorescence magnitudes in the coastal environment in comparison with the open ocean assuming proportionality between PAR and a * Chl.
We would like to stress that the results of comparison of the model and field measurements is limited to show that data derived from field measurements fall inside the boundaries predicted by our radiative transfer model simulations and that expression (19a) can on average be a good estimation of the fluorescence amplitude. In fact, there are many factors which make point-point comparison of the model and field data unreasonable. These include true (versus apparent) variability in the fluorescence quantum yield, spatial and temporal shifts between reflectance and WET Labs measurements which resulted in some changes of water conditions, the 4 nm resolution of WET Labs data in comparison with 1 nm reflectance data which can miss fine features on the spectra, unknown actual specific chlorophyll absorption spectra and complex illumination conditions. Much more detailed and accurate field studies are needed to evaluate the applicability of expression (18) which explicitly relates Fl to [Chl], CDOM absorption and Cnap in a point-point fashion. On the other hand we found that if graphs in Fig. 9 were simulated with fluorescence quantum yield η=0.5% and 2% instead of 1% with respective decrease and increase of Fl in (19), the experimental data would be completely outside modeled boundaries. This makes clear that despite many uncertainties mentioned above the η=1% hypothesis in a statistical sense should be considered highly probable and the resultant Fl model is a good first approximation of fluorescence in coastal waters.
4.5 Contribution of fluorescence to the NIR reflectance peak
To determine the contribution of the fluorescence to the total NIR peak, we calculate the ratio of the fluorescence peak to the total reflectance at 695 nm, which is usually close to the maximum reflectance in the NIR for our datasets 1 and 2 (low NAP and high NAP cases). As shown in Fig. 11(a) for the low NAP case, the fluorescence magnitude is 10–30% of the peak magnitude for our range of [Chl], so its contribution is significant and its value should be distinguishable from total reflectance. However, in the high NAP case Fig. 11(b) the contribution of the fluorescence decreased rapidly with increasing NAP concentrations, due to the relative increase of elastic scattering reflectance. For Cnap>10 g/m3, the contribution of fluorescence to the total peak dropped below 5% and could be ignored in most applications and retrieval algorithms. Even for Cnap=2-10 g/m3 the fluorescence contribution is still below 10% of the peak, making its retrieval questionable.
Relationships between fluorescence amplitudes and concentrations of water constituents developed by us (18)–(19) can be used directly to estimate Fl values (or corresponding components in reflectances) if [Chl], ay(400) and Cnap are known. They can also be applied to algorithms for the retrieval of IOP and water parameters from reflectance spectra. As a first step, these retrievals can be carried out without taking into account the fluorescence component to make preliminary estimation of [Chl], ay(400) and Cnap values. These retrievals then can be repeated after calculation and allowance for fluorescence amplitude. This approach also allows one to separate open ocean and coastal waters and to choose an appropriate expression (14) or (18b) for fluorescence amplitude estimation. On the other hand, if the type of water is known in advance, expressions (14) or (18b) can be incorporated into a retrieval algorithm as an additional constraint.
Datasets with more than 2000 reflectances typical for coastal waters, with high variability of [Chl], CDOM, and NAPs, together with specific chlorophyll absorption spectra and spectral distributions of attenuation and scattering and with results of comprehensive measurements in Chesapeake Bay were used to analyze the magnitude of fluorescence in coastal waters and its dependence on [Chl] and other water components.
Based on these HYDROLIGHT simulations we first found that the fluorescence amplitude in coastal waters is in general substantially lower for the same [Chl] than in the open ocean. This is due to the decrease of photosynthetically available radiation (PAR), attenuated by absorption of CDOM and/or absorption and backscattering of NAPs. This decrease was especially noticeable for [Chl]<50 mg/m3, where fluorescence can be 3–10 times lower than in the open ocean. To facilitate our comparisons, we developed parameterized expressions to quantify the fluorescence amplitude as a function of [Chl] as well as CDOM and NAP concentrations
Using our models within appropriate limits and comparing experimental relations between Fl and [Chl] to our model estimates, we found that the variability of fluorescence magnitude in coastal waters can best be attributed to attenuation effects by water constituents, rather than to the differences in fluorescence quantum yield which we found to be well approximated at around η=1.0% and consistent to field measurement estimates in case 1 waters. In fact, we found that this value of the quantum yield best explains the change in the NIR reflectance maximum wavelength as a function of [Chl]. Our simulations showed that higher η values corresponding to higher fluorescence magnitudes would result in unrealistically small total reflectance shifts of the peak in the NIR from 685 nm with increasing [Chl] which are not observed in the field and unrealistically small shifts if the quantum efficiency is too low.
In addition to the intrinsic value in interpreting our field measurements, the simple parameterized fluorescence expressions can be integrated into existing algorithms for [Chl] and IOP retrieval from reflectance spectra and will presumably improve algorithms which are based on reflectance peak characteristics in the NIR spectral zone.
Finally, our calculations also show that NAP concentration is a critical factor in the contribution of fluorescence to the total reflectance in the NIR. For low NAP concentrations Cnap<2 g/m3, the fluorescence reflectance component contributes 10–30% to the total reflectance in the NIR, which can affect retrieval algorithms unless they are separated using proper techniques and methods from the elastic reflectance. However, with increasing NAP concentration, the fluorescence contribution decreases rapidly because elastic reflectance increases almost proportionally to Cnap as well as the additional attenuation by NAPs. In those cases, including many estuarine and near shore conditions, as well as turbid inland waters, the effect of fluorescence on reflectance spectra is almost negligible.
We would like to thank the following individuals who assisted in field and laboratory measurements: A. Binderup, R. Carlson, L. Chasar, E. Cizek, K. Dillon, B. Elmaanaoui, C. Fan, C. Hladik, C. Holland, R. LaCouture, M. Machmuller, J. Mulder, A. Mustapha, S. Pasko, M. Vargas, and L.Whitehurst. Laboratory facilities and other logistical support for the Chesapeake Bay campaign, including two research boats, were generously provided by K. Clark from Morgan State University’s Estuarine Research Center at Solomon, MD and by J. Bortz at the Maryland Department of Natural Resources. We are also very grateful to the reviewers of the paper whose comments and suggestions helped to improve it significantly.
This research was supported partially by grants from NASA #NCC-1-03009 and NOAA #NA06OAR4810162 and #NA17AE1624 with subcontracts from Environmental Cooperative Science Center, Florida A&M University.
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