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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 21 — Oct. 8, 2012
  • pp: 23300–23317
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Model of the dependence of the sun-induced chlorophyll a fluorescence quantum yield on the environmental factors in the sea

Miroslawa Ostrowska  »View Author Affiliations


Optics Express, Vol. 20, Issue 21, pp. 23300-23317 (2012)
http://dx.doi.org/10.1364/OE.20.023300


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Abstract

The paper discusses a physical model, obtained with the aid of statistical analyses, of the relationships between the sun-induced chlorophyll a fluorescence quantum yield and marine environmental factors. The relationships are based on a large set of empirical data from various ocean regions with basins of different trophicity, at different depths and in different seasons. Underwater spectral radiance and irradiance in the PAR spectral range were used to determine the quantum yield of sun-induced chlorophyll a fluorescence. From a statistical analysis a preliminary mathematical expression was derived to describe the fluorescence quantum yield as a function of the scalar irradiance, basin trophicity and the water temperature in situ. These relationships may be useful for analysing the budget of the light energy absorbed by phytoplankton pigments utilized in chemical and non-chemical quenching.

© 2012 OSA

1. Introduction

Sun-induced chlorophyll fluorescence – SICF (the main abbreviations and symbols used in the text are listed in Table 1

Table 1. List of the abbreviations and symbols used in the text

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) supplies information on the state and functioning of marine plant communities. Numerous attempts have therefore been made to determine, among other things, chlorophyll concentrations and levels of photosynthetic primary production in the sea on the basis of measured SICF values (e.g [1

1. M. Babin, J. C. Therriault, L. Legendre, B. Nieke, R. Reuter, and A. Condal, “Relationship between the maximum quantum yield of carbon fixation and the minimum quantum yield of chlorophyll a in vivo fluorescence in the Gulf of St. Lawrence,” Limnol. Oceanogr. 40(5), 956–968 (1995). [CrossRef]

3

3. Y. Huot, C. A. Brown, and J. J. Cullen, “Retrieval of phytoplankton biomass from simultaneous inversion of reflectance, the diffuse attenuation coefficient and sun-induced fluorescence in coastal waters,” J. Geophys. Res. 112(C6), C06013 (2007), doi:. [CrossRef]

].). However, the use of SICF to determine these properties is severely limited: in spite of intensive research into the dependence of the SICF quantum yield Φfl on environmental conditions (see e.g [4

4. S. Maritorena, A. Morel, and B. Gentili, “Determination of the fluorescence quantum yield by oceanic phytoplankton in their natural habitat,” Appl. Opt. 39(36), 6725–6737 (2000). [CrossRef] [PubMed]

6

6. M. Ostrowska, M. Darecki, and B. Woźniak, “An attempt to use measurements of sun-inducted chlorophyll fluorescence to estimate chlorophyll a concentration in the Baltic Sea,” Proc. SPIE 3222, 528–537 (1997). [CrossRef]

].), no general mathematical description of SICF has yet been formulated. Our preliminary analyses of this dependence were presented at the Ocean Optics conference in 2010 and published in the conference materials (see [7

7. M. Ostrowska, “Dependence of quantum yield of chlorophyll a fluorescence in the sea on environmental factors - the preliminary results,” in Proceedings of Ocean Optics XX conference, (Anchorage, Alaska 2010).

]). The aim of the present work was to derive a more complex version of a mathematical model, based on a larger set of experimental data, of the dependence of the quantum yield of the natural fluorescence of phytoplankton on the three principal factors governing phytoplankton growth in the sea: the trophicity of the water body under scrutiny, the light conditions there, and the temperature at different depths in the water. It was based on a set of more than 1200 values of the above-mentioned principal factors governing phytoplankton growth, and on a set of values of the quantum yield of fluorescenceΦflcorresponding to these environmental conditions, determined from measurements of downward irradiance and upward radiance spectra, and of other spectra necessary for obtaining the relevant parameters. The details of these analyses will be discussed below.

2. Material and methods

2.1 Experiments

In order to achieve the objectives of this work, empirical data gathered in various regions (mainly the southern part) of the Baltic Sea during serial cruises of r/v ‘Oceania’ (IO PAS Sopot) in 1999–2010 were employed. This bank of empirical data was extended by historical data gathered jointly by scientists from the Institute of Oceanology PAS and the Shirshov Institute of Oceanology RAS during the 23rd cruise of the r/v 'Vityaz' in the Atlantic Oceans: (1991) headed by Professor M.E Vinogradov from the Shirshov Institute of Oceanology RAS. These studies were carried out in seas of different trophicity, with chlorophyll concentrations from 0.02 mg m−3 (oligotrophic ocean centres) to ca 80 mg m−3 (supereutrophic waters in Baltic gulfs).

This database contains a large number of different marine environmental parameters and magnitudes characterizing the various properties of phytoplankton and marine photosynthesis. Of these parameters, the following, measured at different depths at 100 stations were used in the present analysis:

  • - chlorophyll a concentration Ca(0) [mgchla m3], measured at different depths in the sea using the traditional spectrophotometric method [8

    8. J. D. H. Strickland and T. R. Parsons, “A practical handbook of seawater analysis. Pigment analysis,” Bull. Fish. Res. Bd. Can. 167, 1–311 (1968).

    ];
  • - the spectra of light absorption by phytoplankton apl(λ,z) [m1], measured in vivo using non-extraction methods (see e.g [9

    9. G. M. Ferrari and S. Tassan, “A method using chemical oxidation to remove light absorption by phytoplankton pigments,” J. Phycol. 35(5), 1090–1098 (1999). [CrossRef]

    11

    11. S. Tassan and G. M. Ferrari, “An alternative approach to absorption measurements of aquatic particles retained on filters,” Limnol. Oceanogr. 40(8), 1358–1368 (1995). [CrossRef]

    ].) in suitably prepared samples of water containing phytoplankton, drawn from different depths in the sea. The relevant spectral measurements were performed on a UNICAM UV4-100 spectrophotometer equipped with a LABSPHERE RSA-UC-40 integrating sphere. This is described in detail in [12

    12. D. Ficek, S. Kaczmarek, J. Stoń-Egiert, B. Woźniak, R. Majchrowski, and J. Dera, “Spectra of light absorption by phytoplankton pigments in the Baltic; conclusions to be drawn from a gaussian analysis of empirical data,” Oceanologia 46(4), 533–555 (2004).

    ];
  • - the downward irradiance in the PAR spectral range (400–700 nm) Ed(λ,z) [μEin m2s1nm1], the total (integrated from 400 to 700 nm) scalar downward irradiance in this range PAR(z) [μEin m2s2], and the spectra of upward radiance at the nadir in the PAR spectral range (400–700 nm) Lu(λ,z) [μEin m2 s1 nm1 srad1] were measured:
  • - in the Atlantic and Indian Oceans with underwater spectrophotometers constructed at IO PAN. With these, the downward irradiance Ed(λ,z) and upward radiance Lu(λ,z) were measured at nine wavelengths λ [nm]: 405, 450, 500, 525, 590, 600, 665, 683 and 710. The physical principles underlying these measurements are explained in e.g [13

    13. J. Dera, “The characteristics of the euphotic zone irradiance in the sea,” Oceanologia 1, 9–98 (in Polish) (1971).

    15

    15. B. Woźniak, R. Hapter, and B. Maj, “The inflow of solar energy and the irradiance of the euphotic zone in the region of Ezcurra Inlet during the Antarctic summer of 1977/78,” Oceanologia 15, 141–174 (1983).

    ];
  • - in the Baltic Sea with MER 2040. With this device the downward irradiance Ed(λ,z) and upward radiance Lu(λ,z)were measured at nine wavelengths λ [nm]: 412, 443, 510, 550, 589, 625, 665, 683 and 710 (the measurement details are given in [16

    16. J. L. Mueller and R. W. Austin, “Ocean optics protocols for Sea-WiFS validation, revision l,” SeaWiFS technical report series. NASA Tech Memo 25, 7–12 (1995).

    ,17

    17. M. Darecki and D. Stramski, “An evaluation of MODIS and SeaWiFS bio-optical algorithms in the Baltic Sea,” Remote Sens. Environ. 89(3), 326–350 (2004). [CrossRef]

    ];
  • - temperature temp [oC] determined in situ with standard STD probes.

These parameters were measured in situ at different depths down to ca 60 m in the sea or in vitro in the laboratory in samples of sea water from different regions and depths but mostly (773 points at different stations and depths) in the Baltic Sea. On this basis 1224 values of the quantum yield of fluorescenceΦflwere obtained indirectly from an analysis of downward irradiance and upward radiance spectra, and of other spectra necessary for obtaining the relevant parameters; this was done in accordance with the two-stage scheme given in Ostrowska et al. (1997) and described below.

2.2 Used computation methods

(Stage 1) The total upward radiance Lint,fl at the nadir in the chlorophyll a fluorescence spectral band was determined from an analysis of spectral upward radiance values at the nadir Lu(λ) (containing effects due to elastic – see Rayleigh and Mie theory – and non-elastic Raman scattering, apart from fluorescence) for a number of wavelengths λ in the spectral region, coinciding with the above-mentioned chlorophyll a fluorescence band centred on 683 nm. To this end we used the algorithm for determining this fluorescence based on measurements of the water-leaving radiance at the nadir Lu(λ,z) for three wavelengths in the region of this chlorophyll a fluorescence band peaking at around 683 nm (see [6

6. M. Ostrowska, M. Darecki, and B. Woźniak, “An attempt to use measurements of sun-inducted chlorophyll fluorescence to estimate chlorophyll a concentration in the Baltic Sea,” Proc. SPIE 3222, 528–537 (1997). [CrossRef]

]). Similar methods for determining the total radiance at the nadir due to chlorophyll fluorescence have often been used by other authors employing the Fluorescence Line Height (FLH) algorithm [2

2. Y. Huot, C. A. Brown, and J. J. Cullen, “New algorithms for MODIS sun-induced chlorophyll fluorescence and a comparison with present data products,” Limnol. Oceanogr. Methods 3, 108–130 (2005). [CrossRef]

,3

3. Y. Huot, C. A. Brown, and J. J. Cullen, “Retrieval of phytoplankton biomass from simultaneous inversion of reflectance, the diffuse attenuation coefficient and sun-induced fluorescence in coastal waters,” J. Geophys. Res. 112(C6), C06013 (2007), doi:. [CrossRef]

,18

18. J. Gower, R. Doerffer, and G. A. Borstad, “Interpretation of the 685nm peak in water-leaving radiance spectra in terms of fluorescence, absorption and scattering, and its observation by MERIS,” Int. J. Remote Sens. 20(9), 1771–1786 (1999). [CrossRef]

20

20. F. E. Hoge, P. E. Lyon, R. N. Swift, J. K. Yungel, M. R. Abbott, R. M. Letelier, and W. E. Esaias, “Validation of Terra-MODIS phytoplankton chlorophyll fluorescence line height. I. Initial airborne lidar results,” Appl. Opt. 42(15), 2767–2771 (2003). [CrossRef] [PubMed]

]. As already mentioned, we realize that the FLH algorithm takes into account the reduced influence of elastic and non-elastic scattering in the total radiance spectrum Lu(λ) to only an approximate extent. It is well-known that the Raman scattering spectrum is shifted in relation to the radiation eliciting it towards long wavelengths and is selective. A more detailed analysis of the influence of this effect on radiation will be found in [21

21. T. K. Westberry and D. A. Siegel, “Phytoplankton natural fluorescence variability in theSargasso Sea,” Deep Sea Res. Part I Oceanogr. Res. Pap. 50(3), 417–434 (2003). [CrossRef]

]. In addition, we would like to draw attention to the fact that CDOM and SPM can also affect the estimated fluorescence yield. When the concentrations of these constituents are high, the effect due to elastic scattering may increase strongly, especially on large suspended particles and phytoplankton; seen against this background, the fluorescence spectrum may be relatively small. We assume, however, that these effects are largely eliminated by the FLH method. In view of the lack of suitable measurements, we have not taken these subtelties into consideration in this discussion. One has to be mindful of the fact that they are of an approximate nature and are simplified, whereas the model descriptions presented here may be a first step to further, more detailed and comprehensive analyses.

(Stage 2) The SICF quantum yield Φfl was calculated on the basis of the above-mentioned values of the radiance Lint,fl. For this we used the approximate method we derived for determining the SICF quantum yield by solving the inverse optical problem (see below).

2.3. The solution to the inverse optical problem

The inherent quantum yield of SICF in the sea at depth z Φfl(z)Φfl,z defines the ratio of the number of quanta (in the spectral band around 685 nm) emitted by phytoplankton in unit volume to the number of quanta from the entire spectral range 400 – 700 nm absorbed by its pigments.

As a result of fluorescence, phytoplankton at depth z’ emits radiation from a layer of thickness dz’ vertically upwards in an amount described by the equation (for a vertically stratified sea):

dLint,fl(z')dz'=14πΦfl(z')a˜pl(z')PAR0(z')
(1)

where

  • Lint,fl(z') [Ein m−2s−1srad−1] – the part of the total upwelling radiance in the chlorophyll a fluorescence band at the nadir due to fluorescence;
  • a˜pl(z')=[PAR0(z')]1400700apl(λ,z')E0(λ,z')dλ [m−1] - the mean phytoplankton light absorption coefficient weighted by the irradiance spectrum;
  • apl(λ,z') [m−1] - spectrum of the phytoplankton light absorption coefficient;
  • PAR0(z')=400700E0(λ,z')dλ ≈1.2PAR(z') [Ein m−2s−1] - scalar irradiance in the 400-700 nm spectral range;
  • E0(λ,z') [Ein m−2s−1nm−1] - spectrum of scalar spectral irradiance;
  • PAR(z')=400700Ed(λ,z')dλ [Ein m−2s−1] - downwelling irradiance in the 400-700 nm spectral range.
  • Ed(λ,z') [Ein m−2s−1nm−1] - spectrum of downwelling vector irradiance;
  • (4π)1 – a factor resulting from the isotropicity of fluorescence.

The contribution to the upward radiance, Lint,fl,z(z'), from the nadir at depth z, derived from the fluorescence at depth z', Lint,fl(z = z'), differs approximately by a factor linked to the coefficient of light absorption by the water body a683nm(z') or the coefficient of attenuation of radiance KL,u,683nm(z'):
dLint,fl,z(z')dz'=dLint,fl(z')dz'ezz'KL,u,683nm(z')dz'dLint,fl(z')dz'ezz'a683nm(z')dz'
(2)
It is assumed in the above equations (see the second approximated term) that the light absorption coefficient in sea water for wavelength λ = 683nm a683nm takes roughly the same value as the upward radiance attenuation coefficient for the same wavelength, i.e. a683nm(z) ≈KL,u,683nm(z). This assumption was made for practical reasons: the light absorption coefficients a683nm were not known, whereas the upward radiance attenuation coefficient KL,u,683nm(z) is defined directly by the measurement of the upward radiance vertical profiles Lu,683nm(z). Analysis of empirical data acquired by our research group back in the 1970s, mainly in the Baltic Sea and in some parts of the Atlantic Ocean [22

22. J. Dera, L. Gohs, R. Hapter, W. Kaiser, H. Prandke, W. Rüting, B. Woźniak, and S. M. Zalewski, “Untersuchungen zur Wechselwirkung zwischen optischen, physikalischen, biologischen und chemischen Umweltfaktoren in der Ostsee Geod. Geophys,” Veröff. IV, 13 (1974).

, 23

23. L. Gohs, J. Dera, D. Gedziorowska, R. Hapter, M. Jonasz, H. Prandke, H. Siegel, G. Schenkel, J. Olszewski, B. Woźniak, and S. M. Zalewski, “Untersuchungen zur Wechselwirkung zwischen den optischen, physikalischen, biologischen und chemischen Umweltfaktoren in der Ostsee aus den Jahren 1974, 1975 und 1976 Geod. Geophys,” Veröff. IV, 25 (1978).

], shows that in the red region the ratio a(λ,z)/KL,u(λ,z) does not diverge from unity by more than 20%, the standard deviation being 0.05. In our assessment this does not, in the majority of cases, introduce errors greater than 5%.

Taking into account Eq. (1), Eq. (2) takes the form:

dLint,fl,z(z')dz'=14πΦfl(z')a˜pl(z')PAR0(z')ezz'KL,u,683nm(z')dz'
(3)

The total radiance Lint,fl,z is obtained by integrating Eq. (3) with respect to depth z’ within the limits (∞ - z). If, further, we assume a simplified, homogeneous model of the medium (K0(z') = K0(z)≡K0,z, KL,u,683nm(z') = KL,u,683nm(z)≡KL,u,683nm,z, a˜pl(z')=a˜pl(z)a˜pl,z are constant and depth-independent) and bearing in mind the relationship PAR0(z')=PAR0(z)eK0(z)(z'z)PAR0,zeK0,z(z'z), the expression for Lint,fl,z can be reduced to the approximate form:

Lint,fl,z=PAR0,za˜pl,z4πzΦfl(z')e(K0,z+KL,u,683nm,z)(z'z)dz'
(4)

where K0,z [m−1] – coefficient of attenuation of scalar irradiance PAR0 with depth;

Φfl,zapp=[ze((K0,z+KL,u683nm,z)(z'z))dz']1zΦfl(z')e((K0,z+KL,u,683nm,z)(z'z))dz'==(K0,z+KL,u,683nm,z)zΦfl(z')e((K0,z+KL,u,683nm,z)(z'z))dz'
(5)

If we accept this definition of the apparent quantum yield of fluorescence, Eq. (4) describing the dependence of the radiation Lint,fl,z on the apparent quantum yield of fluorescence at depth z then takes a relatively straightforward form:
Lint,fl,z=PAR0,za˜pl,z4πΦfl,zapp1K0,z+KL,u,683nm,z
(6)
Thus from Eq. (6) we get the dependence of the apparent quantum yield of fluorescence at depth z, Φfl,zapp, on the values of Lint,fl,z, PAR0,z, a˜pl,z, K0,z and KL,u,683,z measured at that same depth:
Φfl,zapp=4πLint,fl,z[K0,z+KL,u,683nm,z]a˜pl,zPAR0,z4πLint,fl,z[K0,z+a683nm,z]a˜pl,zPAR0,z
(7)
This operational definition was used in the present paper to estimate the apparent fluorescence quantum yield Φfl,zapp at different depths in the sea, which was later used to calculate inherent quantum yields (see below).

Φfl,zΦfl,zapp=K0,z(Φfl,zapp)1dΦfl,zappdz+KL,u,683nm,zK0,z+KL,u,683nm,z
(8)

Substituting this relationship in Eq. (7), we obtain the following operational definition enabling Φfl,z to be determined from measurements of Lint,fl,z, PAR0,z, a˜pl,z, K0,z and KL,u,683nm,z as well as values of Φfl,zapp and its first derivative with respect to depth z, defined additionally for the same depth on the basis of calculations:

Φfl,z=4πLint,fl,z[K0,z(Φfl,zapp)1dΦfl,zappdz+KL,u,683nm,z]a˜pl,zPAR0,z4πLint,fl,z[K0,z(Φfl,zapp)1dΦfl,zappdz+a683nm,z]a˜pl,zPAR0,z
(9)

where the relative value of the derivative (Φfl,zapp)1dΦfl,zappdz is determined approximately from the apparent quantum yields of fluorescence at two depths calculated according to Eq. (7): zu – above depth z, and zd – below depth z, that is, in accordance with the expression:

1Φfl,zappdΦfl,zappdz1zuzdlnΦfl,zuappΦfl,zdapp
(10)

The above equations (Eqs. (7), (9)) are operational definitions of the SICF quantum yield. Similar expressions (with slight differences emerging from the fact that they used various approximation methods) were obtained by other authors (see [4

4. S. Maritorena, A. Morel, and B. Gentili, “Determination of the fluorescence quantum yield by oceanic phytoplankton in their natural habitat,” Appl. Opt. 39(36), 6725–6737 (2000). [CrossRef] [PubMed]

,5

5. J. R. Morrison, “In situ determination of quantum yield of phytoplankton chlorophyll a fluorescence: A simple algorithm, observations, and a model,” Limnol. Oceanogr. 48(2), 618–631 (2003). [CrossRef]

,24

24. D. A. Kiefer, W. S. Chamberlin, and C. R. Booth, “Natural fluorescence of chlorophyll a: relationship to photosynthesis and chlorophyll concentration in the western South Pacific gyre,” Limnol. Oceanogr. 34(5), 868–881 (1989). [CrossRef]

]).

These two differently defined yields of photosynthesis – apparent and inherent – have been calculated in this paper. But the main part of the paper analyses the dependence of the inherent quantum yield on environmental conditions (Eq. (9)). The following two facts lend support to the use of the inherent quantum yield in later analyses. Firstly, this magnitude is formally classified among the inherent optical properties, which describe elementary optical phenomena – in this case the fluorescence of chlorophyll a, which is stimulated by the absorption of solar radiation by the photosynthetic pigments in phytoplankton. It refers to unit volume of sea water, that is, to a single point where we have unequivocally defined values of physical magnitudes (irradiance conditions, temperature, chlorophyll concentration etc.) characterizing the environment and governing the optical processes occurring in it and not, as in the case of the apparent quantum yield, to a column of water of thickness (z - ∞), in which the environmental parameters governing fluorescence do not have unequivocal values and would have to be obtained from appropriate averaging for this water column. Secondly, expression that describes the quantum yield of photosynthesis, used for analysis presented in this paper(see Chapter 4 The principal assumptions and scheme of the model), refers to the unit volume of sea water. It is worth drawing attention to the fact that the apparent quantum yield (Eq. (7)) takes somewhat lower values than the inherent yield. According to our studies the factor differentiating these two yields is on average about Φfl/Φflapp1.3 [6

6. M. Ostrowska, M. Darecki, and B. Woźniak, “An attempt to use measurements of sun-inducted chlorophyll fluorescence to estimate chlorophyll a concentration in the Baltic Sea,” Proc. SPIE 3222, 528–537 (1997). [CrossRef]

].

3. Presentation of the problem

Apart from being dissipated as heat, the solar radiation energy in the sea absorbed by phytoplankton pigments is used either for the primary production of organic matter, the consequence of photosynthesis, or is re-emitted as a result of the fluorescence of chlorophyll. SICF takes place in the band of half-width 5-15 nm in the ca 683 nm wavelength region [25

25. B. Woźniak and J. Dera, Light absorption in sea water (Springer, New York, 2007).

].

Quantitatively, this alternative consumption of the energy absorbed by phytoplankton pigments during the processes of photosynthesis or SICF is correlated with the conditions in the marine environment. Three sets of factors are involved: (1) the level of PAR irradiance and the light absorption capacity of phytoplankton pigments at different depths in the sea (strictly speaking, the quantity of light absorbed by the photosynthetic pigments of phytoplankton); (2) the trophicity of the basin, the index of which is approximately and conventionally given by the chlorophyll a concentration Ca(0) in its surface waters, and (3) the temperature at different depths. Qualitatively, the nature of the relationship between the quantum yield of fluorescence Φfl and the first two sets of factors can be seen on the plots in Fig. 1
Fig. 1 Empirical dependence of the sun-induced chlorophyll a fluorescence quantum yield Φfl on the underwater irradiance PAR, recorded at all measurement points at different depths in different regions of the Baltic Sea and Atlantic Ocean (a); relations averaged for oligotrophic and mesotrophic waters with relatively low chlorophyll a concentrations and for eutrophic waters with relatively high chlorophyll a concentrations. The vertical intervals on the profiles correspond to the standard deviations of Φfl (b).
and Fig. 2
Fig. 2 Empirical dependence of the sun-induced chlorophyll a fluorescence quantum yield Φfl on the chlorophyll a concentration Ca(0)in the surface water layer, i.e. the trophic index of the basin, recorded at all measurement points at different depths in different regions of the Baltic Sea and Atlantic Ocean (a); relation averaged for relatively high levels of underwater PAR(z) irradiance [PAR(z) >20 μEin m−2s−1] and relatively low levels of underwater PAR(z) irradiance [PAR(z) <20 μEin m−2s−1]. The vertical intervals on the profiles correspond to the standard deviations of Φfl (b).
.

These illustrate the positions of the experimental points of the dependence of Φflat different depths and in different seas on PAR irradiances (Fig. 1(a)) and surface chlorophyll a concentrations Ca(0) (Fig. 2(a)). In Fig. 1(b) and Fig. 2(b) the same relations are shown for data averaged in differently defined subsets.

It is evident from the figures that at low levels of PAR irradiance, the quantum yield of fluorescence Φfl tends to rise with increasing irradiance, but decreases abruptly when certain critical threshold values are exceeded. Moreover, values of Φfl are highest in oligotrophic oceanic waters (where chlorophyll concentrations are low) and fall dramatically with increasing trophicity Ca(0). Hence, in the eutrophic waters of the Baltic Sea they may be several times and even several tens of times lower than in the Atlantic.

The dependence of Φfl on the water temperature, temp is rather weak and difficult to define (Fig. 3
Fig. 3 Empirical dependence of the quantum yield of fluorescence Φfl on temperature in the sea temp [°C] recorded at all measurement points at different depths in different regions of the Baltic Sea and Atlantic Ocean (a); averaged plot of interrelationship (dashed line). The respective vertical and horizontal sections depict the changes of standard deviations of recorded values of quantum yield of fluorescence Φfl and the temperature temp (b).
). Typically, there is a slight drop in the value of Φflwith increasing temp, which can be seen from the averaged relationship in Fig. 3(b). But this is not a universal feature, particularly in the case of Φfl recorded at high levels of irradiances in surface waters. In such a situation the tendency is often reversed, with the quantum yield of fluorescence increasing with increasing temp.

It was not possible to capture these subtleties (not shown in Fig. 3(b)) in a standard statistical analysis of our limited empirical database; this was feasible only with more complex analyses. The world literature boasts a number of papers covering various aspects of the problems involving the effects of environmental factors on phytophysiological processes in phytoplankton, including photosynthesis and fluorescence (e.g [1

1. M. Babin, J. C. Therriault, L. Legendre, B. Nieke, R. Reuter, and A. Condal, “Relationship between the maximum quantum yield of carbon fixation and the minimum quantum yield of chlorophyll a in vivo fluorescence in the Gulf of St. Lawrence,” Limnol. Oceanogr. 40(5), 956–968 (1995). [CrossRef]

,3

3. Y. Huot, C. A. Brown, and J. J. Cullen, “Retrieval of phytoplankton biomass from simultaneous inversion of reflectance, the diffuse attenuation coefficient and sun-induced fluorescence in coastal waters,” J. Geophys. Res. 112(C6), C06013 (2007), doi:. [CrossRef]

5

5. J. R. Morrison, “In situ determination of quantum yield of phytoplankton chlorophyll a fluorescence: A simple algorithm, observations, and a model,” Limnol. Oceanogr. 48(2), 618–631 (2003). [CrossRef]

,26

26. M. Babin, A. Morel, and B. Gentili, “Remote sensing of sea surface sun-induced chlorophyll fluorescence: consequences of natural variations in the optical characteristics of phytoplankton and the quantum yield of chlorophyll a fluorescence,” J. Rem. Sens. 17(12), 2417–2448 (1996). [CrossRef]

30

30. M. J. Behrenfeld, T. K. Westberry, E. S. Boss, R. T. O’Malley, D. A. Siegel, J. D. Wiggert, B. A. Franz, C. R. McClain, G. C. Feldman, S. C. Doney, J. K. Moore, G. Dall’Olmo, A. J. Milligan, I. Lima, and N. Mahowald, “Satellite-detected fluorescence reveals global physiology of ocean phytoplankton,” Biogeosc. 6(5), 779–794 (2009). [CrossRef]

].). These problems are better understood where the relationship between photosynthesis and the above-mentioned environmental factors are concerned, whereas knowledge of the dependence of fluorescence on these factors is still somewhat rudimentary. To give an example: mathematical model formulas of the dependence of the quantum yield of photosynthesis in phytoplankton on the most important factors governing phytoplankton growth in the sea have been derived and presented in several papers, including some with the present author’s participation (e.g [31

31. A. Morel, “Light and marine photosynthesis: a spectral model with geochemical and climatological implications,” Prog. Oceanogr. 26(3), 263–306 (1991). [CrossRef]

41

41. B. Woźniak, A. Krężel, M. Darecki, S. B. Woźniak, R. Majchrowski, M. Ostrowska, Ł. Kozłowski, D. Ficek, J. Olszewski, and J. Dera, “Algorithm for the remote sensing of the Baltic ecosystem (DESAMBEM). Part 1: Mathematical apparatus,” Oceanologia 50(4), 451–508 (2008).

]. and others). In contrast, no such general mathematical description in relation to fluorescence has yet been derived. As marine photosynthesis and fluorescence are alternative means of deactivating the excitation energy in phytoplankton pigments, the analysis was based on the existing model of the quantum yield of photosynthesis, derived previously by our research group [38

38. B. Woźniak, J. Dera, D. Ficek, M. Ostrowska, and R. Majchrowski, “Dependence of the photosynthesis quantum yield in oceans on environmental factors,” Oceanologia 44(4), 439–459 (2002).

,40

40. B. Woźniak, D. Ficek, M. Ostrowska, R. Majchrowski, and J. Dera, “Quantum yield of photosynthesis in the Baltic: a new mathematical expression for remote sensing applications,” Oceanologia 49(4), 527–542 (2007).

]; efforts were made to modify it in order to construct a mathematical description of the relationship between SICF of phytoplankton and environmental factors.

4. The principal assumptions and scheme of the model

4.1 Assumption 1

This model of the fluorescence yield makes use of the following mathematical expression, derived with the participation of the present author, for the quantum yield of the alternative process to fluorescence, i.e. photosynthesis (after [38

38. B. Woźniak, J. Dera, D. Ficek, M. Ostrowska, and R. Majchrowski, “Dependence of the photosynthesis quantum yield in oceans on environmental factors,” Oceanologia 44(4), 439–459 (2002).

]);

Φ=ΦMAXfafΔfc(Ca(0))fc(PARinh)fE,t
(11)

It is the product of the maximum possible yield of photosynthesis ΦMAX (equal to 0.125 mol atC Ein−1 or 1 Ein Ein−1) and five dimensionless factors taking values from 0 to 1. Analogous factors for the quantum yield of fluorescence are described below (with the Eq. (13)). Their mathematical relationships with environmental factors were established by means of empirical studies and are given and discussed in detail: the factor fa in [38

38. B. Woźniak, J. Dera, D. Ficek, M. Ostrowska, and R. Majchrowski, “Dependence of the photosynthesis quantum yield in oceans on environmental factors,” Oceanologia 44(4), 439–459 (2002).

] see also [37

37. B. Woźniak, J. Dera, D. Ficek, M. Ostrowska, R. Majchrowski, S. Kaczmarek, and M. Kuzio, “The current bio-optical study of marine phytoplankton,” Opt. Appl. 32(4), 731–747 (2002).

], factor fc(Ca(0)) in [35

35. B. Woźniak, J. Dera, and O. I. Koblentz-Mishke, “Bio-optical relationships for estimating primary production in the ocean,” Oceanologia 33, 5–38 (1992).

], and the other factors in [40

40. B. Woźniak, D. Ficek, M. Ostrowska, R. Majchrowski, and J. Dera, “Quantum yield of photosynthesis in the Baltic: a new mathematical expression for remote sensing applications,” Oceanologia 49(4), 527–542 (2007).

], see also [41

41. B. Woźniak, A. Krężel, M. Darecki, S. B. Woźniak, R. Majchrowski, M. Ostrowska, Ł. Kozłowski, D. Ficek, J. Olszewski, and J. Dera, “Algorithm for the remote sensing of the Baltic ecosystem (DESAMBEM). Part 1: Mathematical apparatus,” Oceanologia 50(4), 451–508 (2008).

]

4.2 Assumption 2

It is well known that the intensity of chlorophyll fluorescence in phytoplankton has two components: the fluorescence constant F0 and the variable fluorescence Fv (e.g [42

42. Z. Kolber and P. G. Falkowski, “Use of active fluorescence to estimate phytoplankton photosynthesis ‘in situ’,” Limnol. Oceanogr. 38(8), 1646–1665 (1993). [CrossRef]

45

45. M. Ostrowska, R. Majchrowski, D. N. Matorin, and B. Woźniak, “Variability of the specific fluorescence of chlorophyll in the ocean. Part 1: theory of classical 'in situ' chlorophyll fluorometry,” Oceanologia 42(2), 203–219 (2000).

].). It was therefore assumed that the quantum yield of fluorescence Φflcould also be expressed as a sum:

Φfl=Φfl,0+Φfl,v
(12)

where Φfl,0is the quantum yield associated with the fluorescence constant F0, and Φfl,vis the quantum yield associated with the fluorescence variable Fv.

The first of these components F0 is always measurable, regardless of whether the reaction centres in the photosynthetic apparatuses of plants (PS2 RC) are open or closed. On the other hand, the variable Fv is detectable only when PS2 RC are closed and fluorescence is taking place instead of photosynthesis.

4.3 Assumption 3

As in the case of photosynthesis, the mathematical expression for the variable component of the quantum yield of fluorescence Φfl,v can be written as the product of its theoretically possible maximum value Φfl,v,MAX (equal to 1 or 1 Ein Ein−1) and five dimensionless factors:

Φfl,v=Φfl,v,MAXffl,affl,Δffl,c(Ca(0))ffl,c(PARinh)ffl,E,t
(13)

Three of the five dimensionless factors ffl,i appearing in Eq. (13) have the same significance (and similar values) as the corresponding factors in expression Eq. (11) describing the quantum yield of photosynthesis Φ. They are:

  • - ffl,a- the non-photosynthetic pigment absorption effect factor. The excitation energy of photoprotecting pigments is not passed on to the reaction centre, so it can be neither utilized for photosynthesis nor re-emitted in the ca 683 nm spectral band by the chlorophyll in that centre. Hence ffl,a=fa;
  • - ffl,Δ- the inefficiency factor in energy transfer and charge recombination. This describes the disturbances to the function of PS2 RC, preventing the uptake of excitation energy from the pigments, which could later be used for photosynthesis or be re-emitted in the form of chlorophyll fluorescence in the ca 683 nm band. Hence ffl,Δ=fΔ;
  • - ffl,c(PARinh) - the factor describing the reduction in the portion of functional PS2 RC as a result of photoinhibition (fc(PARinh)). These centres are damaged, as a result of which, as before, there is no uptake of energy that could later be utilized for photosynthesis or be re-emitted in the form of chlorophyll fluorescence in the ca 683 nm band. Hence ffl,c(PARinh)=fc(PARinh).

On the other hand, the factor fE,t describing the effect of irradiance and temperature on photosynthesis differs from the factor ffl,E,t, which expresses the effect of these parameters on fluorescence. It is well known that fE,t, the classic dependence of photosynthesis on light and temperature (e.g [31

31. A. Morel, “Light and marine photosynthesis: a spectral model with geochemical and climatological implications,” Prog. Oceanogr. 26(3), 263–306 (1991). [CrossRef]

,34

34. J. Dera, Underwater Irradiance as a Factor Affecting Primary Production (Diss. and Mon. IO PAN, Sopot 7, 1995).

,47

47. B. Woźniak, K. Bradtke, M. Darecki, J. Dera, J. Dudzińska-Nowak, L. Dzierzbicka-Głowacka, D. Ficek, K. Furmańczyk, M. Kowalewski, A. Krężel, R. Majchrowski, M. Ostrowska, M. Paszkuta, J. Stoń-Egiert, M. Stramska, and T. Zapadka, “SatBałtyk - a Baltic environmental satellite remote sensing system - an ongoing project in Poland. Part 1: assumptions, scope and operating range,” Oceanologia 53(4), 897–924 (2011), doi:. [CrossRef]

].), also known as the light curve of photosynthetic efficiency at a given temperature, defines the relative number of open PS2 RC, and is consequently proportional to the quantum yield of photosynthesis. But the yield of the alternative process, i.e. fluorescence, is proportional to the relative number of closed PS2 RC, that is, to the factor ffl,E,t, which when summed with fE,tgives unity. Thus ffl,E,t=1fE,t.

Likewise, the trophicity of a water body affects the photosynthetic yield in a different way to the fluorescence yield. So, as in the case of the factors ffl,E,tand fE,t, factor ffl,c,Ca(0), describing the relation between the number of functioning PS2 RC and the trophicity of the water body, when summed with fc,Ca(0)gives unity. This means that ffl,c,Ca(0)=1fc,Ca(0).

Based on the above assumptions, the mathematical description of the dependence of the variable component of the quantum yield of natural phytoplankton fluorescence on the trophicity of a water body, the light conditions there and the temperature at different depths in the water column is expressed by Eq. (13) and by the partial expressions for the individual compnent and factors given below in set of equations:
ffl,a=a˜pl,PSP*a˜pl*
(14)
where a˜pl*=f(Ca(0),τ,PAR(0))anda˜pl,PSP*=f(Ca(0),τ)are given in [37

37. B. Woźniak, J. Dera, D. Ficek, M. Ostrowska, R. Majchrowski, S. Kaczmarek, and M. Kuzio, “The current bio-optical study of marine phytoplankton,” Opt. Appl. 32(4), 731–747 (2002).

,38

38. B. Woźniak, J. Dera, D. Ficek, M. Ostrowska, and R. Majchrowski, “Dependence of the photosynthesis quantum yield in oceans on environmental factors,” Oceanologia 44(4), 439–459 (2002).

]
ffl,Δ0.408±0.105
(15)
ffl,c(PARinh,temp)=exp(4860746PAR22.23temp/10)
(16)
where PAR=PAR(0)eτ
ffl,E,t=1[1exp(PURPSP*5.2371072.03temp10)]5.2371072.03temp10PURPSP*
(17)
where PURpsp*=PARa˜pl,PSP*
ffl,c(Ca(0))=0.440.44+Ca(0)0.66
(18)
where: Ca(0) [mg m−3] – total chlorophyll a concentration in the surface water layer, PAR [μEin m−2s−1] – downward irradiance in the PAR spectral range, PURPSP [μEin m−2s−1]– mass-specific radiation flux absorbed by photosynthetic pigments, temp [C] – ambient water temperature,τ [dimensionless] – optical depth in the sea, a˜pl*,a˜pl,PSP* [m2(mg tot.chla)−1] – mean mass-specific coefficient of light absorption of all, and only photosynthetic (PSP), pigments weighted by the irradiance spectrum, respectively.

4.4 Assumption 4

Values of the quantum yield of fluorescence Φfl,0associated with the fluorescence component F0 were determined for all the measurement points on the basis of the following equation:

Φfl,0=Φfl,measΦfl,v,calc
(19)

where:

Φfl,meas– empirical values of the total quantum yield of fluorescence determined from the measurements mentioned in the Introduction according to the methodology described in 2.3;

Φfl,v,calc– the quantum yield of fluorescence associated with the fluorescence variable Fv and calculated on the basis of Eq. (13) and the factors ffl,i (Eqs. (14) to (18)).

Φfl,0=0.00712Ca(0)0.402
(20)

5. Validation of the model description; final remarks

The mathematical description of the relationship between the quantum yield of fluorescence Φfl and environmental factors, derived and presented in this paper (see Eqs. (12)-(18), (20)), enables its variability under different conditions in the water column down to a depth of ca 60 m to be tracked. Figure 5
Fig. 5 Dependence of the model yield Φfl (calculated on the basis of Eqs. (12)-(18),(20) on the underwater irradiance PAR in different trophic types of basins with surface chlorophyll concentrations Ca(0) varying from 0.035 to 7 mg m−3: for a surface irradiance PAR = 1500 [μEinm2s1] and temp = 15C (a); for a surface irradiance PAR varying from 300 to 1500 (every 300) [μEinm2s1] and temp = 15C(b); for different temperatures in the sea varying from 5 to 30 (every 5) C and a surface irradiance PAR = 1500 [μEinm2s1] (c).
gives the modelled dependences of this yield on the light conditions in different trophic types of water, where surface chlorophyll Ca(0) varies from 0.035 to 7 mg m−3 (a), the surface irradiance PAR varies from 300 to 1500 μEinm2s1 (b), and temp varies from 5 to 30C(c). Detailed analysis of these plots reveals certain limitations of the model, however. For example, the modelled values of this yield for superoligotrophic oceanic waters appear to exceed the empirical values (compare Fig. 1 and Fig. 3); conversely, the fluorescence yield Φfl,calc calculated for supereutrophic waters is somewhat underestimated. This is also evident from Fig. 6(a)
Fig. 6 Comparison of quantum yields of fluorescence: determined empirically (Φfl,meas) in different water basins and at different depths and calculated with the aid of the present model (Φfl,calc) (a); histogram of the ratio Φfl,calc/Φmeas (b).
, which compares the fluorescence yield determined using the present model Φfl,calc with the corresponding empirical values of Φfl,meas based on measurement data. Figure 6(b) shows a histogram of the ratio Φfl,calc/Φfl,meas. The errors of this approximation are given in Table 2

Table 2. Errors of estimation of the fluorescence quantum yield Φfl

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: they are not much greater than those for the earlier model for photosynthesis (standard error factor for photosynthesis x = 1.7 – see [40

40. B. Woźniak, D. Ficek, M. Ostrowska, R. Majchrowski, and J. Dera, “Quantum yield of photosynthesis in the Baltic: a new mathematical expression for remote sensing applications,” Oceanologia 49(4), 527–542 (2007).

], for fluorescence x = 1.74). In the interests of strict accuracy, we should add that the discontinuities and sharp local minima visible on some of the plots in Fig. 5, which are particularly distinct with regard to oligotrophic waters, are not a reflection of reality but represent artifacts due to the imperfections of the statistically approximated functional relationships. The statistical description of these relationships obtained here could, if subjected to statistical analyses of greater penetration, describe the empirical data with greater precision and accuracy. However, such a more detailed analysis would only be meaningful with respect to a much more extensive data set.

To recapitulate, the aim of this work has been achieved. A mathematical model has been derived to describe the dependence of the Sun-induced Chlorophyll Fluorescence on a variety of environmental conditions across a wide range of their recorded natural variability. As mentioned earlier, this model refers to the quantum yield Φfl in the surface waters of basins down to a depth of about 60 m. In the case of oligotrophic basins this corresponds to a surface layer of water of approximately half the thickness of the euphotic layer; in supereutrophic waters, this surface layer may be coincident with the whole euphotic layer and possibly witha layer of water even twice as thick. With the formulation of such a model, it will be possible, among other things, to account for the dependence of the quantum yield of fluorescence on environmental factors in fluorescence methods of determining different characteristics of marine plant communities. Given the rather sparse experimental material available, these analyses are of a preliminary nature; they will be repeated in the future on a richer set of data and expanded to include a larger number of environmental factors affecting the fluorescence and photosynthesis of phytoplankton, in particular, the dependence of the quantum yield of fluorescence on the nutrient content in the sea, based on the mathematical description given in [38

38. B. Woźniak, J. Dera, D. Ficek, M. Ostrowska, and R. Majchrowski, “Dependence of the photosynthesis quantum yield in oceans on environmental factors,” Oceanologia 44(4), 439–459 (2002).

].

These results can be applied in the development of new fluorometric methods (remote or direct) for investigating marine algae, particularly the process of photosynthesis [47

47. B. Woźniak, K. Bradtke, M. Darecki, J. Dera, J. Dudzińska-Nowak, L. Dzierzbicka-Głowacka, D. Ficek, K. Furmańczyk, M. Kowalewski, A. Krężel, R. Majchrowski, M. Ostrowska, M. Paszkuta, J. Stoń-Egiert, M. Stramska, and T. Zapadka, “SatBałtyk - a Baltic environmental satellite remote sensing system - an ongoing project in Poland. Part 1: assumptions, scope and operating range,” Oceanologia 53(4), 897–924 (2011), doi:. [CrossRef]

,48

48. B. Woźniak, K. Bradtke, M. Darecki, J. Dera, J. Dudzińska-Nowak, L. Dzierzbicka-Głowacka, D. Ficek, K. Furmańczyk, M. Kowalewski, A. Krężel, R. Majchrowski, M. Ostrowska, M. Paszkuta, J. Stoń-Egiert, M. Stramska, and T. Zapadka, “SatBałtyk - a Baltic environmental satellite remote sensing system - an ongoing project in Poland. Part 2: practical applicability and preliminary results,” Oceanologia 53(4), doi:. 925, 925–958 (2011). [CrossRef]

].

Where:

ε=N1iεi(εi=(Xi,CXi,M)/Xi,M,Xi,M- measured values, Xi,C - estimated values) - mean systematic error;

σε=(((εi<ε>)2)/N)1/2 - standard deviation (statistical error) of ε; εg=10[log(Xi,C/Xi,M)]1 (log(Xi,C/Xi,M)- mean of log(Xi,C/Xi,M)) - mean logarithmic error);

x=10σlog (σlog- standard deviation of the log(Xi,C/Xi,M)) - standard error factor; σ+=x1σ=(1/x)1 - statistical logarithmic errors.

Acknowledgments

The study was partially financed by MNiSW (Ministry of Science and Higher Education) within the framework of IO PAN's statutory research and also as part of MNiSW research project N306 1391 33 in 2008-2010. Partial support for this study was also provided by the project “Satellite Monitoring of the Baltic Sea Environment – SatBałtyk” funded by the European Union through European Regional Development Fund contract No. POIG 01.01.02-22-011/09

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B. Woźniak, K. Bradtke, M. Darecki, J. Dera, J. Dudzińska-Nowak, L. Dzierzbicka-Głowacka, D. Ficek, K. Furmańczyk, M. Kowalewski, A. Krężel, R. Majchrowski, M. Ostrowska, M. Paszkuta, J. Stoń-Egiert, M. Stramska, and T. Zapadka, “SatBałtyk - a Baltic environmental satellite remote sensing system - an ongoing project in Poland. Part 1: assumptions, scope and operating range,” Oceanologia 53(4), 897–924 (2011), doi:. [CrossRef]

48.

B. Woźniak, K. Bradtke, M. Darecki, J. Dera, J. Dudzińska-Nowak, L. Dzierzbicka-Głowacka, D. Ficek, K. Furmańczyk, M. Kowalewski, A. Krężel, R. Majchrowski, M. Ostrowska, M. Paszkuta, J. Stoń-Egiert, M. Stramska, and T. Zapadka, “SatBałtyk - a Baltic environmental satellite remote sensing system - an ongoing project in Poland. Part 2: practical applicability and preliminary results,” Oceanologia 53(4), doi:. 925, 925–958 (2011). [CrossRef]

OCIS Codes
(010.4450) Atmospheric and oceanic optics : Oceanic optics
(260.2510) Physical optics : Fluorescence

ToC Category:
Atmospheric and Oceanic Optics

History
Original Manuscript: March 6, 2012
Revised Manuscript: September 20, 2012
Manuscript Accepted: September 21, 2012
Published: September 25, 2012

Citation
Miroslawa Ostrowska, "Model of the dependence of the sun-induced chlorophyll a fluorescence quantum yield on the environmental factors in the sea," Opt. Express 20, 23300-23317 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-21-23300


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  48. B. Woźniak, K. Bradtke, M. Darecki, J. Dera, J. Dudzińska-Nowak, L. Dzierzbicka-Głowacka, D. Ficek, K. Furmańczyk, M. Kowalewski, A. Krężel, R. Majchrowski, M. Ostrowska, M. Paszkuta, J. Stoń-Egiert, M. Stramska, and T. Zapadka, “SatBałtyk - a Baltic environmental satellite remote sensing system - an ongoing project in Poland. Part 2: practical applicability and preliminary results,” Oceanologia 53(4), doi:. 925, 925–958 (2011). [CrossRef]

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