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Remote sensing of vertical phytoplankton pigment distributions in the Baltic: new mathematical
expressions. Part 3: Non-photosynthetic pigment absorption factor
Baltic Sea Non-photosynthetic pigments absorption factor fa Vertical distribution Remote sensing
Bogdan Wozniak1'2 Roman Majchrowski2 Miroslawa Ostrowska1 Dariusz Ficek2 Justyna Kunicka1 Jerzy Dera1
1 Institute of Oceanology, Polish Academy of Sciences,
Powstancow Warszawy 55, PL-81-712 Sopot, Poland; e-mail: firstname.lastname@example.org
2 Institute of Physics, Pomeranian Academy,
Arciszewskiego 22B, PL-76-200 Slupsk, Poland; e-mail: email@example.com
Received 1 August 2007, revised 5 November 2007, accepted 9 November 2007.
This paper, part 3 of the description of vertical pigment distributions in the Baltic Sea, discusses the mathematical expression enabling the vertical distributions of the non-photosynthetic pigment absorption factor fa to be estimated. The factor fa is
directly related to concentrations of the several groups of phytoplankton pigments and describes quantitatively the ratio of the light energy absorbed at given depths by photosynthetic pigments to the light energy absorbed by all the phytoplankton pigments together (photosynthetic and photoprotecting). Knowledge of this factor is highly desirable in the construction of state-of-the-art 'light-photosynthesis' models for remote-sensing purposes.
The expression enables fa to be estimated with considerable precision on the basis of two surface parameters (available from satellite observations): the total chlorophyll a concentration at the surface Ca(0) and the spectral downward irradiance Ed(X, 0) just below the sea surface. The expression is applicable to Baltic waters from the surface down to an optical depth of т « 5.
The verification of the model description of fa was based on 400 quasi-empirical values of this factor which were calculated on the basis of empirical values of the following parameters measured at the same depths: Ed(X, z) (or also PAR(z)), api (X, z), and the concentrations of all the groups of phytoplankton pigments Ca(z) and Cj (z) (where j denotes in turn chl 6,chl c, PSC, phyc, PPC). The verification shows that the errors in the values of the non-photosynthetic pigment absorption factor fa estimated using the model developed in this work are small: in practice they do not exceed 4%.
Besides the mathematical description of the vertical distribution of fa,this paper also discusses the range of variation of its values measured in the Baltic and its dependence on the trophic index of a basin and depth in the sea. In addition, the similarities and differences in the behaviour of fa in Baltic and oceanic basins are compared.
This paper is the last in a series of three, whose objective has been to find mathematical formulas to describe the vertical distributions of phytoplankton pigments in the Baltic Sea. These formulas have been adapted for application in remote-sensing algorithms for monitoring the Baltic ecosystem. The two previous articles in this series (Ostrowska et al. 2007 and Majchrowski et al. 2007, both in this volume) give mathematical formulas approximating the vertical distributions of total chlorophyll a and the concentrations of the other phytoplankton accessory pigments (photosynthetic PSP1 and photoprotecting PPP) in the Baltic. They enable the concentrations of these pigments Cj(z) to be estimated at different depths in the sea from known surface total chlorophyll a concentrations Ca(0) and known surface irradiance conditions (the spectral downward irradiance Ed(X,0)), both magnitudes that can be estimated by remote-sensing techniques (see, e.g., Ruddick et al. 2000, Kr^zel 2001, Sathyendranath et al. 2001, Darecki et al. 2003). The present paper discusses
the mathematical description of the vertical distributions in the Baltic of the non-photosynthetic pigment absorption factor fa(z), which is strictly related to the vertical distributions of photosynthetic and photoprotecting pigments in marine phytoplankton. This factor is crucial to the development of 'light-photosynthesis' models, particularly to the modelling of the quantum yield of photosynthesis (see Ficek et al. 2000, Wozniak et al. 2007, this volume). Its significance will be explained below.
Under natural conditions in the sea, phytoplankton produces not only chlorophyll a, but also various types of accessory photosynthetic and photoprotecting pigments that absorb solar energy. By absorbing part of the light reaching the phytoplankton cell, the photoprotecting carotenoids (PPC) protect chlorophyll a from photo-oxidation (Bidigare et al. 1990, Wozniak et al. 2007, this volume). The energy absorbed by photoprotecting pigments is not used for photosynthesis. That is why photoprotecting pigments (PPP) are often referred to as non-photosynthetic pigments (Bidigare et al. 1990, Babin et al. 1996a,b). For photosynthesis, only the energy absorbed by the photosynthetic pigments (PSP), i.e., by chlorophylls a, b, c, photosynthetic carotenoids (PSC) and phycobilins, is consumed. The relations between the part of the energy absorbed by phytoplankton cells that can be used in photosynthesis and the total energy absorbed by these cells are described by the above-mentioned dimensionless factor fa.Itistheratio2 of the solar energy absorbed at a given depth by the photosynthetic pigments in phytoplankton, the so-called photosynthetically usable radiation (PURPSP(z)), to the amount of that energy absorbed by all the phytoplankton pigments together (PUR(z)), that is, the sum of the energy absorbed by the photosynthetic pigments PURPSP(z) and by the photoprotecting pigments PURPPP(z):
fa(z)= PURpsp(z)/PUR(z)= PURpsp(z)/(PURpsp(z) +
The upshot is that fa is determined by the mutual relationship between the concentrations of photosynthetic CPSP and photoprotecting pigments Cppp and can theoretically take values from 0 to 1 (fa =0if no PSP are present in the phytoplankton, i.e., when CPSP = 0,so PURPSP = 0; fa = 1 if no PPP are present in the phytoplankton, i.e., when CPPP = 0,so PURppp = 0).
In our earlier studies on oceanic Case 1 waters (for details, see Ficek et al. 2000), it was found that fa usually takes values from 0.32 to 1, depending on the trophic index of the waters in question, the depth in the sea, and the irradiance conditions. An analytical description of these profiles of fa(T) was compiled as a function of three variables: the trophic index of the basin, Ca(0), the optical depth in the sea т, and the daily mean scalar irradiance just below the sea surface PARn(0) (see eqs. (8),
(9) and (10), and Tables 1, 2 and 3 in Ficek et al. 2000). Figure 1a (see
p. 520, this paper) shows a plot illustrating model depth profiles of fa(T) in Case 1 waters of different trophic indices (calculated for the mean daily irradiance in the temperate zone PAR(0) = 695 //Ein m-2 s-1): in Case 1 waters fa rises with trophic index, its value being the smallest in oligotrophic and the highest in eutrophic waters. At the same time fa usually rises in value with increasing depth in the sea. This observation can be explained as follows: the number of high-energy radiation quanta from the short-wave end of the visible spectrum, i.e., capable of photo-oxidising chlorophyll, decreases with depth; hence, phytoplankton cells need smaller and smaller quantities of photoprotecting carotenoids (PPC) to protect them from this high-energy radiation, and PPC production declines accordingly. That is why the relative content of PPC produced by phytoplankton decreases with increasing depth. Consequently, fa increases with both depth and the trophic index of the waters. In extreme cases, for example, in supereutrophic waters like class E5, the pigments present even at quite shallow depths are mostly photosynthetic ones, and fa takes values close to 1. For the case illustrated in Figure 1a, fa varies from 0.5 to 1. This was the result obtained for the mean irradiance conditions typical of the temperate zone. On the other hand, with the extremely high daily irradiances characteristic of equatorial regions, e.g., PAR(0)= 1300 //Ein m-2 s-1, the minimum value of fa is about 0.32.
In the initial phase of the search for an expression to describe the vertical distributions of this non-photosynthetic pigment factor fa(z)in Baltic waters, the utility of the earlier oceanic model (Ficek et al. 2000) was assessed. The results were not encouraging. Therefore, new model formulas
of this kind had to be developed specially for the Baltic by way of the mathematical modelling procedures and calculations presented below.
2. Analysis and modelling scheme
The following well-known relations between the quantities of energy absorbed (PUR and PURPSP) on the one hand, and the spectral distributions of the downward irradiance Ed(X) (or the scalar irradiance E0(X))and the absorption spectra of photosynthetic pigments only api>psp(X) on the other were substituted in eq. (1):
700 nm 700 nm
J E0(X)api(X)dXи1.2 у Ed(X)api(X)dX, (2)
PUR = J E0(X)api(X)dX и 1.2
400 nm 400 nm
700 nm 700 nm
PURpsp = j E0(X)apipsp(X)dX и 1.2 J Ed(X)Opitpsp(X)dX. (3) 400 nm 400 nm
Then, by applying the relationships apt = ap\/Ca and a*t PSP = apt,psp/Ca, the following expression is obtained for the factor fa at an optical depth in the sea т:
a*i, apt psp - the respective mean specific absorption coefficients of chlorophyll a weighted by the irradiance spectrum in the 400-700 nm range for all phytoplankton pigments and for photosynthetic phyto-plankton pigments only:
700 nm 700 nm
1 / £o(A)a;,(A)dA^-^ J Ed(X)a*pl(X)dX, (5)
PAR0 J "K 'PAR
400 nm 400 nm
psp = paRq J Eo(X)a*l PSP(X)dX^ 400 nm
PAR j EdW4i,PSpWX; (6) 400 nm
PAR0 and PAR - the respective total scalar and downward irradiances in the 400-700 nm spectral range:
700 nm 700 nm
PAR0 = j E0(X)dX and PAR = j Ed(X)dX. (7) 400 nm 400 nm
Note that values of fa(T) can be determined from known chlorophyll-specific coefficients of light absorption by photosynthetic pigments (а*г PSP) and by all phytoplankton pigments (а*г), averaged with the weight of the spectral distributions of the underwater irradiances. According to the definitions of these absorption coefficients (eqs. (5) and (6)), it is possible to determine them, provided that we have the following data:
• the spectrum of scalar irradiance E0(X, z) and the total scalar irradiance in the 400-700 nm spectral range PAR0(z) at different depths in the sea (or the vector irradiance PAR(z),asthereis a simple, approximate relation between them: PAR0 и 1.2 PAR);
• the spectrum of the total absorption coefficients for all phytoplankton pigments api(X, z) and for photosynthetic pigments apl>PSP(X, z), but only at the same depths as E0(X, z).