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Quantum yield of photosynthesis in the Baltic: a new

mathematical expression

for remote sensing applications[1]


Baltic Sea Quantum yield of photosynthesis Remote sensing

Bogdan Wozniak1'2 Dariusz Ficek2 Miroslawa Ostrowska1 Roman Majchrowski2 Jerzy Dera1

1 Institute of Oceanology, Polish Academy of Sciences,

Powstancow Warszawy 55, PL-81-712 Sopot, Poland; e-mail: wozniak@iopan.gda.pl

2 Institute of Physics, Pomeranian Academy,

Arciszewskiego 22B, PL-76-200 Slupsk, Poland; e-mail: ficek@apsl.edu.pl

Received 10 September 2007, revised 26 November 2007, accepted 28 November 2007.

Statistical relationships between the quantum yield of photosynthesis Ф and selected environmental factors in the Baltic have been established on the basis of a large quantity of empirical data. The model formula is the product of the theoreti­cal maximum quantum yield Фмлх =0.125 atomC quantum-1 and five dimension-

less factors fi taking values from 0 do 1: Ф = ФмлхІа ІА fc(ca(0)) fc(PARinh) fE,t.

To a sufficiently good approximation, each of these factors fi appears to be


dependent on one or at most two environmental factors, such as temperature, underwater irradiance, surface concentration of chlorophyll a, absorption properties of phytoplankton and optical depth. These dependences have been determined for Baltic Case 2 waters. The quantum yield Ф, calculated from known values of these environmental factors, is then applicable in the model algorithm for the remote sensing of Baltic primary production. The statistical error of the approximate quantum yields Ф is 62%.

1. Introduction

The quantum yield of phytoplankton photosynthesis Ф1 in the sea is a key function enabling the rate of primary production of organic matter to be defined on the basis of the quantity of light energy absorbed by the pigments of that phytoplankton. Ф expresses the efficiency of the conversion of CO2 molecules fixed in the biomass, or of the evolution of O2 molecules, per quantum of light absorbed (Koblentz-Mishke et al. 1985, Kirk 1994),


pB pB pB

Ф = —-= —--и---, (1)

PUR*     PAR0a*pl     l.2PARa*i V ;


PB [molC (mg tot. chl a)-1 s-1] - rate of photosynthesis, (also known as the assimilation number), i.e., primary production p in unit time referred to unit mass of chlorophyll a;

PUR* [Ein (mg tot. chl a)-1 s-1] - the number of quanta absorbed by phytoplankton pigments in unit time referred to unit mass of chloro­phyll a;

PAR0 [Ein m-2 s-1]and PAR [Ein m-2 s-1] - scalar and downward irradiances by sunlight in the PAR spectral range (400-700 nm);

apt [m2 (mg tot. chl a)-1] - mean chlorophyll-specific absorption coefficient for phytoplankton in vivo weighted by the downward irradiance spectrum Ed(X) [Ein m-2 s-1 nm-1], i.e.,

700 nm

a*pl = (PAR)-1   Ed(\)a*pl(X)d\ (2a)

400 nm


700 nm


400 nm

(PAR,)-11.2  у   Ed(X)a*pi (X)dX, (2b)

The objective of the present research was to derive a mathematical model of the quantum yield of photosynthesis applicable in algorithms for the remote sensing of primary production in the Baltic. Because of the complexity and variability of the mix of substances in Baltic waters, this model of the quantum yield's dependence on the environmental parameters in this sea will necessarily be more of a rough approximation than the oceanic model. The model description of the quantum yield of photosynthesis Ф in the Baltic that we now present is the result of the relevant modelling procedure, preceded by a thorough statistical analysis of the extensive bank of empirical data gathered in various regions of the Baltic during cruises of r/v 'Oceania' (IO PAS[2] Sopot) and r/v 'Baltica' (MIR[3] Gdynia) in 1999-2005.

2. The research: description and results

The following mathematical expression for the quantum yield of photo­synthesis Ф in the Baltic Sea was derived: it is the product of the theoretical maximum yield Фтах (equal to 0.125 molC Ein-1, i.e., 0.125 atomC quantum-1), and five (not six, as for oceanic waters) dimensionless factors:

Ф = ФMAXfa fA fc(Ca(0)) fc(PARinh) fE,t. (4)

The dependence of the separate factors fi on the environmental pa­rameters and their magnitude are given in Table 1, together with their range of variability in the Baltic, estimated from the model. Four out of the five dimensionless factors fi in eq. (4) have the same meaning as their counterparts in the expression for Ф in oceanic waters (see eq. (3)): the factor accounting for the non-photosynthetic pigment absorption effect (fa), the factor accounting for inefficiency in energy transfer and charge recombination (fa), the factor describing the reduction in the portion of functional PS2 RC as a result of photoinhibition (fc(pARinh)), and the factor related to the classic dependence of photosynthesis on light and temperature


However, the effects of the lowering of the quantum yield that result from a smaller number of functional PS2 reaction centres (PS2 RC), in turn due to nutrient deficiency (see factor fc(Ninorg) in eq. (3)), photoinhibition (fc(PARinh) in eq. (3)) and the disappearance of these centres at large depths (fc(r) in eq. (3)), are distributed somewhat differently in the new model expression. The total effect on the value of Ф, which for oceanic waters is

described by the product of three factors - fc = fc{Ninorg) fc(r) fc(PARinh)

Table 1. Factors fi determining the quantum yield of photosynthesis in the Baltic Sea expressed by mathematical formulas describing their dependence on abiotic environmental factors at different optical depths т


Mathematical description of the dependence

Typical range of variability in the Baltic

1 2



t     Ki,psp       .      Ki =f{Ca{0),T,PAR{0)) Та = -, where

0.5-1 (about 2 times)


fA ~ 0.408 ± 0.105

nearly constant



7c(ca(o))     0.15 + Ca(0)2-48


(about 2.5 times)


/ -4860746 PAR2 \

Tc(parinhttsmp) - ЄХР

V      2.23-n^ J

0.85-1 (less than 1.2 times)


Г           /       -PUR*pSp       \\ 5.237ХІ0-7 2.03^ fE,t=   1 exp

\5.237xl0-7 2.03-n^ J\ fuhpsp

0.05-1 (about 20 times)


Ф - as the product, altogether




(about 120 times)


Ф - as observed values

0.001-0.075 (about 100 times)


Ca(0) - surface total chlorophyll a concentration [mg tot. chl a m~3],

PAR - downward irradiance in the PAR spectrum range [Ein m~2 s_1],

PURpSP - radiation flux absorbed by photosynthetic pigments [Ein (mg tot. chl a)-1 s_1 ],

temp - ambient water temperature [°С].

Explanations to item 1 - the full mathematical description of the expression for fa is given by eqs. (4), (9), (10) and in Tables 1, 2, 3 in Wozniak et al. (2007), this volume.

- is described for Baltic waters by the product of two factors: fc = fc(Ca(0)) fc(PARinh). The first of these factors, fc(Ca(0)), describes the relation between the number of functional PS2 RC and the surface concentration of chlorophyll a, Ca(0), i.e., the trophic index. In principle, it describes the same effects as the factor fc(N ) in the oceanic model for Ф and is the upshot of the close links between the nutrient concentration in a basin and its trophic index (see, e.g., Wozniak & Dera (2007), chap. 6.1.1). The second factor, standing for the reduction in the portion of PS2 RC in expression (4) for the Baltic, describes, as in the oceanic model (eq. (3)),

the reduction in this portion of PS2 RC due to photoinhibition fc(PARinh). In our description of Ф for the Baltic we have omitted the factor fc(r).The effects described by this factor seem to be of little significance in the Baltic - we certainly did not notice any in our analyses.

The dependences of the aforementioned five dimensionless factors fi on environmental parameters, set out in Table 1, were established from empirical research followed by statistical analysis and mathematical modelling in the following three stages.

2.1. Stage I analysis of factor fa

To begin with, the effect of the presence of photoprotecting carotenoids (PPC) in the photosynthetic apparatus of phytoplankton on the quantum yield of photosynthesis has to be accounted for. As we know, the energy absorbed by these pigments is not used for photosynthesis. Hence, the true quantum yield of photosynthesis is the ratio of the rate of photosynthesis PB to the number of quanta of PUR*PSP absorbed solely by the photosynthetic pigments (PSP), i.e., = PB/PUR*PSP.The quantum yield Ф defined by eq. (1) is therefore smaller than the true value by the factor fa = PUR*PSP/PUR* (where PUR* = PUR*pl, i.e., the quanta absorbed by all phytoplankton pigments). Since PUR*PSP = PAR0 apl PSP and PUR* = PAR0 a*pl, this factor can be described as the ratio of two mean specific absorption coefficients (by phytoplankton aipl an d by photosynthetic pigments only apl PSP) weighted by the irradiance spectrum (eq. (2)):

fa = apl,PSP/apl. (5)

In our previous papers (Ficek et al. 2000a, Wozniak et al. 2003) we showed that fa measured in oceanic waters ranges from c. 0.3 to almost unity and depends largely on the trophic index of the waters in question Ca(0), the level of natural irradiance just below the sea surface, PAR(0) and the optical depth in these waters т = TPAR.Factor fa usually tends to increase as the values of these three variables do so (Ca(0), PAR(0) and т or z). Our latest analyses of Baltic Sea data have shown that here, too, the values of fa depend primarily on these three parameters, but that this dependence is of a somewhat different nature. In particular, the dependence on the chlorophyll concentration Ca(0) is more complex and harder to define precisely. The point is that at the same optical depths in the Baltic and under the same irradiance conditions, fa measured in different regions of this sea takes different values: these are usually smallest in waters of intermediate trophic index, with concentrations Ca(0) ranging from c. 1.7 to 7.5 mg tot. chl a m-3. On the other hand, they are higher both when Ca(0) is lower in value, i.e., in waters of lower trophic index,

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