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Variability of the specific fluorescence of chlorophyll in the o cean. Part 1. Theory of classical in situ chlorophyll fluorometry*

OCEANOLOGIA, 42 (2), 2000. pp. 203 219. 2000, by Institute of Oceanology PAS.
KEYWORDS

Plant luminescence Phytoplankton fluorescence in the ocean Specific chlorophyll fluorescence in vivo Theory of classical fluorometry Fluorometric method

Miroslawa Ostrowska 1 Roman Majchrowski 2 Dimitrii N. Matorin 3 Bogdan Woniak 1,2
1

Institute of Oceanology, Polish Academy of Sciences, PowstacСw Warszawy 55, PL81712 Sopot, Poland; e-mail: ostra@iopan.gda.pl
2

Institute of Physics, Pedagogical University, Arciszewskiego 22 B, PL76200 Slupsk, Poland
3

Department of Biophysics, Faculty of Biology, Moscow State University, Moscow, 117218 Russia
Manuscript received 17 March 2000, reviewed 12 April 2000, accepted 30 April 2000.

Abstract The range of variability of the fluorescence properties of marine phytoplankton in different trophic types of seas and at different depths in the sea is analysed theoretically. An attempt is also made to interpret artificially induced in situ fluorescence measured with submersible fluorometers. To do this, earlier optical
* This paper was presented at the `Second Workshop on Luminescence and Photosynthesis of Marine Phytoplankton', SopotParaszyno, 1115 October 1999.

204

M. Ostrowska, R. Ma jchrowski D. N. Matorin, B. Woniak

models of light absorption by phytoplankton (see Woniak et al. 2000, this volume) and actual empirical data were applied. A straightforward theoretical model of artificially photoinduced phytoplankton fluorescence accounting for the complex influence of different photophysiological characteristics of phytoplankton and the optical characteristics of the instrument has been worked out. A physical method of determining chlorophyll a concentrations in seawater from fluorescence measured in situ with contact fluorometers can be based on this model.

1. Introduction
The standard techniques for measuring chlorophyll a concentrations in phytoplankton samples taken from the sea using traditional sp ectrophotometry or fluorometry (Lorenzen 1967, Strickland & Parsons 1968, Jeffrey & Humphrey 1975) are exp ensive, time-consuming and ineffective. Researchers have therefore b een trying to find a method of determining the chlorophyll a concentration from in situ fluorescence measurements. These would cover not only fluorescence induced naturally by sunlight (Neville & Gower 1977, Grassl 1986, Babin et al. 1996, Ostrowska et al. 1997) but also that induced by artificial light sources (see, for example, Lorenzen 1966, Loftus & Seliger 1975, Slovacek & Hannan 1977, Karabashev 1987, Hundahl & Holck 1989, Shavykin & Ryzhov 1989, Ostrowska 1990, Shavykin 1990, Kolb er & Falkowski 1993). Measurements of the latter are either contact measurements carried out in situ with submersible fluorometers or remote methods using lidars (see Fadeyev et al. 1979, Brown 1980, Bristov et al. 1981, Demidov et al. 1981, 1988, Vedernikov et al. 1990). The sub ject of this pap er is the determination of chlorophyll a concentration using in situ measurements of artificially induced fluorescence. Phytoplankton fluorescence is due to the emission by chlorophyll a of part of the energy, absorb ed by all photosynthetic pigments, that the plant cannot utilise in photosynthesis. In line with many previous pap ers on this matter, we can assume that the phytoplankton in situ fluorescence intensity (F0 ) is roughly prop ortional to the chlorophyll a concentration (Ca ) in the seawater. This assumption leads to a simple method of determining chlorophyll a concentration using fluorescence in situ measurements: Ca = const F0 , (1)

where const [arbitrary instrument unit ] constant of the particular submersible fluorometer which dep ends among other things on the exciting light intensity and the geometry of the instrument. These methods (based on eq. (1)) or similar simple relationships) and others were applied by e.g. Lorenzen (1966), Loftus & Seliger (1975), Slovacek & Hannan (1977), Karabashev (1987), Hundahl & Holck (1989),

Variability of the specific fluorescence of chlorophyll in the ocean. Part 1.

205

Shavykin & Ryzhov (1989), Ostrowska (1990), Shavykin (1990) and Kolb er & Falkowski (1993). However, the results of determining the chlorophyll a concentration with this method are inaccurate b ecause the intensity of fluorescence dep ends not only on the chlorophyll a concentration, but also on that of accessory photosynthetic pigments. The principal factor in this resp ect is the content of accessory photosynthetic pigments, which act as `antennas' that absorb light energy and transfer it to chlorophyll a. In this pap er we attempt to establish how environmental factors affect fluorescence and the observed relationships b etween the intensity of fluorescence and chlorophyll a concentrations. The main aims of the pap er are: (1) To formulate a simple theoretical model of artificially photoinduced phytoplankton fluorescence which takes into account the complex influence of three groups of factors: the chlorophyll a concentration, the photophysiological characteristics of phytoplankton, and the optical characteristics of the instrument used. (2) To apply this model to work out a physically justified method of determining chlorophyll a concentrations in seawater from in situ fluorescence measurements. A further aim was to find a p ossible universal method of determining Ca , not just for one particular instrument, the lamps and optical filters of which have sp ecific sp ectral characteristics, but for any instrument and modifications of it. This would require the development of ob jective means of calibrating the instruments. The results of our analyses are presented in parts 1 and 2 of this pap er (b oth in the present volume). This part, part 1, focuses on the first, theoretical aim. The practical ob jectives are discussed in part 2 (see Ostrowska et al. 2000, this volume).

2. Principles applied in the theoretical model of fluorescence
In order to achieve our ob jectives, we examined the phytoplankton in situ fluorescence measured following excitation of the photosynthetic apparatus with weak light pulses. Measuring instruments of two fundamentally different constructions were used for this purp ose: · fluorometers in which in situ excitation and measurement take place in the absence of ambient light, · fluorometers in which in situ excitation and measurement take place in the presence of ambient light. According to the convention prop osed by Kolb er & Falkowski (1993), the former, F0 , is the in vivo fluorescence yield induced by a weak prob e

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M. Ostrowska, R. Ma jchrowski D. N. Matorin, B. Woniak

flash in the dark, measured in the ambient light-adapted state. The latter, F , is the in vivo fluorescence yield induced by a weak prob e flash in the presence of ambient light, measured in the ambient light-adapted state. Moreover, the latest results concerning adaptation processes and their influence on the light absorption capacities of phytoplankton were applied while the model relationships of fluorescence as a function of environmental and instrumental factors were b eing worked out (see Ma jchrowski & Ostrowska 2000, Ma jchrowski et al. 2000, Woniak et al. 2000, this volume). The chief aim of this section is to establish a formal relationship b etween the artificially induced fluorescence F0 , the chlorophyll a concentration Ca , the physiological characteristics of phytoplankton, and the optical characteristics of the particular instrument used. Once it has b een tested with actual empirical material, such a relationship could b e useful in achieving the second aim, i.e. working out a practical method of fluorometrically determining the chlorophyll a concentration. The p ower of artificially excited fluorescence p er unit volume of water F0 dep ends on numerous factors. Generally sp eaking, this p ower is a function of the light energy absorb ed by phytoplankton photosynthetic pigments, the efficiency with which this energy is converted into fluorescent light, i.e. the fluorescence quantum yield fl , and intercellular reabsorbance of fluorescent light (Mitchell & Kiefer 1988). This p ower of fluorescence also dep ends on the sp ectral characteristics of the exciting light. We can assume that the quantum yield of the chlorophyll fluorescence fl does not dep end on the wavelength of light absorb ed by the photosynthetic pigments. The expression for F0 can thus b e given as the product:

absorbed energy max

F0 = Ca
mi
n

I ()a pl

, P SP

() d

fl

Q ()ffl () d,
1 - reabsorbance

(2)

where Ca [mg tot. chl a m m-2
-3

] chlorophyll a concentration,

I () [Ein s-1 ] sp ectrum of the exciting light, which dep ends on the light source used by the instrument, min , max [nm] the light wavelengths determining the sp ectral range of the exciting light, a pl
, P SP

nm-1

() [m2 (mg tot. chl a)-1 ] sp ecific absorption coefficient of phytoplankton, photosynthetic, pigments,

Variability of the specific fluorescence of chlorophyll in the ocean. Part 1.

207

fl

[dimensionless] quantum yield of fluorescence,

Q

() [dimensionless] sp ectrum of the package effect function (see, for example, van de Hulst 1981, Woniak et al. 1999),

wavelength range of the light emitted, ffl () [nm-1 ] relative sp ectral distribution of the fluorescent light emitted. Eq. (2) can also b e written as follows: F0 = Ic a pl where Ic [Ein m-2 s Ic =
mi
n

, P SP

()

I ()

Q ()

ffl ()

fl Ca ,

(3)

-1

] total intensity of excitation light: (4)

max

I ()d,

a pl

, P SP

() I () mean sp ecific absorption coefficient of photosynthetic phytoplankton pigments averaged with the weight of sp ectrum of exciting light:
max

a , P S P pl

()

I ()

=

- Ic 1 mi
n

a pl

, P SP

() I () d,

(5)

Q () ffl () mean package effect function averaged with the weight of the sp ectrum of the fluorescent light emitted:
-1

Q ()

f

fl

()

=

ffl () d

Q ()ffl () d.

(6)

The sp ectral distribution of the emitted light ffl () can b e assumed roughly equal to the function describing the sp ectral distribution of light absorb ed by chlorophyll a, a (), in the red sp ectrum range, after the a Stokes shift has b een accounted for. The function a () can be described as a a Gaussian function, (see Table 3 in Woniak et al. 1999, p. 194):
1 a () = a ( = 675) e- 2 ( a a -675 2

),

where the disp ersion = 8.55 nm. Therefore, after taking the Stokes shift into consideration, we assumed the following formula for ffl ():
1 ffl () = e- 2 ( -683 2 8.55

).

(7)

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M. Ostrowska, R. Ma jchrowski D. N. Matorin, B. Woniak

Eq. (3) ab ove describ es the complex relationship b etween fluorescence F0 and three groups of factors: (1) The chlorophyll a concentration (Ca ). (2) The photophysiological prop erties of phytoplankton (a pl ffl (), fl ). (3) The optical characteristics of the instrument (I ()). The very clear division of expression (3) describing the fluorescence F0 as a function of three groups of influential factors is of great significance for the solution of the problems under scrutiny here. First of all, it is evident that the measured phytoplankton fluorescence is not a simple function of chlorophyll a concentration, but is complicated by physiological factors and the characteristics of the measuring device. Secondly, eq. (3) enables different versions of instruments to b e intercalibrated (see section 4.1).
, P SP

(), Q (),

3. Empirical data and methods
To achieve the aims set out in this pap er, a suitable database containing the measured fluorescence, chlorophyll a concentration, light conditions and other factors describing environmental conditions in different seas is required. Our database contains the vertical profiles of the following physical parameters collected by teams from Sop ot and Moscow during various cruises to the Baltic Sea, Norwegian Sea, Black Sea, Atlantic Ocean and Indian Ocean, or determined from model calculations: A. The fluorescence F0 or F measured in arbitrary instrument units with three different fluorometers in different seas: (1) IO PAS Pump Prob e fluorometer (F0 ) measurements in the Baltic Sea, Norwegian Sea and Atlantic Ocean by the Sop ot team, during r/v `Oceania' cruises since 1993. (2) IO PAS submarine `classic' fluorometer (F ) measurements in the Baltic Sea, Norwegian Sea, Black Sea and Indian Ocean by the Sop ot team during r/v `Oceania' cruises since 1986 and r/v `Vityaz' in 1988. (3) Lomonosov University Pump Prob e fluorometer (F0 ) measurements in the Black Sea by the Moscow team in August 1989. In the case of the `classic' fluorometer, only data from an optical depth b elow 1.5 were considered so as to eliminate the influence of sunlight on the measurement of artificial excited fluorescence. In this case F ( 1.5) is practically the same as F0 ( 1.5). Moreover, the following parameters were measured along with the fluorescence:

Variability of the specific fluorescence of chlorophyll in the ocean. Part 1.

209

B. Chlorophyll a concentration Ca [mg tot. chl a m-3 ] measured with standard methods (Lorenzen 1967, Strickland & Parsons 1968, Jeffrey & Humphrey 1975). C. Light conditions: sp ectra of the underwater scalar irradiance E0 (, z ) [Ein m-2 nm-1 s-1 ], and the photosynthetically available radiation PAR0 (z ) [Ein m-2 s-1 ] measured with techniques describ ed by Woniak & Montwill 1973, Woniak et al. 1983. D. Temp erature t [ C] (Siwecki & Kumierz 1985) and inorganic nitrogen concentration Ninorg. [µM] (the total nitrogen in nitrate, nitrite and ammonia) determined with a standard device (Wood et al. 1967, Raimbault et al. 1990). All the parameters were measured at the same depths in the study areas. The numb er of measurements collected with each fluorometer is given in Table 1. Several optical characteristics of phytoplankton were also taken into consideration, such as the sp ectra of: E. The light absorption coefficients of photosynthetic phytoplankton pigments a , P S P (). pl F. The package effect function Q (). These last two characteristics were not measured directly but were calculated using the model describ ed by Woniak et al. (2000), this volume.
Table 1. Number of data measured with different types of fluorometers IO PAS Pump Probe fluorometer 309 309 203 203 IO PAS Submarine `classical' fluorometer 750, (440) 750, (440) 347 280 Lomonosov University Pump Probe fluorometer 331 331 331 302

Parameter

F0 (F ), Ca E0 (, z ), PAR0 (z ) t Ninorg.

data only from 1.5.

4. Results
The analysis takes into consideration the elements of fluorescence theory presented in section 2 and the natural diversity of selected characteristics of phytoplankton photosynthesis (Woniak et. al. 1999, and 2000, this volume, Ma jchrowski & Ostrowska 2000, this volume). It is additionally based on the

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M. Ostrowska, R. Ma jchrowski D. N. Matorin, B. Woniak

empirical material describ ed in section 3. The separate steps of the analysis are now describ ed. 4.1. Fluorescence quantum yield; intercalibration of instruments As we are dealing with measurements done with three different fluorometers measuring fluorescence intensity in different arbitrary instrument units, it is not p ossible without prior intercalibration to combine these three sets of data into a single database and p erform the statistical analyses. In order to combine readings from different fluorometers, a constant quantity indep endent of the environment has to b e found, which p ermits comparison of the empirical data from different fluorometers. The quantum yield of fluorescence is such a quantity. This quantum yield is given by the equation
fl

=

Ic a , P S P pl

F0 () I () Q ()

,
f
fl

(8)

where F0 = F0 /Ca . To obtain the absolute value of the quantum yield of fluorescence requires Ic to b e determined in absolute units, which is usually difficult. We therefore use the quantum yield of fluorescence expressed in arbitrary instrument units: F0 , (9) fl [arbitrary instrument units] = apl, P S P () I () Q () ffl
- where [arbitrary instrument units] [Ic 1 ]. First, the fluorescence quantum yields were determined in arbitrary instrument units for the three fluorometers from measured F0 , Ca , and a , P S P (), Q () calculated from the model. They were then compared pl with different environmental factors, in particular:

· the chlorophyll a concentration (Ca ), · the nitrogen concentration (Ninorg. ), · the temp erature in the sea (t), · the optical depth in the sea, determined from: = ln[PAR0 (0+ )/P AR0 (z )]. Figures 1, 2, 3 and 4 show averaged relationships b etween the fluorescence quantum yield and the ab ove-mentioned environmental factors determined for particular fluorometers. Thus, we can make the rough assumption that there is no clear relationship b etween the quantum yield of fluorescence and these environmental factors. From this we can draw the imp ortant conclusion that the quantum yield of chlorophyll fluorescence

Variability of the specific fluorescence of chlorophyll in the ocean. Part 1.

211

a
fluorescence quantum yield [arbitrary instr. units]
100000 100

b

10000

10

1000

0.01

0.1

1

10

10 0
Я3

1 0.01

0.1

1

10

10 0
Я3

chlorophyll concentration Ca [mg m ]

chlorophyll concentration Ca [mg m ]

Fig. 1. Quantum yield of fluorescence fl as a function of chlorophyll a Ca concentration for: Lomonosov University Pump Probe fluorometer, measurements by the Russian team (Black Sea) (a); IO PAS Pump Probe fluorometer, measurements by the Polish team (Baltic Sea, Norwegian Sea, Atlantic Ocean) (b)

a
fluorescence quantum yield [arbitrary instr. units]
100000 100

b

10000

10

1000

0.01

0.1

1

10

1

0.01

0.1

1

10

Ninorg. [mM] inorganic nitrogen concentration

Ninorg. [mM] inorganic nitrogen concentration

Fig. 2. Quantum yield of fluorescence fl as a function of inorganic nitrogen concentration Ninorg. for: Lomonosov University Pump Probe fluorometer, measurements by the Russian team (Black Sea) (a); IO PAS Pump Probe fluorometer, measurements by the Polish team (Baltic Sea, Norwegian Sea, Atlantic Ocean) (b)

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M. Ostrowska, R. Ma jchrowski D. N. Matorin, B. Woniak

a
fluorescence quantum yield [arbitrary instr. units]
100000 100

b

10000

10

1000

0

10

20
o

30 t [ C]

1

0

10

20
o

30 t [ C]

temperature

temperature

Fig. 3. Quantum yield of fluorescence fl as a function of temperature t for: Lomonosov University Pump Probe fluorometer, measurements by the Russian team (Black Sea) (a); IO PAS Submarine `classic' fluorometer, measurements by the Polish team (Baltic Sea, Norwegian Sea, Black Sea, Indian Ocean) (b)

a
fluorescence quantum yield [arbitrary instr. units]
100000 100

b

10000

10

1000

0

2

4

6

8

10

1

0

2

4

6

8

10

optical depth t

optical depth t

Fig. 4. Quantum yield of fluorescence fl as a function of optical depth in the sea for: Lomonosov University Pump Probe fluorometer, measurements by the Russian team (Black Sea) (a); IO PAS Pump Probe fluorometer, measurements by the Polish team (Baltic Sea, Norwegian Sea, Atlantic Ocean) (b)

Variability of the specific fluorescence of chlorophyll in the ocean. Part 1.

213

in vivo at sea is constant for exciting light over a relatively low intensity range, such as are used in fluorometers in practice. This significance stems from two facts: · it can b e used as a basis for intercalibrating different instruments, · it enables the analysis of fluorescence prop erties, such as the sp ecific fluorescence under the diverse environmental conditions existing in the World Ocean (see section 4.2). We can carry out the intercalibration b etween the ith and j th fluorometers using the following relationship: F0
i-th fluor.

= Calibr F0

j -th fluor.

,

(10)

where F0 i-th fluor. and F0 j -th fluor. of water. The coefficient Calibr is the measured by the fluorometers fl i-th fluor. [arbitrary Calibr = fl j-th fluor. [arbitrary

are determined for the same samples ratio of the relevant quantum yields instrument units for i-th fluor.] (10b) instrument units for j -th fluor.]

The values of Calibr can b e determined using arbitrary, uncorrelated readings from these three fluorometers. In this work intercalibration was carried out with reference to the Moscow group's data. After this op eration we obtained 1080 sets of data covering Ca , , and the fluorescence F0 in units of the Moscow group's fluorometer. These data were used in part 2 (see Ostrowska et al. 2000, this volume) to verify the methods of determining chlorophyll a concentrations. 4.2. The natural variability of the specific fluorescence of chlorophyll The fact that the quantum yield of fluorescence is indep endent of environmental factors allows the relative range of natural variability of the sp ecific fluorescence of chlorophyll in the oceans to b e determined. Assuming fl = const, eq. (3) can b e rewritten to give an expression for the sp ecific fluorescence (F0 = F0 /Ca ): F0 [arbitrary units] = a pl
, P SP

()

I ()

Q ()

ffl ()

,

(11)

where [arbitrary units] [m2 (mg tot. chl a)-1 [Ic ] [fl ]]. The characteristics of the sp ecific fluorescence F0 for different trophic typ es of seas and for various depths can b e determined using our model of absorption prop erties of phytoplankton (see Woniak et al. 2000, this volume), which, among other things, enables the sp ectra of a , P S P () and pl Q () to b e determined. In addition, it is assumed that the sp ectra of the

214

M. Ostrowska, R. Ma jchrowski D. N. Matorin, B. Woniak

light exciting fluorescence (I ()/Ic ) have a certain fixed shap e. Nevertheless, the sp ectra are similar for all the fluorometers actually used. The vertical profiles of the sp ecific fluorescence F0 ( ) or F0 (z ) for different trophic typ es of sea can b e determined from the model of phytoplankton light absorption and eq. (11) (Fig. 5). As one can see in this figure, the sp ecific fluorescence generally falls with increasing water trophicity (we assume the surface chlorophyll a concentration, Ca (0) to b e the trophicity). The sp ecific fluorescence also tends to increase with depth, esp ecially in waters of low trophicity. Such b ehaviour is similar to that of the mean absorption coefficients of phytoplankton photosynthetic pigments (see Fig. 5b in Ma jchrowski et al. 2000, this volume, p. 198). However, the range of variability of the sp ecific fluorescence recorded under natural conditions (ab out 50 times) is greater than that of the sp ecific absorption coefficient (< 20 times). As eq. (11) clearly indicates, this is b ecause the sp ecific fluorescence dep ends not only on the sp ecific absorption but also on the mean package effect function. This latter factor decreases with increasing chlorophyll a concentration and in different typ es of seas varies by ab out one order of magnitude.
a
O1 O2 O3 M

b
z [m]
0
E5

0 2 4 6 8

50 100 150

E4

E3

E2 E1 P M

optical depth t

200

O3

depth

250 300 0 0.01 0.02

O2 O1

10

E5 E4

E3

E2

E1

P

0

0.01

0.02

0.03

0.03

specific fluorescence F0' * [arbitrary units]

specific fluorescence F0' * [arbitrary units]

Fig. 5. Model vertical profiles of specific fluorescence F0 for optical depth (a) and for real depth z (b), determined for different trophic types of sea. The symbols of trophic types correspond to the surface chlorophyll a concentration Ca (0): O1 Ca (0) = 0.035 mg tot. chl a m-3 ; O2 Ca (0) = 0.07 mg tot. chl a m-3 ; O3 Ca (0) = 0.15 mg tot. chl a m-3 ; M Ca (0) = 0.35 mg tot. chl a m-3 ; P Ca (0) = 0.7 mg tot. chl a m-3 ; E1 Ca (0) = 1.5 mg tot. chl a m-3 ; E2 Ca (0) = 3.5 mg tot. chl a m-3 ; E3 Ca (0) = 7 mg tot. chl a m-3 ; E4 Ca (0) = 15 mg tot. chl a m-3 ; E5 Ca (0) = 35 mg tot. chl a m-3

Variability of the specific fluorescence of chlorophyll in the ocean. Part 1.

215

The relationships presented in Fig. 5 were obtained by p erforming the relevant calculations from eq. (11) and using the whole model mathematical apparatus (see Table 1 in Woniak et al. 2000, this volume, pp. 182188) of phytoplankton optical prop erties a , P S P () I () and Q () ffl () . The pl model calculations are very time-consuming. That is why for practical purp oses we have worked out simplified p olynomial approximations of the model results. This allows b oth factors occurring in eq. (11) to b e estimated from the two following p olynomial relationships b etween the a , P S P () I () and Q () ffl () , trophic index of the sea Ca (0) and optical pl depth in the sea: a pl
4 , P SP 4

()

I ()

=
m=0 n=0 4 4

Am, n (log Ca (0))n m, Bm, n (log Ca (0))n m,

(12) (13)

Q ()

f

fl

()

=
m=0 n=0

where the coefficients Am, n and Bm, n of these p olynomials are given in Tables 2 and 3. The estimated errors of these approximations do not exceed 3% of the values of a , P S P () and Q () determined from the pl unabridged version of the model by Woniak et al. (2000) in this volume. Formulae (12) and (13) to a significant extent simplify the determination of the chlorophyll a concentration using eq. (11). This fluorometric method of determining the chlorophyll a concentration is describ ed in part 2 of this pap er by Ostrowska et al. (2000, this volume).
Table 2. Values of coefficient Am, a) for 0.035 < Ca (0) < 1.5 n /m 0 1 2 3 4 0 1 -7 -4 4 1 .566 .158 .709 .181 .068 в в в в в 10 10 10 10 10
-2 -3 -3 -4 -3 n

in eq. (12)

1 -3.258 -7.724 1.912 -1.604 -7.220 в в в в в 10 10 10 10 10
-4 -5 -3 -4 -4

2 1.840 3.924 -6.868 -2.463 1.418 в в в в в 10 10 10 10 10
-4 -5 -4 -5 -4

3 5.949 -2.930 7.373 3.054 4.622 в в в в в 10 10 10 10 10
-7 -5 -5 -5 -6

4 -9 1 -2 -7 -3 .084 .368 .307 .392 .326 в в в в в 10 10 10 10 10
-7 -6 -6 -7 -7

b) for 1.5 Ca (0) < 70 n /m 0 1 2 3 4 0 1 -8 -2 1 -2 .560 .437 .255 .849 .572 в в в в в 10 10 10 10 10
-2 -3 -3 -3 -4

1 -1.390 1.933 -5.655 4.874 -1.276 в в в в в 10 10 10 10 10
-4 -3 -3 -3 -3

2 1.075 -8.726 2.611 -2.313 6.163 в в в в в 10 10 10 10 10
-4 -4 -3 -3 -4

3 1.023 1.018 -3.748 3.424 -9.264 в в в в в 10 10 10 10 10
-5 -4 -4 -4 -5

4 -1.339 -4.436 1.888 -1.753 4.781 в в в в в 10 10 10 10 10
-6 -6 -5 -5 -6

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M. Ostrowska, R. Ma jchrowski D. N. Matorin, B. Woniak

Table 3. Values of coefficient Bm, a) for 0.035 < Ca (0) < 1.5 n /m 0 1 2 3 4 0 8 -1 3 -2 4 .551 .441 .927 .847 .384 в в в в в 10 10 10 10 10
-1 -2 -3 -4 -6

n

in eq. (13)

1 -2.210 -1.289 1.654 -2.761 1.287 в в в в в 10 10 10 10 10
-1 -2 -2 -3 -4

2 -1.408 2.299 -8.461 1.289 -6.064 в в в в в 10 10 10 10 10
-1 -2 -3 -3 -5

3 -2.474 -4.666 -1.311 2.754 -1.412 в в в в в 10 10 10 10 10
-2 -4 -2 -3 -4

4 5 -7 3 1 -5 .512 .357 .961 .028 .566 в в в в в 10 10 10 10 10
-3 -3 -3 -3 -5

b) for 1.5 Ca (0) < 70 n /m 0 1 2 3 4 0 8 5 -2 7 -4 .494 .923 .895 .174 .543 в в в в в 10 10 10 10 10
-1 -4 -3 -4 -5

1 -2.455 4.581 -1.325 1.773 -9.290 в в в в в 10 10 10 10 10
-1 -2 -2 -3 -5

2 -2.961 -3.032 1.366 -1.885 8.950 в в в в в 10 10 10 10 10
-2 -1 -1 -2 -4

3 -1.322 3.154 -1.474 2.044 -9.613 в в в в в 10 10 10 10 10
-1 -1 -1 -2 -4

4 6 -8 4 -5 2 .079 .937 .219 .901 .776 в в в в в 10 10 10 10 10
-2 -2 -2 -3 -4

5. Summary and conclusions
In this work the range of variability of phytoplankton fluorescence prop erties in different trophic typ es of water and at different depths in the sea have b een analysed theoretically. We have also attempted to interpret the in vivo measurements of artificially induced fluorescence carried out with submersible fluorometers. The most imp ortant achievement of this work has b een to produce a simple theoretical model of fluorescence excited with artificial light that takes into account the complex influence of three groups of factors on this phenomenon: chlorophyll a concentrations, the various photophysiological characteristics of phytoplankton and the optical characteristics of the measuring instrument. With this model the range of variability of the sp ecific fluorescence F0 under natural conditions in the world's oceans have b een characterised. The sp ecific fluorescence varies over two orders of magnitude. Its values are lowest in eutrophic waters and increase with decreasing water trophicity. The sp ecific fluorescence also varies with depth, usually increasing. These tendencies are characteristic, esp ecially in oligotrophic waters. The model of fluorescence presented here is a physically justified method determining chlorophyll a in seawater using fluorescence measured with contact fluorometers in situ. The application of this method is describ ed in part 2 (Ostrowska et al. 2000, this volume).

Variability of the specific fluorescence of chlorophyll in the ocean. Part 1.

217

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