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Variability of the specific fluorescence of chlorophyll in the o cean. Part 2. Fluorometric metho d of chlorophyll a determination*

OCEANOLOGIA, 42 (2), 2000. pp. 221 229. 2000, by Institute of Oceanology PAS.
KEYWORDS

Plant luminescence Chlorophyll a determination Fluorometric method

Miroslawa Ostrowska Institute of Oceanology, Polish Academy of Sciences, PowstacСw Warszawy 55, PL81712 Sopot, Poland; e-mail: ostra@iopan.gda.pl Dimitrii N. Matorin Department of Biophysics, Faculty of Biology, Moscow State University, Moscow, 117218 Russia Dariusz Ficek Institute of Physics, Pedagogical University, Arciszewskiego 22 B, PL76200 Slupsk, Poland
Manuscript received 22 March 2000, reviewed 18 April 2000, accepted 4 May.

Abstract Two methods of determining the chlorophyll a concentration in the sea have been formulated on the basis of artificially induced fluorescence measured with the aid of submersible fluorometers. The method of statistical correlation is founded on the empirical relationship between fluorescence and chlorophyll concentration. The theoretical model of fluorescence described in Part 1 of this paper (see Ostrowska et al. 2000, this volume) provides the basis of the other method, the physical method. This describes the dependence of the specific fluorescence of phytoplankton on the chlorophyll concentration, a diversity of photophysiological properties of phytoplankton and the optical characteristics of the fluorometer.
* This paper was presented at the `Second Workshop on Luminescence and Photosynthesis of Marine Phytoplankton', SopotParaszyno, 1115 October 1999.

222

M. Ostrowska, D. N. Matorin, D. Ficek

In order to assess their practicability, the methods were sub jected to empirical verification. This showed that the physical method yielded chlorophyll concentrations of far greater accuracy. The respective error factors of the estimated chlorophyll concentration were x = 2.07 for the correlation method and x = 1.5 for the physical method. This means that the statistical logarithmic error varies from -52 to +107% in the case of the former method but only from -33 to +51% in the case of the latter. Thus, modifying the methodology has much improved the accuracy of chlorophyll determinations.

1. Introduction
Part 1 of this pap er (Ostrowska et al. 2000, this volume) describ ed a theoretical model of artificially photoinduced phytoplankton fluorescence that takes into consideration the complex influence of three groups of factors on this phenomenon: the chlorophyll a concentration Ca , physiological characteristics of phytoplankton and the optical characteristics of the fluorometer. The range of variability of the sp ecific fluorescence F0 with resp ect to seawater trophicity and depth were determined using this model. The practical significance of this is that when determining chlorophyll a concentrations from fluorescence measurements, one should b ear such relationships in mind, since the measured fluorescence F0 and chlorophyll a concentration are variously related in different trophic typ es of sea and at different depths. The ob jectives of Part 2 of this pap er are thus: (1) To derive a method of computing chlorophyll a concentrations from fluorescence measurements that accounts for the ab ove-mentioned variability in sp ecific fluorescence. (2) To compare the accuracy of chlorophyll a determinations obtained with this method and with another that ignores the variability in sp ecific fluorescence. To achieve these ob jectives, two p ossible ways of determining chlorophyll a are formulated and verified on the basis of in situ phytoplankton fluorescence measured by means of submersible fluorometers. They are: · the method of statistical correlation, which is based on simple statistical relationships b etween the chlorophyll a concentration Ca and the measured fluorescence F0 , · the physical method, the foundation of which is the theoretical fluorescence model describ ed in Part 1 (see Ostrowska et al. 2000, this volume). For the empirical verification of these methods we used the database describ ed in Part 1 (see section 3 in Ostrowska et al. 2000, this volume).

Variability of the specific fluorescence of chlorophyll in the ocean. Part 2.

223

2. Method of statistical correlation
There is already sufficient evidence forthcoming that the principal factor influencing the intensity of artificially induced fluorescence in the sea is the concentration of chlorophyll a Ca (e.g. Karabashev 1987, Ostrowska 1990, Kolb er & Falkowski 1993). The relationship b etween fluorescence and Ca with resp ect to our database is presented in Fig. 1a. As one can see, the measured fluorescence F0 usually increases when Ca does so. However, the increase in fluorescence is not as striking as that of Ca . In our empirical data (Fig. 1a) the fluorescence varies over a range of ab out two orders of magnitude, whereas Ca varies over almost four orders. This b ecomes clear from a p erusal of Fig. 1b, which illustrates the dep endence of the slop e F0 /Ca i.e. the sp ecific fluorescence F0 , on Ca .
a
[arbitrary units] [arbit. units]
10000 10000

b

1000

1000

fluorescence F0' * = F0' /Ca

100

100

fluorescence F0'

10

10

1 0.001 0.01 0.1 1 10 Ca [mg tot. chl a mЯ3 ] chlorophyll concentration

1 0.001 0.01 0.1 1 10 100 Ca [mg tot. chl a mЯ3 ] chlorophyll concentration

100 1000

Fig. 1. The relationships between the measured fluorescence F0 and chlorophyll a concentration Ca in the sea; the points correspond to measured data, the line corresponds to a regression curve according to the equation: log F0 = 0.6697 log Ca +1.8429 (a), and the specific fluorescence F0 and chlorophyll a concentration Ca in the sea; the points correspond to measured data, the line corresponds to a regression curve according to the equation: - F0 = 69.65 Ca 0.3303 (b)

It can b e seen that with increasing water trophicity this sp ecific fluorescence F0 decreases significantly in value. It is characteristic of these relationships that the exp erimental p oints are widely scattered. Nevertheless, using the least squares method, we can find relationships connecting

224

M. Ostrowska, D. N. Matorin, D. Ficek

· the fluorescence F0 with the chlorophyll a concentration Ca : log F0 = 0.6697 log Ca +1.8429, or F0 = 69.65 Ca where Ca [mg tot. chl a m
-3 (0.6697-1)

(1)
3303

· the sp ecific fluorescence F0 with the chlorophyll a concentration Ca : = 69.65 Ca-0. , (1a)

] chlorophyll a concentration (tot. chl a or chl a + pheo). The correlation coefficient for these relationships r = 0.84. By transforming eq. (1) we obtain a formula for the dep endence of Ca on F0 : Ca = 10
[1.4932(log F0 -1.8429)]

.

(2)

Formula (2) is the basis of the statistical correlation method for determining the chlorophyll a concentration from fluorescence measurements.

3. Physical method
In using the theoretical mo scrib ed in Part 1 (Ostrowska et measured fluorescence is directly in Part 1 by eq. (11)). This can F0meas where
F0theor. = F0theor. Ca ured

del of the phytoplankton fluorescence deal. 2000, this volume), we assume that the prop ortional to the theoretical value (given b e written thus: (3) (3b) Q () , (3a)

[arbitrary instrument units] = const F0theor. [arbitrary units]

and F0theor. = a pl
, P SP

()

I ()

ffl ()

where a , P S P () [m2 (mg tot. chl a)-1 ] sp ecific absorption coefficient of phytopl plankton photosynthetic pigments, a , P S P () I () mean sp ecific absorption coefficient of photosynthetic pl phytoplankton averaged with the weight of the exciting light sp ectrum: a pl
, P SP

()

I ()

- = Ic 1

max mi
n

a pl

, P SP

() I () d,

I () [Ein m-2 nm-1 s-1 ] the exciting light sp ectrum dep endent on the light source used by the fluorometer, min , max [nm ] wavelengths of light determining the range of exciting light, () sp ectrum of the package effect function, Q

Variability of the specific fluorescence of chlorophyll in the ocean. Part 2.

225

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

Q

()

ffl ()

=

ffl () d

Q ()ffl () d,

ffl () [nm-1 ] relative sp ectral distribution of the emitted light. The value of const in eq. (3) dep ends on the prop erties of the fluorometer employed. In our exp eriments using the least squares method of approximating the relevant observed and theoretical fluorescences (see Fig. 2) it was found to b e const = 103.84 .
a
[arbitrary units] Ca]Я1
10000 1000 100 10 1 0.1 0.0001 PSP

b
100000

(l)>I(l) F0' [ PSP

f fl (l)

10000

fluorescence F0'

1000

100 0.0001 * pl, PSP

0.001

0.01

0. 1
f fl (l)

1 [m Я1]

0.001

0.01

0. 1
f fl (l)

1 [m Я1]

(l)>I(l)

C

a

(l)>I(l)

C

a

Fig. 2. The relationships between the measured fluorescence F0 meas. and theoretical fluorescence F0 theor. ; the points correspond to measurements, the corresponds to a regression curve according to the equation: log F0 meas. = a P S P () I () Q () ffl () Ca +3.84 (a), and the ratio pl, measured and theoretical fluorescence F0 meas. /F0 theor. as a function of theoretical fluorescence F0 theor. ; the points correspond to measurements, the corresponds to a regression curve according to the equation: F0 meas. 103.84 = Ca a () I () Q () f () (b)
pl, P S P fl

the line of the line

Hence, in our exp eriments, the relationships b etween the measured and theoretical (modelled) fluorescence take the form F0
meas.

= 103.

84

a pl

, P SP

()

I () F

Q ()

ffl ()

Ca ,

0 theor.

and the formula describing the chlorophyll a concentration as a function of fluorescence is

226

M. Ostrowska, D. N. Matorin, D. Ficek

Ca =

103.84

a , P S P pl

F0 meas. () I () Q ()

.
ffl ()

(4)

Formula (4) is the foundation of the physical method of estimating the chlorophyll a concentration Ca . However, we also need to know the sp ecific absorption of photosynthetic pigments a , P S P () I () and the package pl effect function Q () ffl () in phytoplankton cells. These quantities can b e determined from a known or given optical depth and surface chlorophyll concentration Ca (0) in the sea with the aid of the simplified p olynomial formulae given in Part 1 (Ostrowska et al. 2000, this volume): 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 ,

(4a) (4b)

Q ()

ffl ()

=
m=0 n=0

where the coefficients Am, n and Bm, n of these p olynomials are given in Tables 2 and 3 in Ostrowska et al. 2000, this volume, pp. 215, 216. The optical depths in our exp eriments were measured simultaneously with fluorescence. But values of Ca (0) are not known. Nevertheless, the latter can b e estimated from the real and optical depth known for each profile using Woniak's bio-optical classification of waters (Woniak et. al 1992a and b).
Table 1. Values of Cm, a) for 0 < < 1 n /m 0 1 2 3 4 0 1.42008 0.325625 1.15793 1.7538 0.876821 1 1.56264 0.168647 2.95813 5.5338 2.97397 2 1.24215 14.5657 33.1223 28.351 7.91305 3 8.6257 35.5867 51.2958 25.3579 1.82888 4 12.3604 20.6688 17.4024 3.3401 0.282705 in eq. (5)

n

b) for 1 < 10 n /m 0 1 2 3 4 0 1.43248 0.243892 1.69258 3.47131 1.95027 1 1.61865 4.74305 9.14493 1.19548 4.54015 2 3.32293 9.13519 2.22602 3.23597 4.83875 3 3.19523 8.5247 22.195 9.73787 4.95673 4 8.29916 18.9029 10.0107 2.03738 0.773145

Variability of the specific fluorescence of chlorophyll in the ocean. Part 2.

227

From this classification we can establish the relationship b etween the trophic index of the sea (which we assume to b e Ca (0)), the optical depth and the real depth z . For the purp ose of the present work, this relationship is describ ed by the following approximate p olynomial:
4 4

log Ca (0) =
m=0 n=0

Cm, n (log z )n log

z

m

.

(5)

The coefficients of this p olynomial are set out in Table 1.

4. Empirical verification of methods
In order to assess their practicability, the two methods of determining the chlorophyll a concentration were verified empirically, that is to say, the resp ective measured data of Ca, M are compared with those calculated from eq. (2) (statistical correlation method) or eqs. (4) and (5) (physical method).

Table 2. The relative errors in estimating chlorophyll a concentrations at different depths in the sea using the statistical correlation method (eq. (2)) and the physical method (eqs. (4) and (5)) Arithmetic statistics Logarithmic statistics
statistical

systematic statistical systematic standard error factor

[%] method of statistical correlations physical method where = (Ca,
C

[%] ± 89.8 ± 5.0

g

[%]

x 2.07

- [%] + [%] 51.7 107

30.9

3.6

16.3

1.5

1.5

33.3

50.8

- Ca,

M

)/Ca,

M

errors,

arithmetic mean of errors, standard deviation of errors (statistical error),
g

= 10

[ log(C

a, C

/C

a, M

)]

- 1 logarithmic mean of errors,
M

log (Ca, C /Ca,
log

M

) mean of log (Ca, C /Ca,

), log (Ca, C /Ca,

M

),

log standard deviation of log (Ca, C /Ca, x = 10 - = standard error factor, - 1 and

M

),

1 x

+ = x - 1.

228

M. Ostrowska, D. N. Matorin, D. Ficek

a
chlorophyll concentration Ca, C [mg tot. chl a mЯ3 ] [%] frequency
1000 100 10 1 0.1 0.01 0.01 0.1 1 10 10 20 30

b

1 00 1000

0

0.0625 ratio C
a, C

0.25
M

1

4

16

Ca, M [mg tot. chl a mЯ3 ] chlorophyll concentration

/ Ca,

Fig. 3. Comparison between measured Ca, M and calculated Ca, C chlorophyll a concentrations using the method of statistical correlation (eq. (2)); comparison of calculated and measured chlorophyll a (a), probability density distribution of the ratio of calculated to measured chlorophyll a (b)

a
chlorophyll concentration Ca, C [mg tot. chl a mЯ3] [%] frequency
1000 100 10 1 0.1 0.01 0.01 0.1 1 10 10 20 30

b

1 00 1000

0

0.0625 ratio C
a, C

0.25
M

1

4

16

Ca, M [mg tot. chl a mЯ3 ] chlorophyll concentration

/ Ca,

Fig. 4. Comparison between measured Ca, M and calculated Ca, C chlorophyll a concentration using the physical method (eq. (4) and (5)); comparison of calculated and measured chlorophyll a (a), probability density distribution of the ratio of calculated to measured chlorophyll a (b)

Variability of the specific fluorescence of chlorophyll in the ocean. Part 2.

229

In the case of the statistical correlation method, actual values of Ca, C were calculated from measurements of F0 . In the case of the physical method, values of depths and z were used in addition. The results of the verifications are given in Figs. 3 and 4, and the errors of estimations are given in Table 2.

5. Conclusion
Clearly, the physical method yields significantly more accurate chlorophyll a concentrations than does the method of statistical correlation. The error factor of the estimated chlorophyll concentration x = 1.5 for the former method but x = 2.07 for the latter. Thus, the statistical logarithmic error of the former varies from -33% to +51%, that of the latter from -52% to +107%. Modifying the method of statistical correlation has thus brought ab out a highly desirable improvement in the accuracy of chlorophyll a determinations.

References
Karabashev G. S., 1987, Fluorescence in the ocean, Gidrometeoizdat, Leningrad, 200 pp., (in Russian). Kolber Z., Falkowski P. G., 1993, Use of active fluorescence to estimate phytoplankton photosynthesis `in situ', Limnol. Oceanogr., 38 (8), 16461665. Ostrowska M., 1990, Fluorescence `in situ' method for the determination of chlorophyl l a concentration in sea, Oceanologia, 29, 175202. Ostrowska M., Ma jchrowski R., Matorin D. N., Woniak B., 2000, Variability of the specific fluorescence of chlorophyl l in the ocean. Part 1. Theory of classical `in situ' chlorophyl l fluorometry, Oceanologia, 42 (2), 203219. Woniak B., Dera J., Koblentz-Mishke O. I., 1992a, Bio-optical relationships for estimating primary production in the Ocean, Oceanologia, 33, 538. Woniak B., Dera J., Koblentz-Mishke O. I., 1992b, Model ling the relationship between primary production, optical properties, and nutrients in the sea, Ocean Optics 11, Proc. SPIE, 1750, 246275.