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

**Variability** **of** **the**

**specific** **fluorescence** **of**

**chlorophyll** **in** **the** **ocean**.

Part 2. Fluorometric

method **of** **chlorophyll** a

determ**in**ation*

OCEANOLOGIA, 42 (2), 2000.

pp. 221–229.

2000, by Institute **of**

Oceanology PAS.

KEYWORDS

Plant lum**in**escence

Chlorophyll a determ**in**ation

Fluorometric method

Mirosława Ostrowska

Institute **of** Oceanology,

Polish Academy **of** Sciences,

Powstańców Warszawy 55, PL–81–712 Sopot, Poland;

e-mail: ostra@iopan.gda.pl

Dimitrii N. Mator**in**

Department **of** Biophysics,

Faculty **of** Biology,

Moscow State University,

Moscow, 117218 Russia

Dariusz Ficek

Institute **of** Physics,

Pedagogical University,

Arciszewskiego 22 B, PL–76–200 Słupsk, Poland

Manuscript received 22 March 2000, reviewed 18 April 2000, accepted 4 May.

Abstract

Two methods **of** determ**in****in**g **the** **chlorophyll** a concentration **in** **the** sea have been

formulated on **the** basis **of** artificially **in**duced **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

**the**oretical model **of** **fluorescence** described **in** Part 1 **of** this paper (see Ostrowska

et al. 2000, this volume) provides **the** basis **of** **the** o**the**r 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 Lum**in**escence and

Photosyn**the**sis **of** Mar**in**e Phytoplankton’, Sopot–Paraszyno, 11–15 October 1999.

222 M. Ostrowska, D. N. Mator**in**, D. Ficek

In order to assess **the**ir practicability, **the** methods were subjected 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, modify**in**g **the** methodology has much improved **the**

accuracy **of** **chlorophyll** determ**in**ations.

1. Introduction

Part 1 **of** this paper (Ostrowska et al. 2000, this volume) described

a **the**oretical model **of** artificially photo**in**duced phytoplankton **fluorescence**

that takes **in**to consideration **the** complex **in**fluence **of** three groups **of** factors

on this phenomenon: **the** **chlorophyll** a concentration C a , physiological

characteristics **of** phytoplankton and **the** optical characteristics **of** **the**

fluorometer. The range **of** variability **of** **the** **specific** **fluorescence** F 0 ′∗ with

respect to seawater trophicity and depth were determ**in**ed us**in**g this model.

The practical significance **of** this is that when determ**in****in**g **chlorophyll** a

concentrations from **fluorescence** measurements, one should bear such

relationships **in** m**in**d, s**in**ce **the** measured **fluorescence** F 0 ′ and **chlorophyll** a

concentration are variously related **in** different trophic types **of** sea and at

different depths. The objectives **of** Part 2 **of** this paper are thus:

(1) To derive a method **of** comput**in**g **chlorophyll** a concentrations from

**fluorescence** measurements that accounts for **the** above-mentioned

variability **in** **specific** **fluorescence**.

(2) To compare **the** accuracy **of** **chlorophyll** a determ**in**ations obta**in**ed

with this method and with ano**the**r that ignores **the** variability **in**

**specific** **fluorescence**.

To achieve **the**se objectives, two possible ways **of** determ**in****in**g

**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 between **the** **chlorophyll** a concentration C a

and **the** measured **fluorescence** F ′ 0 ,

• **the** physical method, **the** foundation **of** which is **the** **the**oretical

**fluorescence** model described **in** Part 1 (see Ostrowska et al. 2000,

this volume).

For **the** empirical verification **of** **the**se methods we used **the** database

described **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 forthcom**in**g that **the** pr**in**cipal factor

**in**fluenc**in**g **the** **in**tensity **of** artificially **in**duced **fluorescence** **in** **the** sea is **the**

concentration **of** **chlorophyll** aC a (e.g. Karabashev 1987, Ostrowska 1990,

Kolber & Falkowski 1993). The relationship between **fluorescence** and C a

with respect to our database is presented **in** Fig. 1a. As one can see, **the**

measured **fluorescence** F ′ 0 usually **in**creases when C a does so. However, **the**

**in**crease **in** **fluorescence** is not as strik**in**g as that **of** C a . In our empirical

data (Fig. 1a) **the** **fluorescence** varies over a range **of** about two orders **of**

magnitude, whereas C a varies over almost four orders. This becomes clear

from a perusal **of** Fig. 1b, which illustrates **the** dependence **of** **the** slope

F ′ 0 /C a i.e. **the** **specific** **fluorescence** F ′∗

0 ,onC a.

**fluorescence** F 0

' [arbitrary units]

10000

1000

100

10

a

1

0.001 0.01 0.1 1 10 100 1000

Ca [mg tot. chl a m ñ3 ]

**chlorophyll** concentration

**fluorescence** F = F /C [arbit. units]

a

'

0 * '

0

10000

1000

100

10

b

1

0.001 0.01 0.1 1 10 100

Ca [mg tot. chl a m ]

**chlorophyll** concentration

ñ3

Fig. 1. The relationships between **the** measured **fluorescence** F 0 ′ and **chlorophyll** a

concentration C a **in** **the** sea; **the** po**in**ts correspond to measured data, **the** l**in**e

corresponds to a regression curve accord**in**g to **the** equation:

log F 0 ′ =0.6697 log C a +1.8429 (a), and **the** **specific** **fluorescence** F 0 ′∗ and

**chlorophyll** a concentration C a **in** **the** sea; **the** po**in**ts correspond to measured data,

**the** l**in**e corresponds to a regression curve accord**in**g to **the** equation:

F 0 ′∗

−0.3303

=69.65 Ca

(b)

It can be seen that with **in**creas**in**g water trophicity this **specific** **fluorescence**

F 0 ′∗ decreases significantly **in** value. It is characteristic **of** **the**se relationships

that **the** experimental po**in**ts are widely scattered. Never**the**less, us**in**g **the**

least squares method, we can f**in**d relationships connect**in**g

224 M. Ostrowska, D. N. Mator**in**, D. Ficek

• **the** **fluorescence** F ′ 0 with **the** **chlorophyll** a concentration C a:

log F 0 ′ =0.6697 log C a +1.8429, or (1)

• **the** **specific** **fluorescence** F 0 ′∗ with **the** **chlorophyll** a concentration C a:

F 0 ′∗ =69.65 C (0.6697−1) a =69.65 Ca −0.3303 , (1a)

where

C a [mg tot. chl a m −3 ] – **chlorophyll** a concentration (tot. chl a or

chl a + pheo).

The correlation coefficient for **the**se relationships r = 0.84.

By transform**in**g eq. (1) we obta**in** a formula for **the** dependence **of**

C a on F 0 ′:

C a =10 [1.4932(log F 0 ′ −1.8429)] . (2)

Formula (2) is **the** basis **of** **the** statistical correlation method for determ**in****in**g

**the** **chlorophyll** a concentration from **fluorescence** measurements.

3. Physical method

In us**in**g **the** **the**oretical model **of** **the** phytoplankton **fluorescence** described

**in** Part 1 (Ostrowska et al. 2000, this volume), we assume that **the**

measured **fluorescence** is directly proportional to **the** **the**oretical value (given

**in** Part 1 by eq. (11)). This can be written thus:

F 0measured ′ [arbitrary **in**strument units] = const F 0**the**or. ′ [arbitrary units]

(3)

where

F 0**the**or. ′ = F 0**the**or. ′∗ C a

(3b)

and

F 0**the**or. ′∗ = 〈a∗ pl, P SP (λ)〉 I(λ)〈Q ∗ (λ)〉 ffl (λ),

(3a)

where

a ∗ pl, P SP (λ) [m2 (mg tot. chl a) −1 ] – **specific** absorption coefficient **of** phytoplankton

photosyn**the**tic pigments,

〈a ∗ pl, P SP (λ)〉 I(λ) – mean **specific** absorption coefficient **of** photosyn**the**tic

phytoplankton averaged with **the** weight **of** **the** excit**in**g light spectrum:

〈a ∗ pl, P SP (λ)〉 I(λ) = I −1

c

∫

λ max

λ m**in**

a ∗ pl, P SP

(λ) I(λ) dλ,

I(λ) [E**in**m −2 nm −1 s −1 ] – **the** excit**in**g light spectrum dependent on **the**

light source used by **the** fluorometer,

λ m**in** , λ max [nm] – wavelengths **of** light determ**in****in**g **the** range **of** excit**in**g

light,

Q ∗ (λ) – spectrum **of** **the** package effect function,

**Variability** **of** **the** **specific** **fluorescence** **of** **chlorophyll** **in** **the** **ocean**. Part 2. 225

〈Q ∗ (λ)〉 ffl (λ) – mean package effect function averaged with **the** weight **of** **the**

emitted light spectrum:

[ ] −1 ∫ ∫

〈Q ∗ (λ)〉 ffl (λ) = f fl (λ) dλ Q ∗ (λ)f fl (λ) dλ,

∆λ

∆λ

f fl (λ) [nm −1 ] – relative spectral distribution **of** **the** emitted light.

The value **of** const **in** eq. (3) depends on **the** properties **of** **the** fluorometer

employed. In our experiments us**in**g **the** least squares method **of** approximat**in**g

**the** relevant observed and **the**oretical **fluorescence**s (see Fig. 2) it

was found to be const = 10 3.84 .

**fluorescence** F 0

' [arbitrary units]

10000

1000

100

10

1

a

ñ1

F [< a () l > C ]

' * *

0 pl, PSP I ( l)

f fl () l a

0.1

100

0.0001 0.001 0.01 0. 1 1 0.0001 0.001 0.01 0. 1 1

< a ( ) > Ca

[m ]

< a * pl, PSP ( l) > I Ca

[m ]

* pl, PSP l I () l

f fl () l

100000

10000

1000

b

() l

f fl () l

Fig. 2. The relationships between **the** measured **fluorescence** F 0meas.

′ and **the**

**the**oretical **fluorescence** F

0**the**or. ′ ; **the** po**in**ts correspond to measurements, **the** l**in**e

corresponds to a regression curve accord**in**g to **the** equation:

log F 0meas. ′ = 〈a ∗ pl, P SP (λ)〉 I(λ)〈Q ∗ (λ)〉 ffl (λ) C a +3.84 (a), and **the** ratio **of**

measured and **the**oretical **fluorescence** F 0meas. ′ /F 0**the**or.

′ as a function **of** **the**

**the**oretical **fluorescence** F 0**the**or. ′ ; **the** po**in**ts correspond to measurements, **the** l**in**e

corresponds to a regression curve accord**in**g to **the** equation:

10 3.84 =

(b)

F ′ 0meas.

C a 〈a ∗ pl, P SP (λ)〉 I(λ)〈Q ∗ (λ)〉 ffl (λ)

Hence, **in** our experiments, **the** relationships between **the** measured and

**the**oretical (modelled) **fluorescence** take **the** form

F 0meas. ′ =10 3.84 〈a ∗ pl, P SP (λ)〉 I(λ) 〈Q ∗ (λ)〉 ffl (λ) C a ,

} {{ }

F 0**the**or.

′

and **the** formula describ**in**g **the** **chlorophyll** a concentration as a function **of**

**fluorescence** is

226 M. Ostrowska, D. N. Mator**in**, D. Ficek

F ′ 0meas.

C a =

10 3.84 〈a ∗ pl, P SP (λ)〉 I(λ)〈Q ∗ . (4)

(λ)〉 ffl (λ)

Formula (4) is **the** foundation **of** **the** physical method **of** estimat**in**g **the**

**chlorophyll** a concentration C a . However, we also need to know **the** **specific**

absorption **of** photosyn**the**tic pigments 〈a ∗ pl, P SP (λ)〉 I(λ) and **the** package

effect function 〈Q ∗ (λ)〉 ffl (λ) **in** phytoplankton cells. These quantities can be

determ**in**ed from a known or given optical depth τ and surface **chlorophyll**

concentration C a (0) **in** **the** sea with **the** aid **of** **the** simplified polynomial

formulae given **in** Part 1 (Ostrowska et al. 2000, this volume):

[

4∑ 4

]

〈a ∗ ∑

pl, P SP (λ)〉 I(λ) = A m, n (log C a (0)) n τ m ,

(4a)

n=0

〈Q ∗ (λ)〉 ffl (λ) =

m=0

[

4∑ ∑ 4

m=0

]

B m, n (log C a (0)) n τ m ,

n=0

(4b)

where **the** coefficients A m, n and B m, n **of** **the**se polynomials are given **in**

Tables 2 and 3 **in** Ostrowska et al. 2000, this volume, pp. 215, 216.

The optical depths τ **in** our experiments were measured simultaneously

with **fluorescence**. But values **of** C a (0) are not known. Never**the**less, **the**

latter can be estimated from **the** real and optical depth known for each

pr**of**ile us**in**g Woźniak’s bio-optical classification **of** waters (Woźniak et. al

1992a and b).

Table 1. Values **of** C m, n **in** eq. (5)

a) for 0

**Variability** **of** **the** **specific** **fluorescence** **of** **chlorophyll** **in** **the** **ocean**. Part 2. 227

From this classification we can establish **the** relationship between **the**

trophic **in**dex **of** **the** sea (which we assume to be C a (0)), **the** optical depth τ

and **the** real depth z. For **the** purpose **of** **the** present work, this relationship

is described by **the** follow**in**g approximate polynomial:

[

4∑ 4∑

] (( ) z m )

log C a (0) = C m, n (log z) n log . (5)

τ

m=0 n=0

The coefficients **of** this polynomial are set out **in** Table 1.

4. Empirical verification **of** methods

In order to assess **the**ir practicability, **the** two methods **of** determ**in****in**g

**the** **chlorophyll** a concentration were verified empirically, that is to say, **the**

respective measured data **of** C a, 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** estimat**in**g **chlorophyll** a concentrations at different

depths **in** **the** sea us**in**g **the** statistical correlation method (eq. (2)) and **the** physical

method (eqs. (4) and (5))

Arithmetic statistics Logarithmic statistics

systematic statistical systematic standard error statistical

factor

〈ε〉 [%] σ ε [%] 〈ε〉 g [%] x σ − [%] σ + [%]

method **of** 30.9 ± 89.8 3.6 2.07 –51.7 107

statistical

correlations

physical method 16.3 ± 5.0 1.5 1.5 –33.3 50.8

where

ε =(C a, C − C a, M )/C a, M – errors,

〈ε〉 – arithmetic mean **of** errors,

σ ε – standard deviation **of** errors (statistical error),

〈ε〉 g =10 [〈log(Ca, C/Ca, M )〉] − 1 – logarithmic mean **of** errors,

〈log (C a, C /C a, M )〉 –mean**of**log(C a, C /C a, M ), 〈log (C a, C /C a, M )〉,

σ log – standard deviation **of** log (C a, C /C a, M ),

x =10 σ log

– standard error factor,

σ − = 1 x − 1 and

σ + = x − 1.

228 M. Ostrowska, D. N. Mator**in**, D. Ficek

ñ3

a, C [mg tot. chl m ]

**chlorophyll** concentration

C a

1000

100

10

1

0.1

0.01

a

frequency [%]

0

0.01 0.1 1 10 100 1000 0.0625 0.25 1 4 16

ñ3

Ca, M [mg tot. chl a m ] ratio C a, C /C a, M

**chlorophyll** concentration

Fig. 3. Comparison between measured C a, M and calculated C a, C **chlorophyll** a

concentrations us**in**g **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)

30

20

10

b

ñ3

a, C [mg tot. chl m ]

**chlorophyll** concentration

C a

1000

100

10

1

0.1

0.01

a

frequency [%]

b

30

20

10

0

0.01 0.1 1 10 100 1000 0.0625 0.25 1 4 16

Ca, M [mg tot. chl a m ]

**chlorophyll** concentration

ñ3

ratio C a, C /C a, M

Fig. 4. Comparison between measured C a, M and calculated C a, C **chlorophyll** a

concentration us**in**g **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** C a, C

were calculated from measurements **of** F 0 ′ . In **the** case **of** **the** physical

method, values **of** depths τ 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%. Modify**in**g **the** method **of** statistical correlation has thus brought

about a highly desirable improvement **in** **the** accuracy **of** **chlorophyll** a

determ**in**ations.

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