# Автор неизвестен - Remote sensing of vertical phytoplankton pigment distributions in the baltic new mathematical - страница 3

0

4.680E-06

-2.074E-06

-2.582E-07

1.580E-08

1

-2.437E-06

1.247E-06

5.668E-08

2

3.190E-07

-1.754E-07

3

-2.155E-09

b) 'summer' (for days in the year 119-260) n\m 0_1_2_3_

0

4.576E-06

-1.941E-06

-3.052E-07 2.422E-08

1

-2.399E-06

1.173E-06

6.711E-08

2

3.222E-07

-1.659E-07

3

-3.622E-09

The relevant values of Ti*pl and (f^ PSP can be determined with the aid of polynomials (8) and (9). The values of the coefficients Amn, Bmn and Cmn are given in Tables 1-3. On the other hand, fa was obtained according to eq. (4) by dividing and Hpl PSP determined from the following polynomials:

3 r 3

apl = Г T.Am.n (log(Ca (0)))n\ тт +

33

£ Y,Am,n (log(Ca (0)))П m=0 L n=0 j

3 Г 3 l £ ^5m,n(l09(Ca (0)))n

m=0 n=0

+ ^ I ^Bm.n(log(Ca (0))Г\тГП +

m=0 n=0

3 Г 3 l +PAR(0)J2 Y,Cm,n(log(Ca(0)))n т", (8)

m=0 n=0

3 Г 3 l ~apipsp =£ Y,Am,n(log(Ca(0)))n т", (9)

m=0 n=0

where

Ca(0) [mg tot. chl a m-3] - surface concentration of chlorophyll a; PAR(0) [//Ein m-2 s-1 ] - downward irradiance at the surface in the PAR spectral range (400-700 nm).

4. Verification of the model relationships; conclusions

Values of the factor fa cannot be measured empirically. This is because it is impossible under in vivo conditions to measure separately the light

absorption by photosynthetic pigments and by photoprotecting pigments. Such a measurement has so far been possible only with respect to the total absorption by all pigments. The verification of the values of fa computed using the model description (see eqs. (4), (8) and (9)) was therefore based on quasi-empirical values of this factor. Such quasi-empirical values of fa were calculated on the basis of empirical values of the following parameters measured at the same depths: Ed(X, z) (or also PAR(z)), apl(X, z) and the concentrations of all the groups of phytoplankton pigments Ca(z) and Cj (z) (where j denotes in turn chl b,chl c, PSC, phyc, PPC). This enabled the respective spectra of the chlorophyll-specific coefficient of light absorption for all phytoplankton pigments apl(X, z) and for photosynthetic pigments apl psp(X, z) to be calculated from generally known relationships (see, e.g., Wozniak & Dera 2007):

apl(X, z) = (Ca(z))-1 Q*(X, z)[a*a(X)C\(z)+a*b(X)Cb(z) +

+a*c (X)Cc(z)+ aPsC(X)CPSC(z)+ a*phyc(X)Cphyc(z) +

+appc(X)Cppc(z)], (10) apipsp(X, z) = (Ca(z))-1 Qb(X, z)[a*a(X)Ca(z) + ab(X)Cb(z) +

+ab(X)Cc (z)+ aPsc(X)CPSC(z)+ a*phyc(X)Cphyc(z)],

where

aa, ab, apSC, aphyc, appc - the respective spectral mass-specific absorption coefficients of light for chlorophylls a, chlorophylls b, chlorophylls c, photosynthetic carotenoids (PSC), phycobilins and photoprotecting carotenoids (PPC) (in solvent). In the calculations the values of these coefficients are those typical of the pigments in Baltic phytoplankton, determined earlier and described by the sum of Gaussian bands (see eqs. (4) and (5), and Table 2 in Ficek et al.

2004);

Q ( X, z) - a spectral dimensionless factor of the change in absorption due to pigment packaging in the phytoplankton cells, the so-called packaging

function (Hulst 1981, Morel & Bricaud 1981, Wozniak & Dera 2007).

The values of this packaging function were calculated by the method of successive approximations based on known empirical spectra of apl(X, z) and empirically determined data on the concentration of pigments Cj(z). The algorithm of such approximate calculations is presented in the Annex in Wozniak et al. 1999. Once the spectra of apl(X, z) and apl PSP(X, z) were established, their mean values (according to eqs. (5) and (6)), weighted by the downward irradiance spectra Ed(X, z) measured empirically at the same depths z,could be defined. Then, according to eq. (4), the quasi-empirical values of the

В. Wozniak, R. Majchrowski, M. Ostrowska et al.

non-photosynthetic pigment factor - fajD (z) (determined quasi-empirically - index D) were calculated.

A total of 400 values of the quasi-empirical non-photosynthetic pigment absorption factor fatp,(z) were determined in the above manner at different depths in the sea over a range of optical depths from т = 0 to5at 50 measuring stations. Figure 1c illustrates examples of such empirical profiles of fa(T). Then, the values of fa>c (computed using model - index C) computed for these stations and depths using eqs. (8), (9) and (4) were compared with those determined quasi-empirically fatp,. Figure 2 compares these modelled and measured values, and Table 4 gives the errors of the estimation.

1.0 I............................и

0.9

0.8

0.7

0.7

0.8 0.9

fa,D

1.0

Figure 2. Comparison of the values of the empirical non-photosynthetic pigment absorption factor fai D with the corresponding values calculated by the polynomial method fai C (using formulas (8), (9) and (4)) in the euphotic zone of the Baltic at different stations in 1999-2004

These plots and the verification show that the errors in the values of the non-photosynthetic pigment absorption factor fa estimated using the model developed in this work (eqs. (4), (8) and (9)) are small: in practice they do not exceed 4%. Likewise, the changes of these model values of fa in Baltic waters of different trophic indices with depth (Fig. 1b) are similar in range and nature, as are the empirical profiles (Fig. 1c). This testifies to the practical utility of this mathematical description of the vertical distribution of the non-photosynthetic pigment absorption factor. The objective of this work has therefore been achieved. These new mathematical expressions, enabling vertical profiles of the factor fa in the Baltic to be estimated from known trophic indices (Ca(0)) and surface irradiances (Ed(X, 0) and/or PAR(0)), can be successfully applied in remote-sensing algorithms for monitoring the Baltic ecosystem.

Table 4. Relative errors in the estimation with formulas (8), (9) and (4) of the non-photosynthetic pigment absorption factor fai C in the euphotic zone of the Baltic Sea.

Arithmetic

statistics

Logarithmic statistics

systematic

statistical

systematic

standard

statistical

error

error

error

error factor

error

<є> [%]

os [%}

< є >g [%}

x

a- [%] a+ [%]

0.06

± 3.96

-0.01

1.04

-3.87 +4.03

where

Є = (fa,C - fa,D) - relative error,

fa d quasi-empirical non-photosynthetic pigment absorption factor - (eqs. (10), (11) and (4)),

fa,C modelled non-photosynthetic pigment absorption factor (eqs. (8), (9) and (4)),

<Є> - arithmetic mean error,

as - standard deviation of errors (statistical error),

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