Автор неизвестен - Remote sensing of vertical phytoplankton pigment distributions in the baltic new mathematical - страница 2

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On the other hand, values of E0(X, z), PAR0(z) and apl(X, z), a*i psp(X, z) can be determined from a knowledge of the surface irradiance PAR0(0) and the trophic index of the waters in question, i.e., the surface chlorophyll a concentration Ca(0), using the following models:

Wozniak's bio-optical model of the optical properties of the Baltic, with which typical scalar and vector irradiances can be determined for different trophic types of seawater and at different depths in the water column (Kaczmarek & Wozniak 1995, Wozniak et al. 2003);

the model of the absorption properties of Baltic phytoplankton (Ficek et al. 2004) and also the model description of the vertical distribution of different pigment concentrations in the Baltic presented in parts 1 and 2 of this work (Ostrowska et al. 2007, Majchrowski et al. 2007, both in this volume). This enables spectra of the total absorption coefficients for all phytoplankton pigments and the absorption coefficient for photosynthetic phytoplankton pigments only to be determined.

3. Results and discussion

Within the framework of the foregoing analysis and modelling scheme, depth distributions of the factor fa were determined by model calculations for a water layer extending from the surface down to an optical depth of т и 5 in Baltic waters of different trophic indices (from mesotrophic with a surface chlorophyll concentration Ca(0) = 0.2 mg tot. chl a m-3 to

supereutrophic with Ca(0) = 70 mg tot. chl a m-3) and for the various mean daily values of the irradiance just below the sea surface PAR(0) (from close to 0 to 1600 fjEin m-2 s-1) measured in these waters. These calculations were performed independently for two seasons in the year: (1) the 'winter' period (from day in the year 1 to 118, and from 261 to 365) and (2) the 'summer' period (from day in the year 119 to 260). Hence, the calculations had to take into consideration the two mathematical descriptions, different for summer and winter, of the vertical distributions of the phytoplankton accessory pigment concentrations in the Baltic postulated in part 2 of this series (Majchrowski et al. 2007, this volume).

Some examples of the results obtained with reference to a mean daily irradiance of PAR(0) = 600 //Ein m-2 s-1 are illustrated graphically in Figure 1b. This figure shows that values of fa vary with depth in the sea and trophic index (surface concentration of chlorophyll Ca(0)); they also depend on the season of the year.

Comparison of these plots for the Baltic (Fig. 1b) with similar plots for oceanic waters (Fig. 1a) shows that they have certain features in common, like the increase in value of fa with depth, but that there are also a number of differences between them. In particular, the dependence of fa on trophic index, i.e., on the concentration Ca(0), is more complex in the Baltic than in the oceans and more difficult to describe mathematically. This is because at the same optical depths in the sea and under the same irradiance conditions, the values of fa measured in different regions of the Baltic (Fig. 1c) are usually the smallest in waters with an intermediate trophic index (values of Ca(0) from 1.7 to 7.5 mg tot. chl a m-3) and increase in waters of higher and lower trophic indices. The situation here is therefore different from that in oceanic Case 1 waters, where the value of fa rises monotonically with increasing Ca(0). Moreover, the range of variation of fa in the Baltic (according our observations from 0.5 to 1) is narrower than that in oceanic waters. Finally, these changes in the Baltic exhibit a certain seasonality that was not detected in the oceans: the values of fa under the same conditions measured in the 'warm' months (from May to September) are generally lower than in the remaining 'cool' months.

These values of fa were obtained as a result of time-consuming calcula­tions using the complex models described in Section 2 of this paper. To make the calculations easier, an alternative, polynomial method was developed to determine the mean absorption coefficients a*pl, Hpl PSP, and then the factor fa (from eq. (4)), from the surface total chlorophyll a concentration Ca(0), the optical depth т and the irradiance PAR(0).Todothis, the computed values of a*pl, Hpl PSP and fa were approximated by means of a polynomial using the complete mathematical apparatus of earlier models.

Figure 1. Vertical profiles of the non-photosynthetic pigment factor fa in waters of different trophic index:

a) modelled profiles for PAR(0) = 695 /jEin m-2 s-1 in oceanicCase1waters - according to Ficek et al. 2000;

b) modelled profiles for PAR(0) = 600 /jEin m-2 s-1 in Baltic Case 2 waters; continuous lines - the 'winter' period (from day in the year 1 to 118 and from 261 to 365), dashed lines - the 'summer' period (from day in the year 119 to 260) according to formulas (1), (8), (9) and Tables 2 and 3;

c) empirical profiles in Baltic case 2 waters; continuous lines - the 'winter' period (from day in the year 1 to 118 and from 261 to 365), dashed lines - the 'summer' period (from day in the year 119 to 260); for the following trophic indices Ca(0) given in [mg tot. chl a m-3] and irradiance PAR(0) given in [/.tEin m-2 s-1]:

M- Ca(0) = 0.42; PAR(0) = 304; data from 17.02.2000;

I - Ca(0) = 0.95; PAR(0) = 321; data from 8.02.2003; Ca(0) = 0.82; PAR(0) = 67; data from 10.02.2003; Ca(0) = 0.54; PAR(0) = 820; data from 10.05.2000; (continued next page)

E1-Ca(0) = 1.04; PAR(0) = 270; data from 03.2001; Ca(0) = 1.38; PAR(0) = 810;

data from 9.05.2000; Ca(0) = 1.62; PAR(0) = 855; data from 23.05.2004;

E2- Ca(0) = 4.04; PAR(0) = 665; data from 21.04.2004; Ca(0) = 2.97; PAR(0) = 855;

data from 11.05.2000; Ca(0) = 4.19; PAR(0) = 811; data from 8.05.2002;

E3- Ca(0) = 5.25; PAR(0) = 381; data from 10.04.2004; Ca(0) = 5.26; PAR(0) = 654;

data from 22.04.2004; Ca(0) = 5.86; PAR(0) = 691; data from 16.09.2004;

E4- Ca(0) = 11.0; PAR(0) = 643; data from 17.04.2004; Ca(0) = 17.0; PAR(0) = 638;

data from 20.04.2004;

E5- Ca(0) = 22.6; PAR(0) = 667; data from 19.04.2004; Ca(0) = 22.7; PAR(0) = 330; data from 27.04.1999; Ca(0) = 32.6; PAR(0) = 690; data from 28.04.1999

Table 1. Values of Am^n in eqs. (8) and (9)

a) 'winter' (for days in the year 1-118 and 261-365)

0 12 3

0

1.921E-02

-1.323E-02

7.601E-03 -2.003E-03

1

-4.388E-03

4.326E-03

-1.655E-04

2

4.319E-04

-8.490E-04

 

3

9.279E-05

 

 

b) 'summer' (for days in the year 119-260)

0123

0

2.059E-02

-2.019E-02

1.348E-02 -3.055E-03

1

-2.941E-03

5.189E-03

-1.246E-03

2

1.633E-04

-4.930E-04

 

3

2.641E-05

 

 

Table 2. Values of Bmn in eq. (8)

a) 'winter' (for days in the year 1-118 and 261-365)

0123

0

2.836E-03

-4.004E-04

-1.808E-04

1.760E-05

1

-1.363E-04

-2.349E-04

1.750E-05

 

2

-1.121E-04

4.973E-05

 

 

3

1.332E-05

 

 

 

b) 'summer' (for days in the year 119-260)

0123

0

2.788E-03

-3.302E-04

-2.138E-04

2.783E-05

1

-1.809E-04

-2.568E-04

2.268E-05

 

2

-8.982E-05

5.022E-05

 

 

3

1.124E-05

 

 

 

Table 3. Values of Cm,n in eq. (8) a) 'winter' (for days in the year 1-118 and 261-365) n\m 0_1_2_3

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