The algorithms for calculation of the bio-optical characteristics remained as before [16]. The chlorophyll concentration, particle backscattering coefficient and the total suspended matter (TSM) concentration were computed. The yellow substance absorption coefficient was not derived because the semi-analytic algorithm cannot work in the Barents Sea due to great errors in the atmospheric correction [12,13].

Data
of spectral bands 510 and 555 nm are used in the SeaWiFS case and
of spectral bands 531 and 547 nm for MODIS-Aqua. At these spectral
bands, the satellite and *in situ
*measured data on the radiance
reflectance are agreed with reasonable accuracy [12]. We used the
normalized water-leaving radiance *L*_{WN}(* λ *_{i})
or the above-surface remote-sensing reflectance * R *_{rs}(* λ *_{i});
the choice between them is of no importance, because these
quantities are related to each other by a simple formula: *L*_{WN}(* λ *_{i})
=*
R*_{rs}(* λ *_{i}) · *F*_{0}(* λ *_{i}),
where*F*_{0}(* λ *_{i})
is the extraterrestrial solar irradiance
(http://oceancolor.gsfc.nasa.gov).

**Algorithm for chlorophyll "a"
concentration **

The
regional algorithm for assessment of chlorophyll "a"
concentration was developed on the basis of the field data
measured in August-September 1998 (the 13-th and 14-th cruises of
R/V Academik Sergey Vavilov). Chlorophyll concentration and the
subsurface radiance reflectance *ρ*(* λ *)
were measured concurrently; the latter was measured by a floating
spectroradiometer [14]. The normalized water-leaving radiance
*L*_{WN}*(** λ **)*
is derived from *ρ*(* λ *)
with a formula given in [15].

For
SeaWiFS spectral bands 510 and 555 nm, the following regression
equation between chlorophyll concentration and the ratio
*L*_{WN}*(*510*)/L*_{WN}*(*555*)*
was derived and used:

Equation
(1) was calculated from the field data covering both the open
regions and the Pechora Sea (n=21); a standard error of the
regression equation is 0.135 mg/m^{3}.
It is assumed to be valid in the whole period of study from May to
September, but the errors can increase during a phytoplankton
bloom in May when the relationship between the phytoplankton
pigment and yellow substance absorption may be changed.

*Chl*=
0.34 [*L*_{WN}(510)/*L*_{WN}(555)]^{
-1.39}. (1)

In the MODIS case,
the ration *R*_{rs
}(531)/*R*_{rs
}(547) was used and the
regression equation took the form:

*Chl*=
0.37 [0.006 * R *_{rs}(531)/* R *_{rs}(547)]^{
-3.25}. (2)

**Algorithm for the particle
backscattering coefficient. **

The algorithm was developed for the cases where the semi-analytic algorithm cannot work properly due to high errors in the atmospheric correction; such situation is just typical in the Barents and White Seas. The simplified algorithm uses only two SeaWiFS spectral bands 510 and 555 nm where errors in atmospheric correction are much less than at 412, 443, and 490 nm [16].

To derive the particle
backscattering coefficient *b*_{bp}(555),
the diffuse attenuation coefficient *K*_{d}(555)
and the parameter of *X*(555)
are calculated:

*X*(555)
=*b*_{b}(555)/[*a*(555)+*b*_{b}(555)], (3)

where
*a*(555)
and *b*_{b}(555)
are the seawater absorption and backscattering coefficients. The
*X*(555)
value is derived through the value of normalized water-leaving
radiance *L*_{WN}(555)
at 555 nm, *K*_{d}(555)
through the ratio *L*_{WN}(510)/*L*_{WN}(555)
of values of the normalized water-leaving radiance at 510 and 555
nm.

Then
the value of [*a*(555)+*b*_{b}(555)]
is found from *K*_{d}(555)
by using the Gordon's formula [17].

The
particle backscattering coefficient *b*_{bp}(555)
is calculated as a difference between the seawater backscattering
coefficient *b*_{b}(555)
and the known value of pure seawater backscattering coefficient
*b*_{bw}(555).
The description of the algorithm in more detail is given in [17] .

In
the MODIS case the particle backscattering coefficient *b*_{bp}(555)
was derived by similar way with *L*_{WN
}(531), and *L*_{WN
}(547) as the input parameters.

**Total suspended matter (TSM)**

Concentration
of total suspended matter (TSM) was derived for the
Barents Sea from SeaWiFS
data by the regional algorithm based on the field data measured in
13 and 14 cruises of RV “Akademik Sergey Vavilov”
(August-September 1998). Data of concurrent measurements of
water-leaving radiances *L*_{WN}*
*(by the floating
spectroradiometer) and *TSM
*were used; first
values of the particle
backscattering coefficient *b*_{bp}
were determined [12]
and then the regression relationship TSM vs. *b*_{bp}
was derived [16]:

*TSM *=
73.5 *b*_{bp}
+0.016, (4)

where *b*_{bp}
is measured in m^{-1}
and *TSM *is
presented in mg/l. The mean error in determination of suspended
matter concentration is about 30%.

**Data
rejection. **

There
is an evident requirement that *L*_{WN}*(*510*)
*and
*L*_{WN}*(*555*)*
in the case of SeaWiFS and *L*_{WN}*(*531*)/L*_{WN}(547)
in the MODIS case must be positive. But our analysis showed that
in some cases these quantities were strongly underestimated due to
errors in the atmospheric correction. According to the obtained
results, it occurred when the values of *L*_{WN}(490)
or *L*_{WN}(670)
(or *L*_{WN}(488)
and *L*_{WN}(667)
in the MODIS case) were negative. To avoid the significantly
erroneous values of *Chl*
or *b*_{bp}
derived through the ratio *L*_{WN}(510)/*L*_{WN}(555)
or *L*_{WN}*(*531*)/L*_{WN}*(*547*)*,
the data with negative values of *L*_{WN}(490)
or *L*_{WN}(670)
(*L*_{WN}(488)
and *L*_{WN}(667)
in the MODIS case) were also rejected out.