The algorithms for calculation of the bio-optical characteristics remained as before . 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 . We used the normalized water-leaving radiance LWN( 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: LWN( λ i) = Rrs( λ i) · F0( λ i), whereF0( 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 . The normalized water-leaving radiance LWN( λ ) is derived from ρ( λ ) with a formula given in .
For SeaWiFS spectral bands 510 and 555 nm, the following regression equation between chlorophyll concentration and the ratio LWN(510)/LWN(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/m3. 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 [LWN(510)/LWN(555)] -1.39. (1)
In the MODIS case, the ration Rrs (531)/Rrs (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 .
To derive the particle backscattering coefficient bbp(555), the diffuse attenuation coefficient Kd(555) and the parameter of X(555) are calculated:
X(555) =bb(555)/[a(555)+bb(555)], (3)
where a(555) and bb(555) are the seawater absorption and backscattering coefficients. The X(555) value is derived through the value of normalized water-leaving radiance LWN(555) at 555 nm, Kd(555) through the ratio LWN(510)/LWN(555) of values of the normalized water-leaving radiance at 510 and 555 nm.
Then the value of [a(555)+bb(555)] is found from Kd(555) by using the Gordon's formula .
The particle backscattering coefficient bbp(555) is calculated as a difference between the seawater backscattering coefficient bb(555) and the known value of pure seawater backscattering coefficient bbw(555). The description of the algorithm in more detail is given in  .
In the MODIS case the particle backscattering coefficient bbp(555) was derived by similar way with LWN (531), and LWN (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 LWN (by the floating spectroradiometer) and TSM were used; first values of the particle backscattering coefficient bbp were determined  and then the regression relationship TSM vs. bbp was derived :
TSM = 73.5 bbp +0.016, (4)
where bbp is measured in m-1 and TSM is presented in mg/l. The mean error in determination of suspended matter concentration is about 30%.
There is an evident requirement that LWN(510) and LWN(555) in the case of SeaWiFS and LWN(531)/LWN(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 LWN(490) or LWN(670) (or LWN(488) and LWN(667) in the MODIS case) were negative. To avoid the significantly erroneous values of Chl or bbp derived through the ratio LWN(510)/LWN(555) or LWN(531)/LWN(547), the data with negative values of LWN(490) or LWN(670) (LWN(488) and LWN(667) in the MODIS case) were also rejected out.