**4.2.
Algorithms **

The only changes in the bio-optical algorithms, as compared with the previous issue [6], were made due to changes in the spectral channels of MODIS-Aqua. The SeaWiFS algorithms remained unchanged.

**Chlorophyll
concentration**

__From
SeaWiFS data__,
chlorophyll concentration in the sub-regions 1-5 was calculated
with the algorithm developed by specialists from MHI NANY [29-31]:

*Chl*=
1.13 [*L*_{WN}(510)/*L*_{WN}(555)]^{
-3.33}. (7)

For the sub-regions 6-8 the algorithm developed by specialists from SIO RAS [32] was used:

*Chl*=
0.88 [*L*_{WN}(510)/*L*_{WN}(555)]^{
-2.24}.
(8)

Comparison
between the two algorithms has shown that the *Chl*–SIO
values (derived with the algorithm (8)) are higher than the
*Chl*–MHI
values (derived with the algorithm (7)) if *Chl*–SIO
< 0.4 mg·m^{-3}.
The *Chl*–SIO
values are lower than the *Chl*–MHI
values if *Chl*–SIO
> 0.7 mg·m^{-3}.
Within the *Chl*–SIO
range from 0.4 to 0.7 mg·m^{-3
}the *Chl*
values derived by the two algorithms differ
by less than 15%.

The
both algorithms are assumed to be valid in warm season
(May-September). They can result in considerable errors in
absolute values of *Ñ**hl*
in cold season. However, it can be assumed that relative changes
of chlorophyll concentration are reproduced adequately with the
both algorithms, and for this purpose our computations were also
carried in cold season.

__From MODIS-Aqua data,__
the algorithm to derive chlorophyll concentration in the
sub-regions 1-5 was complicated:

*Chl*
= 0.5 (*Chl*_{1
}+*
Chl*_{2}),
(9)

where
*Chl*_{1}
= 1.13* *[0.66
*R*_{rs}(488)*/R*_{rs}(547)
+ 0.40]^{–3.33};

*Chl*_{2}
= 1.13* *[2.35
*R*_{rs}(531)*/R*_{rs}(547)
– 1.44]^{–3..33}.

For the sub-regions 6-8 the Chl algorithm with MODIS data was similar to (8):

*Chl
*= 0.83 [0.996 *R*_{rs}(531)/*
R*_{rs}(547)]^{-4.36}.
(10)

**Particle
backscattering**

For
calculation of the particle backscattering coefficient *b*_{bp}
in the Black Sea from SeaWiFS data, the simplified algorithm
described in Section 2.2
was used, but *K*_{d}(555)
was calculated through the ratio *L*_{WN}(490)/
*L*_{WN}(555)
instead of *L*_{WN}(510)/
*L*_{WN}(555)
in the Barents Sea.

Computations of the
particle backscattering coefficient *b*_{bp}
in the Black Sea from MODIS-Aqua data were performed by the same
algorithm as with SeaWiFS data but the ratio of *L*_{WN
}(488)/*L*_{WN
}(547) was used instead of *L*_{WN
}(490)/*L*_{WN
}(555) (our calculations showed
that those ratios differ little from each other).

**Yellow
substance absorption**

In
the Black Sea it is possible to retrieve the values of the yellow
substance absorption coefficient *a*_{g}(440).
The version of a semianalytic algorithm described in [12]
was used. It is difficult to estimate errors of the derived values
of *a*_{g}
because they depend strongly on errors of the atmospheric
correction. Of course, the cases with negative values of *L*_{WN}
were rejected out, but we could not check the errors in *L*_{WN}
which were not so pronounced.