Asymptotic optical attenuation in sea water Marinyuk, V.V.; Sheberstov, S.V.
Journal of quantitative spectroscopy & radiative transfer,
January 2023, 2023-01-00, Letnik:
295
Journal Article
Recenzirano
•A simple method is proposed for calculating the asymptotic value of the diffuse attenuation coefficient of sea water.•The scaling law deduced from the radiative transfer equation is verified for ...realistic ocean scattering models.•Over a wide range of ocean water IOPs, the asymptotic attenuation coefficient is described by a universal analytical formula.
A simple method is proposed for calculating the asymptotic attenuation coefficient K∞ of sea water. The method is based on the scaling analysis of the radiative transfer equation within the small-angle approximation. From the scaling, it follows that K∞ is analytically expressed in terms of the absorption coefficient, the transport scattering coefficient, and two dimensionless numeric constants (scaling exponents) depending on a specific scattering phase function. For a given phase function, the scaling exponents can be determined by numerical calculations of the downwelling irradiance. We test the method on a number of oceanlike scattering models. A direct numerical integration of the radiative transfer equation is carried out with the DISORT code for the Petzold, Morel et al., Fournier–Forand and Kopelevich phase functions. Our numerical results agree perfectly with the small-angle scaling and allow us to establish an explicit expression for K∞ for each phase function. We find that the scaling exponents depend rather weakly on the specific angular profile of the phase function and can be taken equal to their values for the Henyey–Greenstein function (this approximation leads to a relative error in the value K∞ less than 5%). So that, within a few percent accuracy, the coefficient K∞ is governed only by the absorption and transport scattering coefficients and is described by a universal formula.
We present results of validating the algorithms used to estimate sea surface solar radiation at 400-700 nm, photosynthetically available radiation (PAR), from satellite ocean color data and an ...appropriate validation procedure when data are collected using a moving ship. The validation was performed using field measurements of PAR during a transit cruise from the Baltic to the White Sea during the summer of 2014. The PAR was measured at 10-minute intervals using a deck radiometer throughout the daylight hours. The satellite estimate of daily surface PAR with an acceptable error, on the scale of 1 day-10
km, is shown.
The interannual (2002–2021) variability of primary production (PP) of the Kara Sea and associated environmental factors was assessed by MODIS-Aqua data and model calculations. Warming in the Kara Sea ...region during the last two decades was characterized by a pronounced positive trend of the sea surface temperature (
T
0
) and weak positive trend of the ice-free area (
S
) averaged for the growing season (April–October). During the investigated period,
T
0
increased by 3.55°C with a trend of 10% y
–1
and
S
increased by 110 × 10
3
km
2
with a trend of 1.4% y
–1
, on average. The values for the water column PP (IPP) averaged over the growing season statistically significantly (
p
< 0.05) decreased in the all Kara Sea regions (
R
2
= 0.22–0.59). For the entire Kara Sea, IPP declined by 38 mgC m
–2
d
–1
with a moderate trend of 1.1% y
–1
(
R
2
= 0.37). The value of photosynthetically active radiation (PAR) averaged over the growing season weakly, but statistically significantly (
p
< 0.05), decreased in the entire Kara Sea areas (
R
2
= 0.20–0.31). Also, in all regions, significant (
R
2
= 0.24 – 0.38) weak or moderate negative trends of surface chlorophyll (chl)
a
were specified. The total annual PP (PP
tot
) increased insignificantly in accordance with an increase in
S
(0.7% y
–1
,
R
2
= 0.08). The most significant decrease in IPP was specified for spring (
R
2
= 0.28). In autumn, a statistically significant positive trend of
S
(
R
2
= 0.24) was observed. Owing to such an increase in
S
, the notable growth of PP
tot
was noted in autumn. This study demonstrates that the decrease of IPP, resulting from the decrease in PAR and chl, in some degree was the reason for moderation of PP
tot
. It should be concluded that in a period of intense warming, the decrease in IPP of the Kara Sea should affect the productivity of higher trophic levels of the food web.
Studies of the interannual variability of primary production, surface water temperature, photosynthetically active radiation, and sea ice cover in the Laptev Sea were performed based on MODIS-Aqua ...data (2002–2018). For a 17-year period, a statistically significant positive trend of surface temperature (
R
2
= 0.27) and a negative trend of photosynthetically active radiation (
R
2
= 0.24) were established. For the investigated period, the average annual water temperature in the Laptev Sea increased by 1.38°C and photosynthetically active radiation decreased by 3.4 Ein m
–2
d
–1
. The ice-free water area extended insignificantly (0.15% y
–1
). The total primary production declined by 1.87 TgC or by 1.4% y
–1
. This decline was accompanied by a decrease in area-specific primary production. For the investigated period, the average annual area-specific primary production values declined by 37.4 mgC m
–2
d
–1
or by 1.6% y
–1
. The presented results suggest that changes in Laptev Sea primary productivity for the last 17 years were mainly caused by a decrease in photosynthetically active radiation and area-specific primary production rather than the dynamics of the sea ice cover.
We study the total reflectance of an absorbing, multiply scattering medium with large (as compared to the light wavelength) inhomogeneities at grazing incidence of light. To model highly forward ...scattering in the medium, we take advantage of the two-parameter Reynolds-McCormick scattering phase function. Using the scaling analysis for the small-angle radiative transfer equation, we derive simple analytic formulae for the dependence of the reflectance on the medium transport coefficients and the angle of incidence. The results obtained are verified by comparison with results of a direct numerical integration of the radiative transfer equation.
—
Studies of seasonal variability of the East Siberian Sea (ESS) water column primary production (IPP) and evaluation of its total annual value (PP
tot
) were performed using MODIS-Aqua data ...(2002–2018). Region-specific primary production and chlorophyll algorithms were used for the first time to achieve that result. Northeastern and Southwestern regions were distinguished in ESS based on multiyear average daily primary production. Seasonal variations in IPP in the Northeastern region were characterized by the maximum in June (273 mgC m
–2
d
–1
). The maximum of water column primary production value in the Southwestern region was recorded in May (311 mgC m
–2
d
–1
). The maximum of IPP for the entire ESS was registered in June (273 mgC m
–2
d
–1
). Values of daily primary production and PP
tot
in the Southwestern region were, respectively, 1.8 and 2 fold higher than in the Northeastern region. The multiyear averaged value of ESS IPP was equal to 91 mgC m
–2
d
–1
and PP
tot
value was equal to 9 TgC. Productivity of the Siberian seas decreased eastward.
—
Interannual variability (2002–2018) of primary production, surface seawater temperature (
T
0
), photosynthetically active radiation (PAR) and ice cover area in the East Siberian Sea (ESS) was ...studied based on the data of the MODIS-Aqua ocean color scanner. The annual total primary production (PP
tot
) decreased by 1.7 TgC over 17 years. The multi-year negative trend in PP
tot
was 0.1 TgC y
–1
(1.38% y
–1
). The decrease in PP
tot
was accompanied by the decrease in the area-specific primary production (IPP). Over the investigated period the annual mean IPP decreased by 13 mgC m
–2
d
–1
. The multi-year negative trend in IPP was 0.76 mgC m
–2
d
–1
y
–1
(0.84% y
–1
). The decrease in PP
tot
and IPP was accompanied by statistically insignificant increase in
T
0
(
R
2
= 0.09) and statistically significant decline in PAR (
R
2
= 0.29). Over the 17 years,
T
0
in ESS increased by 0.68°С (0.04°С y
–1
or 3.2% y
–1
) and PAR declined by 3.4 Ein m
–2
d
–1
(0.2 Ein m
–2
d
–1
y
–1
or 1.9% y
–1
). The ice-free area slightly diminished during the study period (
R
2
= 0.10) by 64.94×10
3
km
2
. The statistically insignificant negative multi-year trend in the ESS ice-free area was 3.82 × 10
3
km
2
y
–1
(0.87% y
–1
). Long-term variability in PP
tot
in ESS from 2002 to 2018 depended not only on the decrease in the ice cover but also on PAR level and IPP.
The seasonal variability of primary production in the Laptev Sea has been studied and its annual values have been determined using the data of a MODIS-Aqua scanner (mean for 2002–2018). ...Regional-specific algorithms of primary production and chlorophyll are used for this purpose for the first time. Two regions of the Laptev Sea—northwestern and southeastern—are distinguished on the basis of the primary production long-term averaged over many years. Seasonal variations in the primary production in the water column of the northwestern region are characterized by the maximum in June (245 mg C/m
2
per day). The maximal primary production in the southeastern region and over the entire area of the Laptev Sea (273–282 mg C/m
2
per day and 256–281 mg C/m
2
per day, respectively) is recorded from May to July. Daily and annual primary production in the southeastern region are 1.9 and 3 times higher, respectively, than in the northwestern region. The primary production mean for the Laptev Sea is 125 mg C/m
2
per day and the total annual primary production is 8 × 10
12
g C.
Seasonal variations in primary production (PP) in the Kara Sea are underresearched. Previous studies only collected data during autumn or in late summer. However, the middle of summer is close to the ...beginning of the growing season, when PP can contribute significantly to annual water column integrated primary production (IPP). In addition, differences can be expected in the spatial and vertical distribution of phytoplankton communities in this period. This gap in midsummer data was addressed within the framework of a multidisciplinary research cruise by the R/V “Akademik Mstislav Keldysh” (from 15 July to 18 August 2016). High values of IPP (> 200 mgC m
−2
day
−1
) and surface chlorophyll
a
(Chl
a
) concentration (Chl
0
> 1 mg m
−3
) were associated with the Ob–Yenisey river plume, located in the central part of the Kara Sea. Beyond the influence of the plume, in the western and southwestern regions of the Kara Sea, well-pronounced subsurface chlorophyll maxima (SCM) were observed. In some cases, the Chl
a
concentration in SCM exceeded Chl
0
by two orders of magnitude. SCM were often accompanied by subsurface PP maxima (SPM). At stations where SCM was pronounced, IPP values reached 500–800 mgC m
−2
day
−1
, and > 30 % of IPP was accounted for by SPM-integrated PP. Thus, in the middle of summer in the Kara Sea, IPP was linked with the chlorophyll-specific phytoplankton biomass and depended on the strength of the SCM.
We calculate the total transmission coefficient (transmittance) of a disordered medium with large (compared to the light wavelength) inhomogeneities. To model highly forward scattering in the medium ...we take advantage of the Gegenbauer kernel phase function. In a subdiffusion thickness range, the transmittance is shown to be sensitive to the specific form of the single-scattering phase function. The effect reveals itself at grazing angles of incidence and originates from small-angle multiple scattering of light. Our results are in a good agreement with numerical solutions to the radiative transfer equation.
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