We study the spatial and angular distribution of light in a narrow stationary beam propagating in a medium like seawater. For a power-law parametrization of the seawater phase function, using radiative transfer analysis, we derive analytical expressions that determine the radiance distribution in the medium. Both the case of intermediate source-receiver distances, where absorption only begins to affect spreading of the beam, and the asymptotic regime of beam propagation are examined. For the main characteristics of the radiance distribution (the total power, the variance of the angular and radial distributions), scaling relations involving the inherent optical parameters of seawater are found. To validate the expressions obtained we carry out Monte Carlo simulation for commonly adopted seawater scattering models (of Petzold and Morel et al) and their analytical parameterizations. For optical parameters typical to seawater, the predicted analytical laws are in excellent agreement with the results of the Monte Carlo computations.

A method is proposed for characterization of the aerosol contribution to the top-of-atmosphere (TOA) radiance. The method is based on solving the problem of radiative transfer in the atmosphere-ocean system and expanding the solution in powers of the aerosol optical thickness tau(a). We show that the linear term of the expansion is analytically expressed in terms of the bidirectional transmittance/reflectance of the aerosol-free Rayleigh atmosphere. A procedure is also proposed for successively extracting the terms of higher order in tau(a )from the data of the TOA radiance computation with the DISORT code. As analysis shows, the radiance expansion in tau(a) is not purely polynomial. Beginning from the quadratic term, the coefficients of the series expansion in powers of tau(a) become dependent logarithmically on tau(a). The approach proposed enables us to reproduce analytically the tau(a)-dependence of the TOA radiance with controlled accuracy. We determine the expansion coefficients up to the cubic term inclusive and validate our results on the aerosol model embedded in NASA's SeaDAS algorithm for aerosol loadings, representative for the Barents and Kara seas. In the visible and near-infrared spectral ranges, accounting for the terms up to a quadratic one is found to be sufficient for the atmospheric correction of satellite ocean color data typical for the Arctic region. (c) 2024 Optica Publishing Group. All rights, including for text and data mining (TDM), Artificial Intelligence (AI)training, and similar technologies, are reserved

We study the azimuthal asymmetry of the spectral bidirectional reflectance distribution function (BRDF) of an optically thick sea-ice layer. From radiative transfer modeling, we find that the azimuth-dependent part of the BRDF ceases to change rather rapidly with an increase in the optical thickness of the layer and tends to a nearly universal angular dependence, insensitive to the specific law of single scattering in the ice. The effect of the scattering phase function manifests itself only in the value of a pre-factor in the azimuth-dependent part of the BRDF. The universality stems from the refractive index mismatch at the air/ice interface and should occur for any natural ice containing large (compared to the wavelength) inclusions. The specified part of the BRDF is governed by sub-diffusive radiation transport and, at large illumination zenith angles, can make a noticeable contribution to the spectral albedo of the layer in the visible range.

A simple method is proposed for calculating the asymptotic attenuation coefficient Km, of sea water. The method is based on the scaling analysis of the radiative transfer equation within the small-angle approx-imation. From the scaling, it follows that Km, is analytically expressed in terms of the absorption coeffi-cient, 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 num-ber 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 Km, 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 Km, less than 5 % ). So that, within a few percent accuracy, the coefficient Km, is governed only by the absorption and transport scattering coefficients and is described by a universal formula. (c) 2022 Elsevier Ltd. All rights reserved.

The maximal value of the chlorophyll-specific carbon fixation rate in the water column or the optimal assimilation number (Pbopt) is an important parameter used to estimate water column integrated primary production (IPP) using models and satellite-derived data. The spatiotemporal variability in the Pbopt of the total and size-fractionated phytoplankton in the Siberian Seas (SSs) and its links with environmental factors were studied based on long-term (1993–2020) field and satellite-derived (MODIS-Aqua) observations. The average value of Pbopt in the SSs was equal to 1.38 ± 0.76 mgC (mg Chl a)–1 h–1. The monthly average values of Pbopt decreased during the growing season from 1.95 mgC (mg Chl a)–1 h–1 in July to 0.64 mgC (mg Chl a)–1 h–1 in October. The average value of Pbopt for small (<3 μm) phytoplankton 1.6-fold exceeded that for large (>3 μm) phytoplankton. The values of Pbopt depend mainly on incident photosynthetically available radiation (PAR). Based on the relationship between Pbopt and PAR, the empirical region-specific algorithm (E0reg) was developed. The E0reg algorithm performed better than commonly used temperature-based models. The application of E0reg for the calculation of Pbopt will make it possible to more precisely estimate IPP in the SSs.

Inter-annual (2002–2021) variability of the Kara Sea PP 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 the pronounced positive trend of surface water temperature (T0) and weak positive trend of free-ice area (S) averaged for the growing season (April – October). During the investigated period T0 increased by 3.55°C with a trend of 10% y–1 and S increased by 110×103 km2 with a trend of 1.4% y–1, on average. The values of water column PP (IPP) statistically significant (p 0.05) decreased in the all of the Kara Sea regions (R2 = 0.22 – 0.59). For the entire Kara Sea the IPP declined by 38 mgC m–2 d–1 with a moderate trend of 1.1% y–1 (R2 = 0.37). The growing season averaged value of photosynthetically available radiation (PAR) weak, but statistically significant (p 0.05), decreased in the all of the Kara Sea areas (R2 = 0.20 – 0.31). Also, in the all regions the significant (R2 = 0.24 – 0.38) weak or moderate negative trends of surface chlorophyll a (Chl) were specified. The total annual PP (PPtot) increased insignificantly in accordance with increase of S (0.7% y–1, R2 = 0.08). The most significant decline of IPP was specified for spring (R2 = 0.28). In autumn the statistically significant positive trend of S (R2 = 0.24) was observed. Due to such increase of S, the strongest growth of PPtot was noted in autumn. In the present work was shown that decrease of IPP, resulting from decline of PAR and Chl, was the reason of moderation of PPtot. Weak increase in PPtot was observed in autumn and in the north area of the sea. It should be concluded that during the period of intense warming, the decrease in the IPP of the Kara Sea should affect the productivity of the higher trophic levels of the food web.

The paper presents the results of testing the possibility of using empirical orthogonal functions to develop algorithms for estimating the concentration of chlorophyll a and suspended matter, the biomass of cyanobacteria in the eastern part of the Gulf of Finland. To develop the algorithms, we used an array of data from field measurements of the subsurface radiance reflectance in 2012–2014, carried out simultaneously with the determination of bio-optical characteristics. It turned out that in the case of the concentration of chlorophyll a and suspended matter, such algorithms can be created not only using the hyperspectral radiance reflectance, but also for the spectral channels of satellite color scanners MODIS and OLCI. An estimation of the cyanobacteria biomass with the empirical orthogonal functions method is not applicable in the case of using satellite channels. A study of the possibility of the most prone to atmospheric correction errors shortwave MODIS channels exclusion was also made. It turned out that the concentration of chlorophyll a is more sensitive to such exclusion than the concentration of suspended matter. Validation on a MODIS data showed that empirical orthogonal functions algorithms give results no worse than regression ones.

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.

Современные проблемы дистанционного зондирования Земли из космоса

Studies of seasonal variability of the East Siberian Sea (ESS) water column primary production (IPP) and evaluation of its total annual value (PPtot) 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 PPtot 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 PPtot value was equal to 9 TgC. Productivity of the Siberian seas decreased eastward.

We study how intensity fluctuations in transmission through a disordered slab change depending on the regime of wave transport. A system with large (compared to the wavelength of light) inhomogeneities is considered. Within a diagrammatic approach, the variance of the total transmission coefficient is calculated numerically beyond the diffusion approximation. A great enhancement of fluctuations is found in the crossover from the ballistic to the diffusive transport at the grazing angles of incidence on the sample surface. The effect originates from the reflection of waves that propagate nearly parallel to the sample boundaries and experience scattering through small angles, and reveals itself both in transmission and reflection and in correlations between the transmitted and reflected fluxes.

We study the angular distribution of light diffusely reflected from a turbid medium with large (compared to the light wavelength) inhomogeneities. Using Monte Carlo radiative transfer simulations, we calculate the azimuthally averaged bidirectional reflectance for an optically thick plane-parallel medium and analyze its dependence on the parameters of the scattering phase function. To model single scattering in the medium, we take advantage of the Reynolds-McCormick phase function. For grazing angles of incidence, we find that the angular distribution of reflected light becomes very sensitive to the angular profile of the scattering phase function. The more elongated the phase function, the more pronounced the peak that arises around the specular reflection angle. Comparison of our numerical results with an analytic solution of the radiative transfer equation is performed, and it is shown that the bidirectional reflectance can be decomposed into two contributions, namely, the diffusion contribution and the contribution from light experiencing multiple scattering through small angles. The latter relates directly to the angular profile of the scattering phase function and is responsible for the peak in the angular distribution of reflected light. An explicit analytic formula for the azimuthally averaged bidirectional reflectance is obtained.

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 Laptev Sea water column primary production and evaluation of its annual values were performed using MODIS-Aqua data (20022018). To reach that result regional-specific primary production and chlorophyll algorithms were used for the first time. Based on multiyear averaged daily primary production Northwestern and Southeastern regions were distinguished in the Laptev Sea. Seasonal variations in water column primary production in the Northwestern region were characterized by the maximum in June (245 mgC m‑2 d‑1). In the Southeastern region and for all Laptev Sea the maximum water column primary production values were denoted from May to July, 273282 mgC m‑2 d‑1 and 256281 mgC m‑2 d‑1, respectively. Daily primary production and annual values of total primary production in the Southeastern region were, respectively, 1.9 and 3 fold higher than in the Northwestern region. Multiyear averaged value of Laptev Sea water column primary production was equal to 125 mgC m‑2 d‑1 and total annual primary production was equal to 8 1012 gC.

Исследования сезонной изменчивости первичной продукции в столбе воды моря Лаптевых и оценка ее годовых величин выполнены по данным сканера MODIS-Aqua, осредненным за 2002–2018 гг. Для этого впервые использованы региональные модели первичной продукции и хлорофилла. В море Лаптевых выделены два контрастных по продуктивности района: Северо-западный и Юго-восточный. Сезонные изменения первичной продукции в столбе воды в Северо-западном районе характеризовались максимумом в июне (245 мгС/м 2 в день). В Юго-восточном районе и для всей акватории моря Лаптевых максимальные (273–282 мгС/м 2 в день и 256–281 мгС/м 2 в день, соответственно) значения первичной продукции в столбе воды были зарегистрированы с мая по июль. Интенсивность первичного продуцирования и годовая первичная продукция в Юго-восточном районе были, соответственно, в 1.9 и 3 раза выше, чем в Северо-западном районе. Среднее для моря значение первичной продукции в столбе воды составило 125 мгС/м 2 в день, а ее годовая величина равнялась 8 × 10 12 ґС.

Представлены обобщённые результаты исследований биооптических характеристик поверхностного слоя вод Баренцева, Карского морей и моря Лаптевых, полученные по судовым и спутниковым данным, и интерпретация наблюдаемых явлений. Выполнен совместный анализ данных измерений о пространственном распределении биооптических характеристик, полученных в 2018 г. с помощью судового проточного комплекса, и спутниковых наблюдений за период 2003-2017 гг., который позволил выявить роль основных процессов, определяющих это распределение, его сезонные и межгодовые изменения. Показано, что пространственные распределения интенсивности флуоресценции окрашенного растворенного органического вещества и хлорофилла хорошо соответствуют гидрофизическим характеристикам в области влияния речного стока; пространственные распределения показателя ослабления хорошо с ними согласуются. Полученные данные позволили определить положение арктических и атлантических вод и кокколитофоридных цветений в Баренцевом море, выделить границы распространения опресненного слоя в морях Карском и Лаптевых. Представлены статистические оценки связи между биооптическими характеристиками Баренцева и Карского морей по спутниковым данным.

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 (Chl0 > 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 Chl0 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.

Пространственная изменчивость первичной продукции в столбе воды (ИПП) и продукционное районирование Карского моря выполнены впервые с использованием региональных моделей, разработанных и верифицированных на основе базы данных, созданной по материалам экспедиций в Карское море в конце августа -начале октября, и спутниковых данных MODIS-Aqua.Придерживаясь описательной концепции и частного подхода, мы выделили шесть продукционных районов, отличающихся по средним многолетним (2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015) значениям ИПП: Эстуарный район (эстуарии Оби и Енисея) со среднегодовым значением солёности на поверхности ≤10 psu; Внутренний (<100 м) и Внешний (100-200 м) шельфы, круглый год находящиеся под влиянием речного стока; Юго-западный район, на который это влияние распространяется в значительно меньшей степени; Северо-западный (жёлоб Св.Анны) и Северо-восточный (жёлоб Воронина) районы с прилегающими акваториям.Средние многолетние значения ИПП