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Inverse methods in hydrologic optics

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Methods for solving the hydrologic-optics inverse problem, i.e., estimating the inherent optical properties of a water body based solely on measurements of the apparent optical properties, are reviewed in detail. A new method is developed for the inverse problem in water bodies in which fluorescence is important. It is shown that in principle, given profiles of the spectra of up- and downwelling irradiance, estimation of the coefficient of inelastic scattering from any wave band to any other wave band can be effected.
High-latitude fjords, very vulnerable to global change, are impacted by their land and ocean boundaries, and they may be influenced by terrestrial water discharges and oceanic water inputs into them. This may be reflected by temporal and spatial patterns in concentrations of biogeochemically important constituents. This paper analyses information relating to the total suspended matter (TSM) concentration in the Porsanger fjord (Porsangerfjorden), which is situated in the coastal waters of the Barents Sea. Water samples and a set of physical data (water temperature, salinity, inherent optical properties) were obtained during two field expeditions in the spring and summer of 2014 and 2015. Bio-optical relationships were derived from these measurements, enabling optical data to be interpreted in terms of TSM concentrations. The results revealed significant temporal variability of TSM concentration, which was strongly influenced by precipitation, terrestrial water discharge and tidal phase. Spatial distribution of TSM concentration was related to the bathymetry of the fjord, dividing this basin into three subregions. TSM concentrations ranged from 0.72 to 0.132 g m−3 at the surface (0–2 m) and from 0.5 to 0.67 g m−3 at 40 m depth. The average mineral fraction was estimated to be 44% at surface and 53% at 40 m.
Two Spitsbergen fjords, Hornsund and Kongsfjorden, are known for being under different hydrological regimes. The first is cold, separated from warm Atlantic water by East Spitsbergen Current, while Kongsfjorden is frequently penetrated by relatively warm Atlantic water. On the other hand, both are under strong influence of water discharge from glaciers and land freshwater input. During the period of observation in both fjords a dominant water mass was Surface Water, which originates mainly from glacial melt. The presence of suspended matter introduced with melt water in Surface Water is reflected by highest values of light attenuation and absorption coefficients recorded in areas close to glacier both in Hornsund and Kongsfjorden. In Hornsund the maximum light attenuation coefficient cpg(555) was 5.817 m−1 and coefficient of light absorption by particles ap(676) = 0.10 m−1. In Kongsfjorden the corresponding values were 26.5 m−1 and 0.223 m−1. In Kongsfjorden suspended matter of the size class 20–200 μm dominated over fractions smaller than 20 μm while in Hornsund dominating size fraction was 2–20 μm. The results provide an evidence of considerable range of variability of the optical properties mainly due to glacial and riverine runoff. The scale of variability of particulate matter in Kongsfjorden is bigger than in Hornsund. Most of the variability in Hornsund can be attributed to glaciers discharge and a presence of particles of mineral origin, while in Kongsfjorden the organic and mineral particles contribute almost equally to defining the optical properties of water.
The inherent optical properties (IOPs) of suspended particulate matter and their relations with the main biogeochemical characteristics of particles have been examined in the surface waters of the southern Baltic Sea. The empirical data were gathered at over 300 stations in open Baltic Sea waters as well as in the coastal waters of the Gulf of Gdańsk. The measurements included IOPs such as the absorption coefficient of particles, absorption coefficient of phytoplankton, scattering and backscattering coefficients of particles, as well as biogeochemical characteristics of suspended matter such as concentrations of suspended particulate matter (SPM), particulate organic matter (POM), particulate organic carbon (POC) and chlorophyll a (Chl a). Our data documented the very extensive variability in the study area of particle concentration measures and IOPs (up to two orders of magnitude). Although most of the particle populations encoun- tered were composed primarily of organic matter (av. POM/SPM=ca 0.8), the different particle concentration ratios suggest that the particle composition varied significantly. The relations between the optical properties and biogeochemical parameters of suspended matter were examined. We found significant variability in the constituent-specific IOPs (coefficients of variation (CVs) of at least 30% to 40%, usually more than 50%). Simple best-fit relations between any given IOP versus any constituent concentration parameter also highlighted the significant statistical errors involved. As a result, we conclude that for southern Baltic samples an easy yet precise quantification of particle IOPs in terms of the concentration of only one of the following parameters – SPM, POM, POC or Chl a – is not achievable. Nevertheless, we present a set of best statistical formulas for a rough estimate of certain seawater constituent concentrations based on relatively easily measurable values of seawater IOPs. These equations can be implemented in practice, but their application will inevitably entail effective statistical errors of estimation of the order of 50% or more.
The effect of angular structure differences between measured and best-fit analytical phase functions of the equivalent backscattering ratio on calculated reflectance values was studied and shown to be significant. We used a Monte Carlo radiative transfer code to check the effect of choosing different analytical (several Fournier- Forand (1994) and Henyey-Greenstein (1941)) phase functions with backscattering ratios identical to the ‘classical’ average Petzold function. We show that the additional variability of the resulting water leaving radiance is about 7% (4% between the Fournier-Forand functions themselves) for most scenarios. We also show a previously unknown maximum of the discrepancy (up to 10%) for highly scattering waters. We discuss the importance of relative differences in phase function for different angular ranges to this maximum and to the behaviour of the discrepancy as a function of solar zenith angle.
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