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Comparison of chlorophyll a concentration detected by remote sensors and other chlorophyll indices in inhomogeneous turbid waters
Abstract and Figures
A new analytical approach for retrieval of the vertically weighted chlorophyll a concentration ( Chl (rs)) detected by remote sensors is presented. Model calculations were carried out for the turbid waters of Lake Kinneret, Israel, and showed that Chl (rs) may be replaced by the average chlorophyll a concentration ( Chl (p)) within the upper "penetration layer" 0-Z(p). The study also showed a high correlation between Chl (rs) and Chl concentration averaged in the other depth layers, namely, the 0-1 m layer, the euphotic layer (0-Z(e)), and the production layer (0-Z(pr)). Our findings are closely related to models developed for the world ocean, with the exception of periods when the dinoflagellate Peridinium gatunense blooms in the lake. We showed the effect of the pattern of vertical Chl distributions within the penetration layer on the difference between Chl (rs) and other Chl indices was conspicuous when the Chl maximum was in the uppermost 0- m layer of the water column. We assume that the presented approaches are instrumental for further development of optimal, locally adapted algorithms for remote sensing of Chl in any type of natural waters.
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... There are two forward models that were proposed in the past to analytically describe the subsurface reflectance of stratified waters; they are the model in Gordon and Clark [24] and that in Zaneveld et al. [26]. Other models, like the one in Sokoletsky and Yacobi [32], provided minor revisions of these two primary models by use of a different attenuation coefficient, with the essences of the two models remaining the same. Therefore, here we focus on the Gordon-Clark and Zaneveld models. ...
... where the weighting function (termed as W Z hereafter) is [32,35] ...
... Since Chl(λ) is a light-weighted average, Chl(λ) will be wavelength dependent, as represented by Eq. (5) and showing in Fig. 2. In view of this basic nature, any Chl calculated from the use of the diffuse attenuation coefficient of photosynthetic available radiation (Kpar, m −1 ) [22,32] will not be appropriate to model R s (λ), as Kpar is not wavelength resolved, whereas R s (λ) is. More importantly, it appears that a change of γ can have a significant effect on Chl(λ) , at least for the stratified cases here. ...
For waters with stratified chlorophyll concentration (Chl), numerical simulations were carried out to gain insight into the forward models of subsurface reflectance and empirical algorithms for Chl from the ocean color. It is found that the Gordon and Clark (1980) forward model for reflectance using an equivalent homogeneous water with a weighted average Chl (⟨Chl⟩) as the input works well, but depending on the contribution of gelbstoff, the difference in reflectance between stratified and the equivalent homogeneous water can be more than 10%. Further, the attenuation of upward light is better approximated as ∼1.5times that of the diffuse attenuation coefficient of downwelling irradiance. On the other hand, although the forward model for reflectance developed in Zaneveld et al. [Opt. Express13, 9052 (2005)] using equivalent homogeneous water with a weighted average of the backscattering to absorption ratio as the input also works well, this model cannot be used to obtain equivalent ⟨Chl⟩ for reflectance. Further, for empirical Chl algorithms designed for "Case 1" waters, it has been discovered that, for surface Chl in a range of ∼0.06-22.0mg/m3, the predictability of surface Chl is basically the same as that of ⟨Chl⟩ from the blue-green band ratio or the band difference of reflectance. Because ⟨Chl⟩ is wavelength and weighting-formula dependent, and it is required to have profiles of both Chl and the optical properties, these results emphasize that for empirical Chl algorithms, it is easier, less ambiguous, and certainly more straightforward and simple to use surface Chl for algorithm development and then its evaluation, rather than to use ⟨Chl⟩, regardless of whether or not the water is stratified.
... Upwelling plane irradiance at λ nm and water depth z m (W m −2 nm −1 ) Fr(z 1 , z 2 ) Fraction of r rs (λ,0 − ) at the layer between z 1 m and z 2 m G(λ, z) = r rs (λ, z)/(b b (λ, z)/(a(λ, z) + b b (λ, z))) g GC Average weighting function derived by Gordon and Clark (1980) [8] g S Average weighting function derived by Sokoletsky and Yacobi (2011) [9] g x Average weighting function, x represents the different functions g Z Average weighting function derived by Zaneveld et al. (2005) [10] IOP'(λ, z) = b b (λ, z)/(a(λ, z) + b b (λ, z)) L u (λ, z) ...
... Sci. 2019, 9,1635 3 of 23 models of coupled ocean-atmosphere system (e.g., studies in References [30][31][32][33][34][35][36]) were developed to predict the radiance and degree of polarization of the light using various numerical methods. ...
... The relationship between b b (z)/(a(z) + b b (z)) in each water depth and r rs (0 − ) could explain the effects of vertical distribution of phytoplankton on underwater light field. Several approaches have been proposed to reduce the effects of vertical distribution of phytoplankton on R rs (λ) [9,10,17]. The R rs (λ) of stratified Case I waters was interpreted and found to be identical to that of hypothetical homogeneous waters with phytoplankton pigment concentration (C rs ), which is a depth-weighted average of the actual profiles of pigment concentration [8]. ...
Current water color remote sensing algorithms typically do not consider the vertical variations of phytoplankton. Ecolight with a radiative transfer program was used to simulate the underwater light field of vertical inhomogeneous waters based on the optical properties of a eutrophic lake (i.e., Lake Chaohu, China). Results showed that the vertical distribution of chlorophyll-a (Chla(z)) can considerably affect spectrum shape and magnitude of apparent optical properties (AOPs), including subsurface remote sensing reflectance in water (rrs(λ, z)) and the diffuse attenuation coefficient (Kx(λ, z)). The vertical variations of Chla(z) changed the spectrum shapes of rrs(λ, z) at the green and red wavelengths with a maximum value at approximately 590 nm, and changed the Kx(λ, z) from blue to red wavelength range with no obvious spectral variation. The difference between rrs(λ, z) at depth z m and its asymptotic value (Δrrs(λ, z)) could reach to ~78% in highly stratified waters. Diffuse attenuation coefficient of downwelling plane irradiance (Kd(λ, z)) had larger vertical variations, especially near water surface, in highly stratified waters. Three weighting average functions performed well in less stratified waters, and the weighting average function proposed by Zaneveld et al., (2005) performed best in highly stratified waters. The total contribution of the first three layers to rrs(λ, 0−) was approximately 90%, but the contribution of each layer in the water column to rrs(λ, 0−) varied with wavelength, vertical distribution of Chla(z) profiles, concentration of suspended particulate inorganic matter (SPIM), and colored dissolved organic matter (CDOM). A simple stratified remote sensing reflectance model considering the vertical distribution of phytoplankton was built based on the contribution of each layer to rrs(λ, 0−).
... Because the satellite Rrs (λ) has information of Chl at depth in the upper water column, it was then argued that the Chl RS should be compared with the weighted average of Chl. However, the weighted Chl is both wavelength-dependent and weighting-formula-dependent, and there is no consensus on which weighting schemes should be used to compare with Chl RS (André, 1992;Morel & Berthon, 1989;Sathyendranath & Platt, 1989;Sokoletsky & Yacobi, 2011;Werdell & Bailey, 2005). Using numerically simulated data, André (1992) compared weighted Chl at 520 nm with Chl RS derived from Rrs(443)/Rrs(550) band ratio (i.e., R bg ), and concluded that the weighted average is necessary only under conditions of strong stratification near the surface. ...
The Ross Sea is the most productive marginal sea in the Southern Ocean and plays an important role in carbon cycling. However, limited sampling of Chlorophyll-a (Chl) and particulate organic carbon (POC) concentrations from research expeditions constrains our understanding of the biogeochemical processes there. Satellites provide a useful tool for synoptic mapping of surface water properties on regional and global scales, yet the general applicability of the published algorithms in the Ross Sea are poorly known. Based on data collected from 18 cruises in the past 20 years, we analyzed both the NASA standard and locally-developed Chl and POC algorithms applicable to the Ross Sea. Our results show the Chl and POC are markedly underestimated using the NASA standard algorithms, with root mean square difference (RMSD) of 4.72 mg m-3 and 218.0 mg m-3, and mean bias (MB) of -3.48 mg m-3 and -159.1 mg m-3, for a wide range of Chl (0.42-16.3 mg m-3) and POC (46.8-812 mg m-3). Similar poor performances were also found for other algorithms applicable in the Ross Sea. We locally tuned both Chl and POC algorithms, and found the Rrs667-based approach showed the most robust performances in retrieving both Chl and POC, with improved RMSD of 2.86 mg m-3 and 129.7 mg m-3, and limited biases. Our results show that, the algal bloom signals in the Ross Sea in terms of Chl and POC are significantly greater than previously determined. More field observations will further constrain the locally-tuned algorithms.
... The key criteria for the model selection were the minimal errors for the remotely sensed values of diffuse attenuation coefficient computed similar to the remotely sensed values of chlorophyll a concentration [17] and reliable vertical distribution of T and K d . From a comparison between Fig. 1 and Fig. 2, it seems that the lists of the best T and K d models are very similar, and we can recommend them (along with analytical method for the average cosines) for reliable retrievals of transmittances and diffuse attenuation coefficients in the Earth's atmosphere and natural waters. ...
... This hypothesis was accepted and used widely in research on vertically nonuniform waters (Mill an-N uñez et al. 1997;Zaneveld et al. 2005;Bresciani et al. 2014). However, a common view concerning a reliable model for weighted mean pigment concentration detectable by remote sensors has not yet been achieved even for Case 1 waters (Sokoletsky and Yacobi 2011). ...
Cyanobacterial blooms occur frequently in eutrophic lakes and their potentially harmful effects affected the security of drinking water and food sources, biodiversity, and economic activities, and attracted the attention of general public worldwide. Cyanobacteria could move vertically in the water column by regulating their buoyancy, which leads to the assumption of homogeneous water invalid. Ecolight, based on radiative transfer theory, was applied to examine the effects of vertical nonuniform of chlorophyll a concentrations (Chl a(z)) on remote sensing reflectance spectrum (Rrs(λ)) of optically complex inland waters. Simulations for nonuniform water consisting of three Chl a(z) profile classes, including Gaussian, exponential, and power, were compared with simulations for a reference homogeneous water whose Chl a was identical to average value of the nonuniform case. The near-surface aggregation of phytoplankton are shown to have significant influence on Rrs(λ) and Chl a inversion algorithms. Variations of ΔRrs(λ) (relative difference of Rrs(λ) between inhomogeneous and homogeneous waters with same average Chl a concentration) mainly depended on the Chl a(z) structure parameters and wavelength. A correction scheme was developed based on the relationships between ΔRrs(λ) and Chl a(z) structure parameters. With knowledge of Chl a(z) profile parameters, Rrs(λ) of inhomogeneous waters can be corrected to the Rrs(λ) of uniform waters with same average Chl a across the water column. Examples of field data from Lake Chaohu illustrated the effects of phytoplankton variation on the near infrared-to-red ratio of Rrs and the Rrs correction performance. © 2017 Association for the Sciences of Limnology and Oceanography.
... The key criteria for the model selection were the minimal errors for the remotely sensed values of diffuse attenuation coefficient computed similar to the remotely sensed values of chlorophyll a concentration (Sokoletsky and Yacobi, 2011) and reliable vertical distribution of T and Kd. From a comparison between Fig. 1 and Fig. 2, it seems that the lists of the best T and Kd models are very similar, and we can recommend them (along with analytical method for the average cosines) for reliable retrievals of transmittances and diffuse attenuation coefficients in the Earth's atmosphere and natural waters. ...
Transmission of light is one of the key optical processes in the Earth’s atmosphere and natural waters, and transmittance (T) is an optical parameter showing the rate of change of irradiance with the optical depth tau. A knowledge of T or another optical parameter, diffuse attenuation coefficient, Kd, steady connected with the T, allows many practical tasks to be solved regarding the ocean and atmospheric optics, such as water quality, primary production, and atmospheric correction. Therefore, knowledge of the reliable relationships between T (or Kd) and such parameters as incident illumination angle, cloud coverage, and inherent optical properties (such as backscattering probability B, scattering asymmetry parameter g, and single-scattering albedo omega_0) is crucial.
We have analyzed the impact of such parameters as the scattering phase function (having the strictly determined value of B and g), omega_0, t, incident solar zenith angle theta_0, cloudiness C, and diffuseness of irradiance d_E on the T and Kd. The benchmark method used for numerical simulations is the modified discrete ordinates method (MDOM) providing an accuracy of better than 1% and having the best speed among the known radiative transfer numerical methods (Budak & Korkin, 2008). We computed T and Kd using a synthetic dataset covering any possible values of parameters typical for the atmosphere and natural waters by MDOM and 21 analytical models and compared results with the MDOM solutions. An analysis of individual models has shown that the best of them yield average errors for T and Kd better than 10% for the majority of real optical conditions in the Earth’s atmosphere and natural waters.
... A is sampled from the surface to the lowest layer just above the bottom sediment. We found that the vertical distribution of Chl a is fairly uniform within the euphotic zone, save the periods when the lake phytoplankton is dominated by the large dinoflagellate P. gatunense (Yacobi 2006;Sokoletsky and Yacobi 2011). The thermal structure of the water column determines, to a large extent, the degree of homogeneity of Chl a vertical distribution, and an abrupt drop in Chl a concentrations is observed below the thermocline (Fig. 10.8a). ...
The phytoplankton assemblage of Lake Kinneret is dominated by dinoflagellates. Secondary phytoplankton biomass contributors are cyanobacteria, chlorophytes, and diatoms, whereas cryptophytes are always present at a low biomass. The main bloom-forming dinoflagellate, Peridinium gatunense, bloomed every spring till the mid-1990s, but since then, it bloomed only during high-rainfall years. This change and a suite of additional changes in phytoplankton dynamics since 1994, changes that occurred after more than two decades of recorded constancy, were interpreted as early responses to increasing stress at the ecosystem level. In particular, the loss of the previously predictable annual pattern (spring bloom of P. gatunense, summer low-biomass, high-diversity assemblage), the appearance and establishment of toxin-producing cyanobacteria, a major loss in species richness, and a shift to dominance of less grazed species in summer are all manifestations of this change that can be viewed as a regime shift.
Surface and remote sensing of chlorophyll a (Chl a)—a proxy of algal biomass—indicates that phytoplankton concentration extremes at the lake surface mostly do not surpass a ratio of 1:2. Exceptional is a situation when Lake Kinneret is dominated by P. gatunense, and then the spatial heterogeneity of phytoplankton increases to a ratio of 1:50 between extreme concentrations. Chl a concentrations were often higher in the northern part of the lake, near the Jordan River inflow, where nutrient enrichment apparently boosts the growth of phytoplankton. The unique Chl a optical properties enable the identification and quantification of that substance using reflectance spectra emerging from the water surface and are recorded by sensors carried onboard satellites. Since 2006, images derived from optical information acquired by MERIS are utilized for mapping of the spatial distribution of phytoplankton in Lake Kinneret.
... A is sampled from the surface to the lowest layer just above the bottom sediment. We found that the vertical distribution of Chl a is fairly uniform within the euphotic zone, save the periods when the lake phytoplankton is dominated by the large dinoflagellate P. gatunense (Yacobi 2006;Sokoletsky and Yacobi 2011). The thermal structure of the water column determines, to a large extent, the degree of homogeneity of Chl a vertical distribution, and an abrupt drop in Chl a concentrations is observed below the thermocline (Fig. 10.8a). ...
The Kinneret phytoplankton biodiversity has been monitored on a regular basis since 1969, with the taxonomic information stored as a digital online catalog (http://kinneret.ocean.org.il/phyt_cat_listView.aspx) containing photographs and morphological descriptions. Our aim was to upgrade this ID tool by adding to it a consensus DNA sequence as a species identifier—DNA barcode. A two-gene system approach was applied, sequencing DNA fragments from the Ribulose-1,5-bisphosphate carboxylase oxygenase large subunit (rbcL) and the rRNA small subunit and intragenic space (SSU-ITS). Today, 72 species isolated from Lake Kinneret, are at different stages of processing. The barcoding process was completed for 26 of those. Barcoding has enabled us to support current nomenclature, clarify the taxonomic names of species whose identification was previously inconclusive, classify to species level taxa previously identified to genus only, discover species new to the lake, and update current nomenclature. The construction of the DNA barcode database stands as the first brick of knowledge upon which further experimental work can be conducted, enabling fast and accurate identification of the Kinneret phytoplankton.
... This means that the portion of water-leaving radiance backscattered from individual layers decreases with depth, unless a turbid layer is covered by clearer water. Appropriate weighting can be applied to reference profile measurements if vertically resolved attenuation measurements are available (Odermatt et al., 2012a;Sokoletsky and Yacobi, 2011). Due to the lack of such measurements, we average the reference profile measurements taken at 0-5 m as in earlier studies with comparable reference data (Odermatt et al., 2010). ...
An algorithm to determine the spectral total absorption coefficient of water is presented. The algorithm is based on the Gershun’s equation of α = μKE. The spectral underwater average cosine, μ and vertical attenuation coefficient of net irradiance, KE were obtained from radiative transfer simulations using Hydrolight with large in-situ measured data from the coastal and estuarine waters of Goa. A refined algorithm of spectral μ as in Ref. [1] is used to determine the spectral underwater average cosine. The spectral KE was related to the diffuse attenuation coefficient, Kd. The algorithms to derive absorption were validated using an independent NOMAD optical data at wavelengths 412, 440, 488, 510, 532, 555, 650 and 676 nm. The performance of the algorithm was evident from the high R², low bias and low RMSE. The values of R² at wavelengths 412, 440, 488, 510, 532, 555, 650 and 676 nm were 0.95, 0.95, 0.93, 0.93, 0.88, 0.82, 0.62, and 0.65 respectively. The corresponding bias were -0.0064, 0.0076, 0.0038, 0.0044, 0.0122, 0.0124, 0.0362, and 0.0093 respectively. The algorithms for μ and KE provide the spectral weighted average within Z90 and have the advantage of deriving the absorption coefficients from the satellite data.
The two-stream model expresses the vertical attenuation coefficient K and the irradiance ratio R as functions of the absorption coefficient a, the backward scattering coefficient b(b), the downward and upward average cosines micro (d) and micro (u), and the normalized reflectance coefficients of downward and upward scalar irradiance, r(d) and r(u). While K/a and R are almost linear functions of b(b)/a when b(b)/a is small, they will approach asymptotic values, which only depend on r(d), r(u), micro (d), and micro (u) when b(b)/a becomes large. The results agree well with oceanic observations of K and R. They also agree with theoretical results derived by other methods. Still proper testing of the model in turbid waters remains.
The two-stream model expresses the vertical attenuation coefficient K and the irradiance ratio R as functions of the absorption coefficient a, the backward scattering coefficient bb, the downward and upward average cosines μ ¯ d and μ ¯ u, and the normalized reflectance coefficients of downward and upward scalar irradiance, rd and ru. While K/a and R are almost linear functions of bb/a when bb/a is small, they will approach asymptotic values, which only depend on rd, ru, μ ¯ d, and μ ¯ u when bb/a becomes large. The results agree well with oceanic observations of K and R. They also agree with theoretical results derived by other methods. Still proper testing of the model in turbid waters remains.
The problem of the inversion of irradiance measurements for the inherent optical properties of a hydrosol such as the world ocean has been examined with the NOARL optical model. This model is a Monte Carlo simulation of the radiative transfer equation that, given the optical properties of a hydrosol, generates the zonal radiances and the commonly measured n-radiances of that hydrosol. This information allows us to test the optical inversion capability of any irradiance model. We have demonstrated that the two-flow model, used often in atmospheric optics, cannot be inverted to yield the inherent backscattcr coefficient of natural hydrosols due to the extreme asymmetry of the hydrosol volume scattering function. The asymmetry of the volume scattering function interacting with the radiance distribution introduces parameters called shape factors into the models for irradiance inversion. The presence of shape factors in an irradiance model renders it unsolvable; thus, simplifying assumptions are required for an inverse solution. We inquire into the possibilities for irradiance inversion given the existence of shape factors.
Abstract Maps of surface chlorophyllous pigment,(Chl a + Pheo a) are currently produced,from ocean color sensors. Transforming such maps into maps of primary production can be reliably done only by using light-production,models,in conjunction with additional information about the column- integrated pigment content and its vertical distribution. As a preliminary effort in this direction, -4,000 vertical profiles of pigment (Chl a + Pheo a) determined,only in oceanic Case 1 waters have been statistically analyzed. They were scaled according to dimensionless depths (actual depth divided by the depth of the euphotic layer, Z,) and expressed as dimensionless,concentrations (actual concentration divided by the mean,con- centration within the euphotic layer). The depth Z,, generally unknown, was computed with a previously developed bio-optical model. Highly significant relationships were found allowing (C>,,,, the pigment content of the euphotic layer, to be inferred from the sur!ace concentration, C,, observed within the layer of one penetration depth. According to their C,, values (ranging from 0.01 to > 10 mg m-3), we categorized the profiles into seven trophic situations and computed a mean,vertical profile for each. Between a quasi-uniform profile in eutrophic waters and a profile with a strong deep maximum in oligotrophic waters, the shape evolves rather regularly. The well- mixed cold waters, essentially in the Antarctic zone, have been separately examined. On average, their profiles are featureless, without deep maxima, whatever their trophic state. Averaged values of p, the ratio of Chl a to (Chl a + Pheo a), have also been obtained for each trophic category. The energy stored by photosynthesizing algae, once normalized with respect to the integrated chlorophyll biomass (C),,, is proportional to the available photosynthetic energy at the surface via a parameter #*, which is the cross-section for photosynthesis per unit of areal chlorophyll. By taking advantage of the relative stability of #*, we can compute primary production from ocean color data acquired from space. For such a computation, inputs are the irradiance field at the ocean surface, the “surface” pigment from which (C),, can be derived, the mean p value pertinent to the trophic situation as depicted by the ($ or (C),,, values, and the cross-section rc/*. Instead of a constant #* value, the mean profiles can be used; they allow the climatological field of the #* parameter,to be adjusted through the parallel use of a spectral light-production,model. Acknowledgments
A model has been developed to investigate the influence of the subsurface chlorophyll profile on the complete spectral water-leaving radiance (ocean color) from 400 - 700 nm. The spectral reflectivity of vertical chlorophyll layers is modeled and coupled with the spectral incident irradiance at the sea surface. Model results indicate similar water-leaving radiance signatures can be obtained from different subsurface chlorophyll profiles. This model provides an interpretation of remote sensing ocean color signatures and possible subsurface structure. The inherent optical properties of the backscatter and absorption coefficient which are determined from the vertical chlorophyll profile for Case I waters are used to calculate the subsurface spectral reflectivity at layer depths. Subsurface reflectivity models are coupled with an atmospheric model of the incident solar irradiance spectrum. The atmospheric irradiance model was run for different cloud cover and different optical depths (ozone, aerosol). The coupled model results compute the remote sensing color spectrum (upwelling radiance) at the sea surface.
Three-dimensional distributions of inherent optical properties (absorption, a, scattering, b, and single-scattering albedo, omega0) were defined for a coastal region in the north-eastern Gulf of Mexico by coupling surface ocean colour aircraft imagery and models of vertical optical profiles. The study area encompassed the surf zone region and offshore sand bar of an open beach environment to a depth of 10m. During the aircraft overflights, concurrent in situ depth profiles of a and b were collected along an offshore transect, modelled, and assigned to each image pixel based on water depth. The modelled a and b profiles were subsequently integrated over depth (weighted by the diffuse attenuation coefficient) to provide a 'remote sensing' estimate comparable to what the aircraft sensor would see. At each pixel in the image, these initial optical depth profiles were then iteratively adjusted until the integrated values agreed to within 5% of the estimates derived from a bio-optical model using the aircraft-measured water-leaving radiances. Thus, unique vertical distributions of the optical fields were defined at each pixel from the corresponding profile when convergence was achieved. The modelled optical profiles compared favourably both spatially and spectrally with measured values. The 3-D visualization of the optical fields provided insight into the biological and physical processes affecting coloured dissolved organic matter (CDOM) and particle distributions in this coastal area.
We used simplifying assumptions to derive analytical formulae expressing the reflectance of shallow waters as a function of observation depth and of bottom depth and albedo. These formulae also involve two apparent optical properties of the water body: a mean diffuse attenuation coefficient and a hypothetical reflectance which would be observed if the bottom was infinitely deep. The validity of these approximate formulae was tested by comparing their outputs with accurate solutions of the radiative transfer obtained under the same boundary conditions by Monte Carlo simulations. These approximations were also checked by comparing the reflectance spectra for varying bottom depths and compositions determined in coastal lagoons with those predicted by the formulae. These predictions were based on separate determinations of the spectral albedos of typical materials covering the floor, such as coral sand and various green or brown algae. The simple analytical expressions are accurate enough for most practical applications and also allow quantitative discussion of the limitations of remote-sensing techniques for bottom recognition and bathymetry.
The upwelling light field in natural waters is of great importance for the appearance of the water bodies, for visibility of objects seen through the water, and for remote sensing of water properties. As a contribution to the understanding of this radiant flux, a study has been carried out by the Monte Carlo simulation technique of the behaviour of photons scattered upward from the down-welling light stream within water bodies. Immediately after scattering the angular distribution of these photons is biased very much toward small angles to the horizontal. As a consequence, the rate of attenuation of this photon population as it travels upward is initially very high. With increasing distance upward the rate of attenuation progressively diminishes as the more horizontally travelling photons are selectively extinguished. -from Author
