- Email: [email protected]
Retrieval of spectral backscattering from spectral scattering based on spectral partitioning technique
Estuarine, Coastal and Shelf Science 217 (2019) 196–205
Contents lists available at ScienceDirect
Estuarine, Coastal and Shelf Science journal homepage: www.elsevier.com/locate/ecss
Retrieval of spectral backscattering from spectral scattering based on spectral partitioning technique
T
Sayoob Vadakke-Chanat, Palanisamy Shanmugam∗ Ocean Optics and Imaging Laboratory, Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai - 600036, India
A R T I C LE I N FO
A B S T R A C T
Keywords: Optical properties Scattering Backscattering Conversion model Turbid and productive waters
Direct measurement of backscattering using sensors has technological limitations such as saturation in highly turbid waters and the effect of absorption in strongly absorbing highly productive waters. In the present study, a quantitative method is developed to estimate the particulate spectral backscattering coefficient based on spectral partitioning of the scattering coefficient. The input slope of the non-algal backscattering spectra was determined from the scattering slope and the magnitude was quantified from the water turbidity. The contribution of phytoplankton to the backscattering was determined as a linear combination of the spectral dependency factors and the chlorophyll concentration. The proposed method of conversion, from scattering to backscattering, when compared with two existing methods (Haltrin and Petzold average ratio), resulted in lower relative errors (mean relative error: -0.214–0.037, mean net Bias: -0.259–0.019, root mean square error: 0.006–0.015, coefficient of determination: 0.91–0.98), and substantial improvement was also observed in the spectral shape and magnitude of the backscattering coefficients.
1. Introduction Scattering and backscattering are optical properties of fundamental importance in the field of oceanic and atmospheric optics and are categorized as the inherent optical properties (IOP) (Bricaud et al., 1998; Loisel et al., 2006; Morel, 1980; Sun et al., 2010). The backscattering coefficient regulates the Bidirectional Reflectance Distribution Function (BRDF), which is a property of prime importance in the field of ocean remote sensing (Mobley, 1994; Twardowski et al., 2007). Light propagation through oceanic waters is defined by the radiative transfer equation (Sundarabalan et al., 2013), requiring information on the spectral angular scattering and spectral absorption of the water column. A practical approximation of the scattering phase function can be obtained from the backscattering ratio (McKee et al., 2009; Mobley et al., 2002), which is the ratio of the backscattering to the scattering values. The particle size distribution (PSD) is another property which can be related to the particulate backscattering ratio and serves as a proxy for the composition of the particles (Twardowski et al., 2001). The backscattering coefficient (bb) has wider implications in terms of practical applications such as the underwater imaging widely utilized in engineering and environmental studies (Mortazavi et al., 2013), optical target detection in the water column and at the ocean bottom (Rao et al., 2009), marine biological research (Sun et al., 2008), and in the
∗
investigation of underwater structures (Kondo and Ura, 2004). The backscattering enhances the intensity of the recorded pixel, results in an alteration in the measured pixel reflectance spectrum, and introduces contrast loss in the captured image, which is a dominant degradation problem (Gholami and Saghafifar, 2018; Mortazavi et al., 2013) in underwater imaging applications (Mortazavi et al., 2013). Measurement of backscattering coefficients has restrictions imposed by the technological limitations such as the saturation of sensors (McKee et al., 2009) and the influence of absorption on the backscattering measurement (Doxaran et al., 2016), while the scattering coefficient (b) is determined from measurements of absorption and attenuation coefficients, which are appropriately calibrated and corrected for associated measurement errors. Estimation of a complete set of IOPs is a prerequisite for various practical purposes and an appropriate and robust method of converting scattering to backscattering could aid the restoration of the parameters. This is because the measurement of the entire set of the optical properties may not be always feasible due to certain economic, technological or logistical limitations. Therefore, a reliable method for estimating the spectral particulate backscattering coefficient from the spectral particulate scattering coefficient is required. In the present work, a method is presented for converting the particulate spectral scattering coefficient into the particulate spectral
Corresponding author. E-mail address: [email protected] (P. Shanmugam).
https://doi.org/10.1016/j.ecss.2018.11.024 Received 7 June 2018; Received in revised form 16 November 2018; Accepted 16 November 2018 Available online 17 November 2018 0272-7714/ © 2018 Elsevier Ltd. All rights reserved.
Estuarine, Coastal and Shelf Science 217 (2019) 196–205
S. Vadakke-Chanat, P. Shanmugam
manufacturer's guidelines. Temperature (Pegau and Zaneveld, 1993) and Salinity (Pegau et al., 1997) corrections were performed on the measured data and an additional correction for scattering effect was performed on the absorption data (Zaneveld et al., 1994). The scattering coefficient was determined from the above data by subtraction of absorption from attenuation values, cpg(λ) – apg(λ) = bp(λ). A CTD (SeaBird SBE-FASTCAT) instrument was used for measurements of temperature and salinity and an FLNTU sensor (WET Labs) was used for chlorophyll fluorescence and turbidity measurements. The FLNTU sensor determines the turbidity using scattering measurements at 700 nm, and the chlorophyll concentration using fluorescence measurements with excitation at 470 nm and emission at 695 nm. An underwater frame on which these sensors were mounted was lowered in the water using a winch with communication and power cables connected to the shipboard computer (Dev and Shanmugam, 2014; Simon and Shanmugam, 2013). An ECO-BB9 sensor from WET Labs was used to obtain the situ measurements of particulate backscattering coefficient (bbp) for 412, 440, 488, 510, 532, 595, 650, 676, and 715 nm wavelengths. The sensor actually measures the volume scattering function (VSF) (β, m−1sr−1) at these wavelengths at 124° (Doxaran et al., 2016; VadakkeChanat et al., 2018), which are then multiplied by the term 2πχ to obtain the backscattering coefficient bb(λ). Subtracting the pure water backscattering then yields bbp. There is an LED source light with a corresponding detector for each measurement wavelength. The BB9 raw output is expressed in counts, sampling at 1 Hz, from which bbp is calculated. A correction is performed for the effect of absorption in these measurements based on a standard correction procedure (WET Labs ECO BB9 User's Guide (BB9), 2017).
backscattering coefficient in coastal and inland waters based on partitioning methods for scattering and backscattering coefficients (Vadakke-Chanat et al., 2017; Vadakke-Chanat and Shanmugam, 2017) and the robustness of the method is demonstrated together with potential implications in coastal and inland waters. 2. Data and methods 2.1. Sampling locations Contrasting coastal and inland environments were identified for in situ data measurement campaigns: clear to moderately turbid coastal waters around Chennai (13°7′ 37″ N; 80° 22′ 9″ E), highly turbid coastal waters near Point Calimere (10°15′16″N, 80°04′2″E), algal bloomdominated eutrophic waters in the Muttukadu lagoon (12°48′2″N; 80°14′37″E) on the southeast coast of India, and turbid and productive waters of the Ganges River (25°14′25″N; 83°0′39″E). Three field campaigns in the Point Calimere coastal region were conducted during May 2012, August 2012, and August 2013. The May 2012 cruise in the Point Calimere region also included two sampling stations offshore of Karaikal and near Palar River mouth. In optical terms, the Point Calimere region is characterized by inorganic sediment derived from wave-tide induced re-suspended bottom material, having a relatively high proportion/concentration of non-algal particles dominated by clay and silt, together with low concentrations of chromophoric dissolved organic matter (CDOM) and chlorophyll (Damotharan et al., 2010; Gokul et al., 2014). Field campaigns in the coastal waters around Chennai were conducted for two periods in January 2015 and March 2015, and six sampling stations from each period were used in this study. These waters have characteristic optical properties that are normally regulated by phytoplankton and CDOM with comparatively less influence from inorganic sediments. Nevertheless, a high contribution from inorganic sediments was witnessed during coastal erosion events as the result of strong wave activity from July–November (monsoon). A field campaign was carried out in the Muttukadu lagoon waters in November 2014. The Ganges River field measurement campaign was conducted in October 2016, and this included the five stations used in this study. The river water is highly productive and loaded with sediments transported from the course of the river. Field data collection during each campaign in Point Calimere comprised measurements at multiple stations from the coast towards the seaward side of the region, covering diverse hydrological and land-use features and various CDOM and particulate sources. Muttukadu Lake is a turbid and eutrophic shallow water body, having intense phytoplankton activity as indicated by high chlorophyll concentrations and low to moderate values of non-algal particles and CDOM. Green algal blooms dominate these waters in cyclic events. The details of each cruise are provided in Table 1.
2.3. Performance assessment Root Mean Square Error (RMSE), Mean Normalized Bias(MNB), and Mean Relative Error (MRE) were used to evaluate the random and systematic errors for the proposed method. The Slope (S), intercept (I) and coefficient of determination (R2) were used for further evaluation of the goodness of fit of the proposed method. Using Mi for the calculated values, Ii for the in situ measured values, and n for the number of data, the RMSE, MNB, and MRE can be written as:
1 n
RMSE =
MNB =
1 n
n
∑ (Mi − Ii )2
(1)
i=1
n
∑ ((Mi − Ii)/Ii)
(2)
i=1
n
MRE =
∑ ((Mi − Ii)/Ii)
(3)
i=1
2.2. Measurement of optical properties 2.4. Comparison with existing models Non-water absorption and attenuation coefficients from visible to near-infrared regions (at 3.8 nm intervals) were measured with an appropriately calibrated ac-s meter (WET Labs Inc., USA) following the
Two existing models are compared with the present work to assess their relative performance. One of the existing models is taken from
Table 1 Details of the data used from each cruises in this study. Location
Latitude
Longitude
Stations
Period
Chl (mg m−3)
Turbidity (NTU)
Use in the study
Chennai Chennai Point Calimere Muttukkad Lagoon Point Calimere Point Calimere Ganges River
13°7′ 37″ N 13°7′ 37″ N 10°15′16″N 12°48′2″N 10°15′16″N 10°15′16″N 25°14′25″N
80°22′ 9″E 80°22′ 9″E 80°04′2″E 80°14′37″E 80°04′2″E 80°04′2″E 83°0′39″E
6 6 3 6 8 16 5
Jan 2015 Mar 2015 May 2012 Nov 2014 Aug 2012 Aug 2013 Oct 2016
0.22–2.62 0.24–8.16 0.91–2.57 44.64–60.04 0.98–14.9 0.18–7.83 7.44–7.87
0.56–1.64 0.12–1.76 0.29–3.59 7.16–8.74 0.49–7.42 0.32–7.71 11.36–17.58
bp - bbp conversion model evaluation bp - bbp conversion model evaluation bp - bbp conversion model evaluation bp - bbp conversion model evaluation Parametrization of bp -Turbidity Model Validation of bp -Turbidity Model Validation of bp - Turbidity Model
197
Estuarine, Coastal and Shelf Science 217 (2019) 196–205
S. Vadakke-Chanat, P. Shanmugam
Fig. 1. A schematic illustrating the step-wise methodology to determine the bbp coefficient from the in-situ bp coefficient based on the partitioning technique.
Fig. 2. Relationship between bp (450) and turbidity using field data from Point Calimere coastal waters (R2 = 0.96, RMSE = 0.29, N = 54).
Fig. 3. Validation results for turbidity using the cruise data from Aug. 2013 in Point Calimere coastal waters and Oct. 2016 in Ganges River waters (R2 = 0.96, RMSE = 0.51, N = 219).
Haltrin (2002) to calculate the backscattering ratio from bp. This ratio is used to calculate bbp (Dev and Shanmugam, 2014). The other model is based on the Petzold's average backscattering ratio (Petzold, 1972), which can be used to convert the scattering spectra to the backscattering spectra (Gokul et al., 2014).
3. Model description The backscattering ratio, in case of a poly-dispersed distribution following the power law (Junge type) and where the absorption is assumed to be zero, is independent of wavelength as shown by previous studies (Ulloa et al., 1994; Whitmire et al., 2007) and re-confirmed theoretically by a more recent study (Sahu and Shanmugam, 2015). A 198
Estuarine, Coastal and Shelf Science 217 (2019) 196–205
S. Vadakke-Chanat, P. Shanmugam
Fig. 4. Spectral bbp depicting the spectral shape of each model with reference to the in-situ data. (a) In-situ data, (b) New Model, (c) Haltrin model, and (d) Petzold average ratio model (Data used are from field campaigns in Chennai Harbour (Aug. 2012, Jan. and March 2015, Chennai Coastal waters (8 Mar. 2015, 6 Jan. 2015, and May 2012), Karaikal, Point Calimere and E05 (Tuticorin), and Muttukkad Lake (Nov. 2014)).
for the conversion because small variations in the spectral slope value may lead to significant changes in the magnitude of the bbNAP spectra. Therefore, to obtain a more accurate bNAP slope value, normalization of the partitioned coefficients with respect to in situ data is performed following the partition of the scattering spectra. The partitioned bNAP and bph are normalized with respect to in-situ bp so that more accurate values of bNAP can be obtained for the slope parameter and used in this conversion. The bNAP slope can now be used as inputs to the model of Vadakke-Chanat et al. (2017) along with chlorophyll and turbidity, in order to obtain the spectral backscattering coefficients. The equations for calculating the partitioned bph and bNAP are provided below (Eqs. (4) – (8)) (Vadakke-Chanat and Shanmugam, 2017).
spectrally constant backscattering ratio for non-algal particles effectively means that the slope of the scattering spectra is also equal to that of the backscattering spectra. However, theoretical studies demonstrating the wavelength-independent nature of the backscattering ratio follow certain assumptions such as zero or insignificant absorption and Junge type particle size distribution, which do not fit well in the case of phytoplankton assemblages (Ulloa et al., 1994). The internal structure of the phytoplankton as well as its complex morphology are known to influence the backscattering ratio in comparison with theoretically predicted values based on the above assumptions using Mie theory (Gordon, 2006; Kitchen and Zaneveld, 1992; Whitmire et al., 2007). It has been demonstrated theoretically that pigmented particles with a power-law distribution of particle size would have a spectrally variable backscattering ratio due to the effect of the imaginary part of the refractive index (Huot et al., 2008; McKee et al., 2009; Morel and Bricaud, 1981). It has also been established that the power-law distribution for particle size does not work well for pigmented algal particles (Whitmire et al., 2010). Therefore, the constant backscattering ratio across the visible wavelengths should only be considered in case of non-algal particles, which fits well with the assumptions made in previous studies. This work proposes a model for conversion of scattering coefficients to backscattering coefficients using chlorophyll and turbidity as additional inputs. The backscattering partitioning model proposed by Vadakke-Chanat et al. (2017) can be effectively used to obtain backscattering spectra given chlorophyll and turbidity as inputs in addition to the slope values. While chlorophyll and turbidity are measured in situ, the additional data requirement here is the backscattering slope caused by the non-algal particulates. This can be obtained from the scattering spectra with the help of the bp partitioning model (VadakkeChanat and Shanmugam, 2017). The partitioning of the scattering spectra is achieved by using the absorption line height obtained from the absorption spectra. Once the scattering spectra are partitioned into non-algal (bNAP) and algal (bph) components, the slope of the bNAP spectra can be calculated and used as an input in the backscattering partition model to obtain the backscattering spectra. However, direct use of bNAP may be problematic since the scattering partition model assumes the bNAP slope to be almost equal to the bp spectral slope. While this close approximation is suitable for the partitioning method, it may be appropriate to calculate the slope parameter in case of bbNAP spectra
aLH (676) = ap (676) −
(ap (648) − ap (714)) (648 − 714)
× (676 − 648) + ap (648) (4)
(676)0.947
(5)
bph (λ ) = bph (648) × P (λ ) + Q (λ )
(6)
bph (648) = 5.3368 × aLH
bNAP (648) = 0.8777 ×
Turbidity 0.8918
bNAP (λ ) = bNAP (648) × (λ /648)Y
(7) (8)
The spectral dependency factors (P(λ) and Q(λ)) in Eq. (6) can be found in Vadakke-Chanat et al. (2017). An empirical relationship for finding the turbidity from bp (450) was developed in this study for its use in the above equation where an independent measurement of turbidity is not available.
Turbidity = 0.9246 × bp (450)1.071
(9)
The bph and bNAP spectra thus obtained are scaled with respect to the total measured bp. The slope of the new scaled bNAP is then found and used as an input in the backscattering partitioning relationships (Vadakke-Chanat et al., 2017), which estimates the bbNAP and bbph spectra to obtain the total bbp. A schematic diagram illustrating this methodology to determine particulate backscattering from measured scattering is provided in Fig. 1. This method successfully achieves conversion of scattering spectra to backscattering spectra, with the additional parameters of absorption line height, chlorophyll, and turbidity. The proposed method can also be used in the absence of the 199
Estuarine, Coastal and Shelf Science 217 (2019) 196–205
S. Vadakke-Chanat, P. Shanmugam
Fig. 5. Comparison of the new model bbp vs the in situ bbp values at key wavelengths. Left panels are for the Haltrin model, middle panels for the Petzold average model, and right panels for the new model.
200
Estuarine, Coastal and Shelf Science 217 (2019) 196–205
S. Vadakke-Chanat, P. Shanmugam
Fig. 6. Spectral bbp depicting the spectral shape of each model with reference to the in-situ data. ((a) In-situ data, (b) New Model, (c) Haltrin model, and (d) Petzold average ratio model (Data used are from Chennai Harbour waters in January and March 2015)).
Fig. 7. Spectral bbp depicting the spectral shape of each model with reference to the in-situ data. (a) In-situ data, (b) New model, (c) Haltrin model, and (d) Petzold average model for the data from the August 2012 cruise in Point Calimere waters.
this purpose. The independence of the data, the variety, and a wider range of values are all thus ensured in the validation. This confirms the applicability of the method of using bp (450) for turbidity estimations. Validation results further revealed a 1:1 relationship between the measured and modelled values, which proves the adequacy and accuracy of the turbidity formulation.
chlorophyll and turbidity values. The empirical formula derived to obtain the turbidity (Eq. (9)) from the scattering coefficient uses 450 nm because the proportional influence of chlorophyll is significantly less at this band compared to other wavelengths. The chlorophyll concentration can be obtained from the absorption line height, which is already an input for the apportioning of the scattering spectra (Vadakke-Chanat and Shanmugam, 2017). The estimation of turbidity (Eq. (9)) is based on a strong correlation and excellent goodness of fit between the turbidity and particulate scattering values (Fig. 2, R2 = 0.96, RMSE = 0.29 for N = 54). Data from the multiple field campaigns conducted in the Point Calimere region were used for this parameterization because the turbidity values ranged widely, from 0.49 to 7.42 NTU. The chlorophyll values also exhibited a wider variation in these waters (0.98–14.9 mg m−3). This ensures the wide applicability of the derived empirical equation for turbidity estimations. Validation results (Fig. 3) further prove a strong correlation between the measured and estimated turbidity values (R2 = 0.96, RMSE = 0.51, N = 219). An independent data set comprising coastal field measurements from Point Calimere coastal waters in August 2013 and Ganges River waters in October 2016 were used for
4. Results and discussion The results of the proposed method are compared with two existing models (Haltrin model and Petzold average model) used to convert scattering spectra to backscattering spectra (Gokul et al., 2014; Haltrin, 2002). It should be noted that Haltrin's relationship was originally proposed for a wavelength of 515 nm; however, an extended application of the same relationship across the spectra was used for comparative analysis. The entire set of backscattering spectra from the in-situ observations and models are shown in Fig. 4. As expected, the new model is clearly efficient in reproducing the spectral inflections in the backscattering 201
Estuarine, Coastal and Shelf Science 217 (2019) 196–205
S. Vadakke-Chanat, P. Shanmugam
Fig. 8. Spectral bbp depicting the spectral shape of each model with reference to the in-situ data. (a) In-situ data, (b) New model, (c) Haltrin model, and (d) Petzold average model for the data from Chennai Coastal waters in March 2015.
Fig. 9. Spectral bbp depicting the spectral shape of each model with reference to the in-situ data. (a) In-situ data, (b) New model, (c) Haltrin model, and (d) Petzold average model for the data from Chennai coastal waters in January 2015.
coefficients of the field data as compared against the existing methods for a wide range of backscattering values. The results for highly productive waters were greatly overestimated for the existing models, while the new model produced values closely matching the in situ data. It should be noted that the spectral shape of the new model was nearly reproduced by the new model, even for lower magnitude spectra compared with the existing models. The overestimations of the Haltrin and Petzold average methods can clearly be seen in Fig. 5. Use of the Haltrin method consistently overestimated the backscattering values in all types of waters across all wavelengths. The use of Petzold average model resulted in similar overestimation despite the magnitude of the overestimation being lower than the Haltrin model. It was observed that the Petzold average model produced a better relationship with in situ data (especially around 715 nm). In contrast, the new approach was highly efficient in accurately reproducing the backscattering values for all water types and across the visible and NIR wavelengths. The overestimation by the Haltrin and Petzold average method is due to the strong influence of phytoplankton on the total backscattering coefficients. The new model has the clear ability to account for the contribution of phytoplankton,
thus producing more reliable backscattering coefficients. The backscattering coefficients of waters with a strong influence of phytoplankton deviate more from the expected trends obtained from Mie calculations based on the assumption of spherical and non-absorbing particles. The bulk effective featured spectra of phytoplankton backscattering were captured from this method for the study region, despite the phytoplankton particle size distribution being highly featured and not fitting the form of a Junge type distribution (Whitmire et al., 2010). Overall, the new model performed best across all the wavelengths as well as over a broad range of water types (Fig. 5). The data sets of individual cruises classified according to the measurement location are shown in Fig. 6 to Fig. 11. Spectral bbp depicts the spectral shape of each model with reference to the in-situ data for data from Chennai Harbour waters during January and March 2015, which are a subset of the data collected off-Chennai for the period (Fig. 6). These waters are relatively productive and clear to moderately turbid coastal waters with chlorophyll concentrations ranging from 2 to 8.16 mg m−3 and turbidity values ranging from 1.48 to 1.76 NTU. Comparison of these results reveals that the spectral troughs around 440 nm and 650 nm and the peaks between 488 and 532 nm and
202
Estuarine, Coastal and Shelf Science 217 (2019) 196–205
S. Vadakke-Chanat, P. Shanmugam
Fig. 10. Spectral bbp depicting the spectral shape of each model with reference to the in situ data. (a) In-situ data, (b) New model, (c) Haltrin model, and (d) Petzold average model for the data from May 2012. Fig. 11. Spectral bbp depicting the spectral shape of each model with reference to the in-situ data. (a) In-situ data, (b) New model, (c) Haltrin model, and (d) Petzold average model for the data from Muttukkad Lake waters in November 2014. Note that the y-axis limits in the sub-plot (c) are different to accommodate the highly overestimated values.
Similar trends are seen in Fig. 9. Fig. 10 represents the field bbp values from Point Calimere coastal waters during May 2012, where the chlorophyll ranged from 0.91 to 2.57 mg m−3 and the turbidity from 0.29 to 3.59 NTU. The data from highly productive eutrophic lagoons waters in Muttukadu Lake with a chlorophyll range of 44.64–60.04 mg m−3 and a turbidity range of 7.16–8.74 NTU also demonstrate the excellent applicability and robustness of the new model (Fig. 11). The ability to calculate the proportional influence of phytoplankton in the backscattering using the new method is further evident compared to the other models (Fig. 11). The new model is capable of predicting the backscattering coefficient with great accuracy even in extremely productive and strongly scattering inland lagoon waters. Nevertheless, fine-tuning the phytoplankton spectral coefficients in the partitioning model (Vadakke-Chanat et al., 2017) for various other global waters may be required after a careful examination of the validity of the model parameterizations for these waters. Fig. 12 shows the spectral percentage deviation plots of the entire data set for each of the models compared in this study. The new model is observed to have the lowest percentage deviation of all the models. While the two existing methods clearly overestimate the backscattering coefficients in these waters, the new model is consistent and has better accuracy in reproducing the spectral shape of the measured backscattering coefficients. The
715 nm were reproduced by the new model, and the magnitude of the backscattering values is also close. However, the spectra from existing methods in Fig. 6 deviated in terms of the magnitude and shape, and a gap was observed between the different spectral lines, which distinctively differ from the in-situ spectra. To further examine the model results, the bbp spectral inflections in the Point Calimere waters from the in situ data, new model, and the existing models were also examined (Fig. 7). In this coastal region, chlorophyll concentrations reached up to 14.9 mg m−3 and the turbidity ranged between 0.49 and 7.42 NTU. Fig. 8 shows the backscattering coefficients for clear to moderately turbid Chennai Coastal waters in March 2015 (except for Harbour waters). These waters exhibited chlorophyll concentrations of 0.24–2.68 mg m−3 and turbidity values of 0.12–0.72 NTU. Evaluation of these results demonstrates again that the spectral troughs near 440 nm and 650 nm and the crests at 715 nm and between 488 and 532 nm are well replicated in the new model, with the magnitude being almost equal to the in situ data. Conversely, the spectra from the earlier approaches (Fig. 8) deviated from the in situ data in terms of the magnitude and shape, and a gap was observed between the different spectral lines, which are distinct from the in situ spectra. In the Chennai coastal waters sampled on 6 January 2015 (subset of the data other than Harbour waters) (Fig. 9), the chlorophyll ranged from 0.22 to 2.61 mg m−3 and the turbidity from 0.56 to 1.64 NTU. 203
Estuarine, Coastal and Shelf Science 217 (2019) 196–205
S. Vadakke-Chanat, P. Shanmugam
Fig. 12. The spectral percentage deviation plots for Haltrin model (a), for Petzold average ratio model (b) and the new model (c). Note that the x-axis of the Fig. 12(a) is different as compared to the other two images to accommodate the very high SPD values.
more closely reproduced with the new method than in the existing methods. A limitation of the new model includes the slight shift in the spectral crest between 488 and 532 nm in comparison with the in situ data though the overall spectral shape closely follows the in situ spectral backscattering inflections at specific wavelengths. However, the ability of the model to reproduce the in-situ backscattering coefficients with the one-to-one correlation overcomes this limitation in terms of its applicability. Fine tuning of the model to this effect could be a topic of future study. The new model will have practical applications in the field of remote sensing, ocean optics, underwater optical communication and underwater imaging studies, since bbp plays a major role in the algorithms used in these fields (Gholami and Saghafifar, 2018; Mortazavi et al., 2013) by enhancing the data repository where measured backscattering data were not previously available for technological, logistical, or financial reasons. The ability of the proposed model for a more accurate determination of backscattering coefficient will enhance underwater imaging capabilities by enabling scientists to decouple the effect of backscattering in the captured image. Underwater imaging in turn has its applied usages in underwater structure inspection including pipelines, rescue operations, diver visibility, underwater target detection, and biological and environmental studies of oceans. The ocean optics and remote sensing research finds implications in marine environmental protection and sediment transport studies (Zhao et al., 2018) for coastal engineering applications. A better model for backscattering ratio has implications in finding the bulk refractive index (Twardowski et al., 2001), and the present model can be used to calculate the backscattering ratio as well.
Table 2 Statistical comparison of the model results (N = 130). Frequency
Model
MRE
MNB
RMSE
R2
Slope
Intercept
412
New Haltrin Petzold New Haltrin Petzold New Haltrin Petzold New Haltrin Petzold New Haltrin Petzold New Haltrin Petzold New Haltrin Petzold New Haltrin Petzold
−0.183 1.478 0.044 −0.214 1.396 0.012 −0.191 1.214 −0.069 −0.166 1.228 −0.081 −0.061 1.544 0.040 −0.027 1.773 0.170 −0.064 1.829 0.260 0.037 2.207 0.368
−0.194 0.462 0.107 −0.259 0.418 0.029 −0.178 0.238 −0.081 −0.122 0.208 −0.101 −0.029 0.362 0.024 0.004 0.520 0.187 −0.086 0.624 0.301 0.019 0.656 0.328
0.012 0.273 0.035 0.015 0.279 0.040 0.015 0.275 0.034 0.015 0.286 0.033 0.011 0.294 0.034 0.008 0.273 0.034 0.007 0.240 0.035 0.006 0.262 0.035
0.96 0.50 0.72 0.91 0.39 0.62 0.93 0.51 0.73 0.93 0.57 0.77 0.94 0.61 0.80 0.96 0.63 0.81 0.96 0.59 0.77 0.98 0.76 0.89
0.904 4.894 1.264 0.896 4.553 1.219 0.881 4.808 1.206 0.881 5.071 1.219 1.004 5.989 1.402 1.047 6.487 1.556 1.062 6.436 1.660 1.092 7.938 1.862
−0.004 −0.105 −0.010 −0.005 −0.094 −0.009 −0.003 −0.122 −0.013 −0.002 −0.137 −0.014 −0.003 −0.146 −0.015 −0.003 −0.134 −0.014 −0.004 −0.113 −0.013 −0.002 −0.137 −0.014
440
488
510
532
595
650
715
statistical measures of the model performance provided in Table 2 also demonstrate the robustness of the new model compared with the previous models. 5. Conclusions
Acknowledgements
A robust method for conversion of spectral particulate scattering coefficient to the spectral particulate backscattering coefficient with additional inputs of chlorophyll concentration and turbidity has been proposed and its efficiency has been demonstrated in the present study. The new method yielded results much more closely consistent with insitu data than the Haltrin and Petzold methods. It was demonstrated that the new method gives optimum results even in highly scattering, intense algal bloom waters, while the existing methods overestimate the backscattering coefficient for these water types. It is also demonstrated that the spectral inflections of the in-situ backscattering coefficient are
This research work was supported by the Department of Science and Technology (No. OEC1819150DSTXPSHA). We thank D. Rajasekhar, The Head, Vessel Management Cell (VMC), and Director of National Institute of Ocean Technology (NIOT) for facilitating our research work by providing Coastal Research Vessels to Indian Institute of Technology (IIT) Madras with which we were able to make various bio-optical and oceanographic measurements off Chennai and Point Calimere. We sincerely thank Dr. S. Mitchell, Editor, Estuarine, Coastal and Shelf Science, and the three anonymous reviewers for their valuable comments and suggestions which allowed us to greatly improve the 204
Estuarine, Coastal and Shelf Science 217 (2019) 196–205
S. Vadakke-Chanat, P. Shanmugam
scientific content and quality of this manuscript.
near-infrared light in water: dependence on temperature and salinity. Appl. Opt. 36, 6035–6046. https://doi.org/10.1364/ao.36.006035. Pegau, W.S., Zaneveld, J.R., 1993. Temperature-dependent absorption of water in the red and near-infrared portions of the spectrum. Limnol. Oceanogr. 38, 188–192. Petzold, T.J., 1972. Volume Scattering Functions for Selected Ocean Waters. Rao, C., Mukherjee, K., Gupta, S., Ray, A., Phoha, S., 2009. Underwater mine detection using symbolic pattern analysis of sidescan sonar images. In: American Control Conference, 2009. ACC’09, pp. 5416–5421. Sahu, S.K., Shanmugam, P., 2015. Semi-analytical modeling and parameterization of particulates-in-water phase function for forward angles. Optic Express 23, 22291. https://doi.org/10.1364/OE.23.022291. Simon, A., Shanmugam, P., 2013. A new model for the vertical spectral diffuse attenuation coefficient of downwelling irradiance in turbid coastal waters: validation with in situ measurements. Optic Express 21, 30082. https://doi.org/10.1364/OE.21. 030082. Sun, D., Li, Y., Wang, Q., Lv, H., Le, C., Huang, C., Gong, S., 2010. Partitioning particulate scattering and absorption into contributions of phytoplankton and non-algal particles in winter in Lake Taihu (China). Hydrobiologia 644, 337–349. https://doi.org/10. 1007/s10750-010-0198-7. Sun, H., Benzie, P.W., Burns, N., Hendry, D.C., Player, M.A., Watson, J., 2008. Underwater digital holography for studies of marine plankton. Philos. Trans. A. Math. Phys. Eng. Sci. 366, 1789–1806. https://doi.org/10.1098/rsta.2007.2187. Sundarabalan, V.B., Shanmugam, P., Manjusha, S., 2013. Radiative transfer modeling of upwelling light field in coastal waters. J. Quant. Spectrosc. Radiat. Transf. 121, 30–44. https://doi.org/10.1016/j.jqsrt.2013.01.016. Twardowski, M.S., Boss, E., Macdonald, J.B., Pegau, W.S., Barnard, A.H., Zaneveld, J.R.V., 2001. A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters. J. Geophys. Res. 106, 14129. https://doi.org/10.1029/ 2000JC000404. Twardowski, M.S., Claustre, H., Freeman, S.A., Stramski, D., Huot, Y., 2007. Optical backscattering properties of the “clearest” natural waters. Biogeosci. Discuss. 4, 1041–1058. Ulloa, O., Sathyendranath, S., Platt, T., 1994. Effect of the particle-size distribution on the backscattering ratio in seawater. Appl. Opt. 33, 7070–7077. Vadakke-Chanat, S., Shanmugam, P., 2017. Modeling the contributions of phytoplankton and non-algal particles to spectral scattering properties in near-shore and lagoon waters. Continent. Shelf Res. 135. https://doi.org/10.1016/j.csr.2017.01.001. Vadakke-Chanat, S., Shanmugam, P., Ahn, Y., 2017. A model for deriving the spectral backscattering properties of particles in inland and marine waters from in situ and remote sensing data. IEEE Trans. Geosci. Rem. Sens. 55. https://doi.org/10.1109/ TGRS.2016.2624986. Vadakke-Chanat, S., Shanmugam, P., Sundarabalan, B., 2018. Monte Carlo simulations of the backscattering measurements for associated uncertainty. Optic Express 26, 21258. https://doi.org/10.1364/OE.26.021258. WET Labs ECO BB9 User’s Guide (BB9), 2017. Seabird Scientific. Whitmire, A.L., Boss, E., Cowles, T.J., Pegau, W.S., 2007. Spectral Variability of the Particulate Backscattering Ratio 15. pp. 7019–7031. https://doi.org/10.1029/ 2005JC003008. Whitmire, A.L., Pegau, W.S., Karp-Boss, L., Boss, E., Cowles, T.J., 2010. Spectral backscattering properties of marine phytoplankton cultures. Optic Express 18, 15073–15093. https://doi.org/10.1029/2003RG000148.D. Zaneveld, J.R.V., Kitchen, J.C., Moore, C.C., 1994. Scattering error correction of reflecting-tube absorption meters. In: Ocean Optics XII, pp. 44–55. Zhao, J., Cao, W., Xu, Z., Ye, H., Yang, Y., Wang, G., Zhou, W., Sun, Z., 2018. Estimation of suspended particulate matter in turbid coastal waters: application to hyperspectral satellite imagery. Optic Express 26, 10476–10493.
References Bricaud, A., Morel, A., Babin, M., Karima, A., Claustre, H., 1998. Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case-1) waters: analysis and implications for bio-optical models. J. Geophys. Res. 103 (C13), 31033–31044. https://doi.org/10.1029/98JC02712. Damotharan, P., Perumal, N.V., Arumugam, M., Vijayalakshmi, S., Balasubramanian, T., 2010. Seasonal variation of physicochemical characteristics in point calimere coastal waters south east coast of India. Middle East J. Sci. Res. 6, 333–339. Dev, P.J., Shanmugam, P., 2014. New model for subsurface irradiance reflectance in clear and turbid waters. Optic Express 22, 9548–9566. Doxaran, D., Leymarie, E., Nechad, B., Dogliotti, A., Ruddick, K., Gernez, P., Knaeps, E., 2016. Improved correction methods for field measurements of particulate light backscattering in turbid waters. Optic Express 24, 3615–3637. https://doi.org/10. 1364/oe.24.003615. Gholami, A., Saghafifar, H., 2018. Simulation of an active underwater imaging through a wavy sea surface. J. Mod. Optic. 65, 1210–1218. Gokul, E.A., Shanmugam, P., Sundarabalan, B., Sahay, A., Chauhan, P., 2014. Modelling the inherent optical properties and estimating the constituents ׳concentrations in turbid and eutrophic waters. Continent. Shelf Res. 84, 120–138. Gordon, H.R., 2006. Backscattering of light from disklike particles: is fine-scale structure or gross morphology more important? Appl. Opt. 45, 7166–7173. Haltrin, V.I., 2002. One-parameter two-term Henyey-Greenstein phase function for light scattering in seawater. Appl. Opt. 41, 1022–1028. https://doi.org/10.1364/ao.41. 001022. Huot, Y., Morel, A., Twardowski, M.S., Stramski, D., Reynolds, R.A., Villefranche, D., Huot, Y., Morel, A., Twardowski, M.S., Stramski, D., Reynolds, R.A., et al., 2008. Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern South Pacific Ocean. Biogeosciences 5, 495–507. Kitchen, J.C., Zaneveld, J.R., 1992. A three-layered sphere model of the optical properties of phytoplankton. Limnol. Oceanogr. 37, 1680–1690. Kondo, H., Ura, T., 2004. Navigation of an {AUV} for investigation of underwater structures. Contr. Eng. Pract. 12, 1551–1559. https://doi.org/https://doi.org/10. 1016/j.conengprac.2003.12.005. Loisel, H., Nicolas, J.-M., Sciandra, A., Stramski, D., Poteau, A., 2006. Spectral dependency of optical backscattering by marine particles from satellite remote sensing of the global ocean. J. Geophys. Res. 111, C09024. https://doi.org/10.1029/ 2005JC003367. McKee, D., Chami, M., Brown, I., Calzado, V.S., Doxaran, D., Cunningham, A., 2009. Role of measurement uncertainties in observed variability in the spectral backscattering ratio: a case study in mineral-rich coastal waters. Appl. Opt. 48, 4663. https://doi. org/10.1364/AO.48.004663. Mobley, C.D., 1994. Light and Water: Radiative Transfer in Natural Waters. Academic press, San Diego. Mobley, C.D., Sundman, L.K., Boss, E., 2002. Phase function effects on oceanic light fields. Appl. Opt. 41, 1035. https://doi.org/10.1364/AO.41.001035. Morel, A., 1980. In-water and remote measurements of ocean color. Boundary-Layer Meteorol. 18, 177–201. Morel, A., Bricaud, A., 1981. Theoretical results concerning the optics of phytoplankton, with special reference to remote sensing applications. In: Oceanography from Space. Springer, pp. 313–327. Mortazavi, H., Oakley, J.P., Barkat, B., 2013. Mitigating the effect of optical back-scatter in multispectral underwater imaging. Meas. Sci. Technol. 24, 74025. https://doi.org/ 10.1088/0957-0233/24/7/074025. Pegau, W.S., Gray, D., Zaneveld, J.R.V., 1997. Absorption and attenuation of visible and
205
Contents lists available at ScienceDirect
Estuarine, Coastal and Shelf Science journal homepage: www.elsevier.com/locate/ecss
Retrieval of spectral backscattering from spectral scattering based on spectral partitioning technique
T
Sayoob Vadakke-Chanat, Palanisamy Shanmugam∗ Ocean Optics and Imaging Laboratory, Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai - 600036, India
A R T I C LE I N FO
A B S T R A C T
Keywords: Optical properties Scattering Backscattering Conversion model Turbid and productive waters
Direct measurement of backscattering using sensors has technological limitations such as saturation in highly turbid waters and the effect of absorption in strongly absorbing highly productive waters. In the present study, a quantitative method is developed to estimate the particulate spectral backscattering coefficient based on spectral partitioning of the scattering coefficient. The input slope of the non-algal backscattering spectra was determined from the scattering slope and the magnitude was quantified from the water turbidity. The contribution of phytoplankton to the backscattering was determined as a linear combination of the spectral dependency factors and the chlorophyll concentration. The proposed method of conversion, from scattering to backscattering, when compared with two existing methods (Haltrin and Petzold average ratio), resulted in lower relative errors (mean relative error: -0.214–0.037, mean net Bias: -0.259–0.019, root mean square error: 0.006–0.015, coefficient of determination: 0.91–0.98), and substantial improvement was also observed in the spectral shape and magnitude of the backscattering coefficients.
1. Introduction Scattering and backscattering are optical properties of fundamental importance in the field of oceanic and atmospheric optics and are categorized as the inherent optical properties (IOP) (Bricaud et al., 1998; Loisel et al., 2006; Morel, 1980; Sun et al., 2010). The backscattering coefficient regulates the Bidirectional Reflectance Distribution Function (BRDF), which is a property of prime importance in the field of ocean remote sensing (Mobley, 1994; Twardowski et al., 2007). Light propagation through oceanic waters is defined by the radiative transfer equation (Sundarabalan et al., 2013), requiring information on the spectral angular scattering and spectral absorption of the water column. A practical approximation of the scattering phase function can be obtained from the backscattering ratio (McKee et al., 2009; Mobley et al., 2002), which is the ratio of the backscattering to the scattering values. The particle size distribution (PSD) is another property which can be related to the particulate backscattering ratio and serves as a proxy for the composition of the particles (Twardowski et al., 2001). The backscattering coefficient (bb) has wider implications in terms of practical applications such as the underwater imaging widely utilized in engineering and environmental studies (Mortazavi et al., 2013), optical target detection in the water column and at the ocean bottom (Rao et al., 2009), marine biological research (Sun et al., 2008), and in the
∗
investigation of underwater structures (Kondo and Ura, 2004). The backscattering enhances the intensity of the recorded pixel, results in an alteration in the measured pixel reflectance spectrum, and introduces contrast loss in the captured image, which is a dominant degradation problem (Gholami and Saghafifar, 2018; Mortazavi et al., 2013) in underwater imaging applications (Mortazavi et al., 2013). Measurement of backscattering coefficients has restrictions imposed by the technological limitations such as the saturation of sensors (McKee et al., 2009) and the influence of absorption on the backscattering measurement (Doxaran et al., 2016), while the scattering coefficient (b) is determined from measurements of absorption and attenuation coefficients, which are appropriately calibrated and corrected for associated measurement errors. Estimation of a complete set of IOPs is a prerequisite for various practical purposes and an appropriate and robust method of converting scattering to backscattering could aid the restoration of the parameters. This is because the measurement of the entire set of the optical properties may not be always feasible due to certain economic, technological or logistical limitations. Therefore, a reliable method for estimating the spectral particulate backscattering coefficient from the spectral particulate scattering coefficient is required. In the present work, a method is presented for converting the particulate spectral scattering coefficient into the particulate spectral
Corresponding author. E-mail address: [email protected] (P. Shanmugam).
https://doi.org/10.1016/j.ecss.2018.11.024 Received 7 June 2018; Received in revised form 16 November 2018; Accepted 16 November 2018 Available online 17 November 2018 0272-7714/ © 2018 Elsevier Ltd. All rights reserved.
Estuarine, Coastal and Shelf Science 217 (2019) 196–205
S. Vadakke-Chanat, P. Shanmugam
manufacturer's guidelines. Temperature (Pegau and Zaneveld, 1993) and Salinity (Pegau et al., 1997) corrections were performed on the measured data and an additional correction for scattering effect was performed on the absorption data (Zaneveld et al., 1994). The scattering coefficient was determined from the above data by subtraction of absorption from attenuation values, cpg(λ) – apg(λ) = bp(λ). A CTD (SeaBird SBE-FASTCAT) instrument was used for measurements of temperature and salinity and an FLNTU sensor (WET Labs) was used for chlorophyll fluorescence and turbidity measurements. The FLNTU sensor determines the turbidity using scattering measurements at 700 nm, and the chlorophyll concentration using fluorescence measurements with excitation at 470 nm and emission at 695 nm. An underwater frame on which these sensors were mounted was lowered in the water using a winch with communication and power cables connected to the shipboard computer (Dev and Shanmugam, 2014; Simon and Shanmugam, 2013). An ECO-BB9 sensor from WET Labs was used to obtain the situ measurements of particulate backscattering coefficient (bbp) for 412, 440, 488, 510, 532, 595, 650, 676, and 715 nm wavelengths. The sensor actually measures the volume scattering function (VSF) (β, m−1sr−1) at these wavelengths at 124° (Doxaran et al., 2016; VadakkeChanat et al., 2018), which are then multiplied by the term 2πχ to obtain the backscattering coefficient bb(λ). Subtracting the pure water backscattering then yields bbp. There is an LED source light with a corresponding detector for each measurement wavelength. The BB9 raw output is expressed in counts, sampling at 1 Hz, from which bbp is calculated. A correction is performed for the effect of absorption in these measurements based on a standard correction procedure (WET Labs ECO BB9 User's Guide (BB9), 2017).
backscattering coefficient in coastal and inland waters based on partitioning methods for scattering and backscattering coefficients (Vadakke-Chanat et al., 2017; Vadakke-Chanat and Shanmugam, 2017) and the robustness of the method is demonstrated together with potential implications in coastal and inland waters. 2. Data and methods 2.1. Sampling locations Contrasting coastal and inland environments were identified for in situ data measurement campaigns: clear to moderately turbid coastal waters around Chennai (13°7′ 37″ N; 80° 22′ 9″ E), highly turbid coastal waters near Point Calimere (10°15′16″N, 80°04′2″E), algal bloomdominated eutrophic waters in the Muttukadu lagoon (12°48′2″N; 80°14′37″E) on the southeast coast of India, and turbid and productive waters of the Ganges River (25°14′25″N; 83°0′39″E). Three field campaigns in the Point Calimere coastal region were conducted during May 2012, August 2012, and August 2013. The May 2012 cruise in the Point Calimere region also included two sampling stations offshore of Karaikal and near Palar River mouth. In optical terms, the Point Calimere region is characterized by inorganic sediment derived from wave-tide induced re-suspended bottom material, having a relatively high proportion/concentration of non-algal particles dominated by clay and silt, together with low concentrations of chromophoric dissolved organic matter (CDOM) and chlorophyll (Damotharan et al., 2010; Gokul et al., 2014). Field campaigns in the coastal waters around Chennai were conducted for two periods in January 2015 and March 2015, and six sampling stations from each period were used in this study. These waters have characteristic optical properties that are normally regulated by phytoplankton and CDOM with comparatively less influence from inorganic sediments. Nevertheless, a high contribution from inorganic sediments was witnessed during coastal erosion events as the result of strong wave activity from July–November (monsoon). A field campaign was carried out in the Muttukadu lagoon waters in November 2014. The Ganges River field measurement campaign was conducted in October 2016, and this included the five stations used in this study. The river water is highly productive and loaded with sediments transported from the course of the river. Field data collection during each campaign in Point Calimere comprised measurements at multiple stations from the coast towards the seaward side of the region, covering diverse hydrological and land-use features and various CDOM and particulate sources. Muttukadu Lake is a turbid and eutrophic shallow water body, having intense phytoplankton activity as indicated by high chlorophyll concentrations and low to moderate values of non-algal particles and CDOM. Green algal blooms dominate these waters in cyclic events. The details of each cruise are provided in Table 1.
2.3. Performance assessment Root Mean Square Error (RMSE), Mean Normalized Bias(MNB), and Mean Relative Error (MRE) were used to evaluate the random and systematic errors for the proposed method. The Slope (S), intercept (I) and coefficient of determination (R2) were used for further evaluation of the goodness of fit of the proposed method. Using Mi for the calculated values, Ii for the in situ measured values, and n for the number of data, the RMSE, MNB, and MRE can be written as:
1 n
RMSE =
MNB =
1 n
n
∑ (Mi − Ii )2
(1)
i=1
n
∑ ((Mi − Ii)/Ii)
(2)
i=1
n
MRE =
∑ ((Mi − Ii)/Ii)
(3)
i=1
2.2. Measurement of optical properties 2.4. Comparison with existing models Non-water absorption and attenuation coefficients from visible to near-infrared regions (at 3.8 nm intervals) were measured with an appropriately calibrated ac-s meter (WET Labs Inc., USA) following the
Two existing models are compared with the present work to assess their relative performance. One of the existing models is taken from
Table 1 Details of the data used from each cruises in this study. Location
Latitude
Longitude
Stations
Period
Chl (mg m−3)
Turbidity (NTU)
Use in the study
Chennai Chennai Point Calimere Muttukkad Lagoon Point Calimere Point Calimere Ganges River
13°7′ 37″ N 13°7′ 37″ N 10°15′16″N 12°48′2″N 10°15′16″N 10°15′16″N 25°14′25″N
80°22′ 9″E 80°22′ 9″E 80°04′2″E 80°14′37″E 80°04′2″E 80°04′2″E 83°0′39″E
6 6 3 6 8 16 5
Jan 2015 Mar 2015 May 2012 Nov 2014 Aug 2012 Aug 2013 Oct 2016
0.22–2.62 0.24–8.16 0.91–2.57 44.64–60.04 0.98–14.9 0.18–7.83 7.44–7.87
0.56–1.64 0.12–1.76 0.29–3.59 7.16–8.74 0.49–7.42 0.32–7.71 11.36–17.58
bp - bbp conversion model evaluation bp - bbp conversion model evaluation bp - bbp conversion model evaluation bp - bbp conversion model evaluation Parametrization of bp -Turbidity Model Validation of bp -Turbidity Model Validation of bp - Turbidity Model
197
Estuarine, Coastal and Shelf Science 217 (2019) 196–205
S. Vadakke-Chanat, P. Shanmugam
Fig. 1. A schematic illustrating the step-wise methodology to determine the bbp coefficient from the in-situ bp coefficient based on the partitioning technique.
Fig. 2. Relationship between bp (450) and turbidity using field data from Point Calimere coastal waters (R2 = 0.96, RMSE = 0.29, N = 54).
Fig. 3. Validation results for turbidity using the cruise data from Aug. 2013 in Point Calimere coastal waters and Oct. 2016 in Ganges River waters (R2 = 0.96, RMSE = 0.51, N = 219).
Haltrin (2002) to calculate the backscattering ratio from bp. This ratio is used to calculate bbp (Dev and Shanmugam, 2014). The other model is based on the Petzold's average backscattering ratio (Petzold, 1972), which can be used to convert the scattering spectra to the backscattering spectra (Gokul et al., 2014).
3. Model description The backscattering ratio, in case of a poly-dispersed distribution following the power law (Junge type) and where the absorption is assumed to be zero, is independent of wavelength as shown by previous studies (Ulloa et al., 1994; Whitmire et al., 2007) and re-confirmed theoretically by a more recent study (Sahu and Shanmugam, 2015). A 198
Estuarine, Coastal and Shelf Science 217 (2019) 196–205
S. Vadakke-Chanat, P. Shanmugam
Fig. 4. Spectral bbp depicting the spectral shape of each model with reference to the in-situ data. (a) In-situ data, (b) New Model, (c) Haltrin model, and (d) Petzold average ratio model (Data used are from field campaigns in Chennai Harbour (Aug. 2012, Jan. and March 2015, Chennai Coastal waters (8 Mar. 2015, 6 Jan. 2015, and May 2012), Karaikal, Point Calimere and E05 (Tuticorin), and Muttukkad Lake (Nov. 2014)).
for the conversion because small variations in the spectral slope value may lead to significant changes in the magnitude of the bbNAP spectra. Therefore, to obtain a more accurate bNAP slope value, normalization of the partitioned coefficients with respect to in situ data is performed following the partition of the scattering spectra. The partitioned bNAP and bph are normalized with respect to in-situ bp so that more accurate values of bNAP can be obtained for the slope parameter and used in this conversion. The bNAP slope can now be used as inputs to the model of Vadakke-Chanat et al. (2017) along with chlorophyll and turbidity, in order to obtain the spectral backscattering coefficients. The equations for calculating the partitioned bph and bNAP are provided below (Eqs. (4) – (8)) (Vadakke-Chanat and Shanmugam, 2017).
spectrally constant backscattering ratio for non-algal particles effectively means that the slope of the scattering spectra is also equal to that of the backscattering spectra. However, theoretical studies demonstrating the wavelength-independent nature of the backscattering ratio follow certain assumptions such as zero or insignificant absorption and Junge type particle size distribution, which do not fit well in the case of phytoplankton assemblages (Ulloa et al., 1994). The internal structure of the phytoplankton as well as its complex morphology are known to influence the backscattering ratio in comparison with theoretically predicted values based on the above assumptions using Mie theory (Gordon, 2006; Kitchen and Zaneveld, 1992; Whitmire et al., 2007). It has been demonstrated theoretically that pigmented particles with a power-law distribution of particle size would have a spectrally variable backscattering ratio due to the effect of the imaginary part of the refractive index (Huot et al., 2008; McKee et al., 2009; Morel and Bricaud, 1981). It has also been established that the power-law distribution for particle size does not work well for pigmented algal particles (Whitmire et al., 2010). Therefore, the constant backscattering ratio across the visible wavelengths should only be considered in case of non-algal particles, which fits well with the assumptions made in previous studies. This work proposes a model for conversion of scattering coefficients to backscattering coefficients using chlorophyll and turbidity as additional inputs. The backscattering partitioning model proposed by Vadakke-Chanat et al. (2017) can be effectively used to obtain backscattering spectra given chlorophyll and turbidity as inputs in addition to the slope values. While chlorophyll and turbidity are measured in situ, the additional data requirement here is the backscattering slope caused by the non-algal particulates. This can be obtained from the scattering spectra with the help of the bp partitioning model (VadakkeChanat and Shanmugam, 2017). The partitioning of the scattering spectra is achieved by using the absorption line height obtained from the absorption spectra. Once the scattering spectra are partitioned into non-algal (bNAP) and algal (bph) components, the slope of the bNAP spectra can be calculated and used as an input in the backscattering partition model to obtain the backscattering spectra. However, direct use of bNAP may be problematic since the scattering partition model assumes the bNAP slope to be almost equal to the bp spectral slope. While this close approximation is suitable for the partitioning method, it may be appropriate to calculate the slope parameter in case of bbNAP spectra
aLH (676) = ap (676) −
(ap (648) − ap (714)) (648 − 714)
× (676 − 648) + ap (648) (4)
(676)0.947
(5)
bph (λ ) = bph (648) × P (λ ) + Q (λ )
(6)
bph (648) = 5.3368 × aLH
bNAP (648) = 0.8777 ×
Turbidity 0.8918
bNAP (λ ) = bNAP (648) × (λ /648)Y
(7) (8)
The spectral dependency factors (P(λ) and Q(λ)) in Eq. (6) can be found in Vadakke-Chanat et al. (2017). An empirical relationship for finding the turbidity from bp (450) was developed in this study for its use in the above equation where an independent measurement of turbidity is not available.
Turbidity = 0.9246 × bp (450)1.071
(9)
The bph and bNAP spectra thus obtained are scaled with respect to the total measured bp. The slope of the new scaled bNAP is then found and used as an input in the backscattering partitioning relationships (Vadakke-Chanat et al., 2017), which estimates the bbNAP and bbph spectra to obtain the total bbp. A schematic diagram illustrating this methodology to determine particulate backscattering from measured scattering is provided in Fig. 1. This method successfully achieves conversion of scattering spectra to backscattering spectra, with the additional parameters of absorption line height, chlorophyll, and turbidity. The proposed method can also be used in the absence of the 199
Estuarine, Coastal and Shelf Science 217 (2019) 196–205
S. Vadakke-Chanat, P. Shanmugam
Fig. 5. Comparison of the new model bbp vs the in situ bbp values at key wavelengths. Left panels are for the Haltrin model, middle panels for the Petzold average model, and right panels for the new model.
200
Estuarine, Coastal and Shelf Science 217 (2019) 196–205
S. Vadakke-Chanat, P. Shanmugam
Fig. 6. Spectral bbp depicting the spectral shape of each model with reference to the in-situ data. ((a) In-situ data, (b) New Model, (c) Haltrin model, and (d) Petzold average ratio model (Data used are from Chennai Harbour waters in January and March 2015)).
Fig. 7. Spectral bbp depicting the spectral shape of each model with reference to the in-situ data. (a) In-situ data, (b) New model, (c) Haltrin model, and (d) Petzold average model for the data from the August 2012 cruise in Point Calimere waters.
this purpose. The independence of the data, the variety, and a wider range of values are all thus ensured in the validation. This confirms the applicability of the method of using bp (450) for turbidity estimations. Validation results further revealed a 1:1 relationship between the measured and modelled values, which proves the adequacy and accuracy of the turbidity formulation.
chlorophyll and turbidity values. The empirical formula derived to obtain the turbidity (Eq. (9)) from the scattering coefficient uses 450 nm because the proportional influence of chlorophyll is significantly less at this band compared to other wavelengths. The chlorophyll concentration can be obtained from the absorption line height, which is already an input for the apportioning of the scattering spectra (Vadakke-Chanat and Shanmugam, 2017). The estimation of turbidity (Eq. (9)) is based on a strong correlation and excellent goodness of fit between the turbidity and particulate scattering values (Fig. 2, R2 = 0.96, RMSE = 0.29 for N = 54). Data from the multiple field campaigns conducted in the Point Calimere region were used for this parameterization because the turbidity values ranged widely, from 0.49 to 7.42 NTU. The chlorophyll values also exhibited a wider variation in these waters (0.98–14.9 mg m−3). This ensures the wide applicability of the derived empirical equation for turbidity estimations. Validation results (Fig. 3) further prove a strong correlation between the measured and estimated turbidity values (R2 = 0.96, RMSE = 0.51, N = 219). An independent data set comprising coastal field measurements from Point Calimere coastal waters in August 2013 and Ganges River waters in October 2016 were used for
4. Results and discussion The results of the proposed method are compared with two existing models (Haltrin model and Petzold average model) used to convert scattering spectra to backscattering spectra (Gokul et al., 2014; Haltrin, 2002). It should be noted that Haltrin's relationship was originally proposed for a wavelength of 515 nm; however, an extended application of the same relationship across the spectra was used for comparative analysis. The entire set of backscattering spectra from the in-situ observations and models are shown in Fig. 4. As expected, the new model is clearly efficient in reproducing the spectral inflections in the backscattering 201
Estuarine, Coastal and Shelf Science 217 (2019) 196–205
S. Vadakke-Chanat, P. Shanmugam
Fig. 8. Spectral bbp depicting the spectral shape of each model with reference to the in-situ data. (a) In-situ data, (b) New model, (c) Haltrin model, and (d) Petzold average model for the data from Chennai Coastal waters in March 2015.
Fig. 9. Spectral bbp depicting the spectral shape of each model with reference to the in-situ data. (a) In-situ data, (b) New model, (c) Haltrin model, and (d) Petzold average model for the data from Chennai coastal waters in January 2015.
coefficients of the field data as compared against the existing methods for a wide range of backscattering values. The results for highly productive waters were greatly overestimated for the existing models, while the new model produced values closely matching the in situ data. It should be noted that the spectral shape of the new model was nearly reproduced by the new model, even for lower magnitude spectra compared with the existing models. The overestimations of the Haltrin and Petzold average methods can clearly be seen in Fig. 5. Use of the Haltrin method consistently overestimated the backscattering values in all types of waters across all wavelengths. The use of Petzold average model resulted in similar overestimation despite the magnitude of the overestimation being lower than the Haltrin model. It was observed that the Petzold average model produced a better relationship with in situ data (especially around 715 nm). In contrast, the new approach was highly efficient in accurately reproducing the backscattering values for all water types and across the visible and NIR wavelengths. The overestimation by the Haltrin and Petzold average method is due to the strong influence of phytoplankton on the total backscattering coefficients. The new model has the clear ability to account for the contribution of phytoplankton,
thus producing more reliable backscattering coefficients. The backscattering coefficients of waters with a strong influence of phytoplankton deviate more from the expected trends obtained from Mie calculations based on the assumption of spherical and non-absorbing particles. The bulk effective featured spectra of phytoplankton backscattering were captured from this method for the study region, despite the phytoplankton particle size distribution being highly featured and not fitting the form of a Junge type distribution (Whitmire et al., 2010). Overall, the new model performed best across all the wavelengths as well as over a broad range of water types (Fig. 5). The data sets of individual cruises classified according to the measurement location are shown in Fig. 6 to Fig. 11. Spectral bbp depicts the spectral shape of each model with reference to the in-situ data for data from Chennai Harbour waters during January and March 2015, which are a subset of the data collected off-Chennai for the period (Fig. 6). These waters are relatively productive and clear to moderately turbid coastal waters with chlorophyll concentrations ranging from 2 to 8.16 mg m−3 and turbidity values ranging from 1.48 to 1.76 NTU. Comparison of these results reveals that the spectral troughs around 440 nm and 650 nm and the peaks between 488 and 532 nm and
202
Estuarine, Coastal and Shelf Science 217 (2019) 196–205
S. Vadakke-Chanat, P. Shanmugam
Fig. 10. Spectral bbp depicting the spectral shape of each model with reference to the in situ data. (a) In-situ data, (b) New model, (c) Haltrin model, and (d) Petzold average model for the data from May 2012. Fig. 11. Spectral bbp depicting the spectral shape of each model with reference to the in-situ data. (a) In-situ data, (b) New model, (c) Haltrin model, and (d) Petzold average model for the data from Muttukkad Lake waters in November 2014. Note that the y-axis limits in the sub-plot (c) are different to accommodate the highly overestimated values.
Similar trends are seen in Fig. 9. Fig. 10 represents the field bbp values from Point Calimere coastal waters during May 2012, where the chlorophyll ranged from 0.91 to 2.57 mg m−3 and the turbidity from 0.29 to 3.59 NTU. The data from highly productive eutrophic lagoons waters in Muttukadu Lake with a chlorophyll range of 44.64–60.04 mg m−3 and a turbidity range of 7.16–8.74 NTU also demonstrate the excellent applicability and robustness of the new model (Fig. 11). The ability to calculate the proportional influence of phytoplankton in the backscattering using the new method is further evident compared to the other models (Fig. 11). The new model is capable of predicting the backscattering coefficient with great accuracy even in extremely productive and strongly scattering inland lagoon waters. Nevertheless, fine-tuning the phytoplankton spectral coefficients in the partitioning model (Vadakke-Chanat et al., 2017) for various other global waters may be required after a careful examination of the validity of the model parameterizations for these waters. Fig. 12 shows the spectral percentage deviation plots of the entire data set for each of the models compared in this study. The new model is observed to have the lowest percentage deviation of all the models. While the two existing methods clearly overestimate the backscattering coefficients in these waters, the new model is consistent and has better accuracy in reproducing the spectral shape of the measured backscattering coefficients. The
715 nm were reproduced by the new model, and the magnitude of the backscattering values is also close. However, the spectra from existing methods in Fig. 6 deviated in terms of the magnitude and shape, and a gap was observed between the different spectral lines, which distinctively differ from the in-situ spectra. To further examine the model results, the bbp spectral inflections in the Point Calimere waters from the in situ data, new model, and the existing models were also examined (Fig. 7). In this coastal region, chlorophyll concentrations reached up to 14.9 mg m−3 and the turbidity ranged between 0.49 and 7.42 NTU. Fig. 8 shows the backscattering coefficients for clear to moderately turbid Chennai Coastal waters in March 2015 (except for Harbour waters). These waters exhibited chlorophyll concentrations of 0.24–2.68 mg m−3 and turbidity values of 0.12–0.72 NTU. Evaluation of these results demonstrates again that the spectral troughs near 440 nm and 650 nm and the crests at 715 nm and between 488 and 532 nm are well replicated in the new model, with the magnitude being almost equal to the in situ data. Conversely, the spectra from the earlier approaches (Fig. 8) deviated from the in situ data in terms of the magnitude and shape, and a gap was observed between the different spectral lines, which are distinct from the in situ spectra. In the Chennai coastal waters sampled on 6 January 2015 (subset of the data other than Harbour waters) (Fig. 9), the chlorophyll ranged from 0.22 to 2.61 mg m−3 and the turbidity from 0.56 to 1.64 NTU. 203
Estuarine, Coastal and Shelf Science 217 (2019) 196–205
S. Vadakke-Chanat, P. Shanmugam
Fig. 12. The spectral percentage deviation plots for Haltrin model (a), for Petzold average ratio model (b) and the new model (c). Note that the x-axis of the Fig. 12(a) is different as compared to the other two images to accommodate the very high SPD values.
more closely reproduced with the new method than in the existing methods. A limitation of the new model includes the slight shift in the spectral crest between 488 and 532 nm in comparison with the in situ data though the overall spectral shape closely follows the in situ spectral backscattering inflections at specific wavelengths. However, the ability of the model to reproduce the in-situ backscattering coefficients with the one-to-one correlation overcomes this limitation in terms of its applicability. Fine tuning of the model to this effect could be a topic of future study. The new model will have practical applications in the field of remote sensing, ocean optics, underwater optical communication and underwater imaging studies, since bbp plays a major role in the algorithms used in these fields (Gholami and Saghafifar, 2018; Mortazavi et al., 2013) by enhancing the data repository where measured backscattering data were not previously available for technological, logistical, or financial reasons. The ability of the proposed model for a more accurate determination of backscattering coefficient will enhance underwater imaging capabilities by enabling scientists to decouple the effect of backscattering in the captured image. Underwater imaging in turn has its applied usages in underwater structure inspection including pipelines, rescue operations, diver visibility, underwater target detection, and biological and environmental studies of oceans. The ocean optics and remote sensing research finds implications in marine environmental protection and sediment transport studies (Zhao et al., 2018) for coastal engineering applications. A better model for backscattering ratio has implications in finding the bulk refractive index (Twardowski et al., 2001), and the present model can be used to calculate the backscattering ratio as well.
Table 2 Statistical comparison of the model results (N = 130). Frequency
Model
MRE
MNB
RMSE
R2
Slope
Intercept
412
New Haltrin Petzold New Haltrin Petzold New Haltrin Petzold New Haltrin Petzold New Haltrin Petzold New Haltrin Petzold New Haltrin Petzold New Haltrin Petzold
−0.183 1.478 0.044 −0.214 1.396 0.012 −0.191 1.214 −0.069 −0.166 1.228 −0.081 −0.061 1.544 0.040 −0.027 1.773 0.170 −0.064 1.829 0.260 0.037 2.207 0.368
−0.194 0.462 0.107 −0.259 0.418 0.029 −0.178 0.238 −0.081 −0.122 0.208 −0.101 −0.029 0.362 0.024 0.004 0.520 0.187 −0.086 0.624 0.301 0.019 0.656 0.328
0.012 0.273 0.035 0.015 0.279 0.040 0.015 0.275 0.034 0.015 0.286 0.033 0.011 0.294 0.034 0.008 0.273 0.034 0.007 0.240 0.035 0.006 0.262 0.035
0.96 0.50 0.72 0.91 0.39 0.62 0.93 0.51 0.73 0.93 0.57 0.77 0.94 0.61 0.80 0.96 0.63 0.81 0.96 0.59 0.77 0.98 0.76 0.89
0.904 4.894 1.264 0.896 4.553 1.219 0.881 4.808 1.206 0.881 5.071 1.219 1.004 5.989 1.402 1.047 6.487 1.556 1.062 6.436 1.660 1.092 7.938 1.862
−0.004 −0.105 −0.010 −0.005 −0.094 −0.009 −0.003 −0.122 −0.013 −0.002 −0.137 −0.014 −0.003 −0.146 −0.015 −0.003 −0.134 −0.014 −0.004 −0.113 −0.013 −0.002 −0.137 −0.014
440
488
510
532
595
650
715
statistical measures of the model performance provided in Table 2 also demonstrate the robustness of the new model compared with the previous models. 5. Conclusions
Acknowledgements
A robust method for conversion of spectral particulate scattering coefficient to the spectral particulate backscattering coefficient with additional inputs of chlorophyll concentration and turbidity has been proposed and its efficiency has been demonstrated in the present study. The new method yielded results much more closely consistent with insitu data than the Haltrin and Petzold methods. It was demonstrated that the new method gives optimum results even in highly scattering, intense algal bloom waters, while the existing methods overestimate the backscattering coefficient for these water types. It is also demonstrated that the spectral inflections of the in-situ backscattering coefficient are
This research work was supported by the Department of Science and Technology (No. OEC1819150DSTXPSHA). We thank D. Rajasekhar, The Head, Vessel Management Cell (VMC), and Director of National Institute of Ocean Technology (NIOT) for facilitating our research work by providing Coastal Research Vessels to Indian Institute of Technology (IIT) Madras with which we were able to make various bio-optical and oceanographic measurements off Chennai and Point Calimere. We sincerely thank Dr. S. Mitchell, Editor, Estuarine, Coastal and Shelf Science, and the three anonymous reviewers for their valuable comments and suggestions which allowed us to greatly improve the 204
Estuarine, Coastal and Shelf Science 217 (2019) 196–205
S. Vadakke-Chanat, P. Shanmugam
scientific content and quality of this manuscript.
near-infrared light in water: dependence on temperature and salinity. Appl. Opt. 36, 6035–6046. https://doi.org/10.1364/ao.36.006035. Pegau, W.S., Zaneveld, J.R., 1993. Temperature-dependent absorption of water in the red and near-infrared portions of the spectrum. Limnol. Oceanogr. 38, 188–192. Petzold, T.J., 1972. Volume Scattering Functions for Selected Ocean Waters. Rao, C., Mukherjee, K., Gupta, S., Ray, A., Phoha, S., 2009. Underwater mine detection using symbolic pattern analysis of sidescan sonar images. In: American Control Conference, 2009. ACC’09, pp. 5416–5421. Sahu, S.K., Shanmugam, P., 2015. Semi-analytical modeling and parameterization of particulates-in-water phase function for forward angles. Optic Express 23, 22291. https://doi.org/10.1364/OE.23.022291. Simon, A., Shanmugam, P., 2013. A new model for the vertical spectral diffuse attenuation coefficient of downwelling irradiance in turbid coastal waters: validation with in situ measurements. Optic Express 21, 30082. https://doi.org/10.1364/OE.21. 030082. Sun, D., Li, Y., Wang, Q., Lv, H., Le, C., Huang, C., Gong, S., 2010. Partitioning particulate scattering and absorption into contributions of phytoplankton and non-algal particles in winter in Lake Taihu (China). Hydrobiologia 644, 337–349. https://doi.org/10. 1007/s10750-010-0198-7. Sun, H., Benzie, P.W., Burns, N., Hendry, D.C., Player, M.A., Watson, J., 2008. Underwater digital holography for studies of marine plankton. Philos. Trans. A. Math. Phys. Eng. Sci. 366, 1789–1806. https://doi.org/10.1098/rsta.2007.2187. Sundarabalan, V.B., Shanmugam, P., Manjusha, S., 2013. Radiative transfer modeling of upwelling light field in coastal waters. J. Quant. Spectrosc. Radiat. Transf. 121, 30–44. https://doi.org/10.1016/j.jqsrt.2013.01.016. Twardowski, M.S., Boss, E., Macdonald, J.B., Pegau, W.S., Barnard, A.H., Zaneveld, J.R.V., 2001. A model for estimating bulk refractive index from the optical backscattering ratio and the implications for understanding particle composition in case I and case II waters. J. Geophys. Res. 106, 14129. https://doi.org/10.1029/ 2000JC000404. Twardowski, M.S., Claustre, H., Freeman, S.A., Stramski, D., Huot, Y., 2007. Optical backscattering properties of the “clearest” natural waters. Biogeosci. Discuss. 4, 1041–1058. Ulloa, O., Sathyendranath, S., Platt, T., 1994. Effect of the particle-size distribution on the backscattering ratio in seawater. Appl. Opt. 33, 7070–7077. Vadakke-Chanat, S., Shanmugam, P., 2017. Modeling the contributions of phytoplankton and non-algal particles to spectral scattering properties in near-shore and lagoon waters. Continent. Shelf Res. 135. https://doi.org/10.1016/j.csr.2017.01.001. Vadakke-Chanat, S., Shanmugam, P., Ahn, Y., 2017. A model for deriving the spectral backscattering properties of particles in inland and marine waters from in situ and remote sensing data. IEEE Trans. Geosci. Rem. Sens. 55. https://doi.org/10.1109/ TGRS.2016.2624986. Vadakke-Chanat, S., Shanmugam, P., Sundarabalan, B., 2018. Monte Carlo simulations of the backscattering measurements for associated uncertainty. Optic Express 26, 21258. https://doi.org/10.1364/OE.26.021258. WET Labs ECO BB9 User’s Guide (BB9), 2017. Seabird Scientific. Whitmire, A.L., Boss, E., Cowles, T.J., Pegau, W.S., 2007. Spectral Variability of the Particulate Backscattering Ratio 15. pp. 7019–7031. https://doi.org/10.1029/ 2005JC003008. Whitmire, A.L., Pegau, W.S., Karp-Boss, L., Boss, E., Cowles, T.J., 2010. Spectral backscattering properties of marine phytoplankton cultures. Optic Express 18, 15073–15093. https://doi.org/10.1029/2003RG000148.D. Zaneveld, J.R.V., Kitchen, J.C., Moore, C.C., 1994. Scattering error correction of reflecting-tube absorption meters. In: Ocean Optics XII, pp. 44–55. Zhao, J., Cao, W., Xu, Z., Ye, H., Yang, Y., Wang, G., Zhou, W., Sun, Z., 2018. Estimation of suspended particulate matter in turbid coastal waters: application to hyperspectral satellite imagery. Optic Express 26, 10476–10493.
References Bricaud, A., Morel, A., Babin, M., Karima, A., Claustre, H., 1998. Variations of light absorption by suspended particles with chlorophyll a concentration in oceanic (case-1) waters: analysis and implications for bio-optical models. J. Geophys. Res. 103 (C13), 31033–31044. https://doi.org/10.1029/98JC02712. Damotharan, P., Perumal, N.V., Arumugam, M., Vijayalakshmi, S., Balasubramanian, T., 2010. Seasonal variation of physicochemical characteristics in point calimere coastal waters south east coast of India. Middle East J. Sci. Res. 6, 333–339. Dev, P.J., Shanmugam, P., 2014. New model for subsurface irradiance reflectance in clear and turbid waters. Optic Express 22, 9548–9566. Doxaran, D., Leymarie, E., Nechad, B., Dogliotti, A., Ruddick, K., Gernez, P., Knaeps, E., 2016. Improved correction methods for field measurements of particulate light backscattering in turbid waters. Optic Express 24, 3615–3637. https://doi.org/10. 1364/oe.24.003615. Gholami, A., Saghafifar, H., 2018. Simulation of an active underwater imaging through a wavy sea surface. J. Mod. Optic. 65, 1210–1218. Gokul, E.A., Shanmugam, P., Sundarabalan, B., Sahay, A., Chauhan, P., 2014. Modelling the inherent optical properties and estimating the constituents ׳concentrations in turbid and eutrophic waters. Continent. Shelf Res. 84, 120–138. Gordon, H.R., 2006. Backscattering of light from disklike particles: is fine-scale structure or gross morphology more important? Appl. Opt. 45, 7166–7173. Haltrin, V.I., 2002. One-parameter two-term Henyey-Greenstein phase function for light scattering in seawater. Appl. Opt. 41, 1022–1028. https://doi.org/10.1364/ao.41. 001022. Huot, Y., Morel, A., Twardowski, M.S., Stramski, D., Reynolds, R.A., Villefranche, D., Huot, Y., Morel, A., Twardowski, M.S., Stramski, D., Reynolds, R.A., et al., 2008. Particle optical backscattering along a chlorophyll gradient in the upper layer of the eastern South Pacific Ocean. Biogeosciences 5, 495–507. Kitchen, J.C., Zaneveld, J.R., 1992. A three-layered sphere model of the optical properties of phytoplankton. Limnol. Oceanogr. 37, 1680–1690. Kondo, H., Ura, T., 2004. Navigation of an {AUV} for investigation of underwater structures. Contr. Eng. Pract. 12, 1551–1559. https://doi.org/https://doi.org/10. 1016/j.conengprac.2003.12.005. Loisel, H., Nicolas, J.-M., Sciandra, A., Stramski, D., Poteau, A., 2006. Spectral dependency of optical backscattering by marine particles from satellite remote sensing of the global ocean. J. Geophys. Res. 111, C09024. https://doi.org/10.1029/ 2005JC003367. McKee, D., Chami, M., Brown, I., Calzado, V.S., Doxaran, D., Cunningham, A., 2009. Role of measurement uncertainties in observed variability in the spectral backscattering ratio: a case study in mineral-rich coastal waters. Appl. Opt. 48, 4663. https://doi. org/10.1364/AO.48.004663. Mobley, C.D., 1994. Light and Water: Radiative Transfer in Natural Waters. Academic press, San Diego. Mobley, C.D., Sundman, L.K., Boss, E., 2002. Phase function effects on oceanic light fields. Appl. Opt. 41, 1035. https://doi.org/10.1364/AO.41.001035. Morel, A., 1980. In-water and remote measurements of ocean color. Boundary-Layer Meteorol. 18, 177–201. Morel, A., Bricaud, A., 1981. Theoretical results concerning the optics of phytoplankton, with special reference to remote sensing applications. In: Oceanography from Space. Springer, pp. 313–327. Mortazavi, H., Oakley, J.P., Barkat, B., 2013. Mitigating the effect of optical back-scatter in multispectral underwater imaging. Meas. Sci. Technol. 24, 74025. https://doi.org/ 10.1088/0957-0233/24/7/074025. Pegau, W.S., Gray, D., Zaneveld, J.R.V., 1997. Absorption and attenuation of visible and
205