Environ Monit Assess (2015) 187:742 DOI 10.1007/s10661-015-4953-0

An optical method to assess water clarity in coastal waters Anuj Kulshreshtha

&

Palanisamy Shanmugam

Received: 6 June 2015 / Accepted: 2 November 2015 # Springer International Publishing Switzerland 2015

Abstract Accurate estimation of water clarity in coastal regions is highly desired by various activities such as search and recovery operations, dredging and water quality monitoring. This study intends to develop a practical method for estimating water clarity based on a larger in situ dataset, which includes Secchi depth (Zsd), turbidity, chlorophyll and optical properties from several field campaigns in turbid coastal waters. The Secchi depth parameter is found to closely vary with the concentration of suspended sediments, vertical diffuse attenuation coefficient Kd (m−1) and beam attenuation coefficient c (m−1). The optical relationships obtained for the selected wavelengths (i.e. 520, 530 and 540 nm) exhibit an inverse relationship between Secchi depth and the length attenuation coefficient (1/(c + Kd)). The variation in Secchi depth is expressed in terms of undetermined coupling coefficient which is composed of light penetration factor (expressed by z(1 %)Kd(λ)) and a correction factor (ξ) (essentially governed by turbidity of the water column). This method of estimating water clarity was validated using independent in situ data from turbid coastal waters, and its results were compared with those obtained from the existing methods. The statistical analysis of the measured and A. Kulshreshtha : P. Shanmugam (*) Ocean Optics and Imaging Laboratory, Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai 600036, India e-mail: [email protected] A. Kulshreshtha e-mail: [email protected]

the estimated Zsd showed that the present method yields lower error when compared to the existing methods. The spatial structures of the measured and predicted Zsd are also highly consistent with in situ data, which indicates the potential of the present method for estimating the water clarity in turbid coastal and associated lagoon waters.

Keywords Water clarity . Coastal and lagoon waters . Secchi depth . Attenuation coefficient . Water quality Abbreviations AC-S Absorption and attenuation sensors AOPs Apparent optical properties BB9 Backscattering sensors CDOM Coloured dissolved organic matter CTD Conductivity-temperature-depth CV Coefficient of variation FLNTU Turbidity and fluorescence chlorophyll sensors IOPs Inherent optical properties MRE Mean root error NTU Nephelometric turbidity unit RMSE Root mean square error SAV Submerged aquatic vegetation TSS Total suspended sediment Symbols a(λ) at − aw bb ct − cw

Absorption coefficient Particulate absorption coefficient Backscattering coefficient Particulate attenuation coefficient

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Zsd Kd Kd(PAR) c 1/ (c + Kd) ξ Γ C0 CT R2

Secchi depth Vertical diffuse attenuation coefficient Diffuse attenuation coefficient for photosynthetically available radiation Beam attenuation coefficient Length attenuation coefficient Correction factor Coupling coefficient Inherent contrast of the disk (dimensionless) Threshold contrast of the disk (dimensionless) Correlation coefficient

Introduction The water clarity of any regional water body is of prime importance to its legitimate commercial and biological usage in day-to-day life. It is used as an important tool in search and recovery operations, dredging and water quality monitoring programmes (Tyler 1968; Effler 1988; Trees et al. 2005). Accurate estimation of water clarity parameter may assist the researchers in the field of coastal hydrodynamics to enhance the knowledge about seasonal movement of the sediments and to develop and implement a better sediment transport model (Boss et al., 2009a). However, estimation of this parameter becomes a challenging task owing to the variation in inherent optical properties (IOPs) and apparent optical properties (AOPs) and the uncontrollability in environmental illumination conditions especially in turbid coastal waters. Light penetration in these waters is often inhibited due to the presence of various multicomponents such as suspended sediments, coloured dissolved organic matter (CDOM), detritus particles and phytoplankton (indexed by ‘chlorophyll’), which contribute to the complex geometric light field structure and the varying trends of light penetration in the water column (Swift et al. 2006). Moreover, the interaction of light available in the upper mixed layer plays an important role in determining the rate of photosynthesis and growth of phytoplankton (microorganisms) and encompassing the depth of euphotic region (Kirk 1994; Marra et al. 1995; Mcclain et al. 1996). Many of these factors introduce complexity in the estimation of the water clarity parameter in coastal and nearshore environments.

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The vertical Secchi depth (Zsd) acts as a proxy of water transparency and is used to assess the visual water clarity of a particular water body (Cialdi and Secchi 1865; Collier et al. 1968; Tyler 1968; Fleming-Lehtinen & Laamanen, 2012; Trees et al. 2005). The Secchi depth is defined as the discrete depth at which the Secchi disk, when submerged underwater, disappears and is no longer visible to the observer when further lowered vertically downward in the water column (Steel and Neuhausser 2002). Contemporarily, it is used as a robust tool to estimate the water clarity for comparative assessment of the water quality of lakes, rivers and regional water bodies (Holmes 1970; Berkman and Canova 2007; Balali et al. 2013). The monitoring and assessment of water clarity is highly instrumental as it reveals the efficiency of measures adopted to lessen the marine pollution and deterioration (Karydis and Kitsiou 2013). Several methods have been developed in the past to determine Zsd and estimate the water clarity. One of the methods from the previous studies revealed that Zsd was modelled, with a view to determine the diffuse attenuation coefficient (Kd) and beam transmittance coefficient (c) for nearshore turbid waters (Holmes 1970). However, the method lacked precision and accuracy as required by optical oceanographers. In other study, extensive measurements of the diffuse attenuation coefficient, Secchi depth and suspended particulate matter were carried out with an aim to establish the optical relationship between the measured Kd and Zsd (Devlin et al. 2008). The science of the Secchi disk was also studied through the modulation transfer theory which revealed that the Secchi disk is a special case where modulation transfer approach and the radiative transfer approach converge (Hou et al. 2007). In a more recent study, optical methods to derive the spatial and temporal patterns of water clarity from MODIS/Aqua data over shallow waters (e.g. Florida Keys and regional waters) have been proposed (Barnes et al. 2013). Moreover, the conventional methods involved assumptions and complex techniques to determine the factor (essentially known as undetermined coupling coefficient (Γ)), which governs the variation in Zsd. Γ plays a crucial role in estimating Zsd, and its value varies with water types, especially under the conditions of high scattering as encountered in turbid coastal waters. Thereby, it poses a greater challenge to correctly predict and fix its value for different water types. The earlier studies overlooked the variable nature of coupling coefficient whereby assuming it constant; thus,

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existing Zsd algorithms tend to deviate in complex coastal waters (Tyler 1968; Davies-Colley 1988). The present study reveals a new method to closely predict the value of coupling coefficient and, hence, accurately estimates Zsd in various water types within coastal environments. The proposed Zsd algorithm does not require any assumption and the optical properties employed can be easily retrieved from remote sensing techniques. Consequently, it would allow us to estimate and monitor the water clarity parameter spatially and temporally without involving extensive field measurements. The results are validated using independent measured values and compared with those obtained from existing methods.

Material and methods This section describes the study region along with the procedures involved in the in situ data acquisition and processing followed by the derivation of a new method to estimate water clarity. The in situ measurements were made at different stations in coastal waters off Point Calimere (Bay of Bengal) on the southeast part of India. The inherent and apparent optical properties measured from this region were then systematically investigated in order to derive the new method to estimate the water clarity. Study area The in situ data were collected from the coastal region of Point Calimere located near Vadaranniyam wetlands along the coastal zone of the Bay of Bengal and Palk Strait. Seasonal river flows (e.g. Cauvery river) discharge large amounts of suspended matter (2∼690 mg/ l) during the northeast monsoon (Quasim 2003). The increased human activities like salt panning, aquaculture and agriculture have also led to sediment accretion in the eastern part of the wetland, near Point Calimere. Furthermore, Mullipallam and Serattalaikkadu creeks, which have experienced a marginal decrease in the aerial extent over the time, are the important geological features of this region apart from mudflats. Therefore, various fluvial processes and human activities have major contribution in modifying the landform of this region. The study region of Point Calimere and Palk Bay are very shallow, characterized by a number of sand dunes and ridges, and are dominated by suspended

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sediments throughout the year with seasonality in bloom conditions. These sediments are the result of bottom resuspension caused by tides, currents and waves and also contributed by less energetic streams like Mullipallam, Koraiyar, Kilaittangi, Marakkakoraiyar, Valavnar and Manakundan Mulli, particularly during the northeast monsoon (Selvaraj et al. 2005). In situ data acquisition and processing In situ measurements of various optical properties were carried out in clear and turbid waters off Point Calimere, where there are 24 sampling stations adjacently colocated on five different transects (Fig. 1). These measurements were made on four different cruises during and after the southwest monsoon, primarily marked between the period May 2012 and January 2014 (i.e. May 2012, August 2012, August 2013 and January 2014). The sampling stations at Point Calimere are characterized by high level of turbidity with preeminence of heavily laden suspended sediments and detrital particles. Sampling stations at Chennai (not shown here for brevity) are essentially clear waters with a low level of suspended sediments and a relatively high level of chlorophyll concentration. Thus, the sampling stations covered a wide range of waters. The standard protocols of Secchi depth measurements were followed to minimize the error associated with the sensitivity of the human eye (Smith 2001). The recorded measurements included the relevant environmental parameters (e.g. the surface wind speed, atmospheric pressure, cloud condition, water depth) that might have caused likely the fluctuations in the optical conditions of the water column. These environmental parameters were obtained on-board using the instruments installed in the research vessel. Anemometer was used to record wind speed, barometer for atmospheric pressure and echo-sounder recorded the water depth at each station. However, the overhead cloud condition was visually interpreted based on the cloud cover of the sky. The data was acquired for a maximum profiling depth of about 18 m in turbid waters off Point Calimere and 21 m in clear waters off Chennai (Fig. 2). The IOPs were measured using various underwater optical instruments, which included AC-S (absorption and attenuation sensors), BB9 (backscattering sensors), FLNTU (turbidity and fluorescence chlorophyll sensors) and CTD (conductivity-

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Fig. 1 A map showing sampling locations in coastal waters off Point Calimere on the coast of Bay of Bengal between India and Sri Lanka

Bay of Bengal

temperature-depth) sensors. The AC-S sensors were used to measure the beam attenuation coefficient (c(λ)) and absorption coefficient (a(λ)) in the spectral range of 400–700 nm. The measured data were then processed by applying the temperature correction (Pegau and Zaneveld 1993) and salinity correction (Pegau et al. 1997). Finally, the scattering correction (Ronald et al. 1994) was applied to the salinity-temperature corrected absorption data to obtain the particulate absorption coefficient (at − aw) and particulate attenuation coefficient (ct − cw), here the subscripts ‘t’ and ‘w’ represent the total and pure water components of the absorption and attenuation coefficients. The pure water coefficients of absorption and attenuation were added to the respective components to obtain the total absorption and total attenuation coefficients. The total scattering coefficient was calculated by subtracting the total absorption coefficient from the total beam attenuation coefficient. The BB9 sensor was used to measure backscattering at nine wavelengths (i.e. 412, 440, 488, 512, 530, 565, 650, 676 and 715 nm). The FLNTU was used to simultaneously measure turbidity in terms of nephelometric turbidity unit (NTU) along with the chlorophyll concentration of water

sample in μg/l, while the SBE Seabird CTD sensors were used to measure the conductivity-temperaturedepth profiles data. The total suspended sediment (TSS) concentration was calculated based on the power relationship (Ellison et al. 2010), TSSðmg=lÞ ¼ 1:09  ðturbidityÞ1:0774

ð1Þ

The power relationship was employed based on the fact that the range of turbidity employed by Ellison et al. (2010) closely matched the range of measured turbidity for the present study. The radiometric quantities were measured by both underwater and above water radiometers. The underwater radiometric profiling measurements were carried out using three hyperspectral radiometers—one ARC to record the upwelling radiance and two ACC radiometers to record the upwelling irradiance and downwelling irradiance, respectively. The radiance and irradiance data recorded onboard were then exported from the database to the deck PC for further processing. Since the radiance sensor was immersed, the immersion factors (wavelength-dependent correction factors) (Ohde and Siegel 2003) were applied to the measured radiance data. Apart from underwater radiometers, above-

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Fig. 2 The nature of waters sampled at different stations in coastal waters off Point Calimere on the coast of Bay of Bengal between India and Sri Lanka. a, b Clear water stations recorded the maximum profiling depth of 21 m with turbidity as low as 0.124 NTU and chlorophyll concentration as high as 13.81 μg/l. c, d

Moderately turbid water stations recorded the turbidity varying from 0.98 to 5.32 NTU whereas the chlorophyll concentration varied between 2.096 and 5.7 μg/l. e, f Highly turbid water stations showed highest turbidity level in the water column with turbidity as high as 13.87 NTU and chlorophyll concentration of 1.182 μg/l

water radiometers were employed to measure waterleaving radiance, downwelling irradiance and sky radiance. The underwater and above-water radiometers are highly dedicated optical instruments designed to measure radiometric quantities in water and air, respectively. Eventually, underwater radiometric and IOP data were interpolated to common depth and wavelength for further statistical data analyses. In the present study, AC-S (ac-spectra) in situ spectrophotometer was employed to measure absorption and attenuation coefficients in the spectral range of 400– 750 nm. However, the spectral range of 400–700 nm was selected for the present work. The spectra for c, Kd and bb in the wavelength ranging from 400 to 700 nm are shown in Fig. 3a–c. With a view to cover the quality control aspect and assure the quality of data collected, the instruments are calibrated during annual factory service at their respective company premises. The nephelometer has a typical range of 0–200 NTU. Also, the AC-S is calibrated before and after the field data measurements to ensure the good quality data during each cruise. The AC-S, BB9 and FLNTU were procured from the WET Labs (USA), whereas the

SBE Seabird CTD sensor was procured from the Seabird Electronics (USA), and the radiometers were obtained from the RAMSES TriOS (Germany). Model description The pioneer work to model the water clarity parameter was carried out by Preisendorfer, based on the radiative transfer theory, which led to a well-established relationship between Zsd and length attenuation coefficient (1/(c + Kd), where c = beam attenuation coefficient and Kd = diffuse attenuation coefficient) in the particular region of visible spectrum ranging from 400 to 700 nm (Tyler 1968; Preisendorfer 1986; Davies-Colley 1988; Doron et al. 2007; Hou et al. 2007). The relationship also suggested that the Secchi depth is primarily governed by an undetermined coefficient, called the coupling coefficient. Furthermore, various analytical and semi-analytical approaches have been developed to express the undetermined coefficient in terms of optical parameters based on the coupled concepts of radiative transfer equation and the Beer-Lambert law (Zaneveld and Pegau 2003).

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2.5

(a)

(b) 2.0 -1

Kd (m )

15 -1

Fig. 3 The inherent and apparent optical properties measured in the spectral range from 400 to 700 nm from clear and turbid water sampling stations of Point Calimere region. a Beam attenuation coefficient (c). b Vertical diffuse attenuation coefficient (Kd). c backscattering coefficient (bb)

c(m )

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10

5

1.5 1.0 0.5

0 400

500

Wavelength

600 (λ ) (nm)

700

0.0 400 450 500 550 600 650 700

Wavelength (λ ) (nm)

0.3

(c)

-1

bb (m )

0.2

0.1

0.0 400 450 500 550 600 650 700

Wavelength (λ ) (nm)

The length attenuation coefficient is expressed as the sum of beam attenuation coefficient and the vertical diffuse attenuation coefficient (Preisendorfer 1986; Hou et al. 2007). The length attenuation coefficient essentially represents the loss of the intensity of light penetrating through the water column, caused due to the interspersed effect of the inherent and apparent optical properties of the medium, which correspondingly affect the depth of underwater visibility. The key inherent optical property is the beam attenuation coefficient, which is defined as the attenuation of the collimated beam of light intensity caused per unit length of the medium owing to cumulative effect of the absorption and scattering (Jerlov 1976; Effler 1988). The total beam attenuation coefficient is spectrally dependent and is given by c ð λ Þ ¼ að λ Þ þ bð λ Þ

ð2Þ

The spectral vertical diffuse attenuation coefficient (Kd) represents the rate of logarithmic decay of the surface spectral downwelling irradiance along the depth for a particular water column under a

given solar illumination condition. The depth average Kd , λ for the layer z2 −z1can be written as K d;λ ðz2 −z1 Þ ¼


 −1 E d;λ ðz2 Þ ln z2 −z1 E d;λ ðz1 Þ

ð3Þ

The above-stated optical property is used to predict and model the underwater geometric light field structure and, therefore, can be employed comprehensively to ascribe the degree of light penetration and availability in the water column (Baker and Smith 1980; Kirk 1994; Mobley and Mobley 1994; Kirk 2003; Pan and Zimmerman 2010). The variation in Secchi depth (Z sd ) is chiefly governed by the coupling coefficient, also known as the undetermined coefficient, denoted by gamma (Γ) (Eq. 4). The well-known approach to predict the coupling coefficient involves the concepts of Beer-Lambert law and radiative transfer equations (Zaneveld and Pegau 2003; Doron et al. 2007). The methodology requires the measurement of the surface reflectance of the disk and the reflectance of the water column relative to the disk (background reflectance) to estimate the contrast threshold of the disk. Then, the logarithmic

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ratio of the differential contrast to the threshold contrast of the disk is evaluated to determine the coupling coefficient (Holmes 1970). The equation involving these parameters is expressed as Z sd ¼

lnðC 0 =C T Þ Γ ¼ ðc þ K d Þ ðc þ K d Þ

ð4Þ

where C0 = inherent contrast of the disk (dimensionless), CT = threshold contrast of the disk (dimensionless), Γ = coupling coefficient and 1/(c+Kd) = length attenuation coefficient (m−1). The calculation of the coupling coefficient in Eq. (4) requires that the reflectance and apparent contrast of the disk must be assumed at the recorded depth to compensate the reduction in visibility parameter (Tyler 1968). The proposed method provides a better correlation between the Secchi depth and (1/(c + Kd)) and turbidity with an R2 of 0.97 (Fig. 4a, b). The in situ Zsd for the coastal waters has been modelled based on the optical properties at 520 nm, which is a centre wavelength for the blue-green region. Moreover, the selection of 520 nm is based on the fact that the wavelength of maximum penetration shifts from blue to green region as one moves from open oceans to complex turbid coastal waters (Pickard and Emery 1990). When verified the modelled relationship at slightly longer wavelengths (e.g., 530 nm and 540 nm), it estimated Zsd with negligible errors. It is to be well noted that in the present study, 540 nm was not considered the wavelength of maximal penetration. Also, the convolution of the eye photopic response with the radiance was not carried out owing to the fact that the green band is less prone to attenuation than blue band (where light fields are rapidly attenuated by particulate and dissolved substances) and red band (where light fields are attenuated by high absorption by water itself) in complex coastal waters. The degree of light penetration in water column can be expressed in terms of Zsd which depends upon (1/(c + Kd)) and Γ (Tyler 1968; Preisendorfer 1986; Davies-Colley 1988; Doron et al. 2007; Hou et al. 2007). Zsd is given by Z sd ¼

Γ ðc þ K d Þ

ð5Þ

Γ varies between 5.9 and 10.1, depending on the medium characteristics and its significantly higher range of values can be expected under conditions of strong scattering (Hou et al. 2007). Hence, it is required to

model the variation in Γ especially in turbid waters where higher intensity of scattering is encountered. This variation in coupling coefficient is modelled in terms of ‘g’ given by Z sd ¼

g or g ¼ Z sd ððc þ K d ÞÞ ðc þ K d Þ

ð6Þ

The above equation yielded varying values of ‘g’ for different conditions which arise due to various scattering conditions for complex waters and showed a systematic variation with backscattering coefficient (bb) (Fig. 4c). Therefore, bb plays a crucial role in governing the variation in ‘g’, which can be approximated to coupling coefficient (Γ) given by Γ ≈g ¼ 30:44ðbb Þ þ 4:55

ð7Þ

The physical effect of the inherent optical property, backscattering, on the complex geometric underwater light field structure can be well accommodated through the inclusion of turbidity (Effler 1988). Hence, bb is modelled in terms of turbidity given by ‘α’ (Fig. 4d). α ¼ 30:44ðbb Þ ¼ 0:7585ðturbidityÞ þ 0:06

ð8Þ

Substituting Eq. (8) in Eq. (7), we get Γ ¼ 4:6 þ 0:7585ðturbidityÞ

Γ ¼ 4:6 þ ξ

ð9Þ

ð10Þ

where ‘ξ’ = 0.7585(turbidity) and is the correction factor. From the above equation, it can be inferred that Γ is composed of a constant approximately equal to 4.6 and a correction factor (ξ) which takes into account the strong conditions of scattering in complex turbid waters. Thus, Zsd can be estimated with greater accuracy for both clear and turbid coastal and associated lagoon waters. In case of clear waters where the effect of turbidity is negligible, Eq. (10) reduces to Γ ¼ 4:6

ð11Þ

Substituting, Eq. (11) in Eq. (5), we get Z sd ¼

4:6 ðc þ K d Þ

ð12Þ

The above equation also confirms with the experimental investigation of Duntley (1963), who reported that the sighting range of mostly encountered objects

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4

5

(a) Measured Zsd (m)

(b)

4 3 2 1

0

2

4

6

8

10

0

12

2

4

6

8

Turbidity (NTU)

15

8

(d) Alpha (α)

(c) 10

6

4

5 2

0 0.05

0.10

0.15

bb(λ ) (m )

submerged in the water is about 4–5 times the length attenuation coefficient (Duntley 1963). Whereas for complex waters, turbidity is taken into account through an additional ξ, resulting in the final equation of Zsd as ð13Þ

The constant factor of 4.6 in Eq. (13) reveals the fact that there lies a parameter of optical visibility that depends upon the z(1 %) and Kd, with a greater physical significance, in relation to the degree of light penetration along the water column. It can be approximated to be a proxy of the product of Kd and z(1 %) which is mathematical identity given by zð1%ÞK d ðλÞ ¼ 4:6

1

-1

-1

4:6 0:7585½turbidity þ ðc þ K d Þ ðc þ K d Þ

2

(c+kd) (m )

0 0.00

Z sd ¼

3

0

0

Coupling Coefficient (Γ)

Fig. 4 The relationships between a measured Zsd and (c + Kd), b measured Zsd and turbidity (NTU); the in situ data used for these relationships were obtained from relatively low turbid and very turbid coastal waters off Point Calimere and Chennai. c The variation of coupling coefficient highly depended on the backscattering coefficient, bb(λ). d The variation of the variable term ‘α’ in terms of turbidity. Note that the above relationships were verified by in situ data from a wide variety of waters within coastal regions

Measured Zsd (m)

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ð14Þ

It also describes the optical characteristics of the water column in terms of light penetration. The value of z(1 %) pertains to the depth at which the spectral downward irradiance falls to 1 % of the spectral irradiance available at the water surface and is referred as the light extinction depth, whereas the value of ‘Kd’ is the depth averaged

0.20

0.25

0

2

4

6

8

Turbidity (NTU)

value of the vertical diffuse attenuation coefficient. At such depth, the underwater light field geometric structure is regarded as the euphotic zone, an optical region where nearly 99 % of the spectral irradiance (surface downwelling irradiance) decays due to the cumulative effect of vertical diffuse attenuation along the water column (Arst et al. 1997; Tiwari and Shanmugam 2014). This mathematical identity is widely used to estimate the diffuse attenuation coefficient for photosynthetically available radiation, Kd(PAR). The Kd(PAR) determines the level of light intensity available (degree of light penetration in the water column) to submerged aquatic vegetation (SAV) which are considered as the crucial component of coastal ecosystems (Gallegos 2001; Pierson et al. 2008). ξ in Eq. (13) accounts for the effect of turbidity in the water column and suggests that the depth of disappearance is highly governed by the light backscattered from the euphotic region. It is recognized that the most of light (about 90 %) originating from the surface comes from this region, and thereby represents the most important optical characteristic for optical remote sensing investigations (Arst et al. 1997; Ballestro 1999). Therefore, the physical effect of the inherent optical property,

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backscattering, on the complex geometric light field structure has been well accommodated in the modelled relationship through the inclusion of turbidity. The intensity of light backscattered by the suspended particles leads to the formation of the isotropic region which usually occurs at few optical depths, thereby imparting ‘Kd’ the benign behaviour of quasi-inherent optical property (Tiwari and Shanmugam 2013). Apart from the in situ measurement of turbidity, the chlorophyll concentration was also measured for the water samples for each of the four cruises which showed a high seasonal variation. The efficiency of non-photochemical quenching varies with internal and external uncontrollable environmental conditions, thereby posing a greater challenge for physiologists and eco-physiologists to identify its contribution to chlorophyll fluorescence. Therefore, the present work does not cover the quantitative analysis and effect of photo-chemical or non-photochemical quenching on the chlorophyll fluorescence. Moreover, high chlorophyll and TSS concentration complicates the fluorescence measurements in coastal waters resulting in the fluorescence spectrum to overlap with elastic reflectance spectrum (Maxwell and Johnson 2000; Ahmed et al. 2007). In contrast to the turbidity parameter, the coupling coefficient was found to be independent of the variation in chlorophyll concentration.

Existing methods

8:7 ðc þ K d Þ

Z sd ðλÞ ¼

4:8 ðc þ K d Þ

ð16Þ

Thus, the above experimental and scientific investigations carried out by Tyler (1968) and DaviesColley (1988) formed the integral part of this study for evaluating the performance of the present method. Error analyses

In order to evaluate the performance of the present method, two other methods (e.g. Tyler 1968; DaviesColley 1988) are included in the present study. Tyler (1968) predicted the value of undetermined Γ to be 8.7 and derived the following relationship: Z sd ðλÞ ¼

relatively insensitive to the assumed value of C0 and CT. This value of coupling coefficient was exploited and thoroughly tested over the period of time by various researchers, and it was found to be consistent in estimating the water clarity parameter. For instance, it matched the value proposed by Preisendorfer (1986) based on the reflectance and disk contrast thresholds, and a similar value was obtained in the work of Hǿjerslev (1986), Davies-Colley et al. (2003) and Swift et al. (2006). Therefore, Tyler’s theory of Secchi depth is considered as an important application of the contrast transmittance theory. In 1988, Davies-Colley developed a similar model to determine the sighting range based on contrast transmittance theory to characterize the visual clarity of the water. The model was evaluated under the best case scenario of determining the underwater visibility parameter using the black disk target (Davies-Colley 1988). Davies-Colley (1988) model for the water clarity takes the form of the following equation:

ð15Þ

To assess the index of visual clarity in marine and associated lagoon waters, Tyler employed a white Secchi disk to determine the sighting range of the underwater object. The experimental investigation and disk observation yielded the inherent contrast (C0) of about 40 and it depended on the background water illuminance. The threshold contrast (CT) was assumed 0.0066. The value of C0 was estimated based upon the assumption that the white Secchi disk has an inherent reflectance of 82 % while the ocean water reflectance is about 2 %. Γ, being a logarithmic function, was found

The capability of the model to precisely estimate the water clarity parameter can be assessed based on certain standard statistical measures. The random and systematic errors between the predicted and measured values can be defined in terms of the root mean square error (RMSE) and mean root error (MRE), respectively. These matrices are expressed as 2X 3 n   2 1=2 model in situ logZ sd −logZ sd 6 7 i¼1 RMSE ¼ 4 ð17Þ 5 N −2

MRE ¼

n
situ  X logZ model −logZ in sd sd  100 situ logZ in sd i¼1

ð18Þ

By performing the linear regression analysis between the predicted and measured values, one can also obtain

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the values of slope, intercept, bias and correlation coefficient (R2). These statistical values are good measures of the disparity between the predicted and measured values.

Results The present method was successfully implemented and tested over the existing methods (at three wavelengths 520, 530 and 540 nm) using large in situ data collected from coastal and associated lagoon waters. To demonstrate the robustness of present method, the spatial patterns in measured and predicted water clarity were investigated using data from four different cruises. To understand the variation of the measured optical properties, the in situ data obtained from four different cruises from May 2012 to January 2014 are described (Tables 1a–d). In each of these cases, the mean, maximum, minimum and standard deviation were calculated to study the variation in the measured optical properties. For the month of August 2013 and January 2014 measured Zsd was observed with a maximum of 12.5 and 11 m, respectively, whereas for the month of May 2012 and August 2012, it was significantly lower (i.e. 3 and 4.5 m, respectively). However, the minimum value of measured Zsd for each of the cruise did not show much variation. Thus, the coefficient of variation (CV) was calculated to gain further insight into the relative departure of these parameters. The value of coefficient of variation is found to vary appreciably, with the highest variation for the data of August 2013 and January 2014 and the lowest for the data of May 2012 and August 2012, which suggests substantial spatio-temporal variability in optical properties of the study region. Examination of the in situ data obtained from various cruise programmes revealed that Secchi depth varied with length attenuation coefficient and follows the contrast transmittance theory (Fig. 4a). However, it also varied significantly with measured turbidity (Fig. 4b). Therefore, it was concluded that these two properties play a major role in estimating the Secchi depth. The present method estimates the visual water clarity based on the contrast transmittance theory and lays emphasis that the variation in coupling coefficient, governed by the backscattering of the water column, is taken into account through the inclusion of turbidity (Fig. 4c, d). The method required the

Environ Monit Assess (2015) 187:742

measurement of Secchi depth, beam attenuation coefficient, diffuse attenuation coefficient and turbidity. To investigate the spectral nature of penetrating light field in the water column (i.e. spectral downwelling irradiance Ed(λ) along the depth), Ed(λ) spectra for the three consecutive cruises in the study region are shown in Fig. 5. Note that the magnitude of Ed(λ) is reduced and its peak is shifted toward the green region in turbid waters. In clear waters, Ed(λ) spectra are nearly flat with relatively higher magnitude and fluctuation in the bluegreen region. Because the irradiance light fields are rapidly attenuated by particulate and dissolved substances in the blue region (e.g. turbid coastal waters) and by pure water itself in the red/NIR regions, there is a noticeable reduction in the magnitude of Ed(λ) in these spectral regions. Thus, the shift in wavelength of maximum light penetration is restricted to the green wavelengths from 500 to 550 nm for coastal waters and the amount of underwater downwelling irradiance highly correlates to this spectral region (Siegel and Dickey 1988). It also emphasizes the importance of evaluating the suitability of specific bands for predicting the underwater visibility parameters. The present method has been implemented and validated using three independent datasets collected from different water types under various illumination conditions. The data collected in the month of May 2012 was used for parameterization (data points shown in Fig. 4a– d), whereas the other three cruise data were used as independent datasets to validate the results. The independent datasets included both the time series and the discrete stations which were located on five different transects. The present method performs well in the spectral domain of 520–540 nm for a wide range of measured Zsd. The predicted values shows a slight variation in some cases of Zsd measured, which may be due to the prevailing environmental conditions (such as surface wind speed, sky and cloud conditions, tides, currents, ambient light field) or due to the drifting of the vessel and intense wave effects during the on-board radiometric/photometric measurements. The selection of wavelengths from 520 to 540 nm is due to the fact that the most of the underwater imagery system operates within this range, and moreover, the human eye has the maximum sensitivity in this spectral domain (Levin et al. 2013). To examine the overall efficiency and statistical performance of the present method, its results were compared with those of Tyler (1968) and Davies-

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Table 1 Statistical description for a list of variables measured in clear and turbid coastal waters off Point Calimere and Chennai during four different cruises Measured Zsd (m)

Kd (m−1)

c (m−1)

(c + Kd) (m−1)

Turbidity (NTU)

TSS (mg/l)

Chl (μg/l)

No. of data points

Mean Maximum

1.66 3

0.552 1.45

5.52 14.07

6.077 15.53

4.7 7.33

5.288 9.329

1.25 2.543

12

Minimum

0.5

0.08

1.429

1.518

1.01

1.108

0.861

Standard deviation

0.857

0.380

3.75

4.10

3.1

2.82

0.465

CV

0.51

0.688

0.68

0.674

0.66

0.533

0.372

Mean Maximum

2.868 4.5

0.351 0.704

1.992 4.96

2.34 30.18

1.59 5.56

1.84 6.92

6.01 13.81

Minimum

1.5

0.196

1.33

0.48

0.41

0.417

0.808

Statistics

(a) May 2012

(b) August 2012

Standard deviation

0.8

0.116

1.107

1.186

1.39

1.748

3.395

CV

0.279

0.33

0.55

0.506

0.874

0.948

0.564

Mean Maximum

5.552 12.5

0.29 0.563

2.087 4.37

2.37 4.84

2.06 5.32

2.71 6.59

1.364 4.467

Minimum

1.7

0.09

0.281

0.403

0.124

0.11

0.45

Standard deviation

4.067

0.167

1.608

1.766

1.80

2.22

0.935

CV

0.732

0.57

0.77

0.74

0.873

0.82

0.68

Mean Maximum

3.43 11

0.552 1.654

3.814 14.04

4.36 15.69

3.84 13.87

4.79 18.53

1.14 1.57

Minimum

0.5

0.114

0.437

0.565

0.554

0.577

0.954

Standard deviation

2.92

0.437

3.87

4.29

3.77

5.1

0.227

CV

0.851

0.791

1.01

0.984

0.981

1.06

0.199

24

(c) August 2013 21

(d) January 2014 11

Zsd Secchi depth, Kd diffuse attenuation coefficient for downwelling irradiance, c beam attenuation coefficient, Chl chlorophyll concentration

Colley (1988). This comparison exercise included a total of 65 in situ data for the selected wavelengths of 520, 530 and 540 nm (Fig. 6a–c). The deviations arising from the obtained relationship for all the three wavelengths are presented in Tables 2a–c. The statistical analyses based on MRE, RMSE, slope, bias and R2 clearly indicate that the present method outperforms the other two models in turbid coastal waters. For instance, the present method yielded MRE ∼ −0.038, RMSE ∼ 0.077, slope ∼ 1, intercept ∼ −0.025, R2 ∼ 0.94 and bias ∼ −0.017 at 520 nm; MRE ∼ −0.037, RMSE ∼ 0.098, slope ∼ 1, intercept ∼ −0.03, R2 ∼ 0.89 and bias ∼ 0.017 at 530 nm; MRE ∼ −0.023, RMSE ∼ 0.098, slope ∼ 1, intercept ∼ −0.040, R2 ∼ 0.89 and bias ∼ 0.010 at 540 nm. The lower errors and higher slope and R2 values

associated with this method demonstrate its potential in estimating the water clarity with relatively higher accuracy. Concerning the model of Tyler (1968), the linear regression analysis indicated that the slope between measured and predicted values is approximately 0.8∼0.81. However, the mean relative error was significantly higher (MRE −0.260∼0.246 and RMSE 0.157∼0.172). On the contrary, the model of DaviesColley (1988) yielded the slope 0.8∼0.81, MRE −0.31∼−0.32, and RMSE 0.182∼0.195. The biases of approximately −0.11–0.117 and 0.14∼0.147 were observed for the Tyler (1968) and Davies-Colley (1988) models respectively. The performance was further supported by the statistical measures like standard deviation, variance and mean for the respective models. It was found that the model of Tyler (1968) has the highest

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30 25

2

40

Measured E d (mW/cm /nm)

50

2

Fig. 5 Spectral variation of the measured downwelling irradiance (Ed(λ)) in the visible range from 400 to 700 nm for turbid waters (top and middle panels) and clear waters (bottom panels). Note that in turbid waters, Ed(λ) spectra are low in magnitude with a narrow peak around 525–570 nm, whereas in clear waters Ed(λ) spectra are high in magnitude with a broad peak shifting toward the blue wavelengths (i.e. 480–550 nm)

Measured E d (mW/cm /nm)

742

30 20 10 0 400 450 500 550 600 650 700

20 15 10 5 0 400 450 500 550 600 650 700

Wavelength (λ ) (nm)

Wavelength (λ ) (nm) 40

2

20

Measured E d (mW/cm /nm)

2

Measured E d (mW/cm /nm)

25

15 10 5 0 400 450 500 550 600 650 700 Wavelength (λ ) (nm)

20

10

0 400 450 500 550 600 650 700

Wavelength (λ ) (nm) 80

2

2

50

Measured E d (mW/cm /nm)

60

Measured E d (mW/cm /nm)

30

40 30 20 10 0 400 450 500 550 600 650 700

70 60 50 40 30 20 10

E d (2 m )

E d (3 m )

E d (8 m )

E d (9 m )

E d (10 m )

standard deviation, variance and mean of 4.93, 24.38 and 4.97, respectively, whereas the present model yields the relatively low values (2.53, 6.43 and 3.17, respectively) in the selected wavelength regions. DaviesColley (1988) model also gives slightly higher values (standard deviation, variance and mean values of 2.72, 7.42 and 2.74, respectively). These results apparently confirm that the present method yields more accurate Zsd values when compared with the other two models. These results are further supported by the scatter plots at 520, 530 and 540 nm for inter-comparison of models

500

600

700

Wavelength (λ ) (nm)

Wavelength (λ ) (nm) E d (1 m )

0 400

E d (4 m ) E d (11 m )

E d (5 m ) E d (12 m )

E d (6 m ) E d (13 m )

E d (7 m ) E d (14 m )

(Fig. 6), where there is a one-to-one correlation between the results from our method and measured values. To further investigate the robustness of the present method, the consistency in spatial structures of the present method and in situ Zsd maps are examined (Fig. 7). Due to mere impossibility of collecting the in situ data at each and every latitudinal and longitudinal coordinates of transects of the study region, these contour plots were generated by interpolating values between stations corresponding for all four cruises. The spatial aspects of Zsd for the study region has been generated using the Surfer

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25

520nm ZSD Predicted (m)

20 15 10

Z

SD

Predicted (m)

Fig. 6 a–c Comparison between the in situ Zsd and predicted Zsd values (Secchi depth) by the present model and those developed by Tyler (1968) and Davies-Colley (1988) and at three wavelengths (520, 530 and 540 nm). The results from the present model are better compared with the measured Zsd values at all the three wavelengths

5

530 nm

20 15 10 5

(a) 0

(b)

0 0

5 10 15 20 ZSD Measured (m)

ZSD Predicted (m)

25

25

0

5 10 15 20 ZSD Measured (m)

25

540 nm

20 15 10 5

(c) 0 0

5 10 15 20 ZSD Measured (m)

25

Tyler Model (1968) Davies-Colley Model (1988) Present Model

software. The inverse distance to a power gridding operation was performed to generate the spatial pattern which provided the best visual interpretation of the in situ and

predicted Zsd values for the study region. It is evident that the present method results in spatial structures of Zsd closely consistent with the measured data, although there

Table 2 Comparison of the results of statistical analyses performed between measured (in situ) and derived Secchi depth from the new model and existing models in the spectral range of 520–540 nm Wavelength (λ)

MRE

RMSE

Slope

Intercept

R2

Bias

S.D.

Variance

Mean

(a) Present model 520 nm

−0.038

0.077

0.99

−0.025

0.94

−0.017

2.53

6.43

3.17

530 nm

−0.037

0.098

0.99

−0.030

0.90

0.017

2.55

6.53

3.22

540 nm

−0.023

0.098

0.99

−0.040

0.90

0.010

2.54

6.48

3.26

520 nm

0.251

0.157

0.80

−0.001

0.94

−0.113

4.93

24.38

4.97

530 nm

0.246

0.168

0.80

−0.003

0.90

−0.111

4.98

24.82

5.05

540 nm

0.260

0.172

0.81

−0.010

0.90

−0.117

4.96

24.69

5.1

(b) Tyler (1968)

(c) Davies-Colley (1988) 520 nm

−0.322

0.182

0.80

−0.205

0.94

0.145

2.72

7.42

2.74

530 nm

−0.327

0.195

0.80

0.205

0.90

0.147

2.74

7.55

2.78

540 nm

−0.313

0.190

0.81

0.199

0.90

0.141

2.74

7.51

2.81

MRE mean relative error, RMSE root mean square error, R2 coefficient of determination

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Fig. 7 Spatial structures in measured and predicted Zsd (Secchi depth) over the clear and turbid coastal waters off Point Calimere. These contour plots apparently capture a good performance of the present model as its Zsd values are closely matching with measured data from four different cruises

(a) Measured Zsd during May 2012

(b) Modelled Zsd during May 2012

(c) Measured Zsd during August 2012 (d) Modelled Zsd during August 2012

(e) Measured Zsd during August 2013

(f) Modelled Zsd during August 2013

(g) Measured Zsd during January 2014

(h) Modelled Zsd during January 2014

is slight discrepancy at some locations due to the absence of in situ data to capture the spatial variations of IOPs and AOPs. Nevertheless, these results show the confidence level of the present method to predict accurate Zsd values in clear and turbid coastal waters.

Discussion The present method is consistent with the theory of contrast transmittance and provides a new dimension to understand the scientific proficiency related to visual

water clarity. The modelled relationship satisfies the physical constraints imposed by the inherent optical conditions prevalent in the underwater environment, prominently in the euphotic zone of the mixed layer, which has been explicitly expressed by the product of z(1 %) and the depth averaged value of the diffuse attenuation coefficient (Kd). It has been found that the wavelength of 520 nm has a distinctive capability of characterizing the geometric behaviour of underwater light field and the depth of light penetration in turbid waters for the selected visible wavelengths ranging from 520 to 540 nm. The parametric analysis indicated that a

Environ Monit Assess (2015) 187:742

positive correlation exists between turbidity and coupling coefficient in the green waveband. The systematic investigation of various inherent optical properties (IOPs) revealed that the backscattering coefficient (bb) positively correlates to coupling coefficient and governs the variation in coupling coefficient for complex coastal waters. Therefore, it necessitated the inclusion of primary factor (chiefly turbidity) that accrues backscattering, especially in coastal turbid/complex waters (Effler 1988). Thus, a correction factor was included in terms of turbidity which represented the phenomena of backscattering and reflected the variable nature of coupling coefficient for various water types. It has been emphasized evidently that the precise addressal of the coupling coefficient (Γ) through a proper parameterization, based on the optical properties of the underwater environment, can play a central role in estimating the depth of light penetration under various illumination conditions and probably explain the underlying physics of light extinction for various water types. To demonstrate the robustness of the present method, it was successfully implemented and validated using three independent in situ datasets, which confirm its potential in accurately predicting the Secchi depth in clear and turbid coastal waters. Moreover, the present method correlates Secchi depth (Zsd) and turbidity, which serves as the major parameter in assessing the natural condition of water body in terms of water clarity (Cox et al. 2005). All the datasets used in the present study showed significant variability in optical properties of the water column (Arthi and Shanmugam 2013; Pravin and Shanmugam 2014; Sundarabalan et al. 2013). A large number of data points considered for the validation exercise were collected over a period of three consecutive years, in the coastal regions of the Bay of Bengal. The present method when examined indicated that over 95 % of the predicted values were within ±10 % of the measured values and performed well over the entire range of measured turbidity and chlorophyll.

Conclusion In the previous work, similar procedures and conventional conceptual methods were employed to determine the coupling coefficient that involved the complex techniques to measure the contrast reflectance and threshold contrast of the disk. Therefore, these studies neglected the essential contribution of the optical property of the

Page 15 of 18 742

medium that induces the variation in coupling coefficient. In the present work, a new practical method has been revealed to estimate Zsd in both clear and turbid waters through the modelling of Γ. For clear waters, the coupling coefficient is almost constant (approximately 4.6), whereas for turbid waters, an additional correction factor (ξ) is required which takes into account the effect of backscattering on the water clarity through the inclusion of turbidity. Since the in situ turbidity was measured using FLNTU, it can be interpreted that the present algorithm correlates Zsd to bb(700). Also, the present study is restricted in the spectral range of 520–540 nm owing to the fact that the chlorophyll fluorescence affects the backscattering coefficient spectra at 676 nm in marine environment (Jiang et al. 2014). The beam attenuation is a function of acceptance angle and the optical design of the instrument used (Voss 1992; Boss et al., 2009b). The optical instrument to measure beam attenuation is chosen to yield the derived empirical relationship that has minimum possible associated error. Therefore, there will be small difference in regression due to the instruments used. The salient feature of the present method can be attributed to its ability to accurately predict the water clarity for both clear and turbid waters. Thus, its application does not require special partitioning of the entire independent data into further subsets, such as into case 1 and case 2 waters, which otherwise are required to model ocean waters bio-optical algorithms. Therefore, it meets the accuracy and efficiency requirements for underwater visibility studies. The present method has been successful in predicting the Secchi depth with significant closure to the measured value and has potentially enhanced our understanding in the optical theory related to light penetration. Moreover, the present algorithm provides the leverage as the determination of the vertical visibility does not require the assumption or the complex quantitative measurement of the parameters like background reflectance of the disk/contrast threshold of the disk or the dedicated devices/instrumentations that measure the light extinction coefficient of the water body. The underwater application of the modelled relationship can be extended by incorporating the appropriate optically dependent parameter to determine the horizontal visibility in the regions where the existing methods fail. The key concept of contrast transmittance theory plays a crucial role in estimating Zsd. However, the accurate determination of coupling coefficient by remote sensing technique is quite challenging owing to its high variability in

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various water types. Therefore, the existing remote sensing algorithms mainly rely on band rationing techniques to estimate satellite-derived Zsd and ignores contrast transmittance theory (Zhang et al. 2003; Suresh et al. 2006; Chen et al. 2007). The present work aimed to address the important issue that the theory of contrast transmittance cannot be overlooked to estimate satellitederived Zsd. The proposed algorithm would assist in remote sensing of Zsd without deviating from the principle concept of contrast transmittance theory. The improvement in existing Zsd algorithms can be achieved provided the approach of radiative transfer equation is employed to accurately predict Γ and hence, accurately estimate Zsd in various water types. Also, the integral components of time-independent radiative transfer equation can play an imperial role to explore the methodologies that could reduce the percentage error in the predicted values and in incorporating a better analytical technique which would assist to investigate the latent optical parameters that significantly influence the undetermined coupling coefficient and, hence, the Secchi depth in a particular geometric underwater light field structure encountered in various coastal water types. Acknowledgments The present work was supported by the NRB and was carried out by the extensive support of IIT Madras, Chennai-600036. We would like to extend our earnest thanks to D. Rajshekhar, The Head, Vessel Management Cell (VMC) and the Director of National Institute of Ocean Technology (NIOT), for providing the coastal research vessels (SagarPaschimi and SagarPurvi) to IIT Madras for carrying out various underwater light field measurements during the cruises and develop the biooptical models. We also thank scientists N. Ravi and K. Sashikumar for their timely arrangement of the vessel and the VMC members for their valuable on-board help during the in situ measurements. We sincerely thank two anonymous reviewers for their insightful comments on our manuscript.

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