3.1 Data used

We used OLI data for determining pre-monsoon (March 2017) and post-monsoon (September 2017) suspended sediments. OLI provides the multispectral data for the visible and infrared range, and covers the entire Earth in 16 days. The OLI uses the push broom sensor with an 185 km cross-track field of view.

Shuttle radar topography mission is a research effort that obtained digital elevation models to generate a high-resolution digital topography database of the Earth. For extracting the bathymetry, we used a global relief model which is a composite model that incorporates a digital bathymetry model (DBM). SRTM30_PLUS (http://topex.ucsd.edu/WWW_html/srtm30_plus.html, last access: January 2017) consists of both a topography and a bathymetry model; therefore, it provides 30 arcsec (900 m) resolution data for land as well as for ocean, which is derived from depth sounding (SONAR) and satellite altimetry. Finally, the wind direction was derived from the ERA-Interim portal, provided by the ECMWF (European Centre for Medium-Range Weather Forecasts, 2017), which is an independent intergovernmental organization, based on a four-dimensional IFS (Cy31r2) system.

3.2 Conversion of digital number (DN) values to top of atmosphere (TOA) reflectance

Atmospheric correction was applied to determine the water-leaving reflectance (ratio of upwelling radiance just above the water surface and the solar downwelling irradiance) by eliminating the contribution of surface glint and atmospheric scattering from the estimated total reflectance. The total atmospheric reflectance was estimated as the sum of the molecular reflectance (Rayleigh reflectance), specular reflection of the sun, and the reflectance of aerosol, foam, and whitecaps. All of these parameters were determined from the metadata and field measurements, using an empirical relationship (Gordon and Wang, 1994). Solar radiation is totally absorbed by water in the near-infrared band. Thus, water-leaving radiance can be eliminated to directly estimate aerosol. Hence, medium to relatively high suspended particulate matter (SPM) concentrations can be better mapped using the near-infrared and red bands.

These raw data can be converted to TOA reflectance from the DN (Eq. 1) using rescaling factors and parameters found in the metadata file (MTL.txt), which is provided with the data. This can be carried out as follows:

where ${\mathit{\rho }}_{\mathrm{t}}^{\prime }$ is the TOA planetary reflectance (without solar angle correction), M_p is the band-specific multiplicative rescaling factor, A_r is the band-specific additive rescaling factor, and Q_cal is the quantized and calibrated standard product pixel values (DN).

Next, we corrected the ${\mathit{\rho }}_{\mathrm{t}}^{\prime }$ using Eq. (2) for the solar angle:

where ρ_t is the TOA planetary reflectance, θ_SE is the local sun elevation angle, θ_SZ is the local solar zenith angle, and ${\mathit{\theta }}_{\mathrm{SZ}}=\mathrm{90}{}^{\circ }-{\mathit{\theta }}_{\mathrm{SE}}$.

3.3 Molecular/Rayleigh reflectance correction

Most reflectance from air molecules and aerosols must be accurately modelled and removed from the observed signal. At-sensor total reflectance (Eq. 3) can be expressed as the following formula:

After the Rayleigh correction, ground surface + aerosol albedo r_a can be determined as

where ρ_R is the Rayleigh reflectance, the extra terrestrial sun radiation is (π)(E_S)(cos(θ_S))(d_sol)exp[(−m)(τ_net)],

θ_s and θ_v are the angle of solar zenith and sensor zenith, respectively, d_sol is the eccentricity correction factor of the Earth's orbit, and T_R is the Rayleigh atmospheric transmittance.

T_yu = Rayleigh transmittance for sensor

T_yd = Rayleigh transmittance for sun

where τ_Raylight is the Rayleigh optical depth, ${\mathit{\tau }}_{{\mathrm{O}}_{\mathrm{2}}}$ is the oxygen optical depth, τ is the optical depth, and S_R is the Rayleigh spherical albedo.

Rayleigh reflectance (ρ_r) is calculated as follows:

where μ_s=cos of sun zenith, μ_v=cos of sensor zenith, ∅_v is the sun azimuth, ∅_s is the sensor azimuth, ρ_R1 is the single-scattering contribution, and τ is the atmospheric optical depth.

Sensor spectral response-based pre-computed radiative transfer simulations, solar and sensor viewing geometry, and ancillary information were used to estimate most of the components in the above equations. Rayleigh correction was executed by subtracting the Rayleigh reflectance value from the top of atmosphere reflectance as

3.4 Marine reflectance calculation

Aerosol reflectance (ε) over water pixels was derived from the ratio of reflectance in the chosen bands. ε, the proportion of the multiple-scattering aerosol reflectance, was constant over the study period. The value of ε was considered to be 1 for standard processing in the visual and near-infrared bands (Vanhellemont et al., 2014). A linear relation was established between marine reflectance and constant aerosol type (ε). Aerosol can be determined by the slope of the regression line (Neukermans et al., 2009) and the median ratio of the Rayleigh corrected reflectance in bands 4 and 5 (${\mathit{\rho }}_{\mathrm{c}}^{\mathrm{4}}$, ${\mathit{\rho }}_{\mathrm{c}}^{\mathrm{5}}$). Alpha, ∝, the ratio of oceanic reflectance was determined using the average resemblance spectrum for the band central wavelengths:

Gamma, γ is the fraction of diffused atmospheric transmittance in the two bands, which is calculated using the following equation (Eq. 8):

Then, the oceanic reflectance is calculated using ${\mathit{\rho }}_{\mathrm{w}}^{\left(\mathrm{3}\right)}$ and ${\mathit{\rho }}_{\mathrm{w}}^{\left(\mathrm{4}\right)}$ (Eq. 9):

3.5 Spectral analysis of the suspended sediments

The reflectance spectrum of an object is a graph of the radiation reflected to the incident wavelength and serves as a unique signature for the particular object. The water curve is characterized by high absorption in the near-infrared wavelength and beyond, whereas maximum reflectance is found in blue range of the spectrum. The spectral curve for the SSC is plotted for suspended particles in the ocean at a certain wavelength, after establishing the marine reflectance and correcting for aerosol in the data.

3.6 Extraction of suspended sediments and its validation

After obtaining the error free reflectance data, we proceeded with mapping the movement of suspended sediments during the pre-monsoon and post-monsoon seasons. Increments in red reflectance range in turbid water indicate the presence of sediments. We determined suspended solid matter using the single band (the red band) algorithm (Eq. 10) that was also used by Nechad et al. (2010):

where A=327.84 g m⁻³ and C=0.1708.

Using the above-mentioned method, we mapped the solid particles suspended near the shore (within 10 km) in order to explore the transportation of suspended particle along the coast during the pre-monsoon and post-monsoon seasons.

As previously stated, the single band algorithm, which was suitable for the study area, was used as a predictor for assessing the suspended sediments along the coast. The model was validated with samples collected within 5 km of the coast. The root mean square error (RMSE) was calculated (Eq. 11),

to examine the variation between the field-based predicted ($\widehat{y}$) data and the satellite-based observed (y) data values. This study used the concurrent satellite and ground-based data for better calibration.

Figure 2Mean significant wave height along the coast.

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4.1 Spectral signature of water and SSC having different magnitudes

The reflectance curve (Fig. 3) is plotted between the wavelengths utilized and the detected suspended sediment reflectance from a 900 m² area (at 30 m resolution). The reflectance variation of the surface water indicates the presence of suspended sediments in the offshore region (Fig. 3). We note that the regions with high suspended sediment concentrations have high reflectance at near-infrared wavelengths, and regions with comparatively lower suspended sediment concentrations have high reflectance in the red part of the spectrum. The areas with no suspended sediments show high reflectance in the blue region of the spectrum and total absorption at near-infrared wavelengths. Hence, the reflectance curve helps with the determination of the concentration of suspended sediments in the water.

Figure 5Suspended sediments in the post-monsoon period.

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4.2 Monitoring of suspended sediments

The northern part of study area experienced heavy deposition during the post-monsoon, as the suspended particles were swashed by fewer high energy waves; the dominant wave direction during this season was also conducive to deposition (Fig. 4). Whereas, in the pre-monsoon season, circulation of the sediments was found to occur in the lower part of the study area due to the dominate wave and current action along the shore (Fig. 5). Basically, a sediment particle will remain suspended when the vertical velocity of the fluid motion becomes greater than the settling velocity of the particle. Therefore, with respect to the wave field, the vertical motion must result from the combined effects of turbulence and wave orbital motion. Here another phenomenon also acts on the sediments – the gravity of the sediments suspended in the ocean – as the heavy sediments get deposited near shore, whereas the lighter sediments float. The wave directions in the pre-monsoon and post-monsoon periods are shown in Figs. 4 and 5, respectively. It was found that the SSC rapidly decreased with an increase in the distance (0–10 km) from the shoreline as well as an increase in the bathymetry level of 5–10 m. Furthermore, the effect of wave shoaling was deeper water is significantly less, which was found to cause a sparse distribution of sediment concentrations. Suspended sediment concentrations more than 5000 m from the shoreline and below a depth of 10–20 m, are rarely observed as measurement at these depths is not currently possible, which is one of the limitations of the optical data. The movement of SSCs indicates that SSCs have a positive correlation with wave direction and littoral current. We assigned weight to the layer based on the deposition along the shore. Most of the southern part of the study area was found to exhibit high concentrations of suspended matter during pre-monsoon and post-monsoon seasons, which were derived from the single band model with a very small RMS error, i.e. 0.19. The middle part of the study region was found to have cyclic SSCs, as it experienced seasonal erosion of the shore and deposition sediments near the beach. The northern most part of the study area was found have lower concentrations of suspended sediments during the pre-monsoon and post-monsoon seasons.