# Characterisation of Coastal Sediment Properties from Spectral Reflectance Data
## 3 Results
### Spectral Analysis of Sediment Samples
Figure 5: Results of spectral analysis of samples from different geomorphic positions at Oyster Bay. (**a**) Full average spectrum for samples from the different position; detailed results at (**b**) the VNIR (552–1352 nm) and (**c**) SWIR (1852–2450 nm) parts of the spectrum. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Wavelength (nm)** & **CaCO\({}_{3}\)** & **Fine Sand** & **Span** \\ \hline
552 & 0.0928 \({}^{\ast}\) & 0.6264 & 0.9885 \\ \hline
652 & 0.2507 & 0.9883 & 0.4891 \\ \hline
752 & 0.7211 & 0.0928 \({}^{\ast}\) & 0.0734 \({}^{\ast}\) \\ \hline
852 & 0.7343 & 0.0096 \({}^{\ast\ast}\) & 0.1257 \\ \hline
952 & 0.9410 & 0.0026 \({}^{\ast\ast}\) & 0.2164 \\ \hline
1052 & 0.0077 \({}^{\ast\ast}\) & 0.7944 & 0.3640 \\ \hline
1152 & 0.0100 \({}^{\ast}\) & 0.9415 & 0.2201 \\ \hline
1252 & 0.0087 \({}^{\ast\ast}\) & 0.4923 & 0.1494 \\ \hline
1462 & 0.0834 \({}^{\ast}\) & 0.2163 & 0.3150 \\ \hline
1552 & 0.3162 & 0.8246 & 0.2073 \\ \hline
1652 & 0.2605 & 0.9801 & 0.1364 \\ \hline
1752 & 0.1525 & 0.8957 & 0.1300 \\ \hline
1789 & 0.1064 & 0.0480 \({}^{\ast}\) & 0.0158 \({}^{\ast}\) \\ \hline
1962 & 0.0264 \({}^{\ast}\) & 0.7977 & 0.0528 \({}^{\ast}\) \\ \hline
2028 & 0.4413 & 0.4095 & 0.2356 \\ \hline
2082 & 0.9618 & 0.5296 & 0.6334 \\ \hline
2152 & 0.4212 & 0.4293 & 0.7909 \\ \hline
2200 & 0.5897 & 0.5675 & 0.6655 \\ \hline
2252 & 0.3046 & 0.0789 \({}^{\ast}\) & 0.3075 \\ \hline
2300 & 0.0098 \({}^{\ast\ast}\) & 0.4795 & 0.0085 \({}^{\ast\ast}\) \\ \hline
2335 & 0.1032 & 0.8612 & 0.8394 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Analysis of \(p\)-values of linear regression of CaCO\({}_{3}\), fine sand and grain size _span_ with selected wavelengths (see Figure 5). Significance levels are: \({}^{\ast}\) 0.1, \({}^{\ast}\) 0.05, \({}^{\ast\ast}\) 0.01 and \({}^{\ast\ast\ast}\) 0.001. Figure 6: Correlation coefficient between reflectance values at different spectral wavelengths and sediment CaCO\({}_{3}\), and particle size characteristics. CaCO\({}_{3}\) values can be estimated using single wavelength relationships as:  
\[CaCO_{3}=54.1-98.37R_{2335}\,\left(R^{2}=0.718,\,\,\text{n}=94\right) \tag{2}\]  
where \(R_{2335}\) is reflectance at the 2335 nm wavelength. A similar model performance can be achieved at the wavelength between 2038 and 2435 nm. A multilinear relationship can improve the model estimation as follows:  
\[ \begin{split} CaCO_{3}=38.99+460.23R_{2200}-1272.89R_{2300}+1158.99 R_{2335}-409.99R_{2370}\\ \left(R^{2}=0.872,\,\,\text{n}=94\right)\end{split}  \tag{3}\]  
where \(R_{2200}\), \(R_{2300}\), \(R_{2335}\), \(R_{2335}\), and \(R_{2335}\) are reflectances at the 2200, 2300, 2335 and 2370 nm wavelengths, respectively. Fine sand can be estimated using the following linear relationship:  
\[F\,\,Sand=179.06R_{2450}-41.01\,\left(R^{2}=0.463,\,\,\text{n}=94\right) \tag{4}\]  
where \(F\,\,Sand\) is the fine sand percentage, and \(R_{2450}\) is reflectance at the 2450 nm wavelength. Fine sand values can also be estimated using the reflectance from the wavelengths ranging between 552 and 1789 nm. This can also be used to develop an improved model to estimate the fine sand percentage as follows:  
\[F\,\,Sand=21.55-364.86R_{1462}+369.07R_{2082}\,\left(R^{2}=0.721,\,\,\text{n}= 94\right) \tag{5}\]  
where \(F\,\,Sand\) is the fine sand percentage and \(R_{1462}\) and \(R_{2082}\) are reflectances at the 1462 and 2082 nm wavelengths, respectively. \(Span\) had very poor performing models when a single band was utilised. For example, the following model was the best performing single-wavelength model:  
\[Span=2.15-2.43R_{2038}\,\left(R^{2}=0.183,\,\,\text{n}=94\right) \tag{6}\]  
where \(R_{2038}\) is the reflectance at the 2038 nm wavelength. A multilinear model can be developed using highly correlated wavelengths ranging between 852 and 2450 nm, as shown below:  
\[ \begin{split} Span=1.68-24.66R_{852}+29.62R_{952}+59.44R_{2252}- 131.36R_{2300}+79.47R_{2350}-\\ 73.27R_{2400}+62.52R_{2447}\,\left(R^{2}=0.516,\,\,\text{n}=94 \right)\end{split}