*4.1. Image Data*

Our image classification results of the RGB data are consistent with the results of other studies (e.g., [11,12,28,70]). The combination of raw RGB bands, two principle components, and two slope rasters (as proposed by [12]) produced similar results to those of the equally processed multispectral bands. Furthermore, processing of the multispectral data improved the classification results significantly, allowing us to minimise the impact of lighting differences successfully.

Transformation to CIELAB coordinates did not deliver any benefit for the RGB data: Neither replacing the RGB bands with their CIELAB counterparts, nor using the image bands containing chromaticity coordinates a\* and b\* separately led to better clustering results (Online Resource 1 in Supplementary Materials). This is different for the multispectral data, as both the CIELAB data based on the multispectral data and SOC data show a significant influence on the clustering results (Figure 7d,e). A combination of slope bands and CIELAB bands eliminates the influence of slightly shadowed areas on the left and right sides of the profile. This leads to more homogeneous results, which is mostly visible in layer A and the righthand parts of layers B and D. As a consequence layer C is—while grouped with the material of layer A—captured more reliably than with the other multispectral band combinations. Another notable result is the similar performance of (i) the combination of slope bands with all CIELAB bands (Figure 7d) and (ii) the combination of slope bands with the CIELAB chromaticity bands a\* and b\* and the SOC raster (Figure 7e). Classification results are nearly identical, only showing small differences in the lower part of the profile.

We observed similarities between the clustering results of band combinations including the SOC raster and, alternatively, the CIELAB lightness raster. Nevertheless, the transferability of these results to other sites has to be examined critically and individuallyfor each case. The noticed relation between SOC and lightness rasters is already proposed by other authors (e.g., [27,59]), who examined this phenomenon in detail and concluded that the relation is highly dependent on the local circumstances. However, if quantitative examination of SOC as conducted by, e.g., Steffens et al. [62] cannot be included into the workflow due to technical or financial limitations, we propose CIE lightness to be a rough indicator of the spatial variance of SOC, while keeping in mind that water content also influences lightness significantly (e.g., [50,60]). Our results support the strong correlation of CIELAB image bands and SOC, as observed for high-contrast soil profiles, for example, by Zhang and Hartemink [28].

The initially proposed significance of CIELAB chromaticity coordinates for the examination of iron oxide concentrations could not be confirmed for our experimental design. The examination of iron oxides based on CIE a\* and b\* as proven by, e.g., Vodyanitskii and Kirillova [27] possibly requires a more sophisticated approach, including the mathematical prediction via, e.g., partial least squares regression or machine learning algorithms, as applied for other sediment properties by, e.g., Daniel et al. [71], Viscarra Rossel and Behrens [72], or Morellos et al. [73]. Other factors that could be responsible for the poor performance of our approach include the limited presence of iron in the profile examined: Elemental Fe concentration is below 1% (see Online Resource 2 in Supplementary Materials) throughout the examined samples. This would correspond to a maximum of c. 1.4% Fe2O3, given that all Fe would result from hematite. A future approach should consider a camera setup with fewer limitations regarding spectral range and resolution. Using a hyperspectral VIS-NIR device would allow the examination of Fe in far more detail [13,60,74]. This would also allow the analysis of further sediment properties, like grain size based on the spectral signal [50,75–77].

More generally speaking, our results support the usage of the CIELAB colour space as a standard for documentation during archaeological excavations. The observed good performance of the CIELAB datasets supports the scientific relevance of the CIELAB colour space, which was previously proposed by other authors [47,78]. For the last decades, this colour space gained popularity in the geosciences and, meanwhile, is widely used in numerous studies (cf. [14]). Many authors noted the clear advantages over the RGB or Munsell colour systems (e.g., [22,23,26]): CIELAB is a mathematically defined colour space that is free to use and suitable for quantitative analyses. In future studies, the proposed quantitative examination of colour differences throughout archaeological profiles by transformation to CIELAB could be complemented by additional colour difference formulas like CIEDE2000 to assess possible benefits [79].
