Evaluation of Sentinel-2 Spectral Indices for Iron and Aluminum Mapping Using Integrated Remote Sensing and Laboratory Analysis: A Case Study in Kirkuk, Iraq

The identification and mapping of mineral elements, especially iron and aluminum, are very important for mineral exploration, geological analysis, and sustainable resource management. Conventional field surveying and laboratory chemical analysis provide directly measurable information about mineral content, but their use in vast or topographically complicated areas is expensive, time-consuming, and spatially limited [1]. Remote sensing provides an alternative methodology that allows for systematic and spatially continuous observations over large areas. Among modern multispectral satellites, Sentinel-2 has proven itself to be a promising tool for geological and mineral mapping because of its high spatial resolution and spectral range from the visible to near-infrared (VNIR) and short-wave infrared (SWIR) spectral bands. The latter are especially useful for detecting absorption and reflection changes caused by mineral presence on the surface [2].

Previous research has already shown the ability of Sentinel-2 to identify and map minerals using spectral ratios and indices. Research [3] explored iron-related spectra of the Anqian Iron Mine in Anshan, China, and showed the applicability of Sentinel-2 bands in discriminating iron minerals based on their spectral responses. Additionally, mineral distributions, such as those of bauxites, were mapped using Sentinel-2 imagery by applying spectral transformations that highlight mineral-sensitive spectral variations [4, 5]. Overall, these studies show the possibility of using multispectral satellite observations as an addition to conventional geological studies.

A number of band ratio and normalized difference methods have been used in order to increase the spectral response of iron- and aluminum-containing minerals. For example, commonly used iron-based ratios include visible-band spectral ratios, while aluminum-based ratios may include SWIR-based ratios and normalized difference indices [6]. Spectral indices mentioned above provide relatively simple ways to emphasize the differences between certain bands of Sentinel-2 and have therefore been extensively applied in mineral mapping. However, the behavior of such indices may depend on the properties of the surface, geology, soil, vegetation, atmosphere, and spectral mixture of the pixels [7].

However, although the potential of the use of Sentinel-2 has been shown, there is a difficulty in converting the spectral index response to an accurate mineral concentration estimation. The spectral disturbance caused by non-target surface material and environment may cause a reduction in the ability of mineral detection [8]. In addition, spectral indices that were either developed or tested in one particular geological area will not necessarily behave similarly when applied in another location. Thus, satellite-based mineral indicators must be assessed using field and laboratory data instead of interpreting the results based on image contrast alone.

Against this backdrop, this research seeks to evaluate the effectiveness of Sentinel-2 spectral formulas for estimating Fe₂O₃ and Al₂O₃ concentrations in Kirkuk Governorate, Iraq, using laboratory data as a reference. Conventional iron and aluminum spectral formulations are evaluated alongside the alternative formulations proposed for iron and aluminum[9]. The novelty of this study lies primarily in the integrated evaluation of Sentinel-2 spectral transformations using laboratory-derived Fe₂O₃ and Al₂O₃ measurements within the geological setting of Kirkuk, Iraq. Rather than claiming that the alternative formulations represent universally superior spectral indices, this study evaluates their performance against established spectral formulations under the same independent testing framework. The alternative formulations are therefore considered site-specific spectral transformations whose applicability is assessed within the Kirkuk study area and qualitatively in selected external mineralized areas. Instead of judging the performance of the formulas only by visual interpretation or one error measure, these formulas are tested based on an independent test set and several statistical indicators such as root mean square error (RMSE), mean absolute error (MAE), bias, coefficient of determination (R²), and 95% confidence intervals. Thus, the study intends to (i) evaluate the agreement between the spectral estimates from Sentinel-2 and the laboratory data, (ii) compare the predictive performance of conventional and proposed spectral formulas under the same validation process, and (iii) test their suitability for mineral mapping other than the current study area.

A combined methodology framework (Figure 3) was adopted for the characterization and analysis of the spatial distribution of iron and aluminum in Kirkuk Governorate, Iraq. The methodology framework consists of field sampling, chemical analysis, Sentinel-2 remote sensing, and GIS methodologies. In total, 27 field samples were subjected to laboratory analysis of Fe₂O₃ and Al₂O₃ to be considered as ground truth values. Sentinel-2 multispectral images were subjected to band arithmetic and various spectral indices. For iron, conventional Eq. (1) and Eq. (2) ratios were studied and compared with the proposed Eq. (5) ratio. On the other hand, for aluminum, the published Eq. (3) and Eq. (4) were studied and compared with the proposed Eq. (6) ratio. The selection of these band combinations was based on the spectral characteristics of iron- and aluminum-bearing minerals. The visible bands used for the iron formulations are sensitive to spectral variations associated with iron-bearing materials, whereas the SWIR bands used for the aluminum formulations are more relevant to absorption features associated with Al-OH-bearing minerals.

It should be noted that Eq. (5), (B4 + B3)/B3, is algebraically equivalent to Eq. (2), B4/B3, with a constant shift of +1. Because the spectral formulations were evaluated using regression relationships that included an intercept, this constant shift changes only the regression intercept and does not change the fitted predictions or the resulting statistical performance measures.

$Iron =\frac{B 4}{B 2}$         (1)

$Iron =\frac{B 4}{B 3}$          (2)

$Aluminum =\frac{B 11}{B 12 }$                   (3)

$N D A I=\left(\frac{B 11-B 12}{B 11+B 12}\right)$           (4)

$Iron =\left(\frac{B 4+B 3}{B 3}\right)$             (5)

$Aluminum =\left(\frac{B 11+B 12}{B 11}\right)$                 (6)

where,

Iron: Iron spectral index

Aluminum: Aluminum spectral index

NDAI: Normalized Difference Aluminum Index

B2: Blue band

B3: Green band

B4: Red band

B11: SWIR 1 band

B12: SWIR 2 band

To link the field and laboratory data with the spatial analysis, Sentinel-2 Level-2A imagery acquired from the Copernicus Browser on 18 December 2025 was used. The selected scene had approximately 0.006% cloud coverage, and no significant cloud contamination or visible distortion was observed over the study area. The selected acquisition date provided suitable image conditions for the analysis. Sentinel-2 Bands 11 and 12 have a native spatial resolution of 20 m and were resampled to 10 m using the Nearest Neighbor method prior to the spectral calculations to maintain a consistent processing grid. This resampling standardized the pixel size for spatial processing but did not create additional spatial information beyond the native 20 m resolution of the SWIR bands. The geographic coordinates of the field samples were used to match each sampling location with the corresponding Sentinel-2 pixel. The required band values were extracted at each sample location using the Extract Values to Points tool in ArcGIS 10.4.1 and were subsequently linked to the corresponding laboratory-measured Fe₂O₃ and Al₂O₃ concentrations.

3.png

Figure 3. Integrated methodological framework for iron and aluminum mapping using field sampling, laboratory analysis, Sentinel-2 imagery, and statistical validation

The data were divided into a calibration (training) set of 20 samples and an independent test set of 7 samples. Using an approximate 70:30 calibration-to-test allocation, seven samples were selected as the independent test set based on their spatial distribution to ensure coverage of the study area, while the remaining 20 samples were used for calibration. No formal stratification based on Fe₂O₃ or Al₂O₃ concentration levels was applied. The calibration set was used to establish the regression relationships between the Sentinel-2 spectral formulations and the laboratory-measured Fe₂O₃ and Al₂O₃ concentrations, while the independent test set was used to evaluate model performance using RMSE, MAE, bias, R², and the 95% confidence interval of bias.

The sampling locations were selected jointly by the researcher and the supervisor based on field conditions and the objective of achieving comprehensive spatial coverage of the study area. The distance between adjacent sampling points ranged from approximately 0.59 to 5.68 km, reflecting the spatial distribution of the sampling locations across the study area. Sampling locations were preferentially selected from areas with exposed or predominantly exposed soil to minimize the influence of vegetation and other land-cover effects on the Sentinel-2 spectral response. Potential mixed-pixel effects and local soil heterogeneity were considered as sources of uncertainty in the analysis. Cross-validation was not performed in this study. Given the limited sample size, the potential risk of overfitting and the uncertainty associated with model performance should therefore be considered when interpreting the results.

The results obtained in this study demonstrate the possibility of combining the use of multispectral images from the Sentinel-2 satellite and laboratory analysis to evaluate the spatial distribution of iron and aluminum in the Kirkuk Governorate. However, the results obtained from the statistical analysis show that the relationship is rather weak, particularly concerning the value of R². Therefore, the proposed formulations should be considered as alternative spectral transformations rather than superior replacements for the existing indices.

(1) Iron spectral formulations

The Eq. (1) and (2) band ratios are commonly used spectral transformations for enhancing iron-related spectral responses and have been applied in previous mineral-mapping studies [3, 22]. In the present study, the conventional Eq. (1) formulation produced the lowest prediction error for iron, with an RMSE of 0.6196 and MAE of 0.5005, whereas Eq. (2) produced an RMSE of 0.6590 and MAE of 0.5352. The proposed formulation, Eq. (5), yielded an RMSE of 0.6590, MAE of 0.5352, bias of -0.4486, and R² of 0.0683. Consequently, the proposed iron formulation did not outperform Eq. (1) and showed performance comparable to Eq. (2) under the present independent testing framework.

Considering the spectrum, the proposed formulation of iron considers the information of red (B4) and green (B3) bands, which are natively available in Sentinel-2 with 10 m spatial resolution. The resulting transformation is a relatively simple one that can be implemented through band arithmetic without requiring resampling of the bands considered. Previous studies, such as study [3], have pointed out the importance of the spectral information provided by Sentinel-2 for iron mineral mapping. However, in this case, the small values of R²—0.0001 for Eq. (1) and 0.0683 for Eq. (2) and the proposed formulation—suggest that the spectral transformations tested explain a relatively small part of the variation in Fe₂O₃ concentration measured in the lab in the independent test sample. Therefore, the main advantage of the proposed iron formulation lies in its simplicity and its comparable performance to Eq. (2).

(2) Aluminum spectral formulations

Earlier studies have analyzed the use of Sentinel-2 SWIR data for the identification of aluminum-containing and bauxite-associated materials, such as the works by Anifadi et al. [4] and Kasmaeeyazdi et al. [5]. The application can be affected by spectral mixing and interference between the mineralogical and surface components [4]. In the current study, the traditional formula of Eq. (3) provided the results of RMSE of 0.9972, MAE of 0.8419, Bias of -0.3147, and R² of 0.1138, while Eq. (4) gave RMSE of 0.9921, MAE of 0.8416, Bias of -0.3026, and R² of 0.1160. The new formula of (B11+B12)/B11 gave RMSE of 0.9877, MAE of 0.8408, bias of -0.2916, and R² of 0.1180.

Such results demonstrate only a slight numerical improvement of the new aluminum formulation compared to the other two conventional indices. The new aluminum formulation provides the smallest RMSE and MAE, bias closest to zero, and the largest R² among all three aluminum formulations. Nevertheless, the level of improvement is small, and the R² value is relatively low. Therefore, the results obtained do not confirm the assumption that the new aluminum formulation can be considered superior to the traditional indices. Instead, the results show that incorporation of B11 and B12 into the new aluminum formulation can provide a somewhat different description of SWIR variability of aluminum-containing surface materials in the study area.

The comparative error analysis presented in Figure 12 further illustrates the relative performance of the evaluated spectral formulations. For iron, the Eq. (1) ratio produced the lowest RMSE and MAE, whereas the proposed formulation showed error levels comparable to those of Eq. (2). For aluminum, the proposed formulation produced slightly lower RMSE and MAE values than Eqs. (3) and (4). However, the differences among the aluminum formulations were relatively small, indicating a modest improvement rather than a substantial increase in predictive performance.

The 95% confidence intervals for the bias of the evaluated formulations included zero, indicating that the estimated mean prediction errors were associated with considerable uncertainty. The uncertainty, together with the relatively low R² values, must be considered in the context of the small number of observations in the independent test subset. Therefore, the findings clearly demonstrate the necessity of using a number of statistical criteria instead of RMSE only.

The weak relationships observed in the independent test dataset may also be influenced by several characteristics of the surface and the remote sensing data. Soil heterogeneity can produce substantial local variations in mineral composition and spectral response, which may reduce the correspondence between individual field samples and satellite-derived spectral values. In addition, although sampling locations were preferentially selected from exposed or predominantly exposed soil, some Sentinel-2 pixels may contain mixed surface materials, including soil, vegetation, and other components, which can affect the extracted spectral response. Variations in mineral assemblages and the relative abundance of iron- and aluminum-bearing minerals may also modify the spectral response and reduce the direct relationship between simple spectral transformations and laboratory-measured concentrations. Furthermore, although Sentinel-2 Level-2A data provide atmospherically corrected bottom-of-atmosphere reflectance, residual atmospheric effects and differences in illumination and surface conditions may still influence the measured spectral response. These factors, together with the limited sample size, may partly explain the low R² values and should be considered when interpreting the quantitative relationships obtained in this study.

The qualitative applicability assessments provide additional information about the geographical behavior of the alternative formulations. In particular, the suggested formulation for iron shows spatial patterns related to the mineralized area of the Anqian Iron Mine in Anshan, China, while the suggested formulation for aluminum highlights spatial patterns associated with the Itea bauxite zone in Greece, which has been previously studied using Sentinel-2 data [4, 5]. However, since there is no independent laboratory analysis of these external sites in the current research, these findings cannot be considered quantitative proof of predictive ability or universal applicability. Instead, they demonstrate that the suggested formulations retain their spatial sensitivity outside the Kirkuk study site.

In general, the developed formulations can be considered simple alternative spectral transformations for Sentinel-2-based mapping of iron and aluminum. The formula for aluminum showed some improvement numerically compared to the tested conventional aluminum indices, and the formula for iron was comparable in performance to Eq. (2), though it was not better than Eq. (1). Further validation should be done on larger datasets and different geological settings.