Extending Multidimensional Rao’s Quadratic Entropy to Optical–Radar Lava-Flow Mapping Using Sentinel-1 and Sentinel-2: Evidence from the 2021 La Palma Eruption

The 2021 eruption of Cumbre Vieja on La Palma, Canary Islands, produced extensive lava flows and major landscape transformation, providing an opportunity to evaluate remote sensing approaches for mapping the extent of an emplaced lava flow. This study assessed direct spectral, classic Rao’s quadratic entropy (RaoQ), and multidimensional RaoQ approaches using satellite observations acquired before and after the eruption. Optical, radar, thermal infrared, and night-time radiance datasets were evaluated within a common change-detection framework implemented in Google Earth Engine. Difference maps were converted into binary change maps using a histogram-based thresholding procedure calibrated on the reference delineation and evaluated against the Copernicus Emergency Management Service (CEMS) lava-flow reference and no-change validation areas derived from ESA WorldCover using multiple accuracy metrics. Because the change reference is the final CEMS lava-flow delineation and the no-change samples lie outside a 100 m buffer around it, the accuracy figures reported here quantify the mapping of lava-flow extent and not of other eruption-related effects such as ash deposition or vegetation damage beyond the flow margins. Among the direct spectral approaches, the NHI_SWIR index achieved the highest overall classification performance. Among the individual Sentinel-2 bands, B12 achieved the highest overall accuracy, whereas B8A achieved the highest true skill statistic; both exceeded the multidimensional RaoQ configurations in mean prevalence-independent discrimination. Within the classic RaoQ approach, MIRBI produced the strongest single-variable heterogeneity-based results. The best multidimensional configurations combined Sentinel-2 B8A and B12 with Sentinel-1 VV, demonstrating that radar backscatter provided complementary information to optical observations. Although multidimensional RaoQ did not surpass the best direct spectral variables, it produced competitive and spatially coherent representations of lava-flow disturbance. The evaluated thermal infrared and night-time radiance products did not provide competitive discrimination under the selected spatial and temporal conditions for different reasons: a thresholding limitation in the case of the Landsat thermal product, and an unfavourable ratio of pixel size to flow width in the case of the night-time radiance products, while the MODIS product returned no valid validation points and could not be evaluated. These product-specific explanations rest on a small number of comparisons and are provisional. These results show that carefully selected Sentinel-2 SWIR variables remain the strongest benchmark for detailed mapping of fresh lava-flow disturbance, while multidimensional RaoQ provides a framework for optical–radar integration that requires no training data or prior classification. Because the evaluation covers a single eruption in a single landscape, transfer of the framework to other events and settings remains to be demonstrated.