Spectral Mixture Modeling with Laboratory Near-Infrared Data I: Insights into Compositional Analysis of Europa

TL;DR

This study benchmarks linear mixture (LM) and Hapke-based radiative transfer (RT) spectral modeling against laboratory near-infrared spectra of H2O ice and sulfuric acid octahydrate (SAO) mixtures to evaluate how accurately each approach retrieves surface composition relevant to Europa. Using endmember spectra measured at ~77 K with ~100 μm grains across three mixtures, LM treats the surface as areal patches while RT accounts for intimate mixing and multiple scattering, with abundances inferred via Markov Chain Monte Carlo. Results show RT abundances stay within ±5% of the true values for all mixtures, whereas LM deviations are typically ±5–15%, and both methods consistently overestimate SAO and underestimate H2O ice. The work supports using RT intimate-mixing modeling for Europa’s surface composition analyses, while LM remains viable in specific compositional regimes; it also highlights the need for broader laboratory data to extend validation to other surface-constituent species and grain sizes for future missions like JUICE and Europa Clipper.

Abstract

Europa's surface composition and physical characteristics are commonly constrained using spectral deconvolution through linear mixture (LM) modeling and radiative transfer-based (RT) intimate mixture modeling. Here, I compared the results of these two spectral modeling- LM versus RT- against laboratory spectra of water (H$_{2}$O) ice and sulfuric acid octahydrate (SAO; H$_{2}$SO$_{4}$$\cdot$8H$_{2}$O) mixtures measured at near-infrared wavelengths ($\sim$1.2-2.5 $μ$m) with grain sizes of 90-106 $μ$m (Hayes and Li, 2025). The modeled abundances indicate that the RT more closely reproduces the laboratory abundances, with deviations within $\pm$5% for both H$_{2}$O ice and H$_{2}$SO$_{4}$$\cdot$8H$_{2}$O with $\sim$100 $μ$m grains. In contrast, the LM shows slightly larger discrepancies, typically ranging from $\pm$5-15% from the true abundances. Interestingly, both LM and RT tend to consistently overestimate the abundance of H$_{2}$SO$_{4}$$\cdot$8H$_{2}$O and underestimate H$_{2}$O ice across all mixtures. Nonetheless, when H$_{2}$SO$_{4}$$\cdot$8H$_{2}$O either dominates (>80% as observed on Europa's trailing hemisphere; Carlson et al. 2005) or is present only in trace amounts ($\sim$10% on areas in Europa's leading hemisphere; Dalton III et al. 2013; Ligier et al. 2016), both the LM and RT render acceptable results within $\pm$10% uncertainty. Thus, spectral modeling using the RT is preferred for constraining the surface composition across Europa, although the LM remains viable in specific compositional regimes.

Figures (4)

• Figure 1: Left panel: Laboratory reflectance spectra of H2O ice, H2SO4$\cdot$8H2O (sulfuric acid octahydrate; SAO), and their mixtures at varying proportions (%wt) and grain sizes of 90–106 $\mu$m hayes2025insights. The blue spectrum represents the H2O ice endmember, the orange spectrum represents the H2SO4$\cdot$8H2O endmember, and the spectra shown in shades of green correspond to mixtures of H2O ice and H2SO4$\cdot$8H2O at different ratios. All reflectance spectra were collected from hayes2025insights. Right panel: Single scattering albedo spectra corresponding to the reflectance spectra, derived using radiative transfer theory based on the hapke1981bidirectional model (refer to Section 2.2 for conversion details).
• Figure 2: Comparison of linear mixture modeling (left panel) and intimate mixture modeling using the hapke1981bidirectional radiative transfer theory (right panel). In each subplot, the blue spectrum represents the laboratory reflectance spectrum of the H2O–SAO mixture hayes2025insights, while the orange spectrum shows the modeled spectrum from either the LM or Hapke-based RT modeling. The true (laboratory) and estimated (model-derived) mean abundances of H2O ice and sulfuric acid octahydrate (SAO) are indicated in each subplot, along with the root mean square error (RMSE) of the spectral fit.
• Figure 3: Comparison of modeled abundances (mean ± 1$\sigma$) of H2O ice and sulfuric acid octahydrate (SAO) using the linear mixture modeling and the intimate mixture modeling based on the hapke1981bidirectional radiative transfer theory. Left panel: Modeled abundances plotted against the expected (ideal) laboratory abundances. Blue and orange markers represent estimates from the LM and Hapke-based RT modeling, respectively. Circle and cross markers represent H2O ice and SAO abundances, respectively, by the corresponding mixture modeling. Right panel: Difference between the laboratory (true) abundances and the modeled abundances (True-Model abundance) for each component using both modeling approaches (LM and RT).
• Figure 4: Left panel: Patches of dark and bright materials on Europa observed in a high-resolution image from the Galileo Solid State Imaging (SSI) system belton1992galileo. The image is centered at approximately 16°S, 163°45'E, with a spatial resolution of $\sim$50 m/pixel. Right panel: A high-resolution Galileo/SSI image of Europa’s chaos terrains on the trailing hemisphere (near center)—an area exposed to radiolytic processes carlson1999sulfuriccarlson2002sulfuric— showing no discernible dark and bright patches. The image is centered at approximately 9°15'N, 84°50'E, with a spatial resolution of $\sim$50 m/pixel. Both SSI images are adopted from malaska2024updated.