Realistic uncertainties on Hapke model parameters from photometric measurement

TL;DR

This paper uses an advanced Bayesian inversion method to analyze uncertainties in Hapke model parameters, revealing that some observed parameter relationships are artifacts of the retrieval process rather than natural phenomena.

Contribution

It introduces an expanded Bayesian inversion approach to assess uncertainties and biases in Hapke parameter retrievals, and identifies optimal geometric conditions for accurate photometric measurements.

Findings

Uncertainties in parameters follow the hockey stick relation due to parameter coupling.

Full BRDF data are less affected by retrieval artifacts.

Optimal geometric sampling conditions are identified for precise parameter estimation.

Abstract

Hapke proposed a convenient and widely used analytical model to describe the spectro-photometry of granular materials. Using a compilation of the published data, Hapke (2012, Icarus, 221, 1079-1083) recently studied the relationship of b and c for natural examples and proposed the hockey stick relation (excluding b>0.5 and c>0.5). For the moment, there is no theoretical explanation for this relationship. One goal of this article is to study a possible bias due to the retrieval method. We expand here an innovative Bayesian inversion method in order to study into detail the uncertainties of retrieved parameters. On Emission Phase Function (EPF) data, we demonstrate that the uncertainties of the retrieved parameters follow the same hockey stick relation, suggesting that this relation is due to the fact that b and c are coupled parameters in the Hapke model instead of a natural phenomena. Nevertheless, the data used in the Hapke (2012) compilation generally are full Bidirectional Reflectance Diffusion Function (BRDF) that are shown not to be subject to this artifact. Moreover, the Bayesian method is a good tool to test if the sampling geometry is sufficient to constrain the parameters (single scattering albedo, surface roughness, b, c, opposition effect). We performed sensitivity tests by mimicking various surface scattering properties and various single image-like/disk resolved image, EPF-like and BRDF-like geometric sampling conditions. The second goal of this article is to estimate the favorable geometric conditions for an accurate estimation of photometric parameters in order to provide new constraints for future observation campaigns and instrumentations.