Hapke parameters

The Hapke parameters are a set of parameters for an empirical model that is commonly used to describe the directional reflectance properties of the airless regolith surfaces of bodies in the Solar System. The model has been developed by astronomer Bruce Hapke at the University of Pittsburgh.

The main parameters are:^[1]

1. ${\displaystyle {\bar {\omega }}_{0}}$ — Single scattering albedo. This is the ratio of scattering efficiency to total light extinction (which includes also absorption), for small-particle scattering of light. That is, ${\displaystyle K_{s}/(K_{s}+K_{a})}$, where ${\displaystyle K_{s}}$ is the scattering coefficient, and ${\displaystyle K_{a}}$ is the absorption coefficient^[2]
2. ${\displaystyle h}$ — The width of the opposition surge.
3. ${\displaystyle B_{0}}$ or ${\displaystyle S_{0}}$ — The strength of the opposition surge.
4. ${\displaystyle P_{0}}$ or g — The particle phase function parameter, also called the asymmetry factor.
5. ${\displaystyle \theta }$ — The effective surface tilt, also called the macroscopic roughness angle.

The Hapke parameters can be used to derive other albedo and scattering properties, such as the geometric albedo, the phase integral, and the Bond albedo.

Limitations of the Hapke Model

The Hapke model has been criticized for having a large number of unconstrained parameters that can make the parameters difficult to constrain. ^[3][4] In particular, the model has been shown to often require unphysical parameters (e.g., the asymmetry factor) when modeling the albedo of ices. ^[5][6][7][8]

See also

• Albedo
• Geometric albedo
• Bidirectional reflectance distribution function