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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:{{cite journal | author= P. Helfenstein| display-authors= etal| title= Galileo Photometry of Asteroid 243 Ida| journal= Icarus| year= 1996| volume= 120 | issue= 1| pages= 48–65| bibcode= 1996Icar..120...48H| doi= 10.1006/icar.1996.0036| doi-access= free}}

  1. \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, K_s/(K_s+K_a), where K_s is the scattering coefficient, and K_a is the absorption coefficient[http://scienceworld.wolfram.com/physics/SingleScatteringAlbedo.html Single Scattering Albedo], scienceworld.wolfram.com.
  2. h — The width of the opposition surge.
  3. B_0 or S_0 — The strength of the opposition surge.
  4. P_0 or g — The particle phase function parameter, also called the asymmetry factor.
  5. \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. {{Cite journal |last1=Shkuratov |first1=Y. |last2=Kaydash |first2=V. |last3=Korokhin |first3=V. |last4=Velikodsky |first4=Y. |last5=Petrov |first5=D. |last6=Zubko |first6=E. |last7=Stankevich |first7=D. |last8=Videen |first8=G. |date=2012-12-01 |title=A critical assessment of the Hapke photometric model |url=https://www.sciencedirect.com/science/article/pii/S0022407312001926 |journal=Journal of Quantitative Spectroscopy and Radiative Transfer |series=Electromagnetic and Light Scattering by non-spherical particles XIII |volume=113 |issue=18 |pages=2431–2456 |doi=10.1016/j.jqsrt.2012.04.010 |bibcode=2012JQSRT.113.2431S |issn=0022-4073}}{{Cite journal |last=Hapke |first=Bruce |date=2013-02-01 |title=Comment on "A critical assessment of the Hapke photometric model" by Y. Shkuratov et al. |url=https://www.sciencedirect.com/science/article/pii/S0022407312004888 |journal=Journal of Quantitative Spectroscopy and Radiative Transfer |volume=116 |pages=184–190 |doi=10.1016/j.jqsrt.2012.11.002 |bibcode=2013JQSRT.116..184H |issn=0022-4073}} In particular, the model has been shown to often require unphysical parameters (e.g., the asymmetry factor) when modeling the albedo of ices. {{Cite journal |last=Mishchenko |first=Michael I. |date=1994-07-01 |title=Asymmetry parameters of the phase function for densely packed scattering grains |url=https://dx.doi.org/10.1016/0022-4073%2894%2990142-2 |journal=Journal of Quantitative Spectroscopy and Radiative Transfer |volume=52 |issue=1 |pages=95–110 |doi=10.1016/0022-4073(94)90142-2 |bibcode=1994JQSRT..52...95M |issn=0022-4073}}{{Cite journal |last1=Mishchenko |first1=M. I. |last2=Macke |first2=A. |date=1997-06-01 |title=Asymmetry parameters of the phase function for isolated and densely packed spherical particles with multiple internal inclusions in the geometric optics limit |url=https://www.sciencedirect.com/science/article/pii/S0022407397000125 |journal=Journal of Quantitative Spectroscopy and Radiative Transfer |volume=57 |issue=6 |pages=767–794 |doi=10.1016/S0022-4073(97)00012-5 |bibcode=1997JQSRT..57..767M |issn=0022-4073}}{{Cite journal |last1=Warren |first1=Stephen G. |last2=Brandt |first2=Richard E. |last3=O'Rawe Hinton |first3=Patricia |date=1998 |title=Effect of surface roughness on bidirectional reflectance of Antarctic snow |url=https://onlinelibrary.wiley.com/doi/abs/10.1029/98JE01898 |journal=Journal of Geophysical Research: Planets |language=en |volume=103 |issue=E11 |pages=25789–25807 |doi=10.1029/98JE01898 |bibcode=1998JGR...10325789W |issn=2156-2202}}{{Cite journal |last1=Khuller |first1=Aditya R. |last2=Emran |first2=Al |date=2025-05-31 |title=Quantitative evaluation of the delta-Eddington, Hapke, and Shkuratov models for predicting the albedo and inferring the grain radius of ice |url=https://www.sciencedirect.com/science/article/pii/S0019103525002180 |journal=Icarus |pages=116671 |doi=10.1016/j.icarus.2025.116671 |issn=0019-1035}}

See also

References

Category:Radiometry

Category:Scattering, absorption and radiative transfer (optics)

Category:Equations of astronomy

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