Discrepancy in Grain Size Estimation of H${}_{2}$O Ice in the Outer
  Solar System and the Interstellar Medium
  Widespread detection of amorphous and crystalline water (H${}_{2}$O) ice in
the outer solar system bodies and the interstellar medium has been confirmed
over the past decades. Radiative transfer models (RTMs) are used to estimate
the grain sizes of H${}_{2}$O ice from near-infrared (NIR) wavelengths. Wide
discrepancies in the estimation of H${}_{2}$O ice grain size on the Saturnian
moons (Hansen, 2009), as well as nitrogen (N${}_{2}$) and methane (CH${}_{4}$)
ices on Kuiper belt objects have been reported owing to different scattering
models used (Emran and Chevrier, 2022). We assess the discrepancy in the grain
size estimation of H${}_{2}$O ice at a temperature of 15, 40, 60, and 80 K
(amorphous) and 20, 40, 60, and 80 K (crystalline) - relevant to the outer
solar system and beyond. We compare the single scattering albedos of H${}_{2}$O
ice phases using the Mie theory (Mie, 1908) and Hapke approximation models
(Hapke, 1993) from the optical constant at NIR wavelengths (1 - 5 $\mu$m). This
study reveals that the Hapke approximation models - Hapke slab and internal
scattering model (ISM) - predict grain size of the crystalline phase, overall,
much better compared to the amorphous phase at temperatures of 15 - 80 K.
However, the Hapke slab model estimates much approximate grain sizes, in
general, to that of the Mie model's prediction while ISM exhibits a higher
uncertainty. We recommend using the Mie model for unknown spectra of outer
solar system bodies and beyond in estimating H${}_{2}$O ice grain sizes. While
choosing the approximation model for employing RTMs, we recommend using a Hapke
slab approximation model over the internal scattering model.
