Radiative Transfer Benchmark

radiative-transfer-benchmark

Generic Models for Disk-Resolved and Disk-Integrated Phase Dependent Linear Polarization of Light Reflected from Exoplanets — Chakrabarty et al. (2021) (arXiv:2106.09434, 2021)

What this evaluates

Evaluates the accuracy of a numerical vector radiative transfer code by comparing its outputs for scattering phase functions, polarization, and albedo against established reference results from prior literature.

Datasets

• Reference Benchmarks (Stam et al. 2006; Madhusudhan & Burrows 2012) — total ?; splits: reference (-1)

Metrics

• scalar phase function — range: [0, 1]
  • Ratio of scattered intensity to incident intensity as a function of scattering angle, derived from the P11 Stokes matrix element.
• polarization — range: [0, 1]
  • Degree of linear polarization for single scattering, calculated as the ratio P12/P11 from the Stokes parameters.
• disk-integrated total degree of polarization (primary) — range: [0, 1]
  • Total polarization integrated over the visible planetary disk as a function of orbital phase, computed for semi-infinite atmospheres obeying the principle of invariance.
• albedo — range: [0, 1]
  • Ratio of reflected flux at a given phase angle to the incident flux, F(α)/F0.

Input / output format

Input: Atmospheric and scattering parameters: single scattering albedo (ω), depolarization factor, refractive index, particle size distribution (e.g., log-normal), scattering angle, and orbital phase.

Output: Numerical arrays or curves representing phase function, polarization degree, and albedo across varying scattering angles or phases.

Scoring recipe

def evaluate_benchmark(model_outputs, reference_outputs):
    # model_outputs: dict of arrays for scalar phase function, polarization, albedo, disk-integrated polarization
    # reference_outputs: dict of arrays from Stam et al. (2006) or Madhusudhan & Burrows (2012)
    errors = {}
    for metric in ['scalar phase function', 'polarization', 'albedo', 'disk-integrated total degree of polarization']:
        errors[metric] = np.max(np.abs(model_outputs[metric] - reference_outputs[metric]))
    # Agreement is confirmed if errors are within numerical tolerance and curves visually overlap
    return errors

Common pitfalls

• Using the wrong particle size distribution (reference papers used different distributions than the assumed log-normal).
• Failing to set single scattering albedo to exactly 1.0 for conservative scattering benchmarks.
• Confusing disk-resolved azimuth-dependent polarization with disk-integrated total polarization.

Evidence (verbatim from paper)

First, we compare the scalar phase function and the polarization for a single scattering with those calculated by Stam et al. (2006) for both Rayleigh scattering and Mie scattering at 0.55 μm wavelength. In the case of Rayleigh scattering, we adopted a depolarization factor of 0.02 as assumed by Stam et al. (2006). In the case of Mie scattering, we considered the cloud particles of refractive index equal to 1.33 (imaginary part is 0) with a size distribution having the mean at 2.2 μm as assumed by Stam et al. (2006); de Rooij & van der Stap (1984). However, we assume a log-normal size distribution of the particles which is different from what Stam et al. (2006); de Rooij & van der Stap (1984) assumed. Figure 3 and Figure 4 demonstrate the comparisons with the results presented by Stam et al. (2006) regarding the variations in phase function and polarization with the varying scattering angle. Clearly, the figures show that our calculations are in close agreement with that obtained by Stam et al. (2006).

Citation

@misc{chakrabarty2021generic,
  title={Generic Models for Disk-Resolved and Disk-Integrated Phase Dependent Linear Polarization of Light Reflected from Exoplanets},
  author={Chakrabarty et al. (2021)},
  year={2021},
  note={arXiv:2106.09434}
}

• arXiv: 2106.09434