Volume 573, January 2015
|Number of page(s)||20|
|Section||Numerical methods and codes|
|Published online||22 December 2014|
Pre-conditioned backward Monte Carlo solutions to radiative transport in planetary atmospheres
Fundamentals: Sampling of propagation directions in polarising media⋆
ESA Fellow, ESA/RSSD, ESTEC, 2201 AZ
2 Research School of Physics and Engineering and Fenner School of Environment and Society, Australian National University, ACT 0200 Canberra, Australia
3 Space Science Institute, Boulder, CO 80301, USA
Received: 21 April 2014
Accepted: 15 August 2014
Context. The interpretation of polarised radiation emerging from a planetary atmosphere must rely on solutions to the vector radiative transport equation (VRTE). Monte Carlo integration of the VRTE is a valuable approach for its flexible treatment of complex viewing and/or illumination geometries, and it can intuitively incorporate elaborate physics.
Aims. We present a novel pre-conditioned backward Monte Carlo (PBMC) algorithm for solving the VRTE and apply it to planetary atmospheres irradiated from above. As classical BMC methods, our PBMC algorithm builds the solution by simulating the photon trajectories from the detector towards the radiation source, i.e. in the reverse order of the actual photon displacements.
Methods. We show that the neglect of polarisation in the sampling of photon propagation directions in classical BMC algorithms leads to unstable and biased solutions for conservative, optically-thick, strongly polarising media such as Rayleigh atmospheres. The numerical difficulty is avoided by pre-conditioning the scattering matrix with information from the scattering matrices of prior (in the BMC integration order) photon collisions. Pre-conditioning introduces a sense of history in the photon polarisation states through the simulated trajectories.
Results. The PBMC algorithm is robust, and its accuracy is extensively demonstrated via comparisons with examples drawn from the literature for scattering in diverse media. Since the convergence rate for MC integration is independent of the integral’s dimension, the scheme is a valuable option for estimating the disk-integrated signal of stellar radiation reflected from planets. Such a tool is relevant in the prospective investigation of exoplanetary phase curves. We lay out two frameworks for disk integration and, as an application, explore the impact of atmospheric stratification on planetary phase curves for large star-planet-observer phase angles. By construction, backward integration provides a better control than forward integration over the planet region contributing to the solution, and this presents a clear advantage when estimating the disk-integrated signal at moderate and large phase angles.
Key words: polarization / radiative transfer
A one-slab, plane-parallel version of the PBMC algorithm is available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (184.108.40.206) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/573/A72
© ESO, 2014
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