Three-dimensional radiative transfer problems

Selected Applications

• Radiation during a solar eclipse: A solar eclipse is not only a spectacular phenomenon but also one of the most three-dimensional radiative transfer problems one can imagine: Photons reaching the shadow under a total eclipse get there exclusively by horizontal photon transport. Under cloudless conditions, a solar eclipse is therefore an ideal experimental test for a three-dimensional radiative transfer code. [Emde and Mayer, 2007] implemented backward photon tracing and spherical geometry in the MYSTIC model to allow the first exact simulation of radiation during a solar eclipse. The agreement with observations is nearly perfect [Kazantzidis et al., 2007]
  
  
• Remote sensing of inhomogeneous clouds: Clouds are inherently inhomogeneous at all spatial scales. Cloud remote sensing relies on two basic assuptions: 1, that clouds are homogeneous over the field-of-view of the satellite (the "plane-parallel assumption"); and 2, that horizontal photon transport can be neglected, or equivalently, that individual satellite pixels can be treated independently of each other (the "independent pixel approximation"). Both assumtions introduce bias and random noise into the retrieved cloud properties. See a nice example of radiance reflected by an inhomogeneous (cubic) clouds field, compared to the independent pixel assumption. In a systematic study we quantified this uncertainty for different sensors [Zinner et al., 2006], [Zinner and Mayer, 2006].
  
  
• Photon pathlength in clouds: This is a straightforward application because the photon pathlength distribution is a natural by-product of a Monte Carlo model. The average pathlength can also be calculated using any radiative transfer model. Examples and comparisons between both approaches are shown by [Mayer et al., 1998]. This work was the birth of MYSTIC!.
  
  
• Effects of inhomogeneous surface albedo and topography: Many measurement sites are located at places which are far from the ideal (flat and homogeneous) area which is assumed by a one-dimensional model. A typical example is the site of Tromsoe: in winter, the land is covered with snow while the sea is typically snow free. Due to the complicated coast line and the surrounding mountains, the interpretation of the measurements at Tromsoe requires the application of a three-dimensional model capable of handling inhomogeneous surface albedo and topography, see [Kylling et al., 1999]. For some new applications have a look at the simulations for Schneefernerhaus, the Metcrax experiment, or for Weissfluhjoch next to Davos. These calcultions are based on a high-resolution topography and illustrate the new backward photon tracing capabilities of MYSTIC.
  
  
• Radiative transfer in inhomogeneous clouds: There are basically two different approaches to the investigation of inhomogeneous clouds. One is the study of realistic situations, using as many measured properties of clouds as possible (high-resolution satellite measurements, combined with sky photographs, etc.). A different approach are statistical investigations, using well-established properties of clouds, like their fractal dimension, size distribution, etc. An example is shown here. More realistic examples are shown on the MYSTIC page.