I3RC phase 1 results from the MYSTIC Monte Carlo model

This article provides a complete description of the radiative transfer model used in the I3RC (Intercomparison of 3D Radiation Codes) campaign. The MYSTIC model is a forward photon tracing method which solves the equation of radiative transfer for the specified conditions without any simplifying assumptions, simulating the involved physics as closely as possible. The methodology used to calculate the requested parameters is described in detail, and some sample results are presented. 1. Model description The Monte Carlo model used for this study (MYSTIC1) is a forward photon tracing method, similar to those described by Cahalan et al. [1994] and O’Hirok and Gautier [1998]. In addition to three-dimensional atmospheres, it allows the realistic treatment of inhomogeneous surface albedo and topography, see e.g. Kylling et al. [1999]. The model atmosphere consists of a 1D background of molecules and aerosol 1MYSTIC: Monte carlo code for the phYSically correct Tracing of photons In Cloudy atmospheres. 0 1 2 3 4 5 6 7 8 9 10 47.5 50.0 z[km] Figure 1. A simple example of the atmosphere used as input to the MYSTIC model (2D cross section of a 3D geometry). Rayleigh and aerosol scattering as well as molecular absorption are described by the 1D background atmosphere. Embedded are three layers of clouds, over some mountainous terrain. particles and a 3D grid of cloud cells. See Figure 1 for a simple example. A schematic diagram of the algorithm is shown in Figure 2. The involved physics is simulated as closely as possible on the basis of the input atmosphere, without any further simplifying assumptions. All processes involving random numbers are marked with a double-frame. The r250 algorithm of Kirkpatrick and Stoll [1981] was chosen as random number generator. Photons start at the top of the atmosphere (TOA) and travel from one scattering event to the next where the length of each path segment is determined by the scattering coefficient, , and the direction ( , ) by the phase function . At the start and after each scattering event, the photon is assigned an optical depth which it travels before the next scattering. The probability that a photon is traveling the optical depth without being scattered is given by Lambert-Beer’s law, ! " . Using the cumulative probility function, #$ % '&)( * ,+!./ ,+0 1 2 3 ! 4 , the length of an individual path segment is calculated according to 5 2 6 %7984: (1) where : is a random number between 0 and 1. This path segment is then translated from optical depth space to physical space, by integrating the scattering coeffcient along the photon path through as many grid boxes until is reached. Here, periodic boundaries were applied; that is, photons leaving the model domain at one side, re-entered it at the opposite side. At the end of each step – if the photon has not reached the Earth’s surface or left at TOA – a new direction is determined according to the scattering properties at the new location. Scattering by molecules, aerosol particles, and cloud droplets is treated separately, assuming the Rayleigh phase function for molecular scattering, the Henyey-Greenstein (HG) phase function for aerosol scattering, and a HG or arbitrary phase function for cloud scattering. For the Rayleigh and HG phase functions, ? @ ACB D and EGF4 , the new direction is calculated analytically by evaluating the cumu-