3. Model descriptions
Algorithms
Used algorithms are described in Iwabuchi (2006, J. Atmos. Sci.). The model uses Monte Carlo methods for simulating photon trajectories and samples fluxes, heating rates, radiances, and other radiometric quantities. The local estimation method is used for radiance averaged over some specific area or over specific solid angle. The maximum cross section method is used for acceleration of photon tracing in inhomogeneous media. Other methods useful for variance reduction are also used and documented in the scientific paper. The flowing figure is an algorithm flow chart.
Geometry
The position of photon is defined in the 3D Cartesian coordinate system. The direction of photon transport is defined by zenith angle (theta) and azimuth angle (phi) from the X-axis, as in the following figure.
The incident and emergent directions for pixel radiances can be specified by the user. The source zenith and azimuth angles are defined as theta0 and phi0, respectively. Similarly, emergent zenith and azimuth angles are defined as theta1 and phi1, respectively. The x-, y- and z-coordinate is defined in 0–xmax, 0–ymaxand zmin–zmax, respectively. The horizontal boundary condition is cyclic. The vertical boundaries z=zmin and zmax correspond to bottom and top, respectively, of the atmosphere (BOA and TOA, respectively).
Surface
The surface is modeled as one of four models
black (no reflection)
Lambertian model
Diffuse-specular mixture model: diffuse reflection is Lambertian, and specular reflection is Fresnellian for rough surface facets.
Rahman-Pinty-Verstraete BRDF model
Li-Sparse-Ross-Thick BRDF model
Surface model and its parameters can vary two-dimensionally.
Atmosphere
The model atmosphere is divided into cell volumes three-dimensionally. The number of layer is defined as nz.
The user can specify cloud layers ("3D layers") arbitrarily with horizontal inhomogeneity. Other layers are assumed to be horizontally homogeneous. The 3D layers are divided into cells in the vertical and horizontal directions. The numbers of 3D cells in x-, y-, and z-directions are defined as nx, ny, and nz3, respectively. Modeled atmospheric media include the followings:
Scattering media: For each one medium, extinction coefficient, single scattering albedo and a ID number of definition of phase function are arbitrarily specified. The user defines some kinds of phase function. Properties can be specified in 1D (for layers) and/or in 3D (for 3D cells):
three kinds of media specified for each 1D layer
several kinds of media specified for each 3D cell
Gaseous absorbing media: Modeled by correlated k-distribution. The absorption coefficients are specified for both 1D layers and 3D cells
Integrators
Various radiative quantities can be computed by the code:
Upward/downward/direct fluxes at layer interfaces (area-averaged fluxes)
Voxel-averaged 3-D heating rates
Pixel-averaged radiances at arbitrary layer interfaces
Camera images (angle-average radiances looking from arbitrary points)
Local fluxes at arbitrary points (pathlength-resolved)
Average pathlengths normalized by vertical layer depths (so-called air-mass factor)
The area-averaged flux detectors are specified at layer boundaries for upward, downward and direct fluxes. The flux is computed as pixel-averaged quantity.
The area-averaged radiances at layer boundaries are defined by the user with zenith and azimuth angles (therdcand phirdc, respectively). The numbers, nxrand nyr, of pixels along x- and y-axes are given by the user. That definition is independent of flux.
Methods and techniques
Various methods and techniques are used in the code, for better performance. Some of them are described in Iwabuchi (2006, J. Atmos. Sci.).
The maximum cross section technique applied to super-cells
The local estimation method
Variance reduction techniques
Collision-forcing method for optically-thin media
Truncation approximations for forward-peaked phase functions
Numerical diffusion
The Russian roulette method
Parallelization using MPI
The method of truncation of forward peak of phase function is incorporated. The truncation fraction adaptively increases with the order of scattering. The user specifies the number of truncation regimes (nchi), light-diffusivity thresholds (chihi & chilo), and maximum truncation factor (fmax).
