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A new algorithm for modeling radiative transfer in inhomogeneous three-dimensional media is described. The spherical harmonics discrete ordinate method uses a spherical harmonic angular representation to reduce memory use and time computing the source function. The radiative transfer equation is integrated along discrete ordinates through a spatial grid to model the streaming of radiation. An adaptive grid approach, which places additional points where they are most needed to improve accuracy, is implemented. The solution method is a type of successive order of scattering approach or Picard iteration. The model computes accurate radiances or fluxes in either the shortwave or longwave regions, even for highly peaked phase functions. Broadband radiative transfer is computed efficiently with a k distribution. The results of validation tests and examples illustrating the efficiency and accuracy of the algorithm are shown for simple geometries and realistic simulated clouds.

We investigated scaling of the atmospheric neutron soft error rate (SER) which affects reliability of CMOS circuits at ground level and airplane flight altitudes. We considered CMOS circuits manufactured in a bulk process with a lightly-doped p-type wafer. One method, based on the empirical model, predicts a linear decrease of SER per bit with decreasing feature size [L.sub.G]. A different method, based on the MBGR model, predicts even faster decrease of SER per bit than linear. If the increasing number of bits is taken into account, then the SER per chip is not expected to increase faster than linearly with decreasing [L.sub.G]. Index Terms--Circuit reliability, scaling, single event upset, soft error rate, technology characterization.