Efficient unbiased variance reduction techniques for Monte Carlo simulations of radiative transfer in cloudy atmospheres: The solution

摘要

Wepresent five new variance reduction techniques applicable toMonte Carlo simulations of radiative transfer in the atmosphere: detector directional importance sampling,udn-tuple local estimate, prediction-based splitting and Russian roulette, and circumsolar virtual importance sampling. With this set of methods it is possible to simulateudremote sensing instruments accurately and quickly. In contrast to all other known techniques used to accelerate Monte Carlo simulations in cloudy atmospheres – exceptudfor two methods limited to narrow angle lidars – the presented methods do not make any approximations, and hence do not bias the result. Nevertheless, these methods converge as quickly as any of the biasing acceleration techniques, and the probability distribution ofudthe simulation results is almost perfectly normal. The presented variance reduction techniques have been implemented into the Monte Carlo code MYSTIC (‘‘Monte Carloudcode for the physically correct tracing of photons in cloudy atmospheres’’) in order toudvalidate the techniques.