Bxz

where R is another random number between 0 and 1, and the azimuthal rotation of the new direction around the old direction is governed by a further random angle between 0° and 360°. The new optical thickness for the next photon path is then calculated and the process iterated until either the photon is absorbed or it leaves the atmosphere.

For cases where scattered sunlight dominates, the most efficient way of proceeding is to fire a sequence of photons at the planet from the direction of the Sun and track the proportion that are reflected by the atmosphere in different angles. For cases where thermal emission dominates, the most efficient way of proceeding is to fire a sequence of photons at the planet from the observer's position, calculate where in the atmosphere they are absorbed, and then average the Planck functions from these absorption regions. Monte Carlo thermal emission calculations converge much faster than reflected sunlight calculations.

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