There are two main approaches to developing practical algorithms that can extract useful and reliable data about trace gas concentrations from the complex combination of factors that are involved in remote sensing measurements from space.

Monte Carlo Models

These simulate physical processes on individual photons using probability functions. The analysis of a large group of photons yields a probability distribution of photon paths.

• Advantages: transparent implementation, true 3-dimensionality, and straight-forward implementation of additional processes.
• Disadvantage: very slow.

Numerical Solutions of the Radiative Transfer Equation

These simplify the Radiative Transfer Equation by using approximations such as a plane parallel atmosphere or only single scattering. The solution uses standard methods for integral-differential equations.

• Advantages: fast and often also provides weighting functions.
• Disadvantages: requires complex code, and is necessarily based on approximations.