Rain is a form of atmospheric precipitations. On the other hand, precipitations are atmospheric condensations. The process of condensation is the exact opposite of atmospheric evaporations; if one exists the other must either be the cause or the effect. Repeated cycles of evaporations and condensations made the science of weather forecasting possible. Naturally, if one process does not exist the other cannot also exist. However, artificially, rainfall can be created without any evidence of prior process of evaporation as long as a pressure gradient combined with a temperature gradient exists between saturation pressure and vapor pressure.

The mathematics of these temperature-pressure gradients involves only simple formulas or equations from classical mechanics and thermodynamics. However, their joint probability distributions are very complex. The first can be at most linear functions while the second must be nonlinear. Unfortunately, nonlinearity always implies infinite solutions. Furthermore, the number of physical variables must be reduced to an absolute minimum simply by applying approximation and symmetry consideration. Nevertheless, the best possible approach is still the process of linearization by transforming products of functional variables to sums of disjointed functional variables.