Discovered in the page of Angelo Vulpiani, a preminent Italian physicist, I believe this paper on noise by L. Cohen is an amusing paper that can redirect to more technical readings.
Noise, Brownian motions (a nice paper by Cecconi et al.), stochastic equations were never touched in my blog before, but they have indeed an important role Hydrology, and one of the warhorses of my friend and master Ignacio Rodriguez-Iturbe (see Random Functions and Hydrology). As Amilcare Porporato said, part of the recent Ecohydrological way is based upon the writing of Master equations, and solving them, under the appropriate assumptions about noise.
The paper indeed treats noise as the product of atoms and molecules, or, from a deeper perspective, as produced by quantum effects.
Noise in hydrology has problably a different origin, in chaos from one side and on heterogeneity from the other (well heterogeneity is, in a sense, randomness, so the phrase is quite tautological).