Hydrodynamic noise with correlation lengths and times

The theory of hydrodynamic noise of Landau and Lifshitz is extended by the consideration of correlation times and lengths. We restrict our study to the domain of thermodynamic equilibrium. When the intensity of the fluctuations of a phenomenological model is characterized by a phenomenological constant, the same procedure can be applied to nonequilibrium turbulent systems. Applications to one-dimensional climatic models and the fluctuation-dissipation theorem in the atmosphere are discussed.