Penland, C., and L. Matrosova, 1994: A balance condition for stochastic numerical models with application to the El Niño - Southern Oscillation. J. Climate, 7, 1352-1372.
Stochastic forcing due to unresolved processes adds energy to a measurable system. Although this energy is added randomly in time, conservation laws still apply. A balance condition for stochastically driven systems is discussed. This "fluctuation-dissipation relation" may be used either to deduce the geographical properties of the stochastic forcing from data given a model for the evolution of the macroscopic variables or to diagnose energy conservation in a stochastic numerical model.
The balance condition in its first role was applied to sea surface temperatures (SSTs) in the Indo-Pacific basin. A low-dimensional empirical dynamical model of SSTs was generated in such a way that observed statistical properties of the field are preserved. Experiments varying the stochastic forcing in this model indicated how the geographical characteristics of the forcing affect the distribution of variance among the various normal modes thereby determining the dominant timescales of the SST field. These results suggest that the south Indian Ocean and the equatorial Pacific close to the date line are important to the amplitude and timing of the warm phase of El Niño-Southern Oscillation.
Fourier spectra obtained from output of the stochastically forced linear model were found to agree with those obtained from COADS data when time series of equal length were compared. A discussion of how spectra from a multivariate linear system can be confused with those of a nonlinear system is presented.