Sardeshmukh, P. D., C. Penland, and M. Newman, 2003: Drifts induced by multiplicative red noise with application to climate. Europhys. Lett., 63, 498-504.
It is well known that moment equations for a multivariate linear system with multiplicative red noise are not closed: equations for low-order moments involve higher-order moments. Further, the probability density for this system is complicated enough that analytic expressions for the moments are difficult to obtain by direct integration. We introduce a closure approximation so that the vector mean of such systems may be estimated with high accuracy. The approximation is accurate for red noises with a wide range of timescales, and approaches the correct limits for both very small and very large correlation times. We include an application relevant to climate modeling and comment on the implications for numerical model investigations of global warming.