Ewald, B., C. Penland, and R. Temam, 2004: Accurate integration of stochastic climate models with application to El Niño. Mon. Wea. Rev., 132, 154-164.
Numerical models are one of the most important theoretical tools in atmospheric research, and the development of numerical techniques specifically designed to model the atmosphere has been an important discipline for many years. In recent years, stochastic numerical models have been introduced in order to investigate more fully Hasselmann's suggestion that the effect of rapidly varying "weather" noise on more slowly varying "climate" could be treated as stochastic forcing. In this article an accurate method of integrating stochastic climate models is introduced and compared with some other commonly used techniques. It is shown that particular care must be used when the size of rapid variations in the "weather" depends on the "climate." How the implementation of stochasticity in a numerical model can affect the detection of multiple dynamical regimes in model output is discussed.
To illustrate the usefulness of the numerical schemes, three stochastic models of El Niño having different assumptions about the random forcing are generated. Each of these models reproduced by construction the observed mean and covariance structure of tropical Indo-Pacific sea surface temperature. It is shown that the skew and kurtosis of an observed time series representing El Niño is well within the distributions of these statistics expected from finite sampling. The observed trend, however, is unlikely to be explained by sampling. As always, more investigation of this issue is required.