Abstract: A method for simulating the statistical behavior of atmospheric, meteorological, or other geophysical time series having the following steps: (a) assembling an ensemble of observed data; (b) removing any evident cycles; (c) calculating the eigensystem and expansion coefficient according to the Loève theorem; (d) determining the distribution of said coefficients; (e) generating a larger set of coefficients based on the statistical distribution determined in step (d); and (f) using this larger distribution to create an ensemble of simulated atmospheric, meteorological, or other geophysical time series. The procedure can be used to develop a wide variety of climate statistics, including probabilities of severe events such as cold snaps or heat waves covering specific geographic regions and lasting for various periods of time. It can also be used to provide an evolving conditional estimate of the probabilities of extensive climate deviations persisting until the end of a month, season, or other period.