Stochastic modelling provides a tool for exploring the full implications of the statistical behavior of historical records and can be used to predict the changing probabilities that events of various magnitudes will occur for different climatic change scenarios. Two simulation models are presented, one for daily air temperature, and the other for daily precipitation. The simulation procedures are: (1) extract salient parameter values from historical records; (2) simulate long sequences of data using the stochastic models, with or without a climate change scenario as provided by a general circulation model; and (3) using the simulated data as inputs, derive the probability distributions of other variables based on known deterministic or probabilistic relationships between the input and the predicted variables. Given a doubling of carbon dioxide concentration in the atmosphere, the climatic models produce varying degrees of temperature and precipitation changes. Examples of application, including the derivation of snowfall and river-ice data using simulated temperature and precipitation, illustrate that stochastic modelling offers a suitable approach to quantify the possible hydrologic impacts of climatic change.