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A constrained stochastic weather generator (CSWG) for producing daily mean air temperature and precipitation based on annual mean air temperature and precipitation from tree-ring records is developed and tested in this paper. The principle for stochastically generating daily mean air temperature assumes that temperatures in any year can be approximated by a sinusoidal wave function plus a perturbation from the baseline. The CSWG for stochastically producing daily precipitation is based on three additional assumptions: (1) In each month, the total precipitation can be estimated from annual precipitation if there exists a relationship between the annual and monthly precipitations. If that relationship exists, then (2) for each month, the number of dry days and the maximum daily precipitation can be estimated from the total precipitation in that month. Finally, (3) in each month, there exists a probability distribution of daily precipitation amount for each wet day. These assumptions allow the development of a weather generator that constrains statistically relevant daily temperature and precipitation predictions based on a specified annual value, and thus this study presents a unique method that can be used to explore historic (e.g., archeological questions) or future (e.g., climate change) daily weather conditions based upon specified annual values.