Return Period Analysis of Minimum Events Using Sliding Polynomials

ABSTRACT A form-free method has been developed for determination of return periods of minimum values of stochastic events. Such minima represent expectancies of limited availability of natural resources. As such, analyses of minima provide information to assist planners and managers of agricultural production systems. The method for return-period analysis of minimum events is similar to a method recently presented for analysis of maximum events. Both use form-free sliding polynomials as smoothing operators, thus reducing the bias produced by assuming some particular probability function as a smoothing operator. Investigations of minimum rainfall, streamflow and temperatures show a number of unique features in the sample data revealed by flexibility in shaping the smoothing curves while maintaining faithful adherence to the sample data. Simulations were used to compute an expected range of future events associated with any level of risk chosen by the planner or manager. Long-period and short-period possible future minima for different return periods were simulated. These simulations show that the uncertainties faced by planners and managers are highly conditioned by unique features of particular data sets and by the length of the return period over which costs and benefits might be averaged.