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The expected frequency of runs of extreme days is modelled with a seasonal autoregressive representation using two site-specific scalar parameters-autocorrelation and an index of seasonality. Extreme days for a meteorological variable such as temperature, evaporation, sunshine and wind run are defined as days when the variable in question exceeds an arbitrary upper threshold or fails to exceed a lower threshold. The model estimates the frequency of runs as a function of duration (in days) and percentile or absolute threshold.The model is applied to several types of daily variable such as wind run, evaporation, sunshine and pressure, and tested extensively on datasets of daily maximum and minimum temperature for 60 to 70 sites in each of Australia and Europe. Using a priori parameter values of autocorrelation and seasonality, the model often provides fair agreement with the observed frequency of runs of extreme days. With the parameter values tuned to fit the observed frequency of runs, the agreement is typically fair to good. It is concluded that the model has the potential to estimate frequency (or return period) of unusually long runs with very low or high percentile thresholds.

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The frequency, intensity and duration of heatwaves at sites in mid-latitude Australia are modelled by a Markov process model and an autoregressive model with both producing typical relative errors of ten to fifteen per cent. The Markov model requires a location-specific empirical coefficient and this coefficient is shown to have a dependency on the summer-time autocorrelation and a seasonality index. Applying the autoregressive model to simple idealised climates, a very similar dependency is found which serves to demonstrate a connection between the two models. The use of detrended temperature, rather than actual temperature, has no material effect on the results.

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