Stochastic seasonality of rainfall in New Zealand

Seasonality is an important source of variation in many processes and needs to be incorporated into rainfall models. The stochastic seasonal rainfall models for high temporal resolution data [ Sansom and Thomson , 2010] and daily data (T. Carey‐Smith et al., A hidden seasonal switching model for multisite daily rainfall, manuscript in preparation 2012) both depend on the specification of one day of the year for each season being in the particular season. So, if the seasonality is to be represented by four seasons then it is necessary to provide four dates on each of which it can be said that, every year, the season is of the first, second, third or fourth type respectively on that day of the year. The model fitting can only proceed once these dates, the mid‐seasons, have been provided. In a region of large seasonal rainfall variation the determination of these mid‐seasons would not be difficult and the model fitting not sensitive to their choice. However, although it is clearly evident in the annual pattern of monthly accumulations, New Zealand's rainfall seasonality is not strong and careful assessment of the mid‐season dates is necessary. They need to be estimated with a precision of days and the 55‐year long rainfall records of daily data from 141 stations spread across New Zealand were analysed on a regional basis. The analysis found regionally coherent dates when the mean daily rain rate changed significantly and that over the years these dates could be modelled as a four component von Mises distribution with characteristics consistent with stochastic seasonality.