Intermittency, autoregression and censoring: a first-order AR model for daily precipitation

Abstract

Daily precipitation is investigated in this study in terms of simple first order autoregressive models. The methodology is based on combining theory from censored processes with continuous autoregressive models to model intermittent phenomena. The choice of short-memory autoregressive models is corroborated further by recent findings on scaling properties of daily precipitation records. The theory and application to synthetic models are presented. The methodology is then applied to Northern Ireland Armagh Observatory daily precipitation for the period 1950–2001 for each month. Both zero- and non zero-mean processes are considered. The analysis indicates that the model parameters do capture seasonality where, for example, the autocorrelation co-efficient is larger in winter, compared to in the summer. This is arguably a reflection of the stronger effect of large-scale processes on rainfall in winter compared to summer. Interestingly, the parameters of the zero- and non zero-mean processes are found to be quite similar, reflecting the symmetric nature of the truncated processes in the midlatitude and extratropics. It is suggested, in particular, that the process mean can be used as a measure to quantify dryness or wetness of a given region. Ways of model improvement, including power transformation, based on the square root, to represent extremes using exploratory quantile–quantile plots better are also discussed. Copyright © 2012 Royal Meteorological Society