The NSRP model is characterized by a flexible structure in which the model parameters broadly relate to underlying physical features observed in rainfall fields. The model has a total of five parameters, estimated through six sampling statistics computed from the observed data (for each month taking the rainfall seasonality into account): hourly mean, hourly and 24 h variances, lag-one autocorrelation of the daily data, and hourly and 24 h skewness. The estimation procedure of such model parameters was carried out by minimizing an objective function evaluated as a weighted sum of normalised residuals between the statistical properties of the observed time series and their theoretical expression derived from the model.
As shown by previous studies (Camici et al., 2011), the main feature of the model is its ability to preserve statistical properties of a rainfall time series over a range of time
scales. Full details of the NSRP may be found in Cowpertwait (1991). The FARIMA model, unlike classical A. Pierleoni et al. / Procedia Engineering 70 ( 2014 ) 1324 – 1333 1327 ARIMA models that are powerful tool for modelling stationary time series, is able to fit the autocorrelation function which is characterized by a slow decay suggesting the presence of long-term persistence. This dependence was detected in many time series of hydrological data and, very often, in the air temperature series (Moretti and Montanari, 2008). The procedure for the implementation of the FARIMA model is not straightforward and it firstly require to remove the seasonal component as the model is only able to simulate deseasonalized time series. Then, the model parameters are identified following the procedure suggested by Montanari et al. (1997).