The analysis is based on the application of a continuous hydrological model coupled with stochastic generation models of rainfall and temperature at hourly scale. Such a coupling permits to achieve long synthetic series of discharge through which, by extracting the maximum annual flow, the flood frequency of extreme events can be obtained. Then, by considering hypothetical future scenarios of temperature and rainfall predicted by the GCM-HadCM3 of Hadley Centre (http:// www.ipcc-data.org/sres/hadcm3_download.html), the previous stochastic series can be perturbed and a comparison on the flood frequency curves can be addressed.
In particular, for the stochastic rainfall and temperature generation, the NeymanScott Rectangular Pulses (NSRP, ) and the Fractionally Differenced ARIMA models were used (FARIMA, ), respectively. These synthetic time series were used as input data of a continuous rainfall-runoff model (named MISDc, ) that finally allowed determining of the synthetic discharge time series.
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 can be 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 , 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 et al. .
The FARIMA model, unlike classical 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 . The procedure for the implementation of the FARIMA model is not straightforward, particularly in the identification phase for the preliminary evaluation of model parameters. The method employed in this study is the one suggested by Montanari et al. .
Finally, MISDc is a continuous rainfall-runoff model developed for the simulation of flood events in the Upper Tiber River basin at sub-hourly time scale. The model consists of two components: the first is a soil water balance model that simulates the soil moisture temporal pattern and sets the initial conditions for the second component which is an event-based rainfall-runoff model for flood hydrograph simulation. The two models are coupled through a simple linear relationship that was derived from an intense monitoring activity of soil moisture and runoff over experimental catchments located in the region . The model incorporates a limited number of parameters and it is characterized by low computational efforts which make it very attractive for the hydrological practice. For that the MISDc model is an appropriate tool to be used for the generation of long discharge time series at hourly (or less) time scale (e.g. 1,000 or more years). For a detailed description of the model the reader is referred to Brocca et al. .
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