In this work, the multifractal properties of hourly rainfall data recorded at a location in Southern Spain have been related to the scale properties of the corresponding intensity–duration–frequency (IDF) curves. Four parametric models for the IDF curves have been fitted to the quantiles of rainfall obtained using the generalized Pareto frequency distribution function with the extreme data series obtained for the same place. The scaling of the rainfall intensity moments has been analysed, and the empirical moments scaling exponent function has been obtained. The corresponding values of q1 and γ1 have been empirical and theoretically calculated and compared with some characteristics of the different IDF models. Thus, the scaling behaviour of IDF curves has been analysed, and the best model has been selected. Copyright © 2012 John Wiley & Sons, Ltd.

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Abstract:A multifractal analysis of hourly and daily rainfall data recorded at four locations of Andalusia (southern Spain) was carried out in order to study the temporal structure of rainfall and to find differences between both time resolutions. The results show that an algebraic tail is required to fit the probability distribution of the extreme rain events for all the cases. The presence of a multifractal phase transition associated with a critical moment in the empirical moments scaling exponent function was also detected. Both facts indicate that the rainfall process is a case of self-organized criticality (SOC) dynamics, although the results differ for each place according to the time resolution and the nature of the rainfall, either convective or frontal. This SOC behaviour is related to a statistically steady state that implies the presence of clusterization in the time-occurrence sequence of rain events. Such fluctuations have been shown by performing the analysis of the Fano and Allan factors and the count-based periodogram. The values for the "synoptic maximum", the typical lifetime of planetary scale atmospheric structures, have been obtained for each place and some important periodicities have been detected when dealing with extremes.

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The flood and drought cycles suffered of old by the province of Malaga, the variability in the distribution of rainfall throughout the province and the reduced length of the data series make it of interest to carry out a regional analysis (RA) of the yearly maximum daily precipitation data to obtain appropriate rainfall quantiles. By taking these maximum precipitations values from 72 weather stations, and their physiographic parameters latitude and altitude, four regions with similar rainfall patterns have been determined by the principal component analysis statistical technique. Then, carrying out an RA of the yearly maximum daily precipitations for each of the regions discriminated, it was observed that three of them were homogeneous for the parameter being studied. In those homogeneous regions that grouped data of different stations but close rainfall pattern, frequency curves could be calculated for several return periods by means of the functions that best fit the data of each region. With these regional curves, it has been possible to obtain more accurate values of the maximum daily quantiles for each of the stations analysed than through the conventional local frequency analysis.

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Accurate forecast of hydrological data such as precipitation is critical in order to provide useful information for water resources management, playing a key role in different sectors. Traditional forecasting methods present many limitations due to the high-stochastic property of precipitation and its strong variability in time and space: not identifying non-linear dynamics or not solving the instability of local weather situations. In this work, several alternative models based on the combination of wavelet analysis (multiscalar decomposition) with artificial neural networks have been developed and evaluated at sixteen locations in Southern Spain (semiarid region of Andalusia), representative of different climatic and geographical conditions. Based on the capability of wavelets to describe non-linear signals, ten wavelet neural network models (WNN) have been applied to predict monthly precipitation by using short-term thermo-pluviometric time series. Overall, the forecasting results show differences between the ten models, although an effective performance (i.e., correlation coefficients ranged from 0.76 to 0.90 and Root Mean Square Error values ranged from 6.79 to 29.82 mm) was obtained at each of the locations assessed. The most appropriate input variables to obtain the best forecasts are analyzed, according to the geo-climatic characteristics of the sixteen sites studied.