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The article discusses the validation of a rainfall model through the application of a multifractal analysis. In a study of the Iberian Peninsula, a multifractal analysis was done to validate the simulation of rainfall records. Four locations in Andalusia in Southern Spain were observed, where simulated hourly rainfall was carried out. The location was observed in 4-year and 20-year durations in order to determine the influence of the length of the data series. The results of the study indicated that algebraic tails are needed to fit the probability distribution for extreme events of rain. Also, dry event durations were seen to fit when real and synthetic data are taken into consideration. A count-based periodogram and the Fano factor methods were applied in a time clustering analysis.

This article discusses a multifractal analysis of rainfall periodicity on an hourly and daily basis in Andalusia in southern Spain. According to the authors, the rainfall process is controlled by self-organized criticality dynamics. In order to fit the probability distribution of the extreme rainfall events an algebraic tail is required. They found that results differ according to the time resolution and whether the rainfall is convective or frontal at each place. This steady state implies the existence of clusterization in the time-occurrence rainfall sequence.

Tropospheric ozone ( O 3 ) time series have been converted into complex networks through the recent so-called Visibility Graph (VG), using the data from air quality stations located in the western part of Andalusia (Spain). The aim is to apply this novel method to differentiate the behavior between rural and urban regions when it comes to the ozone dynamics. To do so, some centrality parameters of the resulting complex networks have been investigated: the degree, betweenness and shortest path. Some of them are expected to corroborate previous works in order to support the use of this technique; while others to supply new information. Results coincide when describing the difference that tropospheric ozone exhibits seasonally and geographically. It is seen that ozone behavior is fractal, in accordance to previous works. Also, it has been demonstrated that this methodology is able to characterize the divergence encountered between measurements in urban environments and countryside. In addition to that, the promising outcomes of this technique support the use of complex networks for the study of air pollutants dynamics. Particularly, new nuances are offered such as the identification and description of singularities in the signal. Image 1 [ABSTRACT FROM AUTHOR]

• The study climatic variables have multifractal nature. • Multifractal analysis is able to study three climatic variables acting in concert. • The most frequents cases have regular singularities. Previous works have analysed the relationship existing between reference evapotranspiration (ET 0) and other climatic variables under a one-at-a-time perturbation condition. However, due to the physical relationships between these climatic variables is advisable to study their joint influence on ET 0. The box-counting joint multifractal algorithm describes the relations between variables using relevant information extracted from the data singularities. This work investigated the use of this algorithm to describe the simultaneous behaviour of ET 0 , calculated by means of Penman–Monteith (PM) equation, and the two main climatic variables, relative humidity (RH) and air temperature (T), influencing on it in the middle zone of the Guadalquivir river valley, Andalusia, southern Spain. The studied cases were grouped according to the fractal dimension values, obtained from the global multifractal analysis, which were related to their probability of occurrence. The most likely cases were linked to smooth behaviour and weak dependence between variables, both circumstances were detected in the local multifractal analysis. For these cases, the rest of Penman Monteith (PM) equation variables, neither the T nor the RH , seemed to influence on ET 0 determination, especially when low T values were involved. By contrast, the least frequent cases were those with variables showing high fluctuations and strong relationship between them. In these situations, when T is low, the ET 0 is affected by the rest of PM equation variables. This fact confirmed T as main driver of ET 0 because the higher T values the lesser influence of other climate variables on ET 0. This condition could not be extended to RH because the variability in ET 0 singularities was not significantly influenced by low or high values of this variable. These results show that the joint multifractal analysis can be regarded as a suitable tool for describing the complex relationship between ET 0 , T and RH , providing additional information to that derived from descriptive statistics. Although, joint multifractal analysis shows some limitations when it is applied to large number of variables, the results reported are promising and suggest the convenience of exploring the relationships between ET 0 and other climatic variables not considered here with this framework such as wind speed and net radiation. [ABSTRACT FROM AUTHOR]