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Daily maximum, TX, and minimum, TN, temperatures recorded at Fabra Observatory, for the period 1914–2020 (from June to September), have permitted to identify the daytime and night time heatwaves, HWs, at the Barcelona Metropolitan Region, BMR, along 107 years. Four heatwaves indices have been computed both for maximum and minimum tempera- tures: the number of events per season, HWN; their maximum duration, HWD; their frequency of occurrence, HWF; and the amplitude of the hottest day event, HWA. Trends in these indices have been obtained and their statistical significance quantified by means of the Mann-Kendall test. For the whole period (1914–2020), positive significant trends have been detected for the four indices, with a marked positive trend since year 2000 for TX, and since 1985 for TN. Nevertheless, when 31-year moving windows have been analysed, both positive and negative significant trends are obtained, being remarkable the change in trend signs around 1960s. The convenience of using the four HW indices is evaluated applying a Principal Component Analysis, PCA, obtaining two principal components. Additionally, the spatial distributions of the MODIS land surface temperatures, LST, corresponding to some extreme heatwaves, permits the detection of two hotspots in the BMR, one for TX and the other for TN. It is also worth mentioning that correlations between the Western Mediter- ranean Oscillation index, WeMOi, and HW episodes are detected, being notable that, at the beginning of these episodes, WEMOi values are usually lower. These correlations could improve the HWs forecasting., Rainfall data have been supplied by Servei Mete- orològic de Catalunya (Generalitat de Catalunya), Fabra Observa- tory (RACA, Barcelona), Agencia Estatal de Meteorología (AEMET, Spanish Government), MODIS satellite data (NASA), and Wester Mediterranean Oscillation indices (WeMO) supplied by the Climatol- ogy Group of UB (2017SGR1362). This research was supported by the Spanish Ministry of Science, Innovation and Universities: grant number PID2019-105976RB-I00]. The authors also thank the editor and the anonymous reviewers for their valuable comments and sugges- tions to improve the manuscript., Postprint (published version)

The rainfall regime in Catalonia, NE Spain, has a typical Mediterranean behaviour with irregular monthly amounts, sometimes the result of copious and intense torrential episodes for a few months, while for others precipitation is scarce. In addition, the varied topography of this region is related to significant rainfall differences between its different areas. The monthly precipitation from 97 stations spread throughout the territory, from 1950 to 2016, has allowed a detailed study of the spatial distribution of rainfall irregularity, based on the concept of disparity, D. The disparities have been calculated for every calendar month, to characterise the rainfall amount inter-annual oscillations, and also for all the consecutive months, to evaluate the rainfall disparity along the year. The spatial distribution of D has been obtained for all cases, showing a main general increase from North to South, and a secondary increase from West to East, in some months such as July. The winter months, especially January, have the highest values of D, which can reach the value of 2.0. The dependence of D on altitude and distance from the coast has also been analysed. The correlation is predominantly negative in both cases, although in some months, such as January, this correlation is not so clear. Additionally, the histograms of D show statistical characteristics, such as signs of a Gaussian distribution for some calendar months, as well as clear asymmetry in others. The obtained results could be interesting to detect the calendar months with the highest uncertainty on their expected rain amounts, contributing to a better knowledge of the complex structure of the rainfall Mediterranean regime., Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This research was supported by the Spanish Ministry of Science, Innovation and Universities (grant PID2019-105976RB-I00 and grant AGL2017-87658-R)., Postprint (published version)

The effusive–explosive energy emission process in a volcano is a dynamic and complex physical phenomenon. The importance of quantifying this complexity in terms of the physical and mathematical mechanisms that govern these emissions should be a requirement for deciding to apply a possible forecasting strategy with a sufficient degree of certainty. The complexity of this process is determined in this research by means of the reconstruction theorem and statistical procedures applied to the effusive–explosive volcanic energy emissions corresponding to the activity in the Volcán de Colima (western segment of the Trans-Mexican Volcanic Belt) along the years 2013–2015. The analysis is focused on measuring the degree of persistence or randomness of the series, the degree of predictability of energy emissions, and the quantification of the degree of complexity and “memory loss” of the physical mechanism throughout an episode of volcanic emissions. The results indicate that the analysed time series depict a high degree of persistence and low memory loss, making the mentioned effusive–explosive volcanic emission structure a candidate for successfully applying a forecasting strategy., This research has been supported by the European High-Performance Computing Joint Undertaking (JU) as well as Spain, Italy, Iceland, Germany, Norway, France, Finland and Croatia under grant agreement no.101093038, (ChEESE-CoE)., Peer Reviewed, Postprint (published version)

The version of record os available online at: http://dx.doi.org/10.1007/s00704-022-04096-3, Time trends and their statistical significance for daily minimum, Tmin, and maximum, Tmax, temperatures recorded at the Fabra Observatory (Barcelona) along 102 years (1917–2018) permit to analyse the evolution of every one of the 365 calendar days along the recording period. Relevant changes in the daily temperature regime have been quantified not only by time trends and the Mann–Kendall test, but also by the multifractal analysis applied to consecutive segments of daily temperature data. The evolution of several multifractal parameters (the central Hölder exponent, the spectral asymmetry and spectral amplitude, the complexity index and the Hurst exponent) provides a complementary viewpoint to describe the evolution of the thermometric regime along the 102 recorded years. At monthly scale, the effects of the climate change are characterised by significant positive trends from September to December and very moderate negative trends from April to July. With respect to changes in the calendar-day structure, it is noticeable a shift of the highest minimum and maximum daily temperature from July to August (year 2018) to the beginning of September (projections for years 2030 and 2050) and the projected highest maximum calendar-day temperature exceeding 30 °C, Peer Reviewed, Postprint (published version)

A long and complete series of monthly rainfall amounts corresponding to Barcelona city (Catalonia, NE Spain), exceeding two centuries (years 1786–2019), is analysed in detail. The obtained results of periodicity (annual scale), time trends (monthly, seasonal and annual scales), statistical distribution (seasonal and annual scale) and fractal/multifractal structures and self-similarity at monthly scale depict the complex structure of this pluviometric regime, which is characterized by moderate increasing and decreasing trends on rain amounts, varying from +0.08¿mm·year-1 (February) to -0.07¿mm·year-1 (September) and quite evident changes on the pluviometric trends at annual and seasonal scales when the rainfall data are analysed for segments of 50¿years from 1800 up to 2019. A good example could be the relevant change on the annual scale time trend, from +0.77¿mm·year-1 (years 1800–1850) to -0.17¿mm·year-1 (years 1950–2019). Clear evidences of decreasing pluviometry for spring, summer and autumn for the last segment (1950–2019) in comparison with the other three segments, including years 1800–1950, are also detected. Additionally, increasing rainfall patterns complexity, expected difficulties on monthly rainfall forecasting and the increasing irregularity of monthly amounts is also detected by interpreting fractal and multifractal results. Irregularity increases on the monthly rainfall series and on the rainfall regime complexity derived from multifractal parameters, could be associated with the very notable increase of CO2 emissions into the atmosphere, globally varying from 51.1¿×¿106 metric tonnes (year 1820) to 36.6¿×¿109 metric tonnes (year 2019) and the tropospheric concentration increasing from 280.8 ppm (year 1850) to 397.5 ppm (year 2014), being the probable relationship between tropospheric concentrations and changes on rainfall patterns the objective of future researches., Peer Reviewed, Postprint (published version)

Els esdeveniments extrems associats amb altes temperatures tenen un impacte en la salut, els seus ecosistemes i, per tant, en l’economia. Com a part del projecte X-ClimPlan, aquest estudi té com a objectiu estudiar les onades de calor a la ciutat de Barcelona entre el 1971 i el 2020, partint de la definició d’onada de calor segons l’AEMET. Això no obstant, aquesta definició té la limitació de referir-se únicament a temperatures màximes. Tot i que aquestes poden tenir greus conseqüències, especialment per cop de calor, els efectes sobre la salut són més acusats en el cas de la calor nocturna, on la impossibilitat de descansar pot provocar empitjorament de malalties respiratòries i cardiovasculars que produeixen morts prematures. Per això, lestudi diferencia entre onades de calor diürnes i nocturnes. Atès que el clima urbà presenta una variació espacial, la investigació parteix de la informació proporcionada per quatre estacions meteorològiques: Observatori Fabra, CMT, Raval i Aeroport, proposant un model OLS per a les quatre estacions i considerant l’any, el mes i el dia del calendari (cd) com a variables explicatives. Tot i que els increments de temperatura difereixen significativament depenent de la localització de l’estació, els resultats expliquen i confirmen que el procés d’escalfament global per sobre dels 2°C tant a les màximes com a les mínimes ja és una realitat a Barcelona. Així mateix, demostra una marcada diferència en els esdeveniments de calor extrema entre diferents ubicacions urbanes; la proximitat al mar, l’altitud, la diferent densitat urbana i la quantitat i la qualitat del verd urbà tenen un efecte determinant en la resiliència a esdeveniments extrems., Extreme events associated with high temperatures impact on the people’s health and their ecosystem, thus the economy. As part of the X-ClimPlan project, this study aims to study heat waves in the city of Barcelona between 1971 and 2020, using the AEMET definition of a heat wave. However that definition refers only to maximum temperatures. High temperatures can have serious consequences in human health, for example, leading to a heat stroke, but it is during nighttime heat, where the inability to rest can worsen respiratory and cardiovascular diseases that cause premature deaths. For this reason, the study differentiates between daytime and nighttime heat waves. Given that the urban climate presents a spatial variation, the research starts with the information provided by four weather stations: Fabra Observatory, CMT, Raval and Airport, and proposes an OLS model for the four stations, considering the year, month and calendar day (cd) as explanatory variables. Even though the temperature in all stations increase, there are differences depending on the location. The results explain and confirm that the process of global warming above 2°C, both in maximum and in minimums, is already a reality in Barcelona. The results also demonstrate a marked difference in extreme heat events between different urban locations; suggesting sea proximity, altitude, different urban density and the quantity and quality of urban greenery have a determining effect on resilience to extreme events., Los eventos extremos asociados con altas temperaturas tienen un impacto en la salud, sus ecosistemas y por tanto en la economía. Como parte del proyecto X-ClimPlan, este estudio tiene como objetivo estudiar las olas de calor en la ciudad de Barcelona entre 1971 y 2020, partiendo de la definición de ola de calor según la AEMET. No obstante, dicha definición tiene la limitación de referirse únicamente a temperaturas máximas. Si bien éstas pueden tener graves consecuencias, especialmente por golpe de calor, los efectos sobre la salud son más acusados en el caso del calor nocturno, donde la imposibilidad de descansar puede provocar empeoramiento de enfermedades respiratorias y cardiovasculares que producen muertes prematuras. Por ello, el estudio diferencia entre olas de calor diurnas y nocturnas. Dado que el clima urbano presenta una variación espacial, la investigación parte de la información proporcionada por cuatro estaciones meteorológicas: Observatorio Fabra, CMT, Raval y Aeropuerto, proponiendo un modelo OLS para las cuatro estaciones y considerando el año, el mes y el día del calendario (cd) como variables explicativas. Aun cuando los incrementos de temperatura difieren significativamente dependiendo de la localización de la estación, los resultados explican y confirman que el proceso de calentamiento global por encima de los 2°C tanto en las máximas como en las mínimas es ya una realidad en Barcelona. Asimismo, demuestra una marcada diferencia en los eventos de calor extremo entre diferentes ubicaciones urbanas; la proximidad al mar, la altitud, la diferente densidad urbana y la cantidad y calidad del verde urbano tienen un efecto determinante en la resiliencia a eventos extremos., Los autores quieren agradecer a Agència de Salut Pública de Barcelona, por la información proporcionada. También al Ministerio de Economía y Competitividad de España (MINECO) y al Fondo Europeo de Desarrollo Regional (FEDER) que permitieron la realización del proyecto Extreme Spatial and Urban Planning Tool for Episodes of Heat Waves and Flash Floods. Building Resilience for Cities and Regions (X-ClimPlan)., Peer Reviewed

Advantages offered by a pluviometric network in Catalonia (NE Spain) have permitted a detailed analysis of the two primary results derived from the autoregressive ARIMA process applied to monthly rainfall amounts. The first was the spatial distribution of the necessary number of previous monthly amounts needed to predict the next amount. The second was the spatial distribution of discrepancies between the real recorded amount and those derived from the autoregressive process. The heterogeneous spatial distribution of both parameters of the ARIMA process is in accordance with the complex spatial distribution of the monthly rainfall regime in Catalonia and fractal/multifractal analyses of several monthly rainfall time series. The statistical distribution of monthly discrepancies also permits a prediction of the probable evolution at monthly scale of drought episodes in terms of length and accumulated rainfall deficit. The results of the ARIMA algorithm are characterised by a few cases of raingauges with remarkable differences (10-20¿mm/month) between real and autoregressive amounts, a predominant number of emplacements lowering 10¿mm/month and a not negligible number of cases with discrepancies lower than 5¿mm/month. In terms of percentages with respect to average monthly amounts, most of discrepancies do not exceed 15%, and only in a very few cases they are within the 20-40% range. It is also worth mentioning that the discrepancies between real and predicted drought lengths use to be no longer than one month. Results corresponding to monthly series recorded at two Earth Sciences observatories are described with more detail to illustrate the advantages offered by the ARIMA autoregressive process in the prediction of beginning, continuity and end of drought episodes., Postprint (author's final draft)

The estimation of the Earth's surface temperature (LST) from the infrared thermal radiation (TIR) emitted by the Earth detected by means of remote sensing has allowed a giant leap in climate analysis. The specialized literature has highlighted the singular importance of the LST in the generation of the Urban Heat Island (UHI), especially at night. It is during the night that the effects of UHI become more apparent, due to the low cooling capacity of urban construction materials and is during night-time that temperatures can cause higher health risks, leading to the aggravation of negative impacts on people’s health and comfort in extreme events such as heat waves becoming more and more frequent and lasting longer. However, the study of nocturnal UHIs is still poorly developed, due to the structural problems. On the one hand, the scarcity of meteorological stations that allow obtaining the air temperature (Ta) with an adequate degree of spatial resolution. And, on the other, due to the limited temporal availability of medium / high resolution nocturnal satellite images that make it possible to know the LST at night. Traditional methods for obtaining nocturnal UHI have been directed either to extrapolation of data from weather stations, or obtaining Ta through urban transects. In the first case, the lack of weather stations in urban landscapes makes it extremely difficult to obtain data to extrapolate and propose models at a detailed resolution scale. In the second case, there is a manifest difficulty in obtaining data simultaneously and significantly representative of urban and rural zones. Remote sensing images are another methodology used to measure night-time UHI, but the greatest limitation of this method is the scarcity of high-resolution images that allow rigorous night-time LST to be obtained. Only MODIS, or Sentinel 3, offer free mid-resolution night-time thermal imaging for LST and UHI analysis. Furthermore, the integration of LST (obtained from remote sensi, Peer Reviewed, Postprint (author's final draft)

The pluviometric regime in the Western Mediterranean and concretely in Catalonia (NE Spain) is characterised by irregular amounts at monthly and annual scales, sometimes with copious short episodes causing foods and, conversely, sometimes with long dry spells exceeding 1 month length, depending on the chosen threshold level to defne the dry episode. Taking advantage of a dense network of rain gauges, most of them with records length of 50–60 years and some others exceeding 85 years, the evolution of these monthly and annual amounts is quantifed by means of their time trends, statistical signif- cance and several irregularity parameters. In agreement with the evolution of the CO2 emissions into the atmosphere and the increasing concentration, in parts per million (ppm), of this greenhouse gas, diferent time trends at annual scale have been detected up to approximately years 1960–1970 in comparison with the interval 1960–1970 to nowadays. Consequently, besides the greenhouse efects on the temperature regime, the infuence on the pluviometric regime could not be negligible., Rainfall data have been supplied by Servei Mete‑ orològic de Catalunya (Generalitat de Catalunya), Fabra Observatory (RACA, Barcelona) and Ebro Observatory (Ramón Llull University and CSIC, Spanish Government). This research was supported by the Spanish Ministry of Science, Innovation and Universities: grant 460 number PID2019-105976RB-I00] and grant number AGL201787658-R. The authors also thank the editor and the anonymous reviewers for their valuable comments and suggestions to improve the manuscript, Peer Reviewed, Postprint (published version)

Distances between consecutive aftershocks are analysed by means of mono- and multifractal theory with the aim of quantifying the complexity of the physical mechanism governing them, as well as their predictability and predictive instability. Hausdorff, Ha, and Hurst, H, exponents are determined by semivariograms and rescaled analysis, respectively. The exponent ß of the power law describing power spectral contents is also quantified. These three parameters permit a generation of fractional Gaussian noise, fGn, simulating distances. The complexity and predictive instability of physical mechanism generating the series of distances is quantified by means of the correlation dimension, µ*, the Kolmogorov entropy, ¿, and the Lyapunov exponents, ¿i, which are based on the reconstruction theorem formulation. Additionally, the multifractal detrended fluctuation analysis, MF-DFA, contributes with a different point of view to quantify the complexity of the series, in terms of fractal spectral width, W, spectral asymmetry, B, and the critical Hölder exponent, a0. By one hand, the MF-DFA is applied to the complete set of distances characterising the whole aftershock process. By the other hand, the MF-DFA is applied to segments of the series of distances with the aim of determining the evolution of the complexity since the mainshock up to the end of the stress relaxation process. Finally, an ARIMA multilinear regression process is applied to obtain some improvements, in comparison with fGn simulations, on the prediction of distances. The database for this analysis is obtained from the Southern California Seismic Network (SCSN) catalogue. Three series of aftershocks equalling to or exceeding magnitudes of 2.0, assuring seismic catalogue completeness, and associated with Landers (06/28/1992), Northridge (01/17/1994) and Hector Mine (10/16/1999) mainshocks are obtained. It is worth mentioning that common mono-multifractal behaviour for the three aftershocks series is not detected, w, Postprint (author's final draft)

Standardized heavy rainfall profiles may contribute to a best knowledge concerning flash floods, ground erosion and runoff. Taking advantage of the rain rate gauges network of Barcelona city and applying a short integration time of 5 min, the heavy rainfall records with amounts above 25 mm and longer than 60 min have been selected along 15 years, being detected 499 records corresponding to 67 episodes. The amount distribution of these records are analysed at time deciles. By grouping these standardized rainfall profiles according to their similarity by means of the average linkage clustering algorithm, 10 clusters are derived, each one of them characterized by different time evolution of rainfall. The representative standardized rainfall profiles for every one of the clusters, together with maximum 5-min rain amounts and rainfall amounts characterizing them, permit to distinguish rainfall patterns. In addition, the extreme heavy rainfalls which may lead to flash floods are identified, as also their respective synoptic situations. In short, this analysis offers a description of heavy rainfall patterns in Barcelona city, complementing previous papers on the normalized intensity curves and 5-min intensity return periods. These heavy rainfall analyses would be very useful when designing drainage and sewerage systems in urban areas as Barcelona, where flash floods may be expected due to episodes of notable rainfall amount and intensity. The imperviousness density of the soil and an appropriate sewerage structure should be adapted to mitigate the effects of these copious and intense episodes., Peer Reviewed, Postprint (author's final draft)

The multifractal detrended fluctuation algorithm is applied to a series of distances and elapsed times between consecutive earthquakes recorded along the years 2000–2018 in the Canterbury region (New Zealand). The time evolution of several multifractal parameters (Hurst exponent, Hölder central and maximum exponents, spectral amplitude, asymmetry, and complexity index) is analyzed. Peaks of multifractal parameters, with statistical significance exceeding 95%, are associated with three earthquakes of notable magnitude (equaling or exceeding Mw = 5.7). Additionally, some other peaks are also associated with the swarm of earthquakes of moderate magnitude. Possible shortcomings created by this assignment to mainshocks or swarms can be removed by comparing the results corresponding to elapsed times and interevent distances between consecutive events. Additionally, the Buishand test, which is used to verify the statistical significance of the detected peaks, also discriminates between mainshocks of notable seismic magnitude and swarms of earthquakes with moderate magnitude. The obtained results, based on the multifractal structure of the seismic activity, could also represent some advances in predicting, with sufficient time, forthcoming mainshocks of high magnitude and mitigate their destructive effects., The research leading to these results has received funding from the European Union’s Horizon 2020 research and innovation program, under Grant Agreement No. 823844, the ChEESE CoE Project., Peer Reviewed, Postprint (published version)

The metropolitan region of Barcelona (BMR) is one of the most densely populated areas in the Mediterranean countries. The estimation of air temperature at a short scale from satellite measurements would contribute to a better understanding of the varied and complex spatial distribution of temperatures in BMR. This estimation would be a first step to study several patterns of the thermometric regime affecting population life quality and health. Taking advantage of MODIS data, air temperature measurements at 48 thermometric stations along the year 2015, together with their geographic and topographic data, multiple regression analyses have permitted to obtain fine spatial distributions (pixels of 1 km2) of minimum, mean and maximum daily air temperatures. Previous to the multiple regression, Pearson coefficients and principal component analysis offer a first overview of the relevance of the variables on the empiric temperatures. The most relevant variables on the multiple regression process at annual and seasonal scale are land surface temperatures, latitude, longitude and calendar day. At a monthly scale, altitude (maximum temperature) and continentality (cold months for minimum and hot months for maximum temperatures) are also relevant. The best fits between empiric temperatures and those derived from the multiple regression processes have square regression coefficients within the range (0.92–0.96) for the annual case, (0.70–0.92) at seasonal scale and (0.52–0.87) at monthly scale. The root mean square error varies from 1.5 to 2.0 °C (annual case), from 1.3 to 2.0 °C (seasonal scale) and from 1.2 to 2.1 °C (monthly scale). In agreement with these regression coefficients and mean square errors, the obtained spatial distribution of temperatures is of notable quality. As an outstanding application, the detection of several urban heat islands on different conurbations within BMR along the Mediterranean coast becomes possible., Postprint (author's final draft)

The complex non-linear regime of the monthly rainfall in Catalonia (NE Spain) is analyzed by means of the reconstruction fractal theorem and the multifractal detrended fluctuation analysis algorithm. Areas with a notable degree of complex physical mechanisms are detected by using the concepts of persistence (Hurst exponent), complexity (embedding dimension), predictive uncertainty (Lyapunov exponents), loss of memory of the mechanism (Kolmogorov exponent), and the set of multifractal parameters (Hölder exponents, spectral asymmetry, spectral width, and complexity index). Besides these analyses permitting a detailed description of monthly rainfall pattern characteristics, the obtained results should also be relevant for new research studies concerning monthly amounts forecasting at a monthly scale. On one hand, the number of necessary monthly data for autoregressive processes could change with the complexity of the multifractal structure of the monthly rainfall regime. On the other hand, the discrepancies between real monthly amounts and those generated by some autoregressive algorithms could be related to some parameters of the reconstruction fractal theorem, such as the Lyapunov and Kolmogorov exponents. The monthly rainfall regime in Catalonia, NE Spain, is analyzed by means of the fractal theory with the aim of improving the knowledge about its complex physical mechanism., Peer Reviewed, Postprint (author's final draft)

La posible intensificación del ciclo hidrológico debido al cambio climático y sus efectos en la hidrología deben tenerse en consideración con el fin de prevenir problemas futuros en los sistemas de drenaje urbano. Las curvas de intensidad-duración-frecuencia (IDF), una importante herramienta utilizada en el diseño y construcción de diferentes estructuras hidrológicas para la gestión del agua, podrían verse alteradas por un supuesto aumento de las lluvias intensas debido al cambio climático (Rodríguez et al. 2014). Así como en otras latitudes se ha reportado un aumento de la precipitación total debido al calentamiento global (IPCC, 2007), en la zona mediterránea varios estudios apuntan una tendencia dominante decreciente en las últimas décadas (Pérez y Boscolo 2010). No ocurre así con la precipitación de carácter extremo o torrencial, para la cual se prevé un aumento, debido a una mayor ocurrencia de episodios lluviosos más cortos y de mayor intensidad (Christensen y Christensen 2003). La evaluación de estos cambios es especialmente interesante en las zonas urbanas con alta densidad de población, debido a la vulnerabilidad de sus complejos sistemas de alcantarillado frente a la lluvia torrencial (Casas et al. 2010, Rodríguez et al. 2013b).Para describir matemáticamente las curvas IDF de un lugar, es posible utilizar una relación de escala relacionada con la propiedad fractal de invariancia de escala de la intensidad de lluvia (Menabde et al. 1999, Rodríguez-Solà et al. 2017). En el caso monofractal o de escala simple, esta relación de escala queda determinada por un único parámetro o exponente de escala β, cuyo valor parece estar relacionado con el régimen pluviométrico del lugar, o más en particular, con la irregularidad de la lluvia (Casas-Castillo et al. 2018b). Así, este parámetro toma valores cercanos a -1 para áreas en donde la lluvia suele ser muy irregular, con valores máximos aislados repentinos, mientras que toma valores más altos para áreas con un patrón d, La possible intensificació del cicle hidrològic causa de el canvi climàtic i els seus efectes en la hidrologia s'han de tenir en consideració per tal de prevenir problemes futurs en els sistemes de drenatge urbà. Les corbes d'intensitat-durada-freqüència (IDF), una important eina utilitzada en el disseny i construcció de diferents estructures hidrològiques per a la gestió de l'aigua, es podrien veure alterades per un suposat augment de les pluges intenses causa de el canvi climàtic (Rodríguez et al. 2014). Així com en altres latituds s'ha reportat un augment de la precipitació total a causa de l'escalfament global (IPCC, 2007), a la zona mediterrània diversos estudis apunten una tendència dominant decreixent en les últimes dècades (Pérez i Boscolo 2010). No passa així amb la precipitació de caràcter extrem o torrencial, per a la qual es preveu un augment, a causa d'una major ocurrència d'episodis plujosos més curts i de més intensitat (Christensen i Christensen 2003). L'avaluació d'aquests canvis és especialment interessant en les zones urbanes amb alta densitat de població, a causa de la vulnerabilitat dels seus complexos sistemes de clavegueram enfront de la pluja torrencial (Casas et al. 2010, Rodríguez et al. 2013b).Per descriure matemàticament les corbes IDF d'un lloc, és possible utilitzar una relació d'escala relacionada amb la propietat fractal d'invariància d'escala de la intensitat de pluja (Menabde et al. 1999, Rodríguez-Solà et al. 2017). En el cas monofractal o d'escala simple, aquesta relació d'escala queda determinada per un únic paràmetre o exponent d'escala β, el valor sembla estar relacionat amb el règim pluviomètric de el lloc, o més en particular, amb la irregularitat de la pluja (Cases -Castell et al. 2018b). Així, aquest paràmetre pren valors propers a -1 per a àrees on la pluja sol ser molt irregular, amb valors màxims aïllats sobtats, mentre que pren valors més alts per a àrees amb un patró de pluja més regular. És d'esperar doncs que la supo, The possible intensification of the hydrological cycle due to climate change and its effects on hydrology should be taken into account in order to prevent future problems in urban drainage systems. The intensity-duration-frequency (IDF) curves, an important tool used in the design and construction of different hydrological structures for water management, could be altered by a supposed increase in heavy rainfall due to climate change (Willems et al. 2011, Rodríguez et al. 2014). Whereas in other latitudes an increase in total precipitation due to global warming has been reported (IPCC, 2007), in the Mediterranean area several studies point to a decreasing dominant trend in recent decades (Pérez and Boscolo 2010). This is not the case with extreme or torrential precipitation, for which an increase is expected, due to a greater occurrence of shorter and more intense rainy episodes (Christensen and Christensen 2003). The evaluation of these changes is especially interesting in urban areas with high population density, due to the vulnerability of their complex sewage systems to torrential rain (Casas et al. 2010, Rodríguez et al. 2013b).To describe mathematically the IDF curves of a place, it is possible to use a scaling relationship related to the fractal property of scale invariance of rainfall intensity (Menabde et al. 1999, Rodríguez-Solà et al. 2017). In the monofractal case or simple scale, this scaling relationship is determined by a single parameter or scaling exponent β, whose value seems to be related to the rainfall pattern of the place, or more particularly, to the irregularity of the rain (Casas-Castillo et al. 2018b). Thus, this parameter takes values close to -1 for areas where rain is usually very irregular, with sudden maximum isolated values, while it takes higher values for areas with a more regular rainfall pattern. It is to be expected that the supposed tendency of the annual precipitation to decrease and the relative increase in extreme precipitati, Este estudio ha sido financiado en parte por el Canal de Isabel II Gestión para el Plan Maestro de Drenaje de la Comunidad de Madrid, y en parte por CETaqua y R+i Alliance para el proyecto SW0801-phase2. Los autores agradecen a Clavegueram de Barcelona (CLABSA), a Barcelona Cicle de l’aigua (BCASA) y a la Fundación para la Investigación del Clima (FIC) por haber proporcionado parte de los datos de lluvia utilizados., Peer Reviewed

Uno de los rasgos principales de las áreas urbanas es el predominio de las superficies impermeables (suelos sellados). Dependiendo de su densidad y extensión, el sellado de los suelos limita o impide las funciones naturales del suelo, puesto que reduce su capacidad potencial de infiltración del agua y, con ello, la regulación de la escorrentía, aumentando el riesgo de inundaciones. En el caso de precipitaciones muy intensas en áreas urbanas con una elevada proporción de superficies impermeables, el sistema de alcantarillado puede no ser suficiente para hacer frente al exceso de agua de lluvia y, por lo tanto, se pueden producir inundaciones súbitas. En muchas zonas de Europa, la extensión de la urbanización y su densificación han incrementado notablemente la proporción de superficies impermeables (European Environment Agency, 2016). En la conurbación de Barcelona, la mayor parte de las áreas tienen una proporción de suelos sellados del 60-80% y en la ciudad de Barcelona, se supera el 80% (fuente: European Environment Agency, GMES/Copernicus). En esta zona los episodios de precipitación intensa son relativamente frecuentes, especialmente a finales de verano y durante el otoño, y algunos de ellos han dado lugar a inundaciones súbitas. En este trabajo se analizan los registros de una red de 23 estaciones de intensidad de precipitación instaladas en la ciudad de Barcelona. La base de datos consta de series de valores de precipitación acumulada a intervalos de 5 minutos, lo cual proporciona una medida de la intensidad de precipitación (mm/5 minutos). El periodo de registro considerado abarca 16 años (1994-2009). Para los registros de más de 60 minutos de duración y de más de 25 mm (67 episodios, 499 registros) se han calculado el total de precipitación acumulada, la intensidad media y la intensidad máxima. Finalmente, se han estudiado los que exceden al mismo tiempo, el percentil del 95% de estas tres variables. Con ello, se han obtenido 29 registros extremos que podrían, Un dels trets principals de les àrees urbanes és el predomini de les superfícies impermeables (sòls segellats). Depenent de la seva densitat i extensió, el segellat dels sòls limita o impedeix les funcions naturals de terra, ja que redueix la seva capacitat potencial d'infiltració de l'aigua i, amb això, la regulació del vessament, augmentant el risc d'inundacions. En el cas de precipitacions molt intenses en àrees urbanes amb una elevada proporció de superfícies impermeables, el sistema de clavegueram pot no ser suficient per fer front a l'excés d'aigua de pluja i, per tant, es poden produir inundacions sobtades. En moltes zones d'Europa, l'extensió de la urbanització i la seva densificació han incrementat notablement la proporció de superfícies impermeables (European Environment Agency, 2016). A la conurbació de Barcelona, la major part de les àrees tenen una proporció de sòls segellats de l'60-80% i a la ciutat de Barcelona, se supera el 80% (font: European Environment Agency, GMES / Copernicus). En aquesta zona els episodis de precipitació intensa són relativament freqüents, especialment a finals d'estiu i durant la tardor, i alguns d'ells han donat lloc a inundacions sobtades. En aquest treball s'analitzen els registres d'una xarxa de 23 estacions d'intensitat de precipitació instal·lades a la ciutat de Barcelona. La base de dades consta de sèries de valors de precipitació acumulada a intervals de 5 minuts, la qual cosa proporciona una mesura de la intensitat de precipitació (mm / 5 minuts). El període de registre considerat abasta 16 anys (1994-2009). Per als registres de més de 60 minuts de durada i de més de 25 mm (67 episodis, 499 registres) s'han calculat el total de precipitació acumulada, la intensitat mitjana i la intensitat màxima. Finalment, s'han estudiat els que excedeixen a el mateix temps, el percentil de el 95% d'aquestes tres variables. Amb això, s'han obtingut 29 registres extrems que podrien donar lloc a situacions d'inundació sobtada. Aquests, One of the main features of urban areas is the prevalence of impervious surfaces (sealed soils). Depending on its density and extent, soil sealing restricts natural soil functions, since it reduces water infiltration capacity and run-off regulation, thus increasing flash flooding risk. In the case of heavy rainfalls in urban areas with high imperviousness ratio, the sewage system could no longer be able to cope with the excess of rainwater and then pluvial floods develop. In many European zones, urban spread and densification have increased the impervious surface ratio (European Environment Agency, 2016). In Barcelona conurbation, most areas have high fractions of sealed soils (60–80%) and in the city, this fraction exceeds 80% (source: European Environment Agency, GMES/Copernicus). Heavy rainfall episodes are relatively frequent in this area, especially in autumn, and some of them have resulted in flash floods. In this study, rainfall intensity records from an urban network of 23 stations are analysed. The database consists of series of rain amounts collected at 5-minute intervals, which provides a measure of rainfall intensity (mm/5 minutes). The recording period encompasses 16 years (1994-2009). For all the records with durations greater than 60 minutes and total amounts greater than 25 mm (67 episodes, 499 records), the total rain amount, average intensity and maximum intensity are determined. We have selected the records exceeding, simultaneously, the 95th percentile of these three variables, thus obtaining 29 extreme records, which could lead to pluvial flash flood events. These extreme records correspond to seven different episodes, occurred from the end of July to October. Most of these extreme episodes are generated by convective processes at local scale as well as by eastern advections. The seven extreme episodes caused important affectations in road communications, breakdowns at traffic lights and telephone lines, as well as interruption of the service of, Esta investigación ha sido financiada por el Ministerio de Economía y Competitividad (Gobierno de España), a través del proyecto BIA2015-68623-R. Los autores agradecen a CLABSA (Clavegueram de Barcelona, S.A.) los datos pluviométricos facilitados., Peer Reviewed

Heavy rainfall episodes are relatively common in the conurbation of Barcelona and neighbouring cities (NE Spain), usually due to storms generated by convective phenomena in summer and eastern and south-eastern advections in autumn. Prevention of local flood episodes and right design of urban drainage have to take into account the rainfall intensity spread instead of a simple evaluation of daily rainfall amounts. The database comes from 5-min rain amounts recorded by tipping buckets in the Barcelona urban network along the years 1994–2009. From these data, extreme 5-min rain amounts are selected applying the peaks-over-threshold method for thresholds derived from both 95% percentile and the mean excess plot. The return period curves are derived from their statistical distribution for every gauge, describing with detail expected extreme 5-min rain amounts across the urban network. These curves are compared with those derived from annual extreme time series. In this way, areas in Barcelona submitted to different levels of flood risk from the point of view of rainfall intensity are detected. Additionally, global time trends on extreme 5-min rain amounts are quantified for the whole network and found as not statistically significant., Peer Reviewed, Postprint (author's final draft)

El objetivo principal de este estudio es caracterizar la intensidad de la isla de calor urbana en la ciudad de Barcelona a lo largo del periodo octubre 2006 - octubre 2017. La intensidad de la isla de calor es la diferencia de temperatura, en un momento determinado, entre el núcleo urbano y las zonas no urbanas (o periurbanas) próximas. Es el indicador más sencillo para cuantificar el calentamiento de la ciudad, en relación a su entorno, especialmente durante las horas nocturnas. Para que la diferencia de temperaturas se pueda atribuir a los efectos de la urbanización, se requiere que los emplazamientos que se comparan sean suficientemente cercanos como para tener el mismo clima regional y que sus factores geográficos locales (altitud y distancia al mar) sean similares. En este estudio, se calculan, día a día, las diferencias de las temperaturas mínimas registradas en la estación meteorológica de El Raval, situada en el centro de Barcelona, y el observatorio meteorológico del aeropuerto de Barcelona (El Prat), situado en el área metropolitana. El aeropuerto no se ubica en una zona rural, pero es un área muy abierta, con un elevado factor de visión del cielo, por lo tanto, con un remarcable enfriamiento nocturno.El periodo de estudio, que abarca 11 años, proporciona más de 4000 datos diarios de diferencias de temperatura mínima (ΔTmin). Se analiza la distribución de frecuencias de los valores de ΔTmin, así como su valor máximo y medio, a escalas anual, semianual y estacional. Es de destacar que el 94.5% de las noches son más cálidas en la estación urbana (El Raval). Esta proporción asciende hasta el 98.4% durante el invierno. La diferencia máxima es de 7.1ºC y, en promedio, las noches de invierno son 3.0ºC más cálidas en El Raval. El análisis del espectro de potencia muestra la periodicidad anual y semianual de la intensidad de la isla de calor. La distribución de los valores de ΔTmin, en función del día del año, permite explorar la vinculación de la intensidad de la, L'objectiu principal d'aquest estudi és caracteritzar la intensitat de l'illa de calor urbana a la ciutat de Barcelona al llarg del període octubre 2006 - octubre 2017. La intensitat de l'illa de calor és la diferència de temperatura, en un moment determinat, entre el nucli urbà i les zones no urbanes (o periurbanes) properes. És l'indicador més senzill per quantificar l'escalfament de la ciutat, en relació al seu entorn, especialment durant les hores nocturnes. Perquè la diferència de temperatures es pugui atribuir a l'efecte de la urbanització, es requereix que els emplaçaments que es comparen siguin prou propers com per tenir el mateix clima regional i que els seus factors geogràfics locals (altitud i distància al mar) siguin similars. En aquest estudi, es calculen, dia a dia, les diferències de les temperatures mínimes registrades a l'estació meteorològica del Raval, situada al centre de Barcelona, i l'observatori meteorològic de l'aeroport de Barcelona (El Prat), situat a l'àrea metropolitana. L'aeroport no s'ubica en una zona rural, però és una àrea molt oberta, amb un elevat factor de visió del cel, per tant, amb un remarcable refredament nocturn. El període d'estudi, que abasta 11 anys, proporciona més de 4000 dades diàries de diferències de temperatura mínima (ΔTmin). S'analitza la distribució de freqüències dels valors de ΔTmin, així com el seu valor màxim i mig, a escales anual, semianual i estacional. És de destacar que el 94.5% de les nits són més càlides a l'estació urbana (El Raval). Aquesta proporció puja fins al 98.4% durant l'hivern. La diferència màxima és de 7.1ºC i, de mitjana, les nits d'hivern són 3.0ºC més càlides al Raval. L'anàlisi de l'espectre de potència mostra la periodicitat anual i semianual de la intensitat de l'illa de calor. La distribució dels valors de ΔTmin, en funció del dia de l'any, permet explorar la vinculació de la intensitat de l'illa de calor amb els períodes freds o càlids de l'any, especialment, per als casos dels valo, The main goal of this study is the characterization of the intensity of the urban heat island (UHI) in Barcelona city center along the October 2006–October 2017 period. The UHI intensity is evaluated by computing the difference in daily minimum temperatures, on a certain moment, between the city center and the peripheral or non-urban neighboring areas. It is the simplest indicator to quantify the warming of the city, in relation to the surrounding environment, especially at night. In order for the temperature differences can be attributed to the influence of urbanization, the sites to be compared must be nearby enough to have the same regional climate and their local geographical factors (altitude and distance from sea) be very similar. In this study, we compute the differences in daily minimum temperatures recorded at the meteorological station El Raval, in Barcelona downtown, and those recorded at the fix observatory of Barcelona Airport (El Prat), located in the metropolitan area. Although the airport is not placed in a rural environment, it is a broadly open area, with a high sky view factor and, consequently, with a marked night cooling.The recording period spans 11 years, thus providing more than 4000 daily data of minimum temperature differences (ΔTmin). The frequency distribution of daily ΔTmin and their maximum and average values are investigated at annual, half-annual and seasonal scales. It is worth remarking that 94.5% of nights are warmer at the urban site (El Raval), this percentage increasing until 98.4% in winter. The maximum temperature difference is 7.1ºC and, on average, winter nights are 3.0ºC warmer at El Raval. The power spectrum shows that UHI intensity has annual and half-annual periodicities. The distribution of ΔTmin values along the calendar days permits exploring the linkages of UHI intensity to cold and hot periods of the year, especially, for the cases of extreme ΔTmin values, and for the scarce colder nights at El Raval. Finally, the i, Peer Reviewed

La Región Metropolitana de Barcelona (RMB), es una de las áreas del Mediterráneo más densamente pobladas. Por ello, tiene mucho interés conocer con detalle la temperatura del aire, ya que, en situaciones extremas, como olas de frío o de calor, puede afectar a la salud y calidad de vida de la población. Puesto que el número de estaciones termométricas que hay en la actualidad es insuficiente para realizar una interpolación óptima, se opta por estimar la temperatura del aire a partir de la temperatura en superficie, proporcionada por el satélite MODIS, y de otras variables como los índices de vegetación y de edificación y variables topogeográficas. Para ello se ha realizado la Regresión Múltiple en la que las variables dependientes son la temperatura mínima, media y máxima diaria del aire de 48 estaciones termométricas. Las variables independientes de la regresión son: las temperaturas en superficie de día y de noche, los índices de vegetación NDVI y de edificación NDBI, todas ellas correspondientes al año 2015, y variables topogeográficas como la latitud, longitud, distancia al mar, altitud, pendiente y orientación. Además, también se ha tenido en cuenta el día del calendario. De los resultados obtenidos en la regresión múltiple se deduce que las variables que más importancia tienen en la ecuación son: la temperatura en superficie nocturna, la latitud, la longitud y día del calendario, para el caso de la temperatura mínima; las temperaturas nocturna y diurna en superficie para la temperatura media, y las temperaturas nocturna y diurna en superficie, la latitud, la longitud y la altitud, para la temperatura máxima. Los coeficientes de regresión al cuadrado obtenidos son de 0.92 para la temperatura mínima y la máxima y de 0.96 para la temperatura media. Los errores cuadráticos medios obtenidos son de 1.93 ºC para la temperatura mínima, de 1.96 ºC para la temperatura media y de 2.04 ºC para la máxima. A partir de la regresión múltiple se puede representar la distribuc, La Regió Metropolitana de Barcelona (RMB), és una de les àrees del Mediterrani més densament poblades. Per això, té molt interès conèixer amb detall la temperatura de l'aire, ja que, en situacions extremes, com onades de fred o de calor, pot afectar la salut i qualitat de vida de la població. Ja que el nombre d'estacions termomètriques que hi ha actualment és insuficient per a realitzar una interpolació òptima, s'opta per estimar la temperatura de l'aire a partir de la temperatura en superfície, proporcionada pel satèl·lit MODIS, i d'altres variables com els índexs de vegetació i d'edificació i variables topo geogràfiques. Per a això s'ha realitzat la Regressió Múltiple a la que les variables dependents són la temperatura mínima, mitjana i màxima diària de l'aire de 48 estacions termomètriques. Les variables independents de la regressió són: les temperatures en superfície de dia i de nit, els índexs de vegetació NDVI i d'edificació NDBI, totes elles corresponents a l'any 2015, i variables topo geogràfiques com la latitud, longitud, distància al mar, altitud, pendent i orientació. A més, també s'ha tingut en compte el dia del calendari. Dels resultats obtinguts en la regressió múltiple es dedueix que les variables que més importància tenen en l'equació són: la temperatura en superfície nocturna, la latitud, la longitud i dia del calendari, per al cas de la temperatura mínima; les temperatures nocturna i diürna en superfície per a la temperatura mitjana, i les temperatures nocturna i diürna en superfície, la latitud, la longitud i l'altitud, per a la temperatura màxima. Els coeficients de regressió al quadrat obtinguts són de 0.92 per a la temperatura mínima i la màxima i de 0.96 per a la temperatura mitjana. Els errors quadràtics mitjans obtinguts són de 1.93 ºC per a la temperatura mínima, d'1.96 ºC per a la temperatura mitjana i de 2.04 ºC per a la màxima. A partir de la regressió múltiple es pot representar la distribució espacial de temperatura diària de l'RMB am, The Metropolitan Region of Barcelona (RMB), is one of the most densely populated areas of the Mediterranean. Therefore, it is very interesting to know in detail the air temperature, since in extreme situations, such as cold or heat waves, it can affect the health and life quality of the population. Since the number of thermometric stations currently available is insufficient for optimal spatial interpolation, we choose to estimate the air temperature based on the surface temperature provided by the MODIS satellite, and other variables such as the indices of vegetation and building and topo geographic variables. For this purpose, Multiple Regression has been performed, taking as dependent variables the minimum, mean and maximum daily air temperatures of 48 thermometric stations. The independent variables of the regression are: the day and night surface temperatures, the NDVI and NDBI indices, all of them corresponding to the year 2015, and topo geographic variables such as latitude, longitude, distance to the sea, altitude, slope and orientation. In addition, the calendar day has also been taken into account. From the results obtained in the multiple regression, it can be deduced that the most important variables in the equation are: the temperature at night, latitude, longitude and calendar day, for the case of the minimum temperature; the night and day temperatures on the surface for the average temperature, and the night and day temperatures on the surface, latitude, longitude and altitude, for the maximum temperature. The squared regression coefficients obtained are 0.92 for the minimum and maximum temperature and 0.96 for the average temperature. The average square errors obtained are 1.93 ºC for the minimum temperature, 1.96 ºC for the average temperature and 2.04 ºC for the maximum. After applying the multiple linear regressions, the spatial distribution of the daily temperature of the RMB can be represented with a resolution of 1 km2, which is the provided by, Peer Reviewed

For preserving existing structures to the extent possible, vibration-based damage detection techniques are gaining more attention. In specific, tracking the changes in a structure’s natural frequencies employing the Principal Component Analysis (PCA) seems to be a promising technique. This paper presents an on-going research for developing an approach for damage detection based on identifying the natural frequencies of the structure (via dynamic identification or monitoring) followed by applying PCA on the temporal variation of the identified natural frequencies. The processing of the dynamic monitoring data was carried out using a proposed semiautomatic algorithm able to identify and track the natural frequencies of the monitored structures and their changes over time. The algorithm was applied on one historical structure and two modern ones. PCA will to be carried out. The so far developed approach as a whole was applied on a steel structure model tested in lab. It was subjected to dynamic identification tests with and without damage. It was found that PCA applied to frequency variation seems to be a possible tool to know damages in structures. Nevertheless, the simplified point of view correlating directly the number of PCs with the damage importance seems to be not accurate. First results seem to indicate that the variance percentage explained by each of the principal components could be correlated with the kind of damages and the shake used to excite the structure., Postprint (published version)

An analysis of the normalised rainfall intensity curves in Barcelona (NE Spain) has been undertaken from selected rain rate episodes recorded by an urban network of tipping buckets applying a 5-min integration time along the years 1994–2009. These curves, based on cumulative amount and time distributions, are modelled by a power law, this fact suggesting fractal behaviour. Four parameters characterise these curves. One of them is the exponent of the power law. Another one quantifies the intermittency of the rainfall along the episode. The other two are the coordinates of cumulative amount and time distribution from which the power law fits well the normalised curve. The total rainfall amount of the episode, its length and the coefficient of variation of the 5-min amounts are also considered as complementary parameters. Taking advantage of these seven parameters, patterns of rainfall intensity are determined for every episode. These patterns, together with the statistical distribution of 5-min amounts, maximum intensity and rainfall intermittence, should increase the knowledge on the urban rainfall regime with the aim of improving drainage design. In addition to present results, flood prevention should be complemented with extreme value analyses and quantification of return periods., Postprint (author's final draft)

Monthly rain amounts (MRA) recorded at Fabra Observatory (Barcelona, NE Spain) since 1917–2010, are analysed from two complementary points of view. First, mono- and multifractal characteristics of MRA are compared with those corresponding to the monthly Western Mediterranean Oscillation index (WeMOi), which affects the rainfall regime at the western Mediterranean region. Monofractality is analysed through Hurst and Hausdorff exponents, and a power law describing the dependence of MRA power spectra on frequency. The reconstruction theorem permits to quantify the complexity of the physical process by means of the correlation dimension and the Kolmogorov entropy. In agreement with this theorem, the predictive instability is also evaluated through the Lyapunov exponents. The multifractality is characterized by the critical Hölder exponent, as well as by the asymmetry and spectral width of the multifractal spectrum. Second, three predictive processes for MRA are tested. One of them is based on the assumption that MRA could be simulated by fractional Gaussian noise. The other two are, by one hand, an ARIMA(p,1,0) process for MRA; on the other hand, an adaptation of the ARIMA process for MRA taking as arguments preceding WeMOi. Finally, relationships between MRA and WeMOi confirm that outstanding MRA use to be coincident with negative WeMOi. An explanation is also proposed for the non-negligible number of MRA corresponding to positive WeMOi., Postprint (published version)

Dry spell lengths, DSL, defined as the number of consecutive days with daily rain amounts below a given threshold, may provide relevant information about drought regimes. Taking advantage of a daily pluviometric database covering a great extension of Europe, a detailed analysis of the multifractality of the dry spell regimes is achieved. At the same time, an autoregressive process is applied with the aim of predicting DSL. A set of parameters, namely Hurst exponent, H, estimated from multifractal spectrum, f(a), critical Hölder exponent, a0, for which f(a) reaches its maximum value, spectral width, W, and spectral asymmetry, B, permits a first clustering of European rain gauges in terms of the complexity of their DSL series. This set of parameters also allows distinguishing between time series describing fine- or smooth-structure of the DSL regime by using the complexity index, CI. Results of previous monofractal analyses also permits establishing comparisons between smooth-structures, relatively low correlation dimensions, notable predictive instability and anti-persistence of DSL for European areas, sometimes submitted to long droughts. Relationships are also found between the CI and the mean absolute deviation, MAD, and the optimum autoregressive order, OAO, of an ARIMA(p,d,0) autoregressive process applied to the DSL series. The detailed analysis of the discrepancies between empiric and predicted DSL underlines the uncertainty over predictability of long DSL, particularly for the Mediterranean region., Postprint (author's final draft)

The seismic generation rate, SGR, at southern California along the 1981–2007 recording period is analysed with the main purpose of finding out whether there exist some correlations between seismic activity before, after and along aftershock sequences triggered by mainshocks of high magnitude. The possibility that a mainshock could be triggered by another neighbouring mainshock and its aftershock sequence is also investigated. The analyses are based on monthly SGR series, obtained as the number of events detected every month along the recording period considered. These monthly SGR series are derived for three aftershock areas associated with Landers (June 28, 1992, Mw = 7.3), Northridge (January 17, 1994, Mw = 6.7) and Hector Mine (October 16, 1999, Mw = 7.1) mainshocks. The most relevant features of SGR series are investigated through various techniques: 1) the rescaled range analysis and the interpretation of the Hurst exponent in terms of persistence, anti-persistence and randomness; 2) time trend estimation by the Kendall-tau algorithm and assessment of their statistical significance by the Mann-Kendall test; 3) the self-affine character, derived from semivariograms, and the Hausdorff measure; 4) autocorrelation and power spectra; 5) cross-correlation and cross-power spectra; 6) the search for the statistical distribution best reproducing the empirical probability of SGR series. Additionally, a close look at plots of epicenters within the aftershock areas, distinguishing between periods of background and aftershock activity, permits detecting some features of the seismicity. Changes on spatial patterns of seismicity suggest that the effects of tectonic stress redistribution could persist beyond an aftershock period, at short and medium distances of the mainshock. This possibility would be also in agreement with cross-correlation results for SGR series., Postprint (author's final draft)

The complexity, predictability and predictive instability of the Western Mediterranean Oscillation index (WeMOi) at monthly scale, years 1856-2000, are analysed from the viewpoint of monofractal and multifractal theories. The complex physical mechanism is quantified by: (1) the Hurst exponent, H, of the rescaled range analysis; (2) correlation and embedding dimensions, mu* and d(E), together with Kolmogorov entropy, kappa, derived from the reconstruction theorem; and (3) the critical Holder exponent, alpha(o), the spectral width, W, and the asymmetry of the multifractal spectrum, f(alpha). The predictive instability is described by the Lyapunov exponents, lambda, and the Kaplan-Yorke dimension, D-KY, while the self-affine character is characterized by the Hausdorff exponent, H-a. Relationships between the exponent beta, which describes the dependence of the power spectrum S(f) on frequency f, and the Hurst and Hausdorff exponents suggest fractional Gaussian noise (fGn) as a right simulation of empiric WeMOi. Comparisons are made with monthly North-Atlantic Oscillation and Atlantic Multidecadal Oscillation indices. The analysis is complemented with an ARIMA(p,1,0) autoregressive process, which yields a more accurate prediction of WeMOi than that derived from fGn simulations., Postprint (author's final draft)

Peer Reviewed, Postprint (published version)

A spatial analysis of partial duration series, PDS, of the dry spell lengths, DSL, is applied to 267 European stations during years 1951–2000. A DSL is defined as the number of consecutive days with precipitation below 0.1 mm/day. For every station, PDS are made of DSL longer than those corresponding to 95th empirical percentile. The L-skewness and L-kurtosis diagram of the PDS distributions shows that most of the stations fit well a generalised Pareto, GP, model. Only four rain gauge records at the southeast Mediterranean coast notably depart from this model. In addition, DSL maps for return periods of 2, 5, 10, 25 and 50 years are introduced by taking into account GP parameters, which are estimated by fitting the GP distribution to empirical PDS distributions of DSL. A comparative study with those obtained in a previous paper, for the whole DSL series and the corresponding best distribution model (Pearson type III), shows that the differences of DSL for the different return periods keep within ±10 % in most of rain gauges. Moreover, a principal component analysis, PCA, is applied to the four first L-moments of the 267 rain gauges. Then, a regionalization in 11 groups is obtained after the clustering process. Finally, a regional frequency analysis is attempted, being possible to assign a GP parent distribution with different parameters to 7 out of the 11 groups., Postprint (author's final draft)

Peer Reviewed, Postprint (published version)

Several properties of aftershock series related to the main shocks of Landers, Northridge and Hector Mine (southern California, USA) are reproduced by the Dynamic Fiber Bundle Model, DFBM. Optimum values for the three parameters governing DFBM are determined by searching for the best agreement of real aftershock series properties and those of synthetic sequences generated by this model. The analysis of the model parameter values provides details on the underlying physical mechanism of the aftershock sequence generation. First, the ratio of seismic energy radiated as seismic waves and transferred as stress-strain to adjacent faults; second, the degree of stress heterogeneity reproducing the complex behavior of real aftershock series. Additionally, the results of simulations support the coexistence of two types of relaxation processes. One of them is associated with the well-known modified Omori's (MO) law, which involves elapsed times between consecutive aftershocks monotonically increasing; the other is manifested by episodes of sudden stress release, with inter-event times much shorter than those predicted by MO law. These episodes are assumed to be a consequence of the complex distribution of tectonic stresses and fault geometry. The first process is associated to events designed as leading aftershocks, LA. The second process generates series of events which are designed as cascades, CA. It is worth of mention that several properties concerning CAs can be reasonably related to critical changes on stress field along the simulation process., Postprint (updated version)

Peer Reviewed, Postprint (published version)

A compilation of daily extreme temperatures recorded at the Fabra Observatory (Catalonia, NE Spain) since 1917 up to 2005 has permitted an exhaustive analysis of the fractal behaviour of the daily extreme temperature residuals, DTR, defined as the difference between the observed daily extreme temperature and the daily average value. The lacunarity characterises the lag distribution on the residual series for several thresholds. Hurst, H, and Hausdorff, Ha, exponents, together with the exponent beta of the decaying power law, describing the evolution of power spectral density with frequency, permit to characterise the persistence, antipersistence or randomness of the residual series. The self-affine character of DTR series is verified, and additionally, they are simulated by means of fractional Gaussian noise, fGn. The reconstruction theorem leads to the quantification of the complexity (correlation dimension, mu*, and Kolmogorov entropy, kappa.) and predictive instability (Lyapunov exponents, lambda, and Kaplan-Yorke dimension, D-KY) of the residual series. All fractal parameters are computed for consecutive and independent segments of 5-year lengths. This strategy permits to obtain a high enough number of fractal parameter samples to estimate time trends, including their statistical significance. Comparisons are made between results of predictive algorithms based on fGn models and an autoregressive autoregressive integrated moving average (ARIMA) process, with the latter leading to slightly better results than the former. Several dynamic atmospheric mechanisms and local effects, such as local topography and vicinity to the Mediterranean coast, are proposed to explain the complex and instable predictability of DTR series. The memory of the physical system (Kolmogorov entropy) would be attributed to the interaction with the Mediterranean Sea., Postprint (published version)

The multifractal character of the daily extreme temperatures in Catalonia (NE Spain) is analyzed by means of the multifractal detrended fluctuation analysis (MF-DFA) applied to 65 thermometric records covering years 1950–2004. Although no clear spatial patterns of the multifractal spectrum parameters appear, factor scores deduced from Principal Component analysis indicate some signs of spatial gradients. Additionally, the daily extreme temperature series are classified depending on their complex time behavior, through four multifractal parameters (Hurst exponent, Hölder exponent with maximum spectrum, spectrum asymmetry and spectrum width). As a synthesis of the three last parameters, a basic measure of complexity is proposed through a normalized Complexity Index. Its regional behavior is found to be free of geographical dependences. This index represents a new step towards the description of the daily extreme temperatures complexity., Postprint (published version)

Aiming to improve the knowledge of droughts in Europe, three indices related to dry spells, DS, regime have been analysed: the number of DS per year, N; the longest annual DS, L-max; and the mean DS length per year, L, for different daily rainfall thresholds (0.1, 1.0, 5.0 and 10.0 mm/day) at annual and seasonal scales. The database consists of daily records from 267 rain gauges, along the years 1951-2000. First, the mean values at annual and seasonal scales of these three indices are represented for the four thresholds. For 0.1 and 1.0 mm/day, spatial patterns suggest a strong N-S gradient for latitudes south of 45 degrees N, especially at annual scale and in summer season. For 5.0 and 10.0 mm/day, the patterns are different, with a strong gradient in the Scandinavian Peninsula and the largest L-max and L at NE Europe, except for summer. Second, a principal component analysis, PCA, is applied to the 60 variables (three indices at five time scales and four thresholds) characterising the DS regime of every gauge. A clustering process leads to a classification of the 267 rain gauges into 20 spatial clusters, on the basis of five selected principal components replacing the original variables. Most of clusters are spatially coherent, with greater spatial variability on DS regimes towards the south and west than to the north and east of Europe. And third, time trends on the three indices are quantified by the Kendall-tau algorithm, and statistical significances at 95% confidence level are assessed by the Mann-Kendall test. For all thresholds and seasons, there is a clear predominance of significant negative trends for N. Specifically, the highest number of rain gauges with significant negative trends corresponds to summer and winter, with average percentages from -2.7 to -8.1% per decade. In summer, significant negative trends are observed in Western Europe at 40 degrees-60 degrees N and between 10 degrees W and 20 degrees E. In annual and winter periods, negative trends, Postprint (published version)

Mediante el análisis estadístico y utilizando diversas técnicas fractales en esta tesis se estudia el comportamiento temporal y espacial de tres series de réplicas sísmicas ocurridas en el Sur de California, que tuvieron lugar después de los terremotos de Landers (Mw=7.3, 1992), Northridge (Mw=6.7, 1994) y Hector Mine (Mw=7.1, 1999) Se plantean tres objetivos principales en este trabajo: 1) Caracterizar y analizar el proceso de ocurrencia de las réplicas sísmicas, en particular el comportamiento temporal que presentan. De acuerdo con la hipótesis que proponen CORREIG et al. (1997) y MORENO et al. (2001), el análisis de este comportamiento temporal muestra que la producción de las réplicas sísmicas se puede describir como una superposición de dos procesos de relajación de los esfuerzos tectónicos. 2) Simular el comportamiento temporal de las tres series de réplicas sísmicas mediante una versión modificada del modelo del Fiber Bundle, el cual describe el proceso de ruptura de un material heterogéneo previamente fracturado, como la corteza terrestre. El análisis de las réplicas sísmicas simuladas con este modelo modificado, que se introduce en el trabajo de MORENO et al. (2001), (FBMdp), nos permitirá encontrar las similitudes y las diferencias con respecto a las series de réplicas reales. Además, nos proporcionará una interpretación y una posible relación entre la dinámica presente en el modelo y el proceso de ruptura que originan las réplicas sísmicas. 3) Analizar y caracterizar el comportamiento fractal de las tres series de réplicas sísmicas mediante dos series temporales, la de distancia, Δ, y la de tiempo, τ, entre réplicas consecutivas. Para realizar este análisis se aplican diversas técnicas fractales como el análisis de rango reescalado, el posible comportamiento de las series como fractales auto-afines y el análisis de la lacunaridad. Además, se utiliza el teorema de Reconstrucción para caracterizar la predictibilidad del sistema y su posible comportamiento c, In this PhD thesis we are interested in the time and spatial behavior of seismic aftershock sequences. Through statistical analyses and several fractal techniques we intend to analyze three aftershocks sequences occurred at Southern California, after the Landers (Mw = 7.3, 1992), Northridge (Mw = 6.7, 1994) and Hector Mine (Mw = 7.1, 1999) mainshocks. There are three main objectives in this thesis: 1) To characterize and analyze the process of occurrence of aftershocks, particularly the time behavior they exhibit. 2) To simulate the time behavior of the three aftershocks series through a modified version of the Fiber Bundle model, describing the rupture process in heterogeneous and fractured materials, like the Earth crust. 3) To analyze and characterize the fractal behavior of the three aftershock series through two time series, the elapsed distance, ¿, and the elapsed time, t, between consecutive aftershocks. As a summary, the main conclusions are listed below: 1) The kinematic analysis of the aftershock sequences shows a superposition of two different processes of tectonic stress release. The first process describes a long-term time decay of aftershocks, which is well described by the modified Omori law, MO. The aftershocks that satisfy this process are called leading aftershocks. The second process describes the aftershock production at a higher rate, which departs from the behavior described by MO law. These groups of seismic aftershocks are called cascades. Unlike the study by CORREIG et al. (1997) and MORENO et al. (2001), the much larger number of aftershocks belonging to the three sequences (LND, HM and NOR) allows the implementation of additional statistical analyses and fractal techniques to the cascades. The results derived from these analyses lead to conclude that cascades show remarkable features common to the three aftershock series. 2) The FBMdp is a suitable model to describe the process of aftershock generation. The comparison between simulated and, Postprint (published version)