Fractal Characterisation of Geophysical Measuring Networks and its Implication for an Optimal Location of Additional Stations: An Application to a Rain-Gauge Network

Mazzarella, A.; Tranfaglia, G.

doi:10.1007/s007040070040

Cited by 25 publications

(18 citation statements)

References 10 publications

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“…It can be cited Lovejoy and Mandelbrot (1985), Rodríguez-Iturbe et al (1989), Olsson et al (1993), Hubert et al (1993), Tessier et al (1996), Harris et al (1996), Veneziano et al (1996), Svensson et al (1996), Lima and Grasman (1999), Mazzarella (1999), Mazzarella and Tranfaglia (2000), Sivakumar (2001a, b), Sivakumar et al (2001) and Salas et al (2005), among many others. These references include a set of concepts (multifractality, chaotic behaviour, time persistence, predictability) applied to a variety of topics as rain intensity, annual amounts, precipitation caused by convective storms, characterisation and comparison of different climates and design and improvement of rain-gauge networks.…”

Section: State Of the Artmentioning

confidence: 99%

Lacunarity, predictability and predictive instability of the daily pluviometric regime in the Iberian Peninsula

Martínez¹,

Lana

Burgueño³

et al. 2007

Nonlin. Processes Geophys.

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Abstract. The complexity of the daily pluviometric regime of the Iberian Peninsula is analysed from the point of view of its lacunarity, predictability and predictive instability. The database consists of daily pluviometric records obtained from 43 rain gauges in Spain and Portugal for the period . Five different series are generated for every rain gauge. The first series is constituted by the consecutive daily amounts. The other four consist of dry spell lengths with respect to daily amount thresholds of 0.1, 1.0, 5.0 and 10.0 mm/day. A dry spell length is defined as the number of consecutive days with rainfall amounts below one of these thresholds. The empirical lacunarity for every rain gauge is well reproduced by two power laws, the exponents varying notably from one gauge to another. The spatial distribution of the lacunarity is characterised by a north to south or southeast gradient, thus suggesting that this parameter can be a useful tool to distinguish between different pluviometric regimes. The predictability of the five series is quantified by means of the rescaled analysis and the interpretation of the Hurst exponent. Its patterns reveal that most part of the Iberian Peninsula shows signs of persistence for the daily rainfall and the dry spell series, although persistence is only clearly manifested in some small domains. The instability of possible predictive algorithms is analysed through the Lyapunov exponents. They are only computed for the series of daily amounts and for dry lengths respect to the threshold level of 0.1 mm/day due to the short number of dry spells for larger threshold levels. The series of daily amounts depict the highest instability along the Mediterranean coast. The series of dry spells show an increasing instability from NE to SW Spain, with a relevant nucleus of high Lyapunov values in the south-western Atlantic coast. As a summary, lacunarity and Hurst and Lyapunov exponents depict a relevant spatial variation, which is in agreement with well known patterns of Correspondence to: X. Lana (francisco.javier.lana@upc.edu) the pluviometric regime, such as annual amount spatial distribution and return periods of dry spells.

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Section: State Of the Artmentioning

confidence: 99%

Lacunarity, predictability and predictive instability of the daily pluviometric regime in the Iberian Peninsula

Martínez¹,

Lana

Burgueño³

et al. 2007

Nonlin. Processes Geophys.

View full text Add to dashboard Cite

show abstract

“…It can be cited Lovejoy and Mandelbrot (1985), Rodríguez-Iturbe et al (1989), Olsson et al (1993), Hubert et al (1993), Tessier et al (1996), Harris et al (1996), Veneziano et al (1996), Svensson et al (1996), Lima and Grassman (1999), Mazzarella (1999), Mazzarella and Tranfaglia (2000), Sivakumar (2001a, b), Sivakumar et al (2001), Salas et al (2005) and Martínez et al (2007a), among many others. Multifractality, chaotic behaviour, time persistence and predictability have been concepts considered by these authors and many variables closely related to rainfall regimes have been analysed.…”

Section: Introductionmentioning

confidence: 99%

Complex behaviour and predictability of the European dry spell regimes

Lana

Martínez²,

Serra

et al. 2010

Nonlin. Processes Geophys.

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Abstract. The complex spatial and temporal characteristics of European dry spell lengths, DSL, (sequences of consecutive days with rainfall amount below a certain threshold) and their randomness and predictive instability are analysed from daily pluviometric series recorded at 267 rain gauges along the second half of the 20th century. DSL are obtained by considering four thresholds, R 0 , of 0.1, 1.0, 5.0 and 10.0 mm/day. A proper quantification of the complexity, randomness and predictive instability of the different DSL regimes in Europe is achieved on the basis of fractal analyses and dynamic system theory, including the reconstruction theorem. First, the concept of lacunarity is applied to the series of daily rainfall, and the lacunarity curves are well fitted to Cantor and random Cantor sets. Second, the rescaled analysis reveals that randomness, persistence and anti-persistence are present on the European DSL series. Third, the complexity of the physical process governing the DSL series is quantified by the minimum number of nonlinear equations determined by the correlation dimension. And fourth, the loss of memory of the physical process, which is one of the reasons for the complex predictability, is characterized by the values of the Kolmogorov entropy, and the predictive instability is directly associated with positive Lyapunov exponents. In this way, new bases for a better prediction of DSLs in Europe, sometimes leading to drought episodes, are established. Concretely, three predictive strategies are proposed in Sect. 5. It is worth mentioning that the spatial distribution of all fractal parameters does not solely depend on latitude and longitude but also reflects the effects of orography, continental climate or vicinity to the Atlantic and Arctic Oceans and Mediterranean Sea.

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“…gives a value larger than that provided by the Student distribution in correspondence of a number of freedom degrees and of a confidence level equal to n)2 and 99%, respectively (Mazzarella and Tranfaglia, 2000). The value of l 0 is also corrected for sample size in this way:…”

Section: Analysis and Resultsmentioning

confidence: 99%

Power Laws Governing Historical Earthquakes in the Apennine Chain (Southern Italy)

et al. 2005

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Rank-ordering analysis is applied to the intertimes between seismic events recorded in the Apennine belt between 40-42°N and 14-16°E from the 15th century onwards. It shows a power law capable of governing the intertimes between 1529 and 368 months and another power law which approximates a random simulation, for the intertimes shorter than 368 months. Only the first power law allows the computation of the return period of major events. Earthquakes with the same energy that are aligned according to different power laws imply the presence of two different populations, indicating, in turn, that the physics of seismic phenomena in the region examined is not straightforward, that the stress is probably not unidirectional and that it acts on a non-isotropic medium. The most probable estimated intertime value for the next event is found to be equal to 60 ± 20 years.

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Fractal Characterisation of Geophysical Measuring Networks and its Implication for an Optimal Location of Additional Stations: An Application to a Rain-Gauge Network

Cited by 25 publications

References 10 publications

Lacunarity, predictability and predictive instability of the daily pluviometric regime in the Iberian Peninsula

Lacunarity, predictability and predictive instability of the daily pluviometric regime in the Iberian Peninsula

Complex behaviour and predictability of the European dry spell regimes

Power Laws Governing Historical Earthquakes in the Apennine Chain (Southern Italy)

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