Rainfall dynamics at different temporal scales: A chaotic perspective

Sivakumar, Bellie

doi:10.5194/hess-5-645-2001

Cited by 83 publications

(68 citation statements)

References 17 publications

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“…Carbonnel, 1989, 1991;Olsson et al, 1992) and evolved towards the use of multifractal theory (see e.g. Schertzer, 1990, 1995;Ladoy et al, 1991Hubert, 1992Hubert, , 1995Tessier et al, 1992Tessier et al, , 1993Tessier et al, , 1996Hubert et al, 1993;Olsson and Niemczynowicz, 1994;de Lima and Bogardi, 1995;Olsson, 1995Burlando and Rosso, 1996;Harris et al, 1996;Svensson et al, 1996;Bendjoudi et al, 1997;de Lima, 1998de Lima, , 1999de Lima and Grasman, 1999;Kiely and Ivanova, 1999;Deidda, 2000;Sivakumar, 2001;de Lima et al, 2002;Veneziano and Furcolo, 2002;Nykanen and Harris, 2003;Veneziano and Langousis, 2005;Kantelhardt et al, 2006;Veneziano et al, 2006;Venugopal et al, 2006;Langousis and Veneziano, 2007;García-Marín et al, 2007;Royer et al, 2008).…”

Section: Some Aspects Of Scaling Theoriesmentioning

confidence: 99%

Investigating the multifractality of point precipitation in the Madeira archipelago

Lima

2009

Nonlin. Processes Geophys.

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Abstract. The purpose of this work is to contribute to a better understanding of the variability of precipitation in the Madeira archipelago. This archipelago is located in the Atlantic subtropical belt under the direct influence of the Azores high pressure system. It is formed by Madeira Island (728 km 2 ) and Porto Santo Island (42 km 2 ) and by two other groups of very small inhabited islands. The complex topography of the islands in the Madeira archipelago and their small size play a crucial role in the local precipitation regime, which is marked by high spatial variability.This paper explores the invariance of properties manifested across scales and determines the fractal and multifractal behaviour observed in the temporal structure of precipitation using daily and 10-min time series from several locations scattered over the main islands. The period covered by the precipitation records is 34 years for the daily data and almost 4 months for the 10-min data. The results show that the temporal structure of precipitation in the Madeira Archipelago exhibits scale-invariant and multifractal properties. The empirical exponent functions describing the scaling statistical properties of the precipitation intensity were characterized using multifractal parameters; these parameters are increasing our awareness of the dynamics of this process in these islands.

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Section: Some Aspects Of Scaling Theoriesmentioning

confidence: 99%

Investigating the multifractality of point precipitation in the Madeira archipelago

Lima

2009

Nonlin. Processes Geophys.

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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 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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“…Such a question still remains to be answered, and will be investigated in a future study. Nevertheless, our opinion, for the moment, especially based on nonlinear dynamic studies on streamflow (and other hydrologic data) and complex network studies on rainfall at different temporal scales, is that the streamflow network properties (including degree centrality, clustering coefficient, and degree distribution) may change for other temporal scales, despite the possible presence of scaling (or fractal) behavior in streamflow; see Sivakumar (2001), Sivakumar et al (2001Sivakumar et al ( , 2004Sivakumar et al ( , 2007, Regonda et al (2004), Salas et al (2005), Jha and Sivakumar (2017), and Naufan et al (2017) for some details. We hope to provide more reliable and convincing answers to this question in a future study, as we are currently conducting additional research on network properties in terms of scale and network size.…”

Section: Discussion Of Resultsmentioning

confidence: 99%

Temporal dynamics of streamflow: application of complex networks

et al. 2018

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This study employs the concepts of complex networks to study the temporal dynamics of streamflow, with emphasis on annual scale (i.e., year-to-year connections). The study proposes a new approach to construct the streamflow network at the annual scale. It uses the daily streamflow data to construct the annual streamflow network, instead of using the annual (mean or accumulated) streamflow data. With this approach, each year serves as a node in the network, with each node having a time series of daily streamflow values (not a single streamflow value). Streamflow data observed over a period of 151 years (October 1862-September 2013) from the Mississippi River basin at St. Louis, Missouri, USA are considered for implementation of the approach. The properties of the annual streamflow network are investigated using three complex network-based methods: degree centrality, clustering coefficient, and degree distribution. The sensitivity of the results to streamflow correlation threshold is also examined. The results suggest that (1) there are only a few very significant nodes (years) in the annual streamflow network (degree centrality method); (2) the annual streamflow network is not a classical random graph, but may be a small-world network or scale-free network (clustering coefficient method); and (3) the network exhibits a combination of exponential and power-law distribution (degree distribution method). Based on the identification of a significant stretch of period (around the 1950s-1990s) with very weak connections with the rest of the period studied, the results also suggest the influence of dam construction (and other anthropogenic factors) on the evolution of annual streamflow dynamics.

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Rainfall dynamics at different temporal scales: A chaotic perspective

Cited by 83 publications

References 17 publications

Investigating the multifractality of point precipitation in the Madeira archipelago

Investigating the multifractality of point precipitation in the Madeira archipelago

Complex behaviour and predictability of the European dry spell regimes

Temporal dynamics of streamflow: application of complex networks

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