Parallel Algorithms for Multifractal Analysis of River Networks

Primavera, Leonardo; Florio, Emilia

doi:10.1007/978-3-030-39081-5_27

Cited by 6 publications

(4 citation statements)

References 9 publications

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“…where we have introduced the definition of si given in Equation (9). Equation (A3) has the same scaling properties in the limit of vanishing s i and p as Equation (8.1).…”

Section: Institutional Review Board Statement: Not Applicablementioning

confidence: 99%

“…Moreover, it is not truly difficult nowadays to assemble computational facilities by clustering several moderately expensive PCs interconnected with good network switches to allow the computation of parallelizable algorithms on a considerable amount of computational cores. In a previous article [9] (hereinafter we refer to this article as P1), we have discussed in detail a possible implementation of a parallel FMA by using the Message Passing Interface (MPI) paradigm [10], which is nowadays a standard for parallel numerical computations on distributed memory machines (such as the clusters of PCs cited above). Such a paradigm can also be used on shared memory machines, such as single-CPU workstations.…”

Section: Introductionmentioning

confidence: 99%

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A Hybrid MPI-OpenMP Parallel Algorithm for the Assessment of the Multifractal Spectrum of River Networks

Primavera

Florio

2021

Water

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The possibility to create a flood wave in a river network depends on the geometric properties of the river basin. Among the models that try to forecast the Instantaneous Unit Hydrograph (IUH) of rainfall precipitation, the so-called Multifractal Instantaneous Unit Hydrograph (MIUH) rather successfully connects the multifractal properties of the river basin to the observed IUH. Such properties can be assessed through different types of analysis (fixed-size algorithm, correlation integral, fixed-mass algorithm, sandbox algorithm, and so on). The fixed-mass algorithm is the one that produces the most precise estimate of the properties of the multifractal spectrum that are relevant for the MIUH model. However, a disadvantage of this method is that it requires very long computational times to produce the best possible results. In a previous work, we proposed a parallel version of the fixed-mass algorithm, which drastically reduced the computational times almost proportionally to the number of Central Processing Unit (CPU) cores available on the computational machine by using the Message Passing Interface (MPI), which is a standard for distributed memory clusters. In the present work, we further improved the code in order to include the use of the Open Multi-Processing (OpenMP) paradigm to facilitate the execution and improve the computational speed-up on single processor, multi-core workstations, which are much more common than multi-node clusters. Moreover, the assessment of the multifractal spectrum has also been improved through a direct computation method. Currently, to the best of our knowledge, this code represents the state-of-the-art for a fast evaluation of the multifractal properties of a river basin, and it opens up a new scenario for an effective flood forecast in reasonable computational times.

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“…where we have introduced the definition of si given in Equation (9). Equation (A3) has the same scaling properties in the limit of vanishing s i and p as Equation (8.1).…”

Section: Institutional Review Board Statement: Not Applicablementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Hybrid MPI-OpenMP Parallel Algorithm for the Assessment of the Multifractal Spectrum of River Networks

Primavera

Florio

2021

Water

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“…This demonstration is done by means of the reduced order model developed in Vannitsem et al (2015). Indeed, the dynamical properties of physical systems can be related to their support fractal dimension as well as its singularities by means of different established concepts like the box-counting dimension (e.g., Steinhaus, 1954;Mandelbrot, 1967;Ott, 2002), generalized correlation integrals (Grassberger, 1983;Hentschel and Procaccia, 1983;Pawelzik and Schuster, 1987), the pointwise dimension method (Farmer et al, 1983;Donner et al, 2011), and related characteristics (Badii and Politi, 1984;Primavera and Florio, 2020). These methods are based on partitioning the phase space into hypercubes of size to define a suitable invariant measure through the filling probability of the ith hypercube by N k points as p k = N k /N , with N being the total number of points.…”

Section: Introductionmentioning

confidence: 99%

Multiscale fractal dimension analysis of a reduced order model of coupled ocean–atmosphere dynamics

2021

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Abstract. Atmosphere and ocean dynamics display many complex features and are characterized by a wide variety of processes and couplings across different timescales. Here we demonstrate the application of multivariate empirical mode decomposition (MEMD) to investigate the multivariate and multiscale properties of a reduced order model of the ocean–atmosphere coupled dynamics. MEMD provides a decomposition of the original multivariate time series into a series of oscillating patterns with time-dependent amplitude and phase by exploiting the local features of the data and without any a priori assumptions on the decomposition basis. Moreover, each oscillating pattern, usually named multivariate intrinsic mode function (MIMF), represents a local source of information that can be used to explore the behavior of fractal features at different scales by defining a sort of multiscale and multivariate generalized fractal dimensions. With these two complementary approaches, we show that the ocean–atmosphere dynamics presents a rich variety of features, with different multifractal properties for the ocean and the atmosphere at different timescales. For weak ocean–atmosphere coupling, the resulting dimensions of the two model components are very different, while for strong coupling for which coupled modes develop, the scaling properties are more similar especially at longer timescales. The latter result reflects the presence of a coherent coupled dynamics. Finally, we also compare our model results with those obtained from reanalysis data demonstrating that the latter exhibit a similar qualitative behavior in terms of multiscale dimensions and the existence of a scale dependency of the statistics of the phase-space density of points for different regions, which is related to the different drivers and processes occurring at different timescales in the coupled atmosphere–ocean system. Our approach can therefore be used to diagnose the strength of coupling in real applications.

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“…This demonstration is done by means of the reduced order model developed in Vannitsem et al (2015). Indeed, the dynamical properties of physical systems can be related to their support fractal dimension as well as its singularities by means of different established concepts like the box-counting dimension (Ott, 2002), generalized correlation integrals (Grassberger, 1983;Hentschel and Procaccia, 1983;Pawelzik and Schuster, 1987), the pointwise dimension method (Farmer et al, 1983;Donner et al, 2011), and related characteristics (Badii and Politi, 1984;Primavera and Florio, 2020). These methods are based on partitioning the phase-space into hypercubes of size to define a suitable invariant measure through the filling probability of the i−th hypercube by N k points as p k = N k /N , with N being the total number of points.…”

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confidence: 99%

Comment on esd-2020-96

2021

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Atmosphere and ocean dynamics display many complex features and are characterized by a wide variety of processes and couplings across different timescales. Here we demonstrate the application of Multivariate Empirical Mode Decomposition (MEMD) to investigate the multivariate and multiscale properties of a reduced order model of the ocean-atmosphere coupled dynamics. MEMD provides a decomposition of the original multivariate time series into a series of oscillating patterns with time-dependent amplitude and phase by exploiting the local features of the data and without any a priori assumptions on the decomposition basis. Moreover, each oscillating pattern, usually named Multivariate Intrinsic Mode Function (MIMF), represents a local source of information that can be used to explore the behavior of fractal features at different scales by defining a sort of multiscale/multivariate generalized fractal dimensions. With these two approaches, we show that the oceanatmosphere dynamics presents a rich variety of features, with different multifractal properties for the ocean and the atmosphere at different timescales. For weak ocean-atmosphere coupling, the resulting dimensions of the two model components are very different, while for strong coupling for which coupled modes develop, the scaling properties are more similar especially at longer time scales. The latter result reflects the presence of a coherent coupled dynamics. Finally, we also compare our model results with those obtained from reanalysis data demonstrating that the latter exhibit a similar qualitative behavior in terms of multiscale dimensions and the existence of a scale-dependency of topological and geometric features for different regions, being related to the different drivers and processes occurring at different timescales in the coupled atmosphere-ocean system.Our approach can therefore be used to diagnose the strength of coupling in real applications. IntroductionThe atmosphere and the ocean form a complex system whose dynamical variability extends over a wide range of spatial and temporal scales (Liu, 2012; Xue et al., 2020). As an example, the tropical regions are markedly characterized by inter-/multi-1

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Parallel Algorithms for Multifractal Analysis of River Networks

Cited by 6 publications

References 9 publications

A Hybrid MPI-OpenMP Parallel Algorithm for the Assessment of the Multifractal Spectrum of River Networks

A Hybrid MPI-OpenMP Parallel Algorithm for the Assessment of the Multifractal Spectrum of River Networks

Multiscale fractal dimension analysis of a reduced order model of coupled ocean–atmosphere dynamics

Comment on esd-2020-96

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