Review: Fractal Geometry in Precipitation
Rainfall, or more generally the precipitation process (flux), is a clear example of chaotic variables resulting from a highly nonlinear dynamical system, the atmosphere, which is represented by a set of physical equations such as the Navier–Stokes equations, energy balances, and the hydrological cyc...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-01-01
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| Series: | Atmosphere |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-4433/15/1/135 |
| _version_ | 1827372789031501824 |
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| author | Robert Monjo Oliver Meseguer-Ruiz |
| author_facet | Robert Monjo Oliver Meseguer-Ruiz |
| author_sort | Robert Monjo |
| collection | DOAJ |
| description | Rainfall, or more generally the precipitation process (flux), is a clear example of chaotic variables resulting from a highly nonlinear dynamical system, the atmosphere, which is represented by a set of physical equations such as the Navier–Stokes equations, energy balances, and the hydrological cycle, among others. As a generalization of the Euclidean (ordinary) measurements, chaotic solutions of these equations are characterized by fractal indices, that is, non-integer values that represent the complexity of variables like the rainfall. However, observed precipitation is measured as an aggregate variable over time; thus, a physical analysis of observed fluxes is very limited. Consequently, this review aims to go through the different approaches used to identify and analyze the complexity of observed precipitation, taking advantage of its geometry footprint. To address the review, it ranges from classical perspectives of fractal-based techniques to new perspectives at temporal and spatial scales as well as for the classification of climatic features, including the monofractal dimension, multifractal approaches, Hurst exponent, Shannon entropy, and time-scaling in intensity–duration–frequency curves. |
| first_indexed | 2024-03-08T11:06:26Z |
| format | Article |
| id | doaj.art-7e358177d8464e8e961a5a07096735ab |
| institution | Directory Open Access Journal |
| issn | 2073-4433 |
| language | English |
| last_indexed | 2024-03-08T11:06:26Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Atmosphere |
| spelling | doaj.art-7e358177d8464e8e961a5a07096735ab2024-01-26T15:02:39ZengMDPI AGAtmosphere2073-44332024-01-0115113510.3390/atmos15010135Review: Fractal Geometry in PrecipitationRobert Monjo0Oliver Meseguer-Ruiz1Department of Algebra, Geometry and Topology, Complutense University of Madrid, 28040 Madrid, SpainMillennium Nucleus in Andean Peatlands (AndesPeat), Arica 1010069, ChileRainfall, or more generally the precipitation process (flux), is a clear example of chaotic variables resulting from a highly nonlinear dynamical system, the atmosphere, which is represented by a set of physical equations such as the Navier–Stokes equations, energy balances, and the hydrological cycle, among others. As a generalization of the Euclidean (ordinary) measurements, chaotic solutions of these equations are characterized by fractal indices, that is, non-integer values that represent the complexity of variables like the rainfall. However, observed precipitation is measured as an aggregate variable over time; thus, a physical analysis of observed fluxes is very limited. Consequently, this review aims to go through the different approaches used to identify and analyze the complexity of observed precipitation, taking advantage of its geometry footprint. To address the review, it ranges from classical perspectives of fractal-based techniques to new perspectives at temporal and spatial scales as well as for the classification of climatic features, including the monofractal dimension, multifractal approaches, Hurst exponent, Shannon entropy, and time-scaling in intensity–duration–frequency curves.https://www.mdpi.com/2073-4433/15/1/135precipitationfractalmonofractaltime-scalingHurst exponent |
| spellingShingle | Robert Monjo Oliver Meseguer-Ruiz Review: Fractal Geometry in Precipitation Atmosphere precipitation fractal monofractal time-scaling Hurst exponent |
| title | Review: Fractal Geometry in Precipitation |
| title_full | Review: Fractal Geometry in Precipitation |
| title_fullStr | Review: Fractal Geometry in Precipitation |
| title_full_unstemmed | Review: Fractal Geometry in Precipitation |
| title_short | Review: Fractal Geometry in Precipitation |
| title_sort | review fractal geometry in precipitation |
| topic | precipitation fractal monofractal time-scaling Hurst exponent |
| url | https://www.mdpi.com/2073-4433/15/1/135 |
| work_keys_str_mv | AT robertmonjo reviewfractalgeometryinprecipitation AT olivermeseguerruiz reviewfractalgeometryinprecipitation |