Multifractals and resolution-independent remote sensing algorithms: The example of ocean colour

Lovejoy, S.; Schertzer, D.; Tessier, Yves; Gaonac’h, H.

doi:10.1080/01431160151144314

Cited by 50 publications

(41 citation statements)

References 48 publications

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“…Figure 4 also demonstrates the fact that if data from special locations (such as near high mountains) are analysed that we may expect systematic biases in our statistics and parameter estimates. These conditional statistics are discussed quantitatively and theoretically in Lovejoy et al (2001b). This underlines the need for coupled multifractal processes, possible through the use of a state vector and vector mulitfractal processes (based on "Lie cascades" Lovejoy et al, 2001b)).…”

Section: Spurious Breaks In the Scalingmentioning

confidence: 99%

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Multifractal earth topography

Gagnon

Lovejoy

Schertzer

2006

Nonlin. Processes Geophys.

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128

131

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Abstract. This paper shows how modern ideas of scaling can be used to model topography with various morphologies and also to accurately characterize topography over wide ranges of scales. Our argument is divided in two parts. We first survey the main topographic models and show that they are based on convolutions of basic structures (singularities) with noises. Focusing on models with large numbers of degrees of freedom (fractional Brownian motion (fBm), fractional Levy motion (fLm), multifractal fractionally integrated flux (FIF) model), we show that they are distinguished by the type of underlying noise. In addition, realistic models require anisotropic singularities; we show how to generalize the basic isotropic (self-similar) models to anisotropic ones. Using numerical simulations, we display the subtle interplay between statistics, singularity structure and resulting topographic morphology. We show how the existence of anisotropic singularities with highly variable statistics can lead to unwarranted conclusions about scale breaking.We then analyze topographic transects from four Digital Elevation Models (DEMs) which collectively span scales from planetary down to 50 cm (4 orders of magnitude larger than in previous studies) and contain more than 2×10 8 pixels (a hundred times more data than in previous studies). We use power spectra and multiscaling analysis tools to study the global properties of topography. We show that the isotropic scaling for moments of order ≤2 holds to within ±45% down to scales ≈40 m. We also show that the multifractal FIF is easily compatible with the data, while the monofractal fBm and fLm are not. We estimate the universal parameters (α, C 1 ) characterizing the underlying FIF noise to be (1.79, 0.12), where α is the degree of multifractality (0≤α≤2, 0 means monofractal) and C 1 is the degree of sparseness of the surface (0≤C 1 , 0 means space filling). In the same way, we investigate the variation of multifractal parameters betweenCorrespondence to: J.-S. Gagnon (gagnonjs@physics.mcgill.ca) continents, oceans and continental margins. Our analyses show that no significant variation is found for (α, C 1 ) and that the third parameter H , which is a degree of smoothing (higher H means smoother), is variable: our estimates are H =0.46, 0.66, 0.77 for bathymetry, continents and continental margins. An application we developped here is to use (α, C 1 ) values to correct standard spectra of DEMs for multifractal resolution effects.

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Section: Spurious Breaks In the Scalingmentioning

confidence: 99%

“…These conditional statistics are discussed quantitatively and theoretically in Lovejoy et al (2001b). This underlines the need for coupled multifractal processes, possible through the use of a state vector and vector mulitfractal processes (based on "Lie cascades" Lovejoy et al, 2001b)). …”

Section: Spurious Breaks In the Scalingmentioning

confidence: 99%

Multifractal earth topography

Gagnon

Lovejoy

Schertzer

2006

Nonlin. Processes Geophys.

Self Cite

128

131

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“…This purely turbulent regime appears to be limited to spatial scales smaller than a particular scale of the order of 100 m, called the "planktoscale" by Lovejoy et al (2001b). In fact, although phytoplankton can reasonably be described as passively advected, in the sense that its retroaction on the turbulent flow is negligible, it cannot be considered to be totally passive, since it is biologically active.…”

Section: Introductionmentioning

confidence: 99%

Multifractal analysis of oceanic chlorophyll maps remotely sensed from space

Montera¹,

Jouini²,

Verrier

et al. 2011

Ocean Sci.

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Abstract. Phytoplankton patchiness has been investigated with multifractal analysis techniques. We analyzed oceanic chlorophyll maps, measured by the SeaWiFS orbiting sensor, which are considered to be good proxies for phytoplankton. The study area is the Senegalo-Mauritanian upwelling region, because it has a low cloud cover and high chlorophyll concentrations. Multifractal properties are observed, from the sub-mesoscale up to the mesoscale, and are found to be consistent with the Corssin-Obukhov scale law of passive scalars. This result indicates that, in this specific region and within this scale range, turbulent mixing would be the dominant effect leading to the observed variability of phytoplankton fields. Finally, it is shown that multifractal patchiness can be responsible for significant biases in the nonlinear source and sink terms involved in biogeochemical numerical models.

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“…Such variability is often associated with turbulence, and multi-scaling properties of oceanic fields have been reported and studied in many previous studies: sea state (Kerman, 1993); phytoplankton concentration (Seuront et al, 1996a(Seuront et al, , b, 1999Lovejoy et al, 2001a); rainfall and cloud radiance (Tessier et al, 1993;Lovejoy and Schertzer, 2006); and satellite images of ocean colour, chlorophyll a and sea surface temperature (Lovejoy et al, 2001b;Nieves et al, 2007;Pottier et al, 2008;Turiel et al, 2009;de Montera et al, 2011;Renosh et al, 2015). Here we focus on coastal waters and consider particles transported by oceanic currents in this highly energetic medium (Svendsen, 1987;Schmitt et al, 2009).…”

Section: Introductionmentioning

confidence: 99%

Intermittent particle dynamics in marine coastal waters

Renosh

Schmitt

Loisel

2015

Nonlin. Processes Geophys.

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Abstract. Marine coastal processes are highly variable over different space scales and timescales. In this paper we analyse the intermittency properties of particle size distribution (PSD) recorded every second using a LISST instrument (Laser In-Situ Scattering and Transmissometry). The particle concentrations have been recorded over 32 size classes from 2.5 to 500 µm, at 1 Hz resolution. Such information is used to estimate at each time step the hyperbolic slope of the particle size distribution, and to consider its dynamics. Shannon entropy, as an indicator of the randomness, is estimated at each time step and its dynamics is analysed. Furthermore, particles are separated into four classes according to their size, and the intermittent properties of these classes are considered. The empirical mode decomposition (EMD) is used, associated with arbitrary-order Hilbert spectral analysis (AHSA), in order to retrieve scaling multifractal moment functions, for scales from 10 s to 8 min. The intermittent properties of two other indicators of particle concentration are also considered in the same range of scales: the total volume concentration C vol-total and the particulate beam attenuation coefficient c p (670). Both show quite similar intermittent dynamics and are characterised by the same exponents. Globally we find here negative Hurst exponents (meaning the small scales show larger fluctuation than large scales) for each time series considered, and nonlinear moment functions.

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Multifractals and resolution-independent remote sensing algorithms: The example of ocean colour

Cited by 50 publications

References 48 publications

Multifractal earth topography

Multifractal earth topography

Multifractal analysis of oceanic chlorophyll maps remotely sensed from space

Intermittent particle dynamics in marine coastal waters

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