S. Lovejoy

Universal multifractal indices for the ocean surface at far red wavelengths

For some time, ocean wave breaking has been conceptualized as a cascade process in which the large scale wind energy flux driving the system is dissipated by wave breaking at small scales, the two seperated by the “equilibrium” scaling range. Cascades are now known to generically lead to multifractals; with special “universal” multifractals theoretically predicted. In this paper we use far red (0.95 μm) radiances at 1m resolution obtained from aircraft to test the multifractal behavior of the ocean surface and estimate the corresponding universal multifractal parameters of the radiance field.

Scaling Of Turbulence In The Atmospheric Surface-Layer: Which Anisotropy?

This paper aims to provide an insight into the fundamental relationships between large and small scale wind velocity fluctuations within the boundary layer through careful analysis of measuring mast wind velocities. The measuring mast was in a wind farm on top of a mountain (with steep inclines of about 30°) on an island surrounded by the sea which meant the horizontal mean flow fluctuations were dominated by buoyancy forces and vertical shears at large scales (above 500m). Thus using a variety of methods including spectral, integrated spectral, integrated cospectral and multifractal analysis we were able to clearly dispel the relevance of 2D turbulence and give on the contrary some credence to the multifractal anisotropic model.

Multifractal Statistical Methods and Space-Time Scaling Laws for Turbulent Winds

We discuss the results of a universal multifractal (UM) analysis performed on the GROWIAN wind speed dataset. Within this framework the wind speed can be reproduced, including the extremes, at all scales using just three parameters: α, C 1 and H [1]. We exploit the fact that the wind speed is simultaneously recorded at several positions (effectively two grids) on two masts. The first grid allows us to compare the scaling of the horizontal spatial increments of the wind speed (at three heights) with that of the temporal increments, thus enabling us to verify Taylor’s hypothesis of frozen turbulence. The second grid allows us to test the hypothesis of scaling anisotropy between horizontal and vertical shears of the wind speed. The two scaling laws refer to the choice of either Kolmogorov energy or buoyancy force fluxes. The spatial structure function analyses assume the large number of data samples (approximately 150 samples of twenty minutes) reduces the uncertainties from the limited number of spatial points. The proof of universal scaling behaviour for different wind farm sites (see [2] for comparison) is an exciting concept that opens up the possibility of further areas of research and application within the field.

Multifractal characteristics and extremes of high-resolution rainfall, application to climate change detection

The quality of rainfall statistics, especially the Intensity‑Duration‑Frequency curves, closely depends on the reliability of available data. However, it has been shown that most of the time series obtained with tipping bucket rain gauges have a lower measuring frequency than is normally assumed. This question is particularly important for urban hydrology, where it is important to take into account high frequency fluctuations of rainfall. Preliminary studies showed that the estimated number of floods was lower when low time resolution data were used, compared to number of floods obtained with the help of higher time resolution data. The deficit of high frequency data can lead to apparent breaks in the scaling laws, which unnecessarily and notoriously complicate rainfall modelling. It is therefore essential to quantify the quality of data before using them. We present a SERQUAL procedure that enables us to answer this question and we use this procedure to select sub-series having the qualities required for high-resolution analysis. A multifractal approach is then applied to the selected data to characterize the temporal structure and the extreme behaviour of rainfall. In the present paper we present a reliable estimate of the multifractal parameters of the five‑minute high resolution rainfall data for the four departments in France. These parameters can be used to calibrate or validate statistical and stochastic models. On the other hand, the evolution of the multifractal characteristics can also be used to evaluate the hydrological consequences of climate change. The obtained results show that the influence of climate change on precipitation is not perceptible for the studied periods in Ile-de-France.

Reply to comment by Igor Esau on “Do stable atmospheric layers exist?”

[1] We would like to thank Esau (2009) for attempting to save the classical notion of stable layers; his argument is i very close to one raised up by an anonymous reviewer of Lovejoy et al. (2008b). Since a similar argument is often invoked to justify atmospheric applications of linear gravity i wave theories, it appears to be widespread in the community. We therefore hope this debate will clarify the issue.