The elliptical dimension of space-time atmospheric stratification of passive admixtures using lidar data

Radkevich, Alexander; Lovejoy, S.; Strawbridge, K. B.; Schertzer, D.

doi:10.1016/j.physa.2007.03.046

Cited by 12 publications

(7 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In contrast, for cloud liquid water content (LWC), Lovejoy and Schertzer (1995) and Davis et al (1996) have found robust results with H % 0.3 which is close to the value found for the fluctuations in the concentration of a passive scalar advected by the wind field (the theoretical value is H = 1/3 for the passive scalar in the well developed Corrsin-Obukhov theory). Also, Lilley et al (2004) and Radkevich et al (2006) find horizontal values H % 0.33 ± 0.01 for both cirrus clouds and aerosols using lidar data (the value 0.60 ± 0.02 indicating scaling stratification was found in the vertical, close to the theoretical value 3/5). (Note added in press: when the spectrum of the HYDROP LWC is analysed it also shows H % 1/3 at the lower wavenumbers with a transition to a white noise spectrum at the higher wavenumbers, see further comments below).…”

Section: Geophysical Fields and Non-conservative Multifractalssupporting

confidence: 61%

Multifractal large number of drops limit in rain

Lilley

Lovejoy

Desaulniers-Soucy

et al. 2006

Journal of Hydrology

Self Cite

View full text Add to dashboard Cite

Section: Geophysical Fields and Non-conservative Multifractalssupporting

confidence: 61%

Multifractal large number of drops limit in rain

Lilley

Lovejoy

Desaulniers-Soucy

et al. 2006

Journal of Hydrology

Self Cite

View full text Add to dashboard Cite

“…Until now, we have applied ASAT to confirm the anisotropic space-time scaling extensions of the Corrsin-Obukhov law; we did not use it to empirically estimate the theoretical exponents. In Radkevich et al (2007), we show one way of doing this. Here, we return to the method of part II (orthogonal directions), but consider the anisotropy of the moments of all orders (i.e.…”

Section: Discussionmentioning

confidence: 99%

Scaling turbulent atmospheric stratification. III: Space–time stratification of passive scalars from lidar data

Radkevich¹,

Lovejoy²,

Strawbridge³

et al. 2008

Quart J Royal Meteoro Soc

Self Cite

View full text Add to dashboard Cite

ABSTRACT:In this third and final part of the series, we concentrate on the temporal behaviour of atmospheric passive scalars. We first recall that -although the full (x, y, z, t) turbulent processes respect an anisotropic scale invariance -that due to advection -the generator will generally not be a diagonal matrix. This implies that the scaling of (1-D) temporal series will generally involve three exponents in real space: 1/3, 1/2, 3/5, for spectra β τ = 5/3, 2, 11/5, with the first and last corresponding to domination by advection (horizontal and vertical respectively), and the second to pure temporal development (no advection). We survey the literature and find that almost all the empirical β τ values are indeed in the range 5/3 to 2. We then use meteorological analyses to argue that, although pure temporal development is unlikely to be dominant for time-scales less than the eddy turnover time of the largest structures (about 2 weeks), an intermittent vertical velocity could quite easily explain the occasionally observed β τ ≈ 2 spectra.We then use state-of-the-art vertically pointing lidar data of backscatter ratios from both aerosols and cirrus clouds yielding several (z, t) vertical space-time cross-sections with resolution of 3.75 m in the vertical, 0.5-30 s in time and spanning 3-4 orders of magnitude in temporal scale. We first test the predictions of the anisotropic, multifractal extension of the Corrsin-Obukhov law in the vertical and in time, separately finding that the cirrus and aerosol backscatters both followed the theoretical (anisotropic) scalings accurately; three of the six cases show dominance by the horizontal wind, the others by the vertical wind. In order to test the theory in arbitrary directions in this (z, t) space, and in order to get more complete information about the underlying physical scale, we develop and apply a new Anisotropic Scaling Analysis Technique (ASAT) which is based on a nonlinear space-time coordinate transformation. This transforms the original differential scaling into standard self-similar scaling; there remains only a 'trivial' anisotropy. This method is used in real space on 2-D structure functions. It is applied to both the new (z, t) data as well as the (x, z) data discussed in part II. Using ASAT, we verify the theory to within about 10% over more than three orders of magnitude of space-time scales in arbitrary directions in (x, z) and (z, t) spaces. By considering the high-(and low-) order structure functions, we verify the theory for both weak and strong structures; as predicted, their average anisotropies are apparently the same.Putting together the results for (x, z) and (z, t), and assuming that there is no overall stratification in the horizontal (x, y) plane, we find that the overall (x, y, z, t) space is found to have an effective 'elliptical dimension' characterizing the overall space-time stratification equal to D eff,st = 3.21 ± 0.05.

show abstract

“…2) together with the fact that we are looking at instantaneous realizations of fields rather than ensemble average statistics. But in other cases it could be investigated using a different set of UM parameters to describe anisotropy between horizontal and vertical directions (see e.g., Lovejoy et al, 1987;Lazarev et al, 1994;Radkevich et al, 2007).…”

Section: Scaling In Cloud Simulated Fields -3-d Analysismentioning

confidence: 99%

Multifractal properties of embedded convective structures in orographic precipitation: toward subgrid-scale predictability

Nogueira

Barros

Miranda

2013

Nonlin. Processes Geophys.

View full text Add to dashboard Cite

Abstract. Rain and cloud fields produced by fully nonlinear idealized cloud resolving numerical simulations of orographic convective precipitation display statistical multiscaling behavior, implying that multifractal diagnostics should provide a physically robust basis for the downscaling and sub-grid scale parameterizations of moist processes. Our results show that the horizontal scaling exponent function (and respective multiscaling parameters) of the simulated rainfall and cloud fields varies with atmospheric and terrain properties, particularly small-scale terrain spectra, atmospheric stability, and advective timescale. This implies that multifractal diagnostics of moist processes for these simulations are fundamentally transient, exhibiting complex nonlinear behavior depending on atmospheric conditions and terrain forcing at each location. A particularly robust behavior found here is the transition of the multifractal parameters between stable and unstable cases, which has a clear physical correspondence to the transition from stratiform to organized (banded and cellular) convective regime. This result is reinforced by a similar behavior in the horizontal spectral exponent. Finally, our results indicate that although nonlinearly coupled fields (such as rain and clouds) have different scaling exponent functions, there are robust relationships with physical underpinnings between the scaling parameters that can be explored for hybrid dynamical-statistical downscaling.

show abstract

The elliptical dimension of space-time atmospheric stratification of passive admixtures using lidar data

Cited by 12 publications

References 34 publications

Multifractal large number of drops limit in rain

Multifractal large number of drops limit in rain

Scaling turbulent atmospheric stratification. III: Space–time stratification of passive scalars from lidar data

Multifractal properties of embedded convective structures in orographic precipitation: toward subgrid-scale predictability

Contact Info

Product

Resources

About