Mathematics – Logic
Scientific paper
Dec 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007agufm.u52a..07a&link_type=abstract
American Geophysical Union, Fall Meeting 2007, abstract #U52A-07
Mathematics
Logic
1839 Hydrologic Scaling, 1853 Precipitation-Radar, 3311 Clouds And Aerosols, 4440 Fractals And Multifractals
Scientific paper
Numerous studies have shown that over various ranges, atmospheric fields are scaling. However until now, for various technical reasons they have been restricted to relatively small ranges of scale, and to relatively small data sets (with few realizations). In particular, the key question as to the large scale space-time limits of scaling has not been empirically established. Does the scaling extend up to planetary scales? What are the corresponding long time scales? Is space-time differentially stratified or roughly isotropic? In this presentation we answer these questions using the first truly global scale analysis of satellite radiances examining 14 passive channels ranging from visible to infra red to passive microwave as well as (active) radar reflectivities. The spatial resolutions depend somewhat on wavelength but are from several kilometers up to planetary scales (20000km), and from (typically) 2- 4 days in time up to 10 years. Two basic analyses were performed: the first purely spatial analysis at full spatial resolution (but orbit by orbit), the second in space-time using a lower resolution (100 km, 2 - 4 day resolution) space-time grid. The spatial analysis showed that without exception the radiances are remarkably scale invariant displaying statistics typically within ±1 - ±2% of those predicted for multifractal cascades. The high accuracy with which scaling holds makes it one of the most accurately obeyed laws in meteorology. For the wavelengths ≤1.6 cm (passive microwave, visible, near and far infra red), this was true over ranges which extend from 5000 - 10000 km down to the resolution scale (≈ 4 km) with effective outer cascade scales in the range 8000 - 20000 km. For these wavelengths, the statistics were near those of turbulent passive scalars. In comparison, for both the passive microwave at 3 cm and the active microwave channel (precipitation radar, 2.2 cm), the cascade was much sparser and the outer scale was around 32000 km indicating that even at planetary scales there was residual variability due to interaction with other processes. In all cases, the outer scale was about twice as large in the east-west direction compared to the north-south direction. Finally, the space-time analyses on the gridded data showed that for the passive scalar - like radiances, the scaling extends to about 22 days (the lifetime of the largest planetary scale structures). The resulting space-time transformation implies a velocity of about 6m/s, and also that space-time is not differentially stratified. We note that for the (precipitation) reflectivity data - the scaling extends to at least 190 days and implies a space-time transformation with a much larger smaller velocity (50 cm/s). Since the data cover the principle wavebands responsible for incoming and outgoing radiative fluxes, and since the latter are strongly nonlinearly coupled with the atmosphere, it is hard to avoid the conclusion that the atmosphere is a scale invariant dynamical process.
Allaire V.
King Simon
Lovejoy Shaun
Pinel J.
Schertzer Daniel
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