Mathematics – Logic
Scientific paper
May 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007agusm.h41a..06l&link_type=abstract
American Geophysical Union, Spring Meeting 2007, abstract #H41A-06
Mathematics
Logic
1840 Hydrometeorology, 1869 Stochastic Hydrology, 4415 Cascades, 4440 Fractals And Multifractals, 4480 Self-Organized Criticality
Scientific paper
The hydrologic cycle begins with precipitation input followed by topography modulated runoff leading to streamflow distributed over river networks. Each of these parts of the cycle involve spatial structures varying over planetary down to millimetric scales; in time, the precipitation and streamflow are strongly variable from climatological scales down to less than a second. In the last 25 years much progress has been made in understanding scaling processes which generically generate variability over huge ranges. Scaling processes have nonlinear dynamical mechanisms which repeat scale after scale from large to small scales leading to non- classical multifractal resolution dependencies. This means that the statistical properties vary systematically in strong, power law ways with the resolution, that classical geostatistics - which assume strong regularity and homogeneity assumptions - do no apply. We can now broadly understand hydrological variability as a consequence of scale invariant dynamics - although as we discuss - the notion of scale invariance must be suitably generalized to take into account the strong (spatial and space-time) anisotropies of the processes. These nonclassical scaling "cascade" processes have the particularity that the variability builds up scale by scale so that at any given scale the variability is precisely the consequence of the huge dynamical range of the phenomena. Due to the existence of stable, attractive multifractal processes, in the limit of a large number of interacting processes or scales, only three "universal" parameters are generally important. These generic features of scaling imply that at a given finite scale, the variability due to the effects of the larger scales is enough to give rise to long-tailed lognormal and log-Levy distributions. However if we also take into account the "hidden" subgrid variability, then we find that the extremes are even stronger; they are generically power laws, "fat-tailed". In this way, cascades provide a nonclassical route to Self-Organized Criticality. We illustrate these ideas on both precipitation data from the recent HYDROP stereophotography experiment which directly determined the size and position of drops and - at the other scale extreme - the planetary TRMM (Tropical Rainfall Monitoring Mission) satellite radar data from 5 - 20,000km scales. We then review recent analyses of streamflow showing how the mean flow information - coupled with universal multifractal parametrizations with power law tails - can be used to estimate return times for extreme flood events.
Lovejoy Shaun
Schertzer Daniel
Tchigirinskaya Y.
No associations
LandOfFree
Scaling and Extremes in precipitation and streamflow does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Scaling and Extremes in precipitation and streamflow, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Scaling and Extremes in precipitation and streamflow will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1035200