HR: 10:50h
AN: NG41D-03 INVITED     [PDF]
TI: Low Rain-Rates, Spurious Scale Breaks and a new Depth Based Analysis Technique
AU: * de Lima, M P
EM: lima@dec.uc.pt
AF: IMAR/ESAC-Coimbra Polytechnic Inst., Bencanta, Coimbra, 3040-316 Portugal
AU: Lovejoy, S
EM: lovejoy@physics.mcgill.ca
AF: McGill Univ., 3600 University st., Montreal, Quebec, H3A 2T8 Canada
AU: Schertzer, D
EM: schertze@ccr.jussieu.fr
AF: Pierre and Marie Curie Univ., 4 Place Jussieu, Paris, 75005 France
AB: The non-linear variability of rainfall is present over a broad range of time and space scales; in addition, at a given scale it involves a huge dynamic range. Both of these characteristics challenge traditional measuring techniques; they require explicit modeling of the rain and the response of measurement devices - including tipping-bucket and siphon type rain gauges. Since they generically produce extreme variability over wide scale ranges, multifractal models of rain are the natural choice. The generic multifractal process is a multiplicative cascade. From the point of view of multifractals, there is an enormous difference between low but finite rain rates and exactly zero rates. This leads to a fundamental modeling question: is a single rain process adequate to model rain (perhaps with a very low rate cut-off to zero) or does one require separate processes for determining where and when it rains and another for the rates in the raining regions? In more mathematical terms, is the support of the rain process a fractal subset of space-time? On the other hand, the low and zero rain rates are particularly difficult to measure; for example, a tipping-bucket type rain gauge does not have a fixed temporal resolution, but rather a fixed depth resolution so that at the low rain rate limit, the temporal resolution becomes infinite. We show that this problem leads to spurious breaks in the scaling at scales which can be of the order of an hour even though the depth resolution can be very small (0.1 mm). In order to overcome these problems an alternative is explored, which analyses the rain as a function of total rain-depth rather than time. This method is particularly suitable for tipping-bucket rain data, because it uses the raw data rather than reconstructed time-series. By comparing results from two climatological regions we show that whereas the statistics from reconstructed series are very different, those with the new depth based series are almost identical (since they are insensitive to the low/zero rain rate problem). In addition, it eliminates the scale breaks so that rain is clearly seen to be scaling from the smallest resolvable scales to the synoptic maximum (roughly 2 weeks).
DE: 1800 HYDROLOGY
DE: 1854 Precipitation (3354)
DE: 3210 Modeling
DE: 3220 Nonlinear dynamics
DE: 3250 Fractals and multifractals
SC: Nonlinear Geophysics [NG]
MN: 2003 Fall Meeting