The intensity returns obtained by a radar from precipitation are well known to fluctuate violently in space and time. We present a systematic study of the resolution dependence time series with overlapping time resolutions spanning 10 orders of magnitude (0.77 ms to 4 months), of the fluctuating radar echo from precipitation. The results undermine the current assumptions of homogeneity of rainfield at scales smaller than the radar resolution, due to Marshall and Hitschfeld (1953), by showing that the only length scales identifiable in the time series are those of the radar pulse volume, the wavelength, and a very small inner scale of the order of millimeters. An analysis of the multiscaling nature of the time series of echo fluctuations reveals multiscaling behaviour at scales down to the resolution or pulse volume scale. Since there are no a priori scales in the rainfield we proceed to model the fluctuating radar echo by assuming a multiscaling model of rainfield variability which extends to sub-resolution scales. A systematic analysis of the statistical behaviour of computed reflectivities from this variability gives a full statistical description of reflectivity originating from multiscaling variability, and solves the scalar multifractal radar observer's problem. Computation of time series of reflectivities from a time-space representation of this variability reveals quantitative and qualitative behaviours consistent with those of observed echo fluctuation time series. We conclude that a multiscaling model of the rainfield which extends to the smallest scales of the rainfield is consistent with observation.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.41364 |
| Date | January 1993 |
| Creators | Duncan, Mike R. (Mike Ross) |
| Contributors | Lovejoy, Shaun (advisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Natural Resource Sciences.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001386326, proquestno: NN94614, Theses scanned by UMI/ProQuest. |
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