HR: 1400h
AN: H53B-13    [Abstracts]
TI: The scale dependence of rain: from raindrop stereophotography to global TRMM orbits
AU: * Lovejoy, S
EM: lovejoy@physics.mcgill.ca
AF: Physics, McGill University, 3600 University st., Montreal, Qc H3A 2T8, Canada
AU: Schertzer, D
EM: Daniel.Schertzer@cereve.enpc.fr
AF: CEREVE, ENPC, 6-8 Ave. Blaise Pascale, Marne-la-Vallée, 77455, France
AU: Allaire, V
EM: vincent.allaire@mail.mcgill.ca
AF: Physics, McGill University, 3600 University st., Montreal, Qc H3A 2T8, Canada
AB: Rain is a highly turbulent process over enormous ranges of scale. The stereophotography of rain drops directly demonstrates that rain is strongly coupled with the wind field down to a "relaxation" scale of the order 30-50cm below which drop inertia makes them free. Using the results of this "HYDROP" experiment, we show that while the liquid water density (ro) follows a multifractal generalization of the classical Corrsin-Obukov passive scalar law; deltaro=l**1/3, on the contrary, the drop number density (n) follows the new law deltan=l**1/2. We show how both laws can be derived from dimensional analysis using appropriate turbulent fluxes. The HYDROP experiment only determines the statistical properties of precipitation over the range of scales 3cm to 2m; for larger but intermediate scales (3m- 5km), we use lidar and radar data which also show scaling of the backscatter cross-section and radar reflectivity factors respectively. To extend this up to planetary scales (5 - 20,000km), we use 3 months (1166 orbits) of the TRMM (Tropical Rainfall Monitoring Mission) satellite radar data at heights 250m above the surface. This global data set (over the region ±38 degrees latitude) is remarkable for it's relatively complete and uniform coverage over a range of =4,000 in scale; it is also nearly free of the range dependent biases which plague ground based radar data. Ignoring for the moment the statistics from the weak reflectivities (which are biased due to the rather higher minimum detectable signal), we find that over the observed range 5-20000km, the moments Mean(Z(lambda)**q) for q less than 2 follow the theoretically predicted form Mean(Z(lambda)**q)= lambda**K(q) to within a maximum deviation of 6 percent where lambda=Leff/Lres and Lres, is the resolution of the reflectivities and Leff is the effective outer scale of the cascade. We find Leff= 40000km indicating that at planetary scales (20000km), there is residual variability from other interactions. Analyzing the exponent K(q) we show that it is well reproduced by a theoretically predicted two parameter ("universal") form, with codimension of the mean field C1=0.63 and Levy index α (characterizing the degree of multifractality) =1.5. Finally over the range 20,000 - 5km using multifractal simulations we show that if the minimum detectable signal is =0.5 times the mean, then the slight deviations in the scaling of the low order moments (q less than 0.5) are explained to within 7 percent. These findings allow us to make stochastic precipitation models which reproduce these isotropic statistics over huge ranges of scale. On the one hand, we can make compound Poisson / multifractal/ models of the distribution of individual drops which respect the basic turbulence laws, on the other hand, the same model can be used at much larger scales to accurately model the TRMM reflectivities.
DE: 1840 Hydrometeorology
DE: 1869 Stochastic hydrology
DE: 4415 Cascades
DE: 4440 Fractals and multifractals
SC: Hydrology [H]
MN: 2007 Joint Assembly