Abstract

A novel coherent technique—the so-called yield-signature analysis—is used to estimate multiparametric particle-size distributions. This is an extension of our previous research, which used yield-signature analysis to estimate effective particle size and mean number density. A general technique is proposed here for estimation of particle-size-distribution functions (SDF’s) with an arbitrary number of parameters. The proposed inversion algorithm compares the experimental yield signature Y_e with the model yield signature Y(v), where v is the vector of parameters of the estimated SDF. Then the inversion algorithm searches for a value of v such that Y(v) is closest (according to a certain criterion) to the experimental yield signature Y_e. The corresponding value of v is accepted as the estimate of the vector of parameters. Many search and gradient techniques are available in numerical mathematics for solution of this problem. One such technique is the quasi-Newton method. Computer simulations show that application of the quasi-Newton method in conjunction with the least-mean-squares proximity criterion leads to a reliable inversion algorithm for the considered problem. The example chosen for computer simulations is estimation of raindrop-size distributions for both showers and thunderstorms. The actual particle-size distribution is given by the log-normal SDF in the considered case, so that three parameters must be estimated. Analysis of simulation results shows that the signal-to-noise ratio (SNR) of 30 dB is sufficient when at least 16 yield measurements are taken. This conclusion is valid for rain rates as low as 5 mm/h. A larger SNR and/or a larger number of measurements is needed for smaller rain rates.

© 1984 Optical Society of America

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