An Investigation of the Relation between Slope and Shape Parameters of Gamma Rain Drop Size Distribution: Measurement and Simulation

On the basis of disdrometer-measured rain drop size distribution (DSD) for 8 years (2000-2008), the shape (μ) and slope (Λ) parameters of the measured Gamma DSD in the form of N(D)=NoD^μexp(-ΛD) are analyzed. We find that the relation between the shape and the precipitation terminal velocity (Vt) follows an empirical exponential form. With the help of this empirical μ-Vt relation, we derive an analytical μ– relation. Comparison shows that the analytical expression is in excellent agreement with the empirical 2nd order polynomial obtained from the least squares fit. An attempt is also made in this paper to use Monte Carlo experiment to simulate the μ–Λ relation. It is found that the probability density functions of lnNo, μ and Λ of the Gamma DSD are characterized by lognormal, Gamma and lognormal functions, respectively. With these statistical properties, the simulated Gamma DSD is randomly generated and the corresponding μ–Λ relation can thus be obtained by best fitting a 2nd order polynomial to the simulated data. Examination shows that the μ–Λ relation obtained from the numerically simulated data is in good agreement with that obtained from the measured DSD data.