Wednesday, 6 August 2003

A Simulation Study of the Effects of “Small Sample” Problem in the Use of Disdrometer Data for Power Law Relations involving Radar Measurables

It is now well known through the studies of Kostinski and Jameson that the exponent of the

*Z*-*R*relation based on disdrometer data is strongly affected by the small sample problem. The retrieval of dsd parameters (using dual-polarized radar data) also involves power law relations of the form*Z*_{h}/N_{w}_{ }=_{ }*a*,_{ }D_{0}^{b}*D*=_{0}_{ }*c*or_{ }Z_{dr}^{d}*Z*_{h}/N_{w}_{ }=_{ }*a*, and it is of interest to know if these exponents also suffer from the ‘small sample’ problem as distrometer data are also used to develop these relations. Note that_{ }(R/N_{w})^{b}*N*is the ‘intercept’ parameter of a normalized gamma dsd while_{w}*D*is the median volume diameter. We show via simulations of the gamma pdf (with parameters_{0}*µ*and*D*) scaled by the number density, that the exponents of the above (normalized) power law relations are not as sensitive to the small sample problem as the_{0}*Z*-*R*power law. We also address the use of distrometer data to calculate the exponent (*b*) of ‘scaling’ law formulations of the dsd as proposed by Sempere-Torres. The evaluation of*b*is based on various moments of the measured dsd, which can be significantly affected by the small sample problem which we demostrate via simulations.Supplementary URL: