Analysis of collection equation solutions under truncated size spectrum assumption for hydrometeors

The solutions of the collection equation are analyzed regarding the size range of hydrometeor spectra with exponential size distributions. The real spectra that contain the hydrometeors with sizes within the observed boundaries are introduced instead of widely used idealized spectra that range from 0 to infinity. The main differences that occur between the real and the idealized spectra are due to the lack of raindrops less than 100 µm in diameter in the real spectrum and the lack of large graupel with diameters greater than 0.5 cm. These differences can produce collection rates that differ by up to 70% when using the real or truncated spectra. The advantage of the new approach is demonstrated in the case where collection rates for the interaction between hail and rain are calculated. Due to the finite boundaries in sizes for the hydrometeor categories that exist when using the real spectra, the collection rates for hail and rain interaction are always positive, whereas they can be negative when the size spectra span the range from 0 to infinity. This means that the use of the real spectra can provide a computationally inexpensive analytical solution for this case, which is not available for these interactions when using the idealized spectra. The findings performed may be of interest for modellers that use the cloud-resolving mesoscale models.