On the sensitivity of the continuous accretion rate equation used in bulk-water parameterization schemes

The analytical solutions of the continuous accretion rate equation are compared regarding two different size distributions for cloud and rain water, two hail terminal velocities for different turbulent regimes and two solution types. The Khrgian-Mazin and Marshall-Palmer size distributions are assumed for rain water fraction, while the Khrgian-Mazin and monodisperse ones are applied to cloud water. In all cases the exponential-type size distribution for hail is used. In the calculation procedure for hail terminal velocity we take into consideration that the drag coefficient may be fixed or dependent on Reynolds number. Both approximate and exact solutions of the accretion rate under the same other conditions are also compared. Results show that the Khrgian-Mazin size distribution makes the approximate accretion rate between hail and rain considerably higher compared to its former parameterization for both hail terminal velocity assumptions. On the other side, the new treatment of hail terminal velocity with a variable drag coefficient produces lower accretion rates compared to the fixed drag coefficient case for all size distributions used. The approximate solution of the accretion rate equation is mainly lower than the exact one. Only in the case of raindrops-cloud droplets interaction it is much higher than the exact one with the Khrgian-Mazin size distribution used.