4 5 6 Diagnosing the Intercept Parameters of the Exponential Drop Size Distributions in a 7 Single - Moment Microphysics Scheme and Impact on Supercell Storm Simulations

38 39 In this study, power-law relations are developed between the intercept parameter of the 40 exponential particle size distribution and the water content for the rain, hail, graupel and snow 41 hydrometeor categories. The derived relations are implemented within the Milbrandt and Yau 42 microphysics scheme. Simulations of the 3 May 1999 Oklahoma tornadic supercell are 43 performed using the diagnostic relations for rain only, and alternately for all four precipitating 44 species, and results are compared with those from the original single-and double-moment 45 versions of the microphysics schemes. Diagnosing the intercept parameter for rain is found to 46 improve the results of the simulation in terms of reproducing the key features of the double-47 moment simulation while still retaining the computational efficiency of a single-moment scheme. 48 Improvements were seen in general storm structure, cold pool structure and intensity, and the 49 number concentration fields. Diagnosing the intercept parameters for all four species, including 50 those for the ice species, within the single-moment scheme yields even closer alignment with the 51 double-moment simulation results. The decreased cold pool intensity is very similar to that 52 produced by the double-moment simulation, and the areal extent of the storm is more accurately 53 reproduced. This study suggests that significant improvements over traditional fixed-intercept 54 parameters in typical single-moment microphysics schemes can be achieved through the use of 55 diagnostic relations for the parameters of the particle size distribution, without a significant 56 increase in computational cost. 57