Polarimetric radar characteristics of melting hail. Part I: Theoretical simulations using spectral microphysical modeling

Spectral (bin) microphysics models are used to simulate polarimetric radar variables in melting hail. Most computations are performed in a framework of a steady-state, one-dimensional column model. Vertical profiles of radar reflectivity factor Z, differential reflectivity Z_DR, specific differential phase K_DP, specific attenuation A_h, and specific differential attenuation A_DP are modeled at S, C, and X bands for a variety of size distributions of ice particles aloft. The impact of temperature lapse rate, humidity, vertical air velocities, and ice particle density on the vertical profiles of the radar variables is also investigated. Polarimetric radar signatures of melting hail depend on the degree of melting or the height of the radar resolution volume with respect to the freezing level, which determines the relative fractions of partially and completely melted hail (i.e., rain). Simulated vertical profiles of radar variables are very sensitive to radar wavelength and the slope of the size distribution of hail aloft, which is correlated well with maximal hail size. Analysis of relative contributions of different parts of the hail/rain size spectrum to the radar variables allows explanations of a number of experimentally observed features such as large differences in Z of hail at the three radar wavelengths, unusually high values of Z_DR at C band, and relative insensitivity of the measurements at C and Xbands to the presence of large hail exceeding 2.5cm in diameter. Modeling results are consistent with S- and C-band polarimetric radar observations and are utilized in Part II for devising practical algorithms for hail detection and determination of hail size as well as attenuation correction and rainfall estimation in the presence of hail.