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Ice crystal aggregates and their melting process are modeled with a new approach for determining their microwave scattering characteristics and are compared with those obtained using effective dielectric constant representations. The aggregates are constructed from columnar crystals of random lengths (with the width being a function of the length), which are composed of a string of touching ice spheres with diameters equal to the column's width. The aggregates are melted using a model that incorporates the primary aspects of experimentally observed features of the melting process. The generalized multiparticle Mie method is used for computing the scattering cross sections of the dry and melting aggregates. The T-matrix method is used for computations involving a bulk representation of each aggregate with an effective dielectric constant model and an oblate spheroidal shape. The 3- and 35.6-GHz backscattering cross sections show significant differences between the two methods for both dry and melting aggregates. For sizes larger than 3 mm, these differences range from several decibels at 3 GHz to well over 7 dB at 35.6 GHz. Significant differences are also observed in the extinction cross sections during the melting process. It is concluded that the effective dielectric constant models of dry and melting ice crystal aggregates do not represent the interactions between the constituent crystals (and water droplets during melting) of the aggregates very well. Hence, bulk models must be used with caution particularly at millimeter wavelengths.