Introduction

A heat budget is used to derive the melting equation; this accounts for heating owing to conduction, vapor diffusion, and sensible heat from the collection of rain, drizzle, and cloud drops that might be warmer than the collector ice-water particle. The collection process is complicated in most models if the temperature of any of the hydrometeor types is not predicted. In this case, the temperature of liquid hydrometeors is assumed to relax to the environmental temperature instantaneously. In the case where hydrometeor temperatures are predicted, the rate of condensation or evaporation on a melting ice-water particle can be more accurately computed (Walko et al. 2000). Diagnosing the instantaneous hydrometeor-species' temperature can lessen the accuracy of melting computations as compared to predicting hydrometeor temperatures. The influence of energy storage and the relaxation times of the hydrometeor-species' temperature to the temperature of the environment will be investigated later in the chapter.

Melting of ice-water hydrometeors can be made very simplistic; or for the case of particle trajectory models, hybrid-bin models and bin models, can be quite sophisticated. For parameterizations, difficulties arise when the Reynolds number of a particle is taken into account. The equations from Rasmussen and Heymsfield (1987a) generally cannot be used for bulk parameterization models whereas they can be used for bin-type models where each bin has its own characteristics. For bulk parameterization models, melting can be treated with one set of equations, say for frozen drizzle, which has a small Reynolds number Nre compared to larger particles.