Parametrization of ice-particle size distributions for mid-latitude stratiform cloud

Particle size distributions measured by the UK C-130 aircraft in ice stratiform cloud around the British Isles are analysed. Probability distribution functions over large scales show that the zeroth, second and fourth moments (equivalent to concentration, ice water content and radar reflectivity) as well as mean particle size have monomodal distributions. Rescaling of the size distributions requiring knowledge of two moments reveals a 'universal' distribution that has been fitted with analytically integrable functions. The existence of the 'universal' distribution implies that two-moment microphysics schemes are adequate to represent particle size distributions (PSDs). In large-scale models it may be difficult to predict two moments, and so power laws between moments have been found as functions of in-cloud temperature. This means that a model capable of predicting ice water content and temperature can predict ice PSDs to use for calculations requiring knowledge of the size distribution (e.g. precipitation rate, radar reflectivity) or to make direct use of the power laws relating moments of the size distribution.