A Scheme for Calculation of the Liquid Fraction in Mixed-Phase Stratiform Clouds in Large-Scale Models

Abstract

A scheme for calculation of the liquid fraction fl in mixed-phase stratiform clouds has been developed for use in large-scale models. An advantage of the scheme, compared to the interpolation in temperature that is typically used, is that it makes it possible to simulate the life cycles of mixed-phase clouds, and the differences between deep and shallow clouds. The central part of the scheme is a physically based calculation of the growth of cloud ice crystals by vapor deposition at the expense of coexisting cloud liquid water, the so-called Bergeron?Findeisen mechanism. Versions of this calculation have been derived for three different ice-crystal habits (spheres, hexagonal plates, or columns) and for two different assumed spatial relationships of the coexisting cloud ice and liquid water (horizontally adjacent or uniformly mixed). The scheme also requires a parameterization of the ice crystal number concentration Ni. The variation with temperature of fl looks broadly realistic compared to aircraft observations taken in the vicinity of the British Isles when the scheme is used in the CSIRO GCM, if Ni is parameterized using a supersaturation-dependent expression due to Meyers et al. If Fletcher?s earlier temperature-dependent expression for Ni is used, the scheme generates liquid fractions that are too large. There is also considerable sensitivity to the ice-crystal habit, and some sensitivity to model horizontal resolution and to the assumed spatial relationship of the liquid water and ice. A further test shows that the liquid fractions are lower in cloud layers that are seeded from above by falling ice, than in layers that are not seeded in this way. The scheme has also been tested in limited-area model simulations of a frontal system over southeastern Australia. Supercooled liquid water forms initially in the updraft, but mature parts of the cloud are mostly glaciated down to the melting level. This behavior, which is considered to be realistic based on observations of similar cloud systems, is not captured by a conventional temperature-dependent parameterization of fl. The variation with temperature of fl shows a marked sensitivity to the assumed spatial relationship of the liquid water and ice. The results obtained using the uniformly mixed assumption are considered to be more realistic than those obtained using the horizontally adjacent assumption. There is also much less sensitivity to the time step when the former assumption is used.