A scheme for calculation of the liquid fraction in mixed-phase stratiform clouds in large-scale models

A scheme for calculation of the liquid fraction f(l) in mixed-phase stratif orm clouds has been developed for use in large-scale models. An advantage o f the scheme, compared to the interpolation in temperature Chat is typicall y used, is that it makes it possible to simulate the life cycles of mixed-p hase clouds, and the differences between deep and shallow clouds. The centr al 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 l iquid water, the so-called Bergeron-Findeisen mechanism. Versions of this c alculation have been derived for three different ice-crystal habits (sphere s, hexagonal plates, or columns) and for two different assumed spatial rela tionships of the coexisting cloud ice and liquid water (horizontally adjace nt or uniformly mixed). The scheme also requires a parameterization of the ice crystal number concentration N-l. The variation with temperature of f(l) looks broadly realistic compared to aircraft observations taken in the vicinity of the British Isles when the s cheme is used in the CSIRO GCM, if N-l is pammeterized using a supersaturat ion-dependent expression clue to Meyers et al. If Fletcher's earlier temper ature-dependent expression for N-l is used, the scheme generates liquid fra ctions that are too large. There is also considerable sensitivity to the ic e-crystal habit, and some sensitivity to model horizontal resolution and to the assumed spatial relationship of the Liquid water and ice. A further te st shows that the liquid fractions are lower in cloud layers that are seede d from above by failing ice, than in layers that are not seeded in this way . The scheme has also been tested in Limited-area model simulations of a fron tal system over southeastern Australia. Supercooled liquid writer forms ini tially in the updraft, but mature parts of the cloud are mostly glaciated d own to the melting level. This behavior, which is considered to be realisti c based an observations of similar cloud systems, is not captured by a conv entional temperature-dependent par;parameterization of f(l). The variation with temperature of f(l) shows a marked sensitivity to the assumed spatial relationship of the liquid water and ice. The results obtained using the un iformly mixed assumption are considered to be more realistic than those obt ained using the horizontally adjacent assumption. There is also much less s ensitivity to the time step when the former assumption is used.