## Joint Centre for Mesoscale Meteorology (JCMM)

**JCMM INTERNAL REPORT NO.59**

*Investigation of different representations of rain in a 1-D evaporation model*

by Hugh Swann

The bulk-microphysics scheme previously used in the UK Met. Office Large Eddy Model has single-moment bulk-water representation of precipitating particles, in common with most other cloud resolving models (eg Flateau *et al* 1989, Lin *et al* 1983). In such schemes, precipitating particles are represented by just one variable (**q**, the mass-mixing ratio) so the number concentration and the mean drop diameter both increase monotonically as a function of **q**. More recently, however, a double-moment bulk-water scheme has been implemented, which uses two variables to represent precipitating particles (the mass-mixing ratio and **n**, the particle number concentration). This reduces the number of adjustable coefficients and allows some processes to be modelled in a more realistic way than is possible with the simpler schemes because the number concentration (and hence the mean diameter) is allowed to vary independently of the mass-mixing ratio.

One feature of cloud simulations that the double-moment scheme is expected to model more accurately is the reduction of the number of small drops compared to larger drops in the evaporation region of rain. The single-moment schemes, especially when an exponential drop size distribution is assumed, implies generation of small drops at a rate faster than they would be generated through the evaporation of large drops, as found by Clough and Franks (1991). A simple 1-D evaporation model with a 'passive' atmosphere is used to model rain falling through subsaturated air to the surface, causing rainfall rates of up to 10mm/h.

Three different representations of rain are compared, a single-moment scheme, a double-moment scheme and an explicit scheme. The shape of the initial drop size distribution is assumed to be either an exponential or a generalised gamma distribution (the explicit scheme is able to deviate from this initial shape, whereas the bulk water schemes can not). The explicit scheme uses a large number of variables each representing a size bin of rain drops. this method is too computationally expensive to be used in a 3-D model, but can be used in this 1-D model to produce an exact solution to the precipitation and evaporating equations, for evaluating the bulk-water approximations.