Parameterization of cloud microphysics
Cloud and precipitation are formed by the evolution of individual drops and ice
particles in an ensemble of hydrometeor particles, having sizes ranging from micrometer in the early life stage up to cm for e.g., a large snow flake. Horizontal mesh sizes of weather prediction and climate models are typically (much) larger than 1 km. Neither one is interested nor is it feasable to simulate the life cycle of individual particles with such models. Instead, one aims at catching the overall effect of the particles' evolution on the variables defined at the grid points, such as liquid water content and precipitation rate. This is called parameterization of cloud microphysics.
Common parameterization concepts characterize the state of the drop ensemble by few properties, which are the moments of the size distribution of the drop ensemble. Such moment variables are e.g., number density and liquid water content. The rain drop ensemble is then characterized by one or two moments for computational efficiency. All other properties relevant to the evolution of the drop ensemble, as e.g., precipitation rate and evaporation rate, have to be traced back to these few moments.
Vertical profiles of the number density N (moment of order 0), liquid water concenetration L (proportional to moment of order 3), and radar reflectivity Z (moment of order 6), valid at 300 s and at 600 s, btained from the -moment model (with L as prognostic variable), the -moment model (with N and L as prognostic moment), the 3-moment model (with N, L, and Z as prognostic moments) together with the reference solution from the microphysical ('spectral') model. Dotted line denotes the initial condition.
The graphic shows the results from a comparative study for the sedimentation of rain drops. Given are the vertical profiles of number density N, liquid water concentration L, and radar reflectivity Z for various simulation times. The four model runs distinguish in the way, the profiles were calculated: in the parameterization scheme one, two, and three, resp., moments of the size distribution have been forecasted as independent properties. The black line refers to the solution of the microphysical ('spectral') model for reference. All model runs start with the same initial conditions (black dotted lines). The comparison shows that the more moments are forecasted, the better is the agreement with the reference solution: The blue line reproduces the reference solution reasonably well. This holds in particular for the differential settling for the various moments, which is caused by the increase of drop sedimentation velocity with drop size. On the other hand, when only a single moment is forecasted, this feature cannot be reproduced, and all signals are shifted alike.
This example illustrates some severe weaknesses of currently used methods in weather and climate modelling. Improvement of the parameterization is an enduring important research task.
For more details see:
Wacker, U., Luepkes, C. (2009): On the selection of prognostic moments in parameterization schemes for drop sedimentation. Tellus 61A, 498-511.
Ziemer, C., Wacker, U. (2011): Parameterization of the sedimentation of raindrops with finite maximum diameter. Submitted.
Parts of the research are supported by Priority Research Programm 'MetStroem', funded by the Deutsche Forschungsgemeinschaft, grant WA1334/8.