Dept. of Atmospheric Sciences, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
Abstract. In the last decade there has been only one study that discussed time integration scheme (TIS) applied to advance governing differential equations in bulk microphysics (BLK) schemes. Recently, Morrison and Gettelman (2008) examine numerical aspects of double-moment BLK scheme with diagnostic treatment of precipitating hydrometeors implemented into Community Atmosphere Model, version 3 (CAM) to find an acceptable level of accuracy and numerical stability. However, stability condition for their explicit non-positive definite TIS was not defined.
It is conventionally thought that the Weather Research and Forecasting (WRF) model can be applied for a broad range of spatial scales from large eddy up to global scale simulations if time steps used for model integration satisfy to a certain limit imposed mainly by dynamics. However, numerics used in WRF BLK schemes has never been analyzed in detail.
To improve creditability of BLK schemes we derive a general analytical stability and positive definiteness criteria for explicit Eulerian time integration scheme used to advanced finite-difference equations that govern warm rain formation processes in microphysics packages in Community models (CAM and WRF) and define well-behaved, conditionally well-behaved, and non-well-behaved Explicit Eulerian Bulk Microphysics Code (EEBMPC) classes.
We highlight that source codes of BLK schemes, originally developed for use in cloud-resolving models, implemented in Community models belong to conditionally well-behaved EEBMPC class and exhibit better performance for finer spatial resolutions when time steps do not exceed seconds or tenths of seconds. For coarser spatial resolutions used in regional and global scale simulations time steps are usually increased from hundredths up to thousands of seconds. This might lead to a degradation of conditionally well-behaved EEBMPCs ability to calculate the amount of precipitation as well as its spatial and temporal distribution since both stability and positive definiteness conditions are not met in the TIS. The correction through the so called “mass conservation” technique commonly used in many models with bulk microphysics is a main characteristic of non-well-behaved EEBMPC, whose utilization leads to erroneous conclusions regarding relative importance of different microphysical processes. Moreover, surface boundary conditions for ocean, land, lake, and sea ice models are dependent on the precipitation and its spatial and temporal distribution. Uncertainties in calculations of temporal and spatial patterns of accumulated precipitation influence the global water cycle. In fact, numerics in non-well-behaved EEBMPCs, which are used in Community Earth System Model, act as a hidden climate forcing agent, if relatively long time steps are used for the host model integration.
By analyzing numerics of warm rain processes in EEBMPCs implemented in Community models we provide general guidelines regarding appropriate choice of integration time steps for use in these models.