Improving numerics of the WRF model bulk microphysics schemes: time integration scheme impacts on precipitation

 

Authors

Igor Sednev — Lawrence Berkeley National Laboratory
Nancy Jeanne Brown — Lawrence Berkeley National Laboratory
Surabi Menon — Lawrence Berkeley National Laboratory
Aditya Murthi — Lawrence Berkeley National Laboratory

Category

Modeling

Description

Implementation of bulk cloud microphysics (BLK) parameterizations in atmospheric models of different scales has been of interest for the last two decades. From the perspective of cloud physics, time steps, on the order of a few seconds, used for the host model integration are justifiable. However, when BLK schemes are used in regional and global models with time steps on the order of hundreds and thousands of seconds, the numerics and the physics are often affected. This research analyzes the numerics used in BLK schemes and demonstrates analytically the time steps needed to maintain stability and positive definiteness of the time integration schemes for various cloud microphysics processes. In this study, we focus on warm clouds.

The Eulerian forward‐in‐time integration scheme used in numerous BLK schemes, implemented in the Weather Research and Forecasting (WRF) model, is conditionally stable and not positive-definite. As a result, WRF BLK schemes might have improved performance at more refined spatial resolution when the time steps used to advance the microphysical finite‐difference equations have an order of magnitude reduction from seconds to tenths of seconds. For coarser spatial resolution simulations, time steps are often increased from hundreds to thousands of seconds. This can lead to a degradation of performance of the WRF BLK schemes due to the application of corrective approaches such as “mass conservation” (for single‐moment schemes) and additional “concentration adjustments” (for double-moment schemes).

Our analysis, based on analytic stability and positive definiteness criteria, will assess the impact of Eulerian forward‐in‐time (EFTI), adaptive sub‐stepping (ADSS), semi‐implicit (SITI), and fully implicit (FITI) time integration techniques on precipitation formation processes in different BLK schemes implemented in the WRF model. We also analyze spatial and temporal distributions of accumulated precipitation obtained in idealized large‐scale WRF simulations. Differences between the control simulation (Morrison‐Curry‐Khvorostyanov BLK scheme with EFTI) and simulations with ADSS, SITI, and FITI will be presented and discussed. This is the first step in a longer-term research effort, and future efforts will focus on examining the implications of these findings through regional and global simulations and analyses.