Forward Semi-Lagrangian Advection with Mass Conservation and Positive Definiteness for Falling Hydrometeors Journal Article uri icon



  • Abstract; A semi-Lagrangian advection scheme is developed for falling hydrometeors in hopes of replacing the conventional Eulerian scheme that has been widely used in the cloud microphysics scheme of numerical atmospheric models. This semi-Lagrangian scheme uses a forward advection method to determine the advection path with or without iteration, and advected mass in a two-time-level algorithm with mass conservation. Monotonicity is considered in mass-conserving interpolation between Lagrangian grids and model Eulerian grids, thus making it a positive definite advection scheme. For mass-conserving interpolation between the two grid systems, the piecewise constant method (PCM), piecewise linear method (PLM), and piecewise parabolic method (PPM) are proposed. The falling velocity at the bottom cell edge is modified to avoid unphysical deformation by scanning from the top layer to the bottom of the model, which enables the use of a large time step with reasonable accuracy. The scheme is implemented and tested in the Weather Research and Forecasting (WRF) Single-Moment 3-Class Microphysics Scheme (WSM3).; In a theoretical test bed with constant terminal velocity, the proposed semi-Lagrangian algorithm shows that the higher-order interpolation scheme produces less diffusive features at maximal precipitation. Results from another idealized test bed with mass-weighted terminal velocity demonstrate that the accuracy of the proposed scheme is still satisfactory even with a time step of 120 s when the mean terminal velocity averaged at the departure and arrival points is employed. A two-dimensional (2D) squall-line test using the WSM3 scheme shows that the control run with the Eulerian advection scheme and the semi-Lagrangian run with the PCM method reveal similar results, whereas behaviors using the PLM and PPM are similar with higher-resolution features, such as mammatus-like clouds.

publication date

  • May 1, 2010

has restriction

  • hybrid

Date in CU Experts

  • June 16, 2021 7:59 AM

Full Author List

  • Henry Juang H-M; Hong S-Y

author count

  • 2

Other Profiles

International Standard Serial Number (ISSN)

  • 0027-0644

Electronic International Standard Serial Number (EISSN)

  • 1520-0493

Additional Document Info

start page

  • 1778

end page

  • 1791


  • 138


  • 5