Abstract
A new rain-drop scheme named box-Lagrangian rain-drop scheme is developed. In the Eulerian raindrop scheme, since the change of the mixing ratio of rainwater q during unit time is calculated from ∂q/∂t=V∂q/∂z, the time step interval Δt is restricted by the Courant-Friedrichs-Lewy (CFL) condition for rain falling: VΔt/Δz<1, where V is the terminal velocity of rain falling, Δz the vertical grid spacing. In the box-Lagrangian rain-drop scheme, the above numerical constraint can be relaxed by the following method. The bulk of rainwater in a vertical grid box is dropped while keeping V constant during a time step interval, and it is partitioned into grid boxes existing in the space where it is dropped.
When Δt is less than the critical value, Δtc, which is calculated from the CFL condition (i. e., Δtc=Δz/V), the box-Lagrangian scheme coincides with the Eulerian scheme. Furthermore, even when Δt is several times larger than Δtc, the box-Lagrangian scheme drops rainwater stably with sufficient accuracy. The box-Lagrangian scheme is effective especially when many vertical layers are employed in the lower part of the model domain to express the atmospheric boundary layer in detail.
