Abstract
A new rain-drop scheme named box-Lagrangian rain-drop scheme is developed. In the Eulerian rain-drop 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: V Δt/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, Δz c , which is calculated from the CFL condition (i.e., Δt c =Δz/V), the box-Lagrangian scheme coincides with the Eulerian scheme. Furthermore, even when Δt is several times larger than Δt c , 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
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