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 Δ
t is restricted by the Courant-Friedrichs-Lewy (CFL) condition for rain falling:
VΔ
t/Δ
z<1, where
V is the terminal velocity of rain falling, Δ
z 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 Δ
t is less than the critical value, Δ
tc, which is calculated from the CFL condition (
i. e., Δ
tc=Δ
z/
V), the box-Lagrangian scheme coincides with the Eulerian scheme. Furthermore, even when Δ
t is several times larger than Δ
tc, 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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