Abstracted Procedures of the RDC Scheme

First uploaded on 2022/10/05
Last updated on 2024/10/04
Copyright(C)2022 jos <jos@kaleidoscheme.com> All rights reserved.

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The following is a brief summary of the basic concepts and computational procedures of RDC parameterization in sequence. Please refer to it together with reading the main part A New Scheme of Cumulus Parameterization Based on RDC.

1. Designation of Supplying Source Domains
   The supplying source domains (corresponding to the cumulus domains) are designated in the calculation area, as in the dynamical detrainment models.


2. The second law of thermodynamics
   The cumulus cloud is merely a mixing domain between the lower and upper troposphere, and its mixing motion (fine eddies inside) is too small in physical scale to contribute to outward transport or to force outside.


3. Radiative cooling in a radiative-convective equilibrium atmosphere with no dynamical forcing
   The tropospheric atmosphere is maintained in a state of radiative-convective equilibrium, which is different from (warmer than) radiative equilibrium, so that radiative cooling occurs constantly without any dynamical forcing from the cumulus motion at all.


4. Local thermodynamical balance
   In order to maintain the current radiative-convective equilibrium state under radiative cooling, an arbitrary air parcel in the troposphere sinks with a subsidence velocity w_R corresponding to the radiative cooling rate.


5. Air motion dynamically bound to the subsidence
   Since the air parcel is dynamically constrained to the subsidence velocity w_R under the restoring force of positive and negative buoyancy, it is difficult for the air parcel to move differently from the subsidence motion.
   As the result, all the air parcels in the troposphere must follow the subsidence velocity w_R.


6. Mass divergence of the subsidence flow due to density stratification of the atmosphere
   Because the atmospheric density ρ is steeply stratified, the mass flux ρw_R corresponding to the subsidence velocity w_R has a divergent field throughout the troposphere.


7. Continuity of the atmosphere
   In order to prevent the formation of a vacuum everywhere in the atmosphere, convergent horizontal mass fluxes (ρu_R, ρv_R) are induced from the supplying source domains to compensate for the divergence of the subsidence mass flux ρw_R.


8. Numerically solving the boundary-value problem for RDC
   For the given supplying source domains of mass/heat/water vapor, the horizontal mass flux field (ρu_R, ρv_R) can be obtained by solving the boundary value problem on the horizontal plane at each altitude.


9. RDC velocity
   Dividing the three-dimensional mass fluxes (ρu_R, ρv_R, ρw_R) obtained as above by the atmospheric density ρ, we obtain the three-dimensional velocity field (u_R,v_R,w_R) due to RDC.