6.7 Summary of the rigid lid streamfunction method

In summary, the rigid lid streamfunction method allows for the computation of the total velocity field using the following algorithm:

• Baroclinic mode

  1.

  Compute the forcing terms for the ``primed'' momentum equation, which include all terms except the lid pressure and atmospheric pressure (Section 6.6).

  2.

  Solve the primed momentum equation at each model level to get the primed velocity at the next time step.

  3.

  Subtract the vertically averaged primed momentum from the primed momentum in order to get the baroclinic velocity field at the next time step.

• Barotropic mode

  1.

  Compute the forcing terms in the barotropic vorticity equation (Section 6.4).

  2.

  Solve the elliptical boundary value problem for the time tendency of the barotropic streamfunction.

  3.

  Time step the streamfunction forward and compute the barotropic velocity field at the new time step.

• Add the baroclinic velocity to the barotropic velocity to then have the full velocity field.