Convergence acceleration

Attention

This is only relevant to you, if you want to do force the potential temperature to a specific potetential temperature in the GCM.

The functionality of convergence acceleration (CA) relates to a procedure that forces the potential temperature to a specific potetential temperature in the GCM.

The details of this procedure can be found in the Appendix of Schneider et al. (2022b).

Note

Convergence acceleration is activated/deactivated by setting the following two parameters:

File	Parameter	Warning
`input/data.exo`	`EXORAD_DEEP_CONVERGENCE =.TRUE.`	only enable when actually doing the CA
`code/EXORAD_OPTIONS.h`	`#define ALLOW_EXORAD_CA`	pre compilation

The CA is used whenever EXORAD_DEEP_CONVERGENCE =.TRUE. is set to true and is then used within the first iterations of the GCM run. Make sure to only use it when you actually want to use it and set EXORAD_DEEP_CONVERGENCE =.FALSE. in any other case!

The CA is intended to be used, when you restart the GCM from a pickupfile and then disabled after!

data.exoca

You need a data.exoca file in the input folder that controls the parameters used for the forcing towards the goal theta.

You can find an example with some random CA parameters (used for testing purposes) in the respective verification folder (CA) in the github repo of exorad.

Here is an example (used in Schneider et al. 2022b):

# EXORAD_CA_APPL :: Timespan over which the forcing is applied
# EXORAD_CA_PDAMP :: pressure, above which we want the full artificial forcing
# EXORAD_CA_PMIN :: minimum pressure, where you want to start the artificial forcing
# EXORAD_CA_GOAL_THETA :: The final potential temperature to which you want to force

&EXORAD_CA_NML
  EXORAD_CA_APPL = 864000.0
  EXORAD_CA_PDAMP = 10e5
  EXORAD_CA_PMIN = 1e5
  EXORAD_CA_GOAL_THETA = 4658.899408445296
/

Note

Please note that the potetential temperature for MITgcm is calculated with reference to the lower interface of the deepest pressure layer.

CA in detail

There are two different smoothing schemes in the CA that are of importance:

time based smoothing
vertical smoothing

The time based smoothing is a way to make sure that the forcing from the CA is applied in a way that is stable enough to make sure that the GCM does not crash. It works such that you set a timespan (EXORAD_CA_APPL) over which you want to go to the desired final theta (EXORAD_CA_GOAL_THETA) This time should be typially in the order of a few days. The CA will then force towards the goal theta following a smooth function (first half of a sinuscurve), where the forcing towards the goal theta is the strongest at the middle of the timespan.

The vertical smoothing makes sure that the forcing towards the final theta has a smooth transition to the upper atmosphere. It is done in such a way that it applies the the CA only to the layers below EXORAD_CA_PMIN. It then has a smooth transition between EXORAD_CA_PMIN to EXORAD_CA_PDAMP, from which it does the full forcing towards the goal potential temperature.

You can easily extract the smoothing functions in the code (pkg/exorad/exorad_ca.F).

The final potential temperature (for layers below EXORAD_CA_PMIN) can be written as:

\[\Theta = \Theta_0 + v\cdot(\Theta_\mathrm{goal}-\Theta_0),\]

where \(\Theta\) is the potential temperature after the CA, \(\Theta_0\) is the potential temperature before CA, \(\Theta_\mathrm{goal}\) is the potential temperature to which we want to force (EXORAD_CA_GOAL_THETA) and \(v\) is the vertical smoothing factor. The vertical smoothing factor goes from 0 to 1 between EXORAD_CA_PMIN and EXORAD_CA_PDAMP.