[MITgcm-support] SHELFICE Package: stability parameter

Wed Oct 5 13:43:16 EDT 2022

Hi Martin,

Yes that’s right.

The ‘buoyancyflux’ corresponds to the buoyancy flux at the ice-ocean interface so it can be calculated based on melt rate from the previous timestep. But I need to make sure I check the sign convention that is used in SHELFICE package (depending on whether B>0 means melting or freezing L0 should be equal to ustar^3/(Kvon*B) or -ustar^3/(Kvon*B)).

Assuming B<0 means freezing, then when B<0, etaStar would be set to 1.
When B>0, if B-->0+ (i.e. when melt-induced buoyancy production of TKE is negligible compared with shear production of TKE, which is what is assumed in the current version of the code),  then etaStar-->1

I’ll give you an update once I have tested this.

Thank you
Josephine

From: MITgcm-support <mitgcm-support-bounces at mitgcm.org> On Behalf Of Martin Losch
Sent: 05 October 2022 15:57
To: MITgcm Support <mitgcm-support at mitgcm.org>
Subject: Re: [MITgcm-support] SHELFICE Package: stability parameter

Hi Josephine,

do I get this right?
etaStar = 1/ sqrt(1+zetaN*Kvon*buoyancyflux./(abs(f)*uStar**2*Rc))?

should go to zero for buoyancyFlux -> Inf, and to one for buoyanceFlux -> 0 (for positive buoyanceFlux), right?
That should work. Let me know if this works for you and maybe you can even add it to the code, once you are confident that it works.

Martin

On 5. Oct 2022, at 14:13, Josephine Anselin - BAS <joslin53 at bas.ac.uk<mailto:joslin53 at bas.ac.uk>> wrote:

Hi Martin,

Thank you very much for your reply. I will try to implement the formula using Lo=ustar^3 / (Kvon * buoyancyflux) and check if the jump that you pointed out causes an issue.

Thank you
Josephine

From: MITgcm-support <mitgcm-support-bounces at mitgcm.org<mailto:mitgcm-support-bounces at mitgcm.org>> On Behalf Of Martin Losch
Sent: 30 September 2022 08:50
To: MITgcm Support <mitgcm-support at mitgcm.org<mailto:mitgcm-support at mitgcm.org>>
Subject: Re: [MITgcm-support] SHELFICE Package: stability parameter

Note that said equation 18 is not defined for Lo<0 for which etaStar should be set to 1, but the formula goes to 0 for Lo -> 0, so that there will be jump/discontinuity at Lo = 0 (from 0 to 1). This may be one of the reasons (appart from the unclear Lo), why this formula was never implemented.

Martin

On 29. Sep 2022, at 07:54, Martin Losch <Martin.Losch at awi.de<mailto:Martin.Losch at awi.de>> wrote:

Hi Josephine,

I am not aware of any attemps, but there’s a code sketch that is commented out (see around lines 482-484 in shelfice_thermodynamics.F).

The H+J99 paper does not describe, how to evaluate the Obukhov length Lo, but otherwise is should be straightforward to implement this (f=fCori(i,j,bi,bj), Rc=0.2, zetaN=0.052 according to table1 in H+J99).

Martin

On 28. Sep 2022, at 19:11, Josephine Anselin - BAS <joslin53 at bas.ac.uk<mailto:joslin53 at bas.ac.uk>> wrote:

Hi all,

In shelfice_thermodynamics.F (within the SHELFICE Package), the stability parameter (etastar) is set to 1.

Has anyone tried to modify the code to compute the stability parameter as per Equation 18 in Holland & Jenkins (1999). If yes, is the modified version available online?

Many thanks,
_________________________________________
Joséphine Anselin
Physical Oceanography PhD Student
British Antarctic Survey, Polar Oceans Team
University of Cambridge, Applied Mathematics

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