Fix in `zpshde.F90` to prevent results differing between `nn_hls`

Closed Daley Calvert requested to merge fix_zpshde_halo_results into main

This fixes the issue raised by @smasson in his 20/01/22 email:

When activating sn_cfctl%l_prtctl = .true., and running ORCA2_ICE_PICES twin experiments (nn_hls = 1 or 2) on 1 core for 1 time step, I found that the first différence between the 2 mono.output_0000 files is for slp wj (array wslpj in ldfslp).

After some digging, I identified that the problem is coming from an optimization on pgrv in zpshde that came with the last merge related to the tiles:

IF (nn_hls==1) CALL lbc_lnk( 'zpshde', pgru , 'U', -1.0_wp , pgrv , 'V', -1.0_wp ) ! Lateral boundary conditions

A quick and dirty solution is to suppress the "IF (nn_hls==1)”. The real problem is that I don’t understand why suppressing this “IF" solves the problem... Up to know, I was not able to figure out the list of dependancies that would explain why this call to lbc_lnk on pgrv is always needed (it should not! I agree with the use of this IF). I suspect a tricky trick somewhere in the way something is computed on each side of the north pole folding...but I could not find it...

I think the issue is to do with the IF statements dependent on ze3wu/ze3wv, which appear several times in the code:

DO_2D( nn_hls-1, nn_hls-1, nn_hls-1, nn_hls-1 )              ! Gradient of density at the last level
   iku = mbku(ji,jj)
   ikv = mbkv(ji,jj)
   ze3wu  = e3w(ji+1,jj  ,iku,Kmm) - e3w(ji,jj,iku,Kmm)
   ze3wv  = e3w(ji  ,jj+1,ikv,Kmm) - e3w(ji,jj,ikv,Kmm)
   IF( ze3wu >= 0._wp ) THEN   ;   pgru(ji,jj) = umask(ji,jj,1) * ( zri(ji  ,jj    ) - prd(ji,jj,iku) )   ! i: 1
   ELSE                        ;   pgru(ji,jj) = umask(ji,jj,1) * ( prd(ji+1,jj,iku) - zri(ji,jj    ) )   ! i: 2
   IF( ze3wv >= 0._wp ) THEN   ;   pgrv(ji,jj) = vmask(ji,jj,1) * ( zrj(ji,jj      ) - prd(ji,jj,ikv) )   ! j: 1
   ELSE                        ;   pgrv(ji,jj) = vmask(ji,jj,1) * ( prd(ji,jj+1,ikv) - zrj(ji,jj    ) )   ! j: 2
IF (nn_hls==1) CALL lbc_lnk( 'zpshde', pgru , 'U', -1.0_wp , pgrv , 'V', -1.0_wp )   ! Lateral boundary conditions

pgrv(ji,Nje0+1) will be calculated in place when nn_hls = 2 and set by lbc_lnk when nn_hls = 1. The issue is that, due to the mirroring of the north fold, the value of ze3wv used to calculate pgrv(ji,Nje0+1) in the nn_hls = 1 case will have the opposite sign to that in the nn_hls = 2 case. Due to the various IF statements, this means that different paths are taken through the code. Therefore while the value of pgrv(ji,Nje0+1) is arithmetically correct for both nn_hls cases, it is not bitwise identical.

The solution is to remove the lbc_lnk calls for pgru/pgrv/pgrui/pgrvi, which causes results to change in the nn_hls = 1 case.

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