New Velocity Potential and Stream Function Calculations

[KarinaAsmar-NOAA]

This PR adds the CPC-requested streamfunction and velocity potential at 200mb to SFS. It is meant to resolve [Issue #902 ] and update on the runtime issues from the previous PR #951 . Job scripts used for testing are in WCOSS2: /lfs/h2/emc/vpppg/noscrub/karina.asmar/vpot_strm/UPP (submit_run_gfsv16_wcoss2.sh and submit_run_sfs_wcoss2.sh).

[KarinaAsmar-NOAA]

@WenMeng-NOAA We have updated the computation for streamfunction and velocity potential for compatibility with UPP parallelization. The subroutine now uses a poisson solver with a convergence tester to reduce runtimes. Comparison of spectral and numerical results is here

[GeorgeVandenberghe-NOAA]

The poisson solver works but is substantially slower than the gather --> stptranf --> scatter operation to solve the equation spectrally. The gather is much cheaper than it sounds because it is TWO fields, (U and V) at one level, not the several hundred such fields that comprise state plus derivative variables. A gather of two fields takes about 0.06 seconds on hera at GFS (high) resolution and it hard to even measure at CFS resolution. The relaxations take about 10 seconds on hera for chi and psi together and less than a second for the spectral solver. Spectral solver takes 27 seconds for the GFS (high) resolution case while the poisson solver takes 161 seconds. Spectral solver takes less than a second for the CFS case while the poisson solver takes about three seconds.

[WenMeng-NOAA]

@KarinaAsmar-NOAA Clean up the debugging code.

[KarinaAsmar-NOAA]

@GeorgeVandenberghe-NOAA Would you please clean up the debugging part of COLLECT_LOC.f? Let me know when done and I'll push it to this branch.

[WenMeng-NOAA]

Here are the runtime tests for the offline post:

GFS(C768) 120 tasks || develop: 142 seconds  ||  PR #1072: 188 seconds
GEFS (C384) 48 tasks || develop: 52 seconds   || PR #1072: 77 seconds
SFS (C96) 48 tasks  ||  develop: 3.86 seconds   || PR #1072: 5.4 seconds

[WenMeng-NOAA]

Here are the runtime test for the inline post with the UFS RT 'cpld_control_sfs' on Hera:

Without  velocity potential and stream function generation: 5 seconds
   run directory: /scratch1/NCEPDEV/stmp2/Wen.Meng/FV3_RT/rt_449231-develop/cpld_control_sfs_intel
With velocity potential and stream function generation: 9 seconds
   run directory: /scratch1/NCEPDEV/stmp2/Wen.Meng/FV3_RT/rt_2703606-sfs/cpld_control_sfs_intel

@DusanJovic-NOAA and @junwang-noaa Please let me know your comments on this PR.

[WenMeng-NOAA]

The UPP RTs have been completed on WCOSS2 with no baseline changes.

[WenMeng-NOAA]

@gspetro-NOAA You may start the UPP RTs on R&D machines. There should be no baseline changes with this PR.

[gspetro-NOAA]

RTs pass on Orion, Hera, and Hercules with no baseline changes.

[WenMeng-NOAA]

This PR is ready for merging.