Add Spectral Nudging Option and Fix Nudging Behavior When Files Are Missing

[patcal]

This pull request addresses issues #1393 and #1273

For Issue #1273 an error exit with a message is invoked if a missing nudging file is encountered.

For Issue #1393 a module for computing spherical harmonics on the physics grid is implemented. The nudging module has additional functionality that uses this module to optionally filter nudging tendencies to scales larger then a specified truncation scale.

This functionality is controlled by 2 additional variables in the &nudging_nl namelist.
Nudge_SpectralFilter- LOGICAL Option to apply spherical harminic filtering to
the model state and target data so that nudging
tendencies are only applied to scales larger than
the specified truncation.

Nudge_SpectralNtrunc - INT The number of meridional spherical harmonic modes used
for spectral filtering. The nominal horizontal scale of
the filtering can be estimated as:

                                                          Hscale = PI*6350/Nudge_SpectralNtrunc

                                          i.e. Nudge_SpectralNtrunc=40 corresponds to a horizontal 
                                                 nudging scale  Hscale~500km.

[fvitt]

Some initial questions and comments. Do you have a test case for spectral nudging that you can point me to? I can implement a regression test case.

[fvitt]

I am not seeing where Nudge_SpectralNbasis gets sets. Is it always -1?

[fvitt]

Should a namelist switch to turn on / off the abort behavior? I agree that aborting the run should be the default behavior.

[fvitt]

As far as I can tell, these spherepack routines are duplicates of the spherepack routines in zonal_mean_mod.F90. If so, the spherepack routines in zonal_mean_mod should be removed and zonal_mean_mod should use the routines here.

[fvitt]

This looks like a duplicate of Invert_Matrix in zonal_mean_mod

[fvitt]

Could the existing ZonalMean class be replaced by "special" use of this SphericalHarmonic class (m=0)?

[jtruesdal]

Thanks @patcal I'll see if I can update this to the head of the trunk.

[jtruesdal]

Suggested change

	! for spectral filtering. The nominal horizontal scale of
	! for spectral filtering. The nominal horizontal scale (km) of

[jtruesdal]

Nudge_SpectralNtrunc should have a check in readnl to make sure its set to something other than the default of -1 along with a message letting the user know about the missing truncation value before attempting the initialization

[jtruesdal]

Samping -> Sampling here and another 3 times below.

[jtruesdal]

This shr_reprosum_calc call within the level loop will be a bottleneck. Can you compute the local covariance with input data and basis functions for all levels first and then make a single reprosum call. Something like this. Not tested.

! Flatten the vertical and basis dimensions to allow a single MPI reduction
nbas_x_nlev = this%nbas * nlev
allocate(Bamp_flat(nbas_x_nlev), stat=astat)
allocate(Csum(nlcols, nbas_x_nlev), stat=astat)

do ll= 1,nlev
do nn= 1,this%nbas
idx = (ll - 1) * this%nbas + nn
count = 0
do lchnk=begchunk,endchunk
ncols = get_ncols_p(lchnk)
do cc = 1,ncols
count=count+1
Csum(count,idx) = I_Gdata(cc,ll,lchnk)*this%basis(cc,lchnk,nn)*this%area(cc,lchnk)
end do
end do
end do
end do

call shr_reprosum_calc(Csum, Bamp_flat, count, nlcols, nbas_x_nlev, gbl_count=ngcols_p, commid=mpicom)

! Unpack the flattened amplitudes into the 2D output array
do ll= 1,nlev
do nn=1,this%nbas
idx = (ll - 1) * this%nbas + nn
O_Bamp(nn,ll) = Bamp_flat(idx)
end do
end do

[jtruesdal]

Pull reprosum out of level loop like in calc_SphericalHarmonic_3Damps_GS. Since this%map(n2, nn) is applied after the reduction, you can unpack Gcov into a temporary Gcov_by_level(nbas) array for each level, and then perform the map multiplication against Gcov_by_level.

[jtruesdal]

Same as other 2 3d routines, pull shr_reprosum_calc out of level loop.

[jtruesdal]

This is a nice refactor. I didn't test the code to pull shr_reprosum out of the level loop it was just an example but something like that should work.