Add GL90 parameterization for stacked shallow water #268
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This adds a new vertical viscosity parameterization as in Greatbatch and Lamb (1990), Ferreira & Marshall (2006) and Zhao & Vallis (2008), hereafter referred to as the GL90 vertical viscosity parameterization. This vertical viscosity scheme redistributes momentum in the vertical, and is the equivalent of the Gent & McWilliams (1990) parameterization, but in a TWA (thickness-weighted averaged) set of equations. The vertical viscosity coefficient nu is computed from kappa_GM via thermal wind balance, and the following relation: nu = kappa_GM * f^2 / N^2. The vertical viscosity del_z ( nu del_z u) is applied to the momentum equation with stress-free boundary conditions at the top and bottom. In the current implementation, kappa_GM is assumed either (a) constant or as (b) having an EBT structure. A third possible formulation of nu is depth-independent: nu = f^2 * alpha The latter formulation would be equivalent to a kappa_GM that varies as N^2 with depth. Currently, the GL90 parameterization is only implemented in stacked shallow water (SSW) mode, in which case we have 1/N^2 = h/g'. More specifically, this commit adds a new subroutine that computes the couping coefficient associated with GL90 via a_cpl_gl90 = nu / h = kappa_GM * f^2 / g' or a_cpl_gl90 = nu / h = f^2 * alpha / h. Further, a_cpl_gl90 is multiplied by a function (botfn), which is 0 within the GL90 bottom boundary layer, whose depth is set by Hbbl_gl90, and 1 otherwise. This modification is necessary to avlid fluxing momentum into vanished layers that ride over steep topography. Finally, a_cpl_gl90 is added to a_cpl, where the latter is the coupling coefficient associated with the remaining vertical stresses, used in the vertical viscosity solver. More information can be found in Loose et al. (https://www.essoar.org/doi/abs/10.1002/essoar.10512867.1), Appendix B.
NoraLoose
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Codecov Report
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## dev/gfdl #268 +/- ##
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- Coverage 37.11% 37.09% -0.03%
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Files 263 263
Lines 73493 73582 +89
Branches 13700 13718 +18
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+ Hits 27279 27296 +17
- Misses 41185 41251 +66
- Partials 5029 5035 +6
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@marshallward any ideas why the style / doxygen test fails? I didn't even touch line 90 in |
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The log seems to not understand the I'm not sure why it's getting confused here, where there are other working cases, but I will try to have a look soon. (I'm out of action today and possibly a bit longer, but will try to get to it.) |
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Oh, I remember a similar issue happening before. Sometimes a docstring of a previous variable will break, and the error won't manifest until a later line. Have a look at one of the previous lines. |
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It's something about the apostrophe No idea why, but it doesn't like that apostrophe. |
Change g' --> g^prime because doxygen and style test does not like the apostrophe.
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Nice catch, that fixed it! Thanks. It looks like there is a separate issue with codecov. |
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The codecov one is unfortunately server-side (current theory is they limit the number of uploads within a certain timeframe). Resubmitting it usually works, though sometimes you have to wait a bit. |
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Ok, we can re-run the github action in a bit? In any case, I'll leave this PR in draft mode until #263 is reviewed and merged because this PR depends on it. |
This variable is analogous to KHTH_USE_EBT_STRUCT, but is specifically for the GL90 scheme. If the user sets KD_GL90_USE_EBT_STRUCT = True, an EBT structure will be applied to KD_GL90. Before this commit, KHTH_USE_EBT_STRUCT took the two-fold role of imposing an EBT structure on KHTH (used in the GM scheme) and KD_GL90 (used in the GL scheme), which may have been confusing.
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This PR is ready for review now. @Hallberg-NOAA or @adcroft would be great reviewers as they have seen this code before, while it was being developed. |
Hallberg-NOAA
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Dec 13, 2022
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Overall this excellent PR looks like it is close to being ready to go, but before we merge it into dev/gfdl, I have a few minor specific comments (see below), that I think should be considered. Thank you for this contribution, @NoraLoose!
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All get_param calls that are for variables that are only used when GL90 is in use get the argument do_not_log = .not.CS%use_GL90_in_SSW. Prior, these variables have been wrapped by an if-statement.
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Hallberg-NOAA
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Dec 22, 2022
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Because of all of the corrections and the merging onto this branch, I am recommending that when this is accepted, it should be done via a squash merge. @NoraLoose would you object to this? |
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This PR is undergoing pipeline testing at https://gitlab.gfdl.noaa.gov/ogrp/MOM6/-/pipelines/17774. |
@Hallberg-NOAA sounds good. |
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Gaea regression: https://gitlab.gfdl.noaa.gov/ogrp/MOM6/-/pipelines/17774 ✔️ 🟡 |
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This was referenced Apr 6, 2023
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Apr 9, 2024
* Fix biharmonic Leith
Biharmonic Leith uses Del omega at is-1 and js-1. This unavoidably requires
u at js-3 and v at is-3, which are unavailable. It also requires Del omega
at Ieq+1 and Jeq+1, which requires v at Ieq+3 and u at Jeq+3, which are
unavailable. This necessitates a halo update.
Fixes several bugs in Leith+E.
- Fixes indexing when computing smoothed vorticity and its gradient
- Crucially, computes `vert_vort_mag` when using Leith+E
- Fixes some logic in the smoothing code
- Other minor indexing fixes
* Leith+E Logic Update
Ah is required at h and q points. The original code computed Ah at
h points, then packed into Ah_h, then applied upper bounds to Ah.
If Ah_h is in the diag_table or if debug is true, then the value of
Ah with upper bounds get packed into Ah_h. Then, at q points the
code unpacks Ah_h. This update makes sure that the upper bound
gets applied to q points, not just h points.
* Leith+E halo updates
The main thing that this commit does is to perform smoothing of u and v
outside of the loop over layers. This swaps nz 2D blocking halo updates
for a single blocking 3D halo update.
* Leith+E smoothing
This commit adds a runtime flag, SMOOTH_AH. If True (default) then
`m_leithy` and `Ah` are both smoothed, which leads to many blocking
communications. If False then these fields are rougher, but there
is less communication.
* Leith+E eliminate pass-var
This commit removes one halo update in Leith+E. To achieve this
requires re-indexing two assignments. The value of Ah and Kh are
computed at h points, then re-used at q points. Without the halo
update it is necessary to offset the assignment at h and q
points, e.g. Kh(I,J) = Kh_h(i+1,j+1,k), to avoid accessing
values that have not been computed.
* Leith+E OBC
Adds code so that Leith+E works with OBC.
* Leith+E eliminate halo update
This commit eliminates one more halo update in Leith+E.
* *Correct rotational symmetry with USE_LEITHY
This commit revises the smoothing code used when USE_LEITHY = True to give
answers that respect rotational symmetry and it also corrects some horizontal
indexing bugs and problems with the staggering in some halo update and smooth_x9
calls and reduces some loop ranges to their minimal required values. The
specific changes include:
1. Corrected a horizontal indexing bug when interpolating Kh_h and Ah_h to
corner (q) points when USE_LEITHY = True. These had previously been
inappropriately copied from the thickness point to the southwest of the
corner point. This required symmetric-memory-mode calculations of the
thickness point viscosities whenever USE_LEITHY is true, but to avoid adding
complicated logic, the symmetric-memory loop bounds are used for the
calculation of Kh.
2. Revised smooth_x9 to give rotationally symmetric answers and split it into
the two routines smooth_x9_h and smooth_x9_uv to reduce the memory used by
this routine and reduce the use of optional arguments.
3. Eliminated 4 unneeded halo update calls, and added error handling for the
case where Leith options are used with insufficiently wide halos.
4. Added new integers to indicate the loop ranges over which the viscosities
and related variables should be calculated, depending on which options are
active, and then adjusted 91 do-loop extents horizontal_viscosity code to
reflect the loop ranges over which arrays are actually used.
5. Added a new 2-d variable for the squared viscosity for smoothing that can
be used for halo updates and to avoid having a variable with confusingly
inconsistent dimensions at various points in the code.
6. Corrected the position arguments on 2 smooth_x9 calls and 4 pass_var calls
that are used when USE_LEITHY=.true. and SMOOTH_AH=.true. As previously
written, these smooth_x9 and pass_var calls would work when in non-symmetric
memory mode but would give incorrect answers when in symmetric memory mode.
These revisions change answers when USE_LEITHY is true, but answers are
bitwise identical in all other cases.
---------
Co-authored-by: Robert Hallberg <Robert.Hallberg@noaa.gov>
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GL90 parameterization
This adds a new vertical viscosity parameterization as in Greatbatch and Lamb (1990), Ferreira & Marshall (2006) and Zhao & Vallis (2008), hereafter referred to as the GL90 vertical viscosity parameterization. This vertical viscosity scheme redistributes momentum in the vertical, and is the equivalent of the Gent & McWilliams (1990) parameterization, but in a TWA (thickness-weighted averaged) set of equations. The vertical viscosity coefficient
nuis computed fromKD_GL90(corresponding tokappa_GM) via thermal wind balance, and the following relation:Currently, the GL90 parameterization is only implemented in stacked shallow water (SSW) mode, in which case we have
1/N^2 = h/g'.The vertical viscosity
del_z ( nu del_z u)is applied to the momentum equation with stress-free boundary conditions at the top and bottom.GL90 viscosity coefficient: Current options
In the current implementation,
KD_GL90is assumed either (a) constant or (b) horizontally varying. In both cases, (a) and (b), one can additionally impose an EBT structure in the vertical forKD_GL90. Another possible formulation of nu is depth-independent:The latter formulation would be equivalent to a
kappa_GMthat varies asN^2with depth.Figure: Vertical viscosity coefficient
Kv_vfor(upper left) baseline with GL90 parameterization turned off;
(upper right) GL90 parameterization turned on and spatially constant
KD_GL90;(lower left) GL90 parameterization turned on and
KD_GL90which is horizontally constant but varies in the vertical with and EBT structure;(lower right) GL90 parameterization turned on with vertically constant GL90 viscosity, achieved by setting
alpha_GL90 = 3 * 10^7 m^2 s.Note that in the last panel, the diagnostic
Kv_vis not exactly constant in the vertical becausewhere
h_vis the layer thickness used at a v-velocity points in the vertical viscosity scheme. The third factor is the composition of a harmonic and arithmetic mean, and is not equal to the identity.Implementation done via coupling coefficients
More specifically, this commit adds a new subroutine that computes the coupling coefficient associated with GL90 via
or
Further,
a_cpl_gl90is multiplied by a function (botfn), which is 0 within the GL90 bottom boundary layer, whose depth is set byHbbl_gl90, and 1 otherwise. This modification is necessary to avoid fluxing momentum into vanished layers that ride over steep topography.Finally,
a_cpl_gl90is added toa_cpl, where the latter is the coupling coefficient associated with the remaining vertical stresses, used in the vertical viscosity solver.More information can be found in Loose et al. (https://www.essoar.org/doi/abs/10.1002/essoar.10512867.1), Appendix B.
Follow-up PR
There will be a follow-up PR which implements diagnostics related to the GL90 parameterization.