Add flux-corrected transport scheme to MALI #70

trhille · 2023-03-07T20:35:20Z

This merge adds a flux-correct transport (FCT) scheme to MALI for thickness and tracer advection, ported over with MALI-relevant modification from MPAS-Ocean's routines, which are based on Skamarock and Gassmann (2011) (https://doi.org/10.1175/MWR-D-10-05056.1). This uses a blend of 3rd and 4th order fluxes to achieve monotonicity. The FCT routine is only used for tracers in MPAS-Ocean, whereas here it is modified for use with both thickness and tracers. The user can specify 2nd, 3rd, or 4th order advection with the config_horiz_tracer_adv_order option, but only config_horiz_tracer_adv_order = 3 with 0 < config_advection_coef_3rd_order < 1 is truly FCT. The config_advection_coef_3rd_order option specifies the blend between 3rd and 4th order fluxes used in the flux correction. config_advection_coef_3rd_order = 1.0 is purely 3rd order, while config_advection_coef_3rd_order = 0.0 is purely 4th order. The default value of 0.25 is taken from the MPAS-Ocean default and may not be appropriate for all situations. Note that all higher-order advection must reduce to 1st order at the boundaries.

This also adds a new variable passiveTracer2d, that can be used to verify advection schemes.

Currently supported combinations of thickness and tracer advection with fct include:

config_thickness_advection = 'fo'; config_tracer_advection = 'fct'
config_thickness_advection = 'fct'; config_tracer_advection = 'fct'
config_thickness_advection = 'fct'; config_tracer_advection = 'none'
FCT tracer advection with no thickness advection and FCT thickness advection with FO tracer advection could be added, but we do not currently anticipate using them. Therefore, we have left them out of this PR as they would add unnecessary complexity to the code.

When used with forward Euler time integration, FCT requires a severely reduced time step relative to first order advection. Testing shows that CFL fraction on the order of 0.1 is likely sufficiently small, but this is probably case-dependent. Once Runge-Kutta time integration is operational, it is recommended to use that instead of forward Euler.

At the time of merging, there is a very slight conservation error (<0.1% in the grounded slab test shown below) for tracers when using FCT for both thickness and tracer advection, while mass is fully conserved. Tracers are conserved when using FO thickness advection with FCT tracer advection. The convergence order has not yet been verified, but testing is under way using a new mesh convergence COMPASS test: MPAS-Dev/compass#690.

Add an option to use the flux-corrected transport advection scheme provided in MPAS framework, and make calls to those modules from mpas_li_advection. Compiles, but not yet tested. No expectation that it will run yet.

We have decided to use modified versions of the routines for higher-order advection from MPAS-Ocean. This commit copies over the modules from the ocean model, but does not modify or call them yet.

Update Makefile to include fct modules. Currently does not compile because of undefined variables.

Initialize fct from tracer_setup. Also rename public routines to start with "li_"

Add li_mesh module that is called during init to make all mesh parameters public. This is copied from mpas-ocean, with modifications appropriate for MALI.

Comment out irrelevant parameters and routine in li_mesh that are specific to MPAS-Ocean and caused build errors.

Add li_config module so other modules can get all configs with 'use li_config'

Also general cleanup to get rid of build errors stemming from these modules.

Some fields need to be revisited for accuracy, but these changes fix build errors.

Remove call to tracer_advection_vert_flx from li_tracer_advection_fct_tend. We will probably want to add this back, but for now just trying to get this to compile without vertical fct. And now it compiles!

trhille · 2023-03-09T22:52:57Z

Code finally compiles as of 414eac6!

Differences between ocean and land ice mesh variables were causing segmentation faults at run time. This clean-up commit allows full_integration to run and pass, which does not test the fct code at all, but shows that li_mesh is now operational.

trhille · 2023-03-10T17:54:07Z

full_integration passes as of 83f5168, which does not test the fct at all, but indicates that the new li_mesh and li_config modules are operational.

Fix issues with public parameter allocations. This now allows the code to run using config_tracer_advection='fct' without invalid memory reference errors, although results are not yet valid.

Clean up li_advection_fct_tend to get rid of runtime errors. All vertical advection code is currently commented out and not operational. This runs with config_thickness_advection='fo' and config_tracer_advection='fct', but it currently seems to give the same results for the humboldt 3km test case in full_integration as using 'fo' for both thickness and tracer advection. Need to look further into that.

Currently fct advection for thickness is not supported, but fo thickness advection wtih fct tracer advection is operational, although not validated.

trhille · 2023-03-14T22:41:14Z

Testing on a364f7a shows that the code will run with config_thickness_advection = 'fo' and config_tracer_advection = 'fct', but from examining damage output, tracers don't seem to actually be advecting.

Previous commit neglected to actually update tracers after calculating tendencies. This corrects that.

trhille · 2023-03-16T15:02:29Z

As of e85d3fd, fct tracer advection is at least doing something, although is not yet verified. Here are three MISMIP runs after 100 years with velo solver turned off, no sub-shelf melt, calculate-damage = true. All use 'fo' thickness advection. Left: no tracer advection; Middle: fo tracer advection; right: fct tracer advection:

White contour is damage = 0.4 from the 'fo' case.

Pass layerThicknessOld instead of layerThickness to fct tracer advection routine because the fct routine calculates a provisional advected layerThickness based on the normalThicknessFlux, which is layerThicknessEdge (before advection) * layerNormalVelocity.

Add support for fct thickness advection by passing layerThickness to li_tracer_advection_fct_tend as a tracer. Note that this seems to require small time steps to avoid terracing effects in the thickness field.

trhille · 2023-03-16T21:47:05Z

As of 8734303, fct thickness advection is operational, and seems to be working correctly. One issue is that it seems to require a very small CFL fraction to avoid terracing effects.
From left to right: fo thickness advection with CFL fraction = 0.8; fct thickness advection w/ CFL fraction 0.8; fct thickness advection w/ CFL fraction 0.1:

CFL fraction of 0.1 (~40 day time steps) seems to be sufficiently low here. I tested another run w/ a CFL fraction of 0.01 (~4 days) and the differences at year 100 are generally <1 m:

What we are seeings seems to be a known issue w/ FCT: "Another infamous byproduct of FCT manifests itself in distortions of a smooth profile. This phenomenon is known as terracing and represents ‘an integrated, nonlinear effect of residual phase errors’ [64] or, loosely speaking, ‘the ghosts of departed ripples’ [7]. A particularly severe form of terracing is caused by the linear instability of the high-order scheme. For this reason, we do not recommend the use of the forward Euler time-stepping (θ = 0) even though the flux-corrected scheme proves positivity-preserving under the CFL-like time step restriction (62)."
(found on page 178 of https://link.springer.com/content/pdf/10.1007/978-94-007-4038-9.pdf)

trhille · 2023-03-16T22:03:10Z

Adding to comment above: CFL fraction of 0.4 also drastically reduces the terracing and gives a thickness field visually indistinguishable from CFL fractions of 0.1 and 0.01, so that's great news! Differences between runs w/ CFL fractions of 0.4 and 0.1:

trhille · 2023-03-17T14:20:23Z

Just for comparison, here are the thickness differences at year 100 when using FO thickness advection with CFL of 0.8 vs 0.1:

So the FCT solution is definitely more sensitive to the time step than the FO solution, even when the time step is quite small.

trhille · 2023-03-17T17:26:38Z

Testing on Thwaites mesh indicates issue with FCT thickness advection during advance, which is not surprising. It turns out that boundaryCell is not being calculated, and thus neither is advMaskHighOrder. This leads to very high velocities and strange geometries in areas where ice advances beyond the initial extent.

First order flux needs to be masked when subtracted from higher order flux, because they don't have the same valid spatial extent. This seems to largely fix the issue with thickness ramps growing at the ice margin in tests on the Thwaites domain. It also leads to a bit more diffusion of the ice mask in the slotted cylinder test, but it also gets rid of the noisy artifacts in the thickness field, so that's great!

trhille · 2023-04-24T15:48:10Z

I have confirmed that results are BFB for restarts and decomposition tests (64 and 128 cores) using the slotted cylinder test case. I should also put together a version of full_integration that uses fct.
Here are the restart test results, with the full run on top, a restart run branching from year 10 in the middle and the difference at year 25 on bottom. This uses 3rd order, beta = 0.5, and CFL fraction = 0.25 (hence the ugliness)

And here is the same for the decomp test. Top is 128 procs, middle is 64 procs, bottom is difference:

trhille · 2023-04-24T16:03:45Z

Here are results at year 25 with CFL fractions of 0.25 (top), 0.1 (middle) and 0.05 (bottom):

trhille · 2023-08-01T19:27:23Z

Uh oh, it appears that passiveTracer is not being conserved in test runs with fct. I ran the notched slab test that I was using above for 100 years and summed up passiveTracer at each time step: ncap2 -s 'tracer_sum = (passiveTracer * thickness * areaCell).sum($nCells)' output_all_timesteps.nc tmp.nc.
fct:

fo conserves just fine:

Both runs do conserve mass, however. Blue is fo, orange is fct:

Update:
I rewound the branch to 4c87809 and the issue is still there, but it is less egregious and drifts the opposite way:

Fix a bug in fct tracer advection that caused tracers to not be conserved due to an inconsistent treatment of the thickness flux. The previous implementation inadvertently used first-order upwind thickness flux to calculate higher-order tracer flux, which led to loss of conservation when both thickness and tracers used fct. Note that this still does not conserve tracers to machine precision, even though mass is conserved to machine precision. But testing shows the tracer volume conserved to within about 0.02%.

trhille · 2023-08-03T18:51:48Z

8d2f023 fixed the tracer conservation issue detailed above! It still doesn't conserve to machine precision, but a 100 year test run on the grounded slab test case showed about 0.06% drift by the end of the simulation. That seems pretty close!

Compare this with the drift above

matthewhoffman · 2023-08-16T16:16:19Z

@dengwirda, see note about slight non-conservation of tracers in Trevor's current implementation (#70 (comment)). Should we be expecting machine precision conservation? If so, do you think we should worry that we're not achieving that given how small the non-conservation is?

I suppose we would be introducing energy conservation errors, given that we will be advecting temperature with this scheme.

matthewhoffman

@trhille , I've made it through these changes and have a number of requests and questions to address, but this seems very close to being ready to merge. Thanks for you hard work and what turned out to be a much more involved project than initially anticipated!

components/mpas-albany-landice/src/Registry.xml

components/mpas-albany-landice/src/mode_forward/mpas_li_advection.F

matthewhoffman · 2023-08-15T15:51:23Z

components/mpas-albany-landice/src/mode_forward/mpas_li_advection_fct.F

+        ! Determine bounds on tracer (tracerMin and tracerMax) from
+        ! surrounding cells for later limiting.
+
+#ifdef MPAS_OPENACC


remove accelerator stuff?

We decided to save removing accelerator stuff for a separate PR.

matthewhoffman · 2023-08-16T15:53:09Z

components/mpas-albany-landice/src/mode_forward/mpas_li_advection.F

+             ! This does conserve mass:
+             layerThickness(:,:) = layerThickness(:,:) + tend(nTracers,:,:) * dt
+             ! Reset tracers after thickness advection for tracer advection
+             ! TODO: determine whether we need to treat other tracer tendencies


@trhille , have you looked into this question?

Yes, it doesn't work for tracers, for some reason.

components/mpas-albany-landice/src/mode_forward/mpas_li_advection_fct_shared.F

components/mpas-albany-landice/src/mode_forward/mpas_li_advection_fct.F

matthewhoffman · 2023-08-16T16:12:05Z

components/mpas-albany-landice/src/mode_forward/mpas_li_advection.F

             call li_tracer_advection_fct_tend(&
                  tend, advectedTracers, layerThicknessOld, &
                  layerThicknessEdge * layerNormalVelocity, 0 * normalVelocity, dt,    &
-                  nTracers, computeBudgets=.false.)!{{{
+                  nTracers, activeTracerHorizontalAdvectionEdgeFlux, computeBudgets=.false.)!{{{


We may want to move activeTracerHorizontalAdvectionEdgeFlux to Registry so it could be output given its importance in the algorithm. But we'd want to refactor things to avoid it being nTracers big first. So let's wait until we encounter a need to visualize it before worrying about that.

Add explanatory comments, remove commented code, clarify desciriptions in Registry.xml

Throw error forr fct thickness with fo tracer, as this combination is currently not supported.

Make activeTracerHorizontalAdvectionEdgeFlux an optional argument when calling fct code.

components/mpas-albany-landice/src/Registry.xml

This fixes an error introduced in the previous commit that prevented code from compiling.

Fix a bug that disabled thickness advection when tracer advection is turned off.

Only pass layer thickness tracer instead of all tracers for thickness advection step, which is the first call to fct when using fct for both thickness and tracers.

Change passiveTracer to passiveTracer2d

matthewhoffman

@trhille , thanks for all the clean up on this PR. I would like to proceed with merging the version you have now and resolve additional issues related to conservations and convergence in follow up PRs as we learn more.

However, it would be nice to first add the logic to support FCT thickness advection with no tracer advection. That would be useful for the horizontal_advection convergence test using the thickness bump and for the halfar convergence test. I think disabling tracer advection would speed those tests up considerably.

One solution would be to fold it into this option:

         elseif ((trim(config_thickness_advection) .eq. 'fct') .and. &
                  trim(config_tracer_advection) .eq. 'fct') then

and then only do the tracer bit if tracer advection is set to fct.

Enable fct thickness advection without tracer advection and throw error if using unsupported combination of thickness and tracer advection. Also initialize some previously uninitialized allocatable arrays.

matthewhoffman · 2023-09-06T03:01:23Z

Testing

@trhille , thanks for making the final (more complicated than expected) adjustment. I tested one more time and all tests pass:

Test Runtimes:
00:19 PASS landice_dome_2000m_sia_restart_test
00:19 PASS landice_dome_2000m_sia_decomposition_test
00:16 PASS landice_dome_variable_resolution_sia_restart_test
00:06 PASS landice_dome_variable_resolution_sia_decomposition_test
00:26 PASS landice_enthalpy_benchmark_A
00:24 PASS landice_eismint2_decomposition_test
00:23 PASS landice_eismint2_enthalpy_decomposition_test
00:29 PASS landice_eismint2_restart_test
00:28 PASS landice_eismint2_enthalpy_restart_test
00:22 PASS landice_greenland_sia_restart_test
00:12 PASS landice_greenland_sia_decomposition_test
00:20 PASS landice_hydro_radial_restart_test
00:12 PASS landice_hydro_radial_decomposition_test
00:44 PASS landice_humboldt_mesh-3km_decomposition_test_velo-none_calving-none_subglacialhydro
00:30 PASS landice_humboldt_mesh-3km_restart_test_velo-none_calving-none_subglacialhydro
00:26 PASS landice_dome_2000m_fo_decomposition_test
00:30 PASS landice_dome_2000m_fo_restart_test
00:11 PASS landice_dome_variable_resolution_fo_decomposition_test
00:16 PASS landice_dome_variable_resolution_fo_restart_test
00:18 PASS landice_circular_shelf_decomposition_test
00:44 PASS landice_greenland_fo_decomposition_test
00:44 PASS landice_greenland_fo_restart_test
00:41 PASS landice_thwaites_fo_decomposition_test
00:32 PASS landice_thwaites_fo_restart_test
00:15 PASS landice_thwaites_fo-depthInt_decomposition_test
00:22 PASS landice_thwaites_fo-depthInt_restart_test
00:58 PASS landice_humboldt_mesh-3km_restart_test_velo-fo_calving-von_mises_stress_damage-threshold_faceMelting
00:32 PASS landice_humboldt_mesh-3km_restart_test_velo-fo-depthInt_calving-von_mises_stress_damage-threshold_faceMelting
Total runtime 12:04
PASS: All passed successfully!

I will also test the FCT tests you have in MPAS-Dev/compass#650

matthewhoffman · 2023-09-06T03:15:03Z

Testing, Part 2

The FCT suite all passes. I did not look at any of the output, but they all run and pass validation. For the sake of merging this PR as a checkpoint, I think that is sufficient.

Test Runtimes:
00:19 PASS landice_dome_2000m_fo_fct_decomposition_test
00:35 PASS landice_dome_2000m_fo_fct_restart_test
00:16 PASS landice_dome_variable_resolution_fo_fct_decomposition_test
00:14 PASS landice_dome_variable_resolution_fo_fct_restart_test
00:42 PASS landice_greenland_fo_fct_decomposition_test
00:47 PASS landice_greenland_fo_fct_restart_test
00:38 PASS landice_thwaites_fct_decomposition_test
00:34 PASS landice_thwaites_fct_restart_test
00:35 PASS landice_humboldt_mesh-3km_restart_test_velo-fo_advec-fct_calving-von_mises_stress_damage-threshold_faceMelting
Total runtime 04:46
PASS: All passed successfully!

matthewhoffman

The long-awaited for day is upon us! Awesome work @trhille !

trhille added 2 commits March 7, 2023 12:26

Add calls to higher order advection scheme

119cfd9

Add an option to use the flux-corrected transport advection scheme provided in MPAS framework, and make calls to those modules from mpas_li_advection. Compiles, but not yet tested. No expectation that it will run yet.

Copy higher-order ocean advection routines

7532330

We have decided to use modified versions of the routines for higher-order advection from MPAS-Ocean. This commit copies over the modules from the ocean model, but does not modify or call them yet.

trhille added enhancement New feature or request in progress Still being worked on, don't merge yet! labels Mar 7, 2023

trhille added 11 commits March 8, 2023 08:10

Update Makefile to include fct modules

aac672a

Update Makefile to include fct modules. Currently does not compile because of undefined variables.

Initialize fct from tracer_setup

47d6154

Initialize fct from tracer_setup. Also rename public routines to start with "li_"

Add li_mesh module

5dd26c6

Add li_mesh module that is called during init to make all mesh parameters public. This is copied from mpas-ocean, with modifications appropriate for MALI.

Comment out irrelevant parameters and routine in li_mesh

e549c55

Comment out irrelevant parameters and routine in li_mesh that are specific to MPAS-Ocean and caused build errors.

Add li_config module

f97dd56

Add li_config module so other modules can get all configs with 'use li_config'

Add fct variables to Registry

ab8ec14

Remove ocean variables from li_advection_fct and li_advection_fct_shared

494d092

Also general cleanup to get rid of build errors stemming from these modules.

Update shared Makefile to include li_config

d9f9317

Fix call to li_advection_fct_tend

9518f49

Some fields need to be revisited for accuracy, but these changes fix build errors.

Fix typo in call to li_config

30d387c

Remove call to tracer_advection_vert_flx

414eac6

Remove call to tracer_advection_vert_flx from li_tracer_advection_fct_tend. We will probably want to add this back, but for now just trying to get this to compile without vertical fct. And now it compiles!

trhille added 3 commits March 13, 2023 11:46

Fix public parameter allocations

79edb95

Fix issues with public parameter allocations. This now allows the code to run using config_tracer_advection='fct' without invalid memory reference errors, although results are not yet valid.

Add support for fo thickness with fct tracer advection

a364f7a

Currently fct advection for thickness is not supported, but fo thickness advection wtih fct tracer advection is operational, although not validated.

Apply tendencies to tracers with fct advection

e85d3fd

Previous commit neglected to actually update tracers after calculating tendencies. This corrects that.

trhille added 2 commits March 16, 2023 08:28

Add support for fct thickness advection

8734303

Add support for fct thickness advection by passing layerThickness to li_tracer_advection_fct_tend as a tracer. Note that this seems to require small time steps to avoid terracing effects in the thickness field.

trhille removed the in progress Still being worked on, don't merge yet! label Apr 24, 2023

trhille requested a review from matthewhoffman April 24, 2023 15:56

trhille mentioned this pull request Jun 28, 2023

Add suite of flux-corrected transport tests for landice integration MPAS-Dev/compass#650

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matthewhoffman requested changes Aug 16, 2023

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trhille added 3 commits August 18, 2023 09:42

Simple cleanup after code review

38f3f2b

Add explanatory comments, remove commented code, clarify desciriptions in Registry.xml

Throw error forr fct thickness with fo tracer

7cff4b7

Throw error forr fct thickness with fo tracer, as this combination is currently not supported.

Make activeTracerHorizontalAdvectionEdgeFlux optional

9530ad5

Make activeTracerHorizontalAdvectionEdgeFlux an optional argument when calling fct code.

matthewhoffman reviewed Aug 19, 2023

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components/mpas-albany-landice/src/Registry.xml Outdated Show resolved Hide resolved

trhille added 4 commits August 20, 2023 12:18

Fix bug with activeTracerHorizontalAdvectionEdgeFlux

aa2999a

This fixes an error introduced in the previous commit that prevented code from compiling.

Fix the case of fo thickness, none tracer advection

35a89ae

Fix a bug that disabled thickness advection when tracer advection is turned off.

Only pass layer thickness tracer for first call to fct

f43c26b

Only pass layer thickness tracer instead of all tracers for thickness advection step, which is the first call to fct when using fct for both thickness and tracers.

Change passiveTracer to passiveTracer2d

8f218c3

Change passiveTracer to passiveTracer2d

trhille force-pushed the add_higher_order_advection branch from 9de6e44 to 8f218c3 Compare August 28, 2023 19:08

matthewhoffman self-requested a review August 31, 2023 17:37

matthewhoffman requested changes Aug 31, 2023

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Enable fct thickness advection without tracer advection

52d9a0b

Enable fct thickness advection without tracer advection and throw error if using unsupported combination of thickness and tracer advection. Also initialize some previously uninitialized allocatable arrays.

trhille force-pushed the add_higher_order_advection branch from 358431a to 52d9a0b Compare September 1, 2023 20:34

matthewhoffman self-requested a review September 6, 2023 16:45

matthewhoffman approved these changes Sep 6, 2023

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matthewhoffman merged commit 7ac9859 into MALI-Dev:develop Sep 6, 2023

trhille mentioned this pull request Oct 19, 2023

Fix small conservation error when using fct thickness and tracer advection #95

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Add flux-corrected transport scheme to MALI #70

Add flux-corrected transport scheme to MALI #70

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Add flux-corrected transport scheme to MALI #70

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Testing, Part 2

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