From f3649c9e5c9ef1abc8ca828e60e3fe726cdc79e4 Mon Sep 17 00:00:00 2001 From: Christopher Bull <5499680+chrisb13@users.noreply.github.com> Date: Fri, 5 Jun 2026 17:15:22 +1000 Subject: [PATCH 1/3] Placeholder for AG-Vertical-Lagrangian-Remapping --- documentation/docs/pages/season2.md | 3 +++ 1 file changed, 3 insertions(+) diff --git a/documentation/docs/pages/season2.md b/documentation/docs/pages/season2.md index 8b0dea8..c45e895 100644 --- a/documentation/docs/pages/season2.md +++ b/documentation/docs/pages/season2.md @@ -1027,6 +1027,9 @@ You may note that this final equation is similar in form to the approximate equa ## Vertical Lagrangian remapping +Date: 18/06/2026. + +Presenter: Angus Gibson (@angus-g). ## Pressure forces ## Coriolis term From 7cd7451846b31de652bcd374b9e039acbf095363 Mon Sep 17 00:00:00 2001 From: Angus Gibson Date: Tue, 16 Jun 2026 17:08:13 +1000 Subject: [PATCH 2/3] Add notes for VLR --- documentation/docs/assets/regridding.png | Bin 0 -> 52226 bytes 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pyn*XD1plvPXT^R0UqhmwQPZ~pS4SqTtFK-TMOihOS}C)T{{e&5=57E0 literal 0 HcmV?d00001 diff --git a/documentation/docs/pages/season2.md b/documentation/docs/pages/season2.md index c45e895..ebe2b7f 100644 --- a/documentation/docs/pages/season2.md +++ b/documentation/docs/pages/season2.md @@ -1029,7 +1029,59 @@ You may note that this final equation is similar in form to the approximate equa Date: 18/06/2026. -Presenter: Angus Gibson (@angus-g). +Presenter: Angus Gibson (@angus-g). + +With **generalised vertical coordinates**, we know that vertical velocities permit +a range of grid evolution from fully Lagrangian (zero dia-surface transport) to fully +Eulerian (zero grid velocity). For the *vertical Lagrangian-remap* method, we tend +toward the fully Lagrangian side: the GVC $s$ follows fluid elements so that the +dia-surface volume flux $w^{(\dot{s})} = 0$. + +If the model is using a purely Lagrangian coordinate, how do we have any control +over it? In general, these coordinates drift to a less useful representation of the +water column. For example, volume injection at the surface would inflate the +upper-most layer, losing resolution for the representation of boundary layer +processes. Even more simply, there is indeed irreversible mixing across surfaces +that must be captured somehow. + +The method has three steps: +1. the Vertical Lagrangian step: evolve the model as above; +2. the Vertical Regrid step: explicitly set the generalised coordinate; +3. the Vertical Remap step: ensure consistency between the ocean state + and the new coordinate. + +![Vertical regrid](../assets/regridding.png) + +The *Vertical Regrid* step is where we have the most freedom and flexibility. At +this stage, we explicitly set the generalised coordinate $s(x,y,z,t)$. The choice +is arbitrary: it could be predetermined (like a fixed geopotential or +terrain-following coordinate); state-dependent (following particular isopycnals by +solving for density levels); or even evolutionary (relaxing the current field +toward some target value). In fact, you could even change the number of +vertical levels! + +There is a slight issue after the Vertical Regrid step: the underlying ocean +state is no longer consistent with the GVC. The *Vertical Remap* step fixes +this by interpolating (or extrapolating) the state onto the new grid. In the +continuous limit, this doesn't change the ocean state. However, since we have +limited resolution there is necessarily a spurious change to the state due to +interpolation error. Ideally, this numerical mixing is reduced while integrated +quantities are conserved. + +![Vertical Lagrangian remapping](../assets/vertical-lagrange-remap.png) + +There are two big advantages to using this method: +1. There is no vertical CFL limit! As long as the remapping can handle + interpolation over more than a single cell, the target grid can be + arbitrary. +2. Grid evolution can occur on a different timestep to state evolution. You may + take several Lagrangian timesteps before performing the regrid/remap steps. + Particularly with several tracers (as with BCG), this may give some + performance improvements. + +A third advantage is that there is a built-in method for remapping the state onto +an arbitrary grid, which is useful for diagnostics. You may have a lower-resolution +diagnostic grid, or want density-space diagnostics, etc. ## Pressure forces ## Coriolis term From 4e356e0d5df6c3b3679ccb9fe6a91220fd28019f Mon Sep 17 00:00:00 2001 From: Angus Gibson Date: Wed, 17 Jun 2026 17:15:45 +1000 Subject: [PATCH 3/3] Improve order of definition and use of terms --- documentation/docs/pages/season2.md | 12 +++++++----- 1 file changed, 7 insertions(+), 5 deletions(-) diff --git a/documentation/docs/pages/season2.md b/documentation/docs/pages/season2.md index ebe2b7f..0d51cbb 100644 --- a/documentation/docs/pages/season2.md +++ b/documentation/docs/pages/season2.md @@ -1031,11 +1031,10 @@ Date: 18/06/2026. Presenter: Angus Gibson (@angus-g). -With **generalised vertical coordinates**, we know that vertical velocities permit +With **generalised vertical coordinates (GVC)**, we know that vertical velocities permit a range of grid evolution from fully Lagrangian (zero dia-surface transport) to fully -Eulerian (zero grid velocity). For the *vertical Lagrangian-remap* method, we tend -toward the fully Lagrangian side: the GVC $s$ follows fluid elements so that the -dia-surface volume flux $w^{(\dot{s})} = 0$. +Eulerian (zero grid velocity). In MOM6, the dynamics are written in the fully Lagrangian sense: +the GVC $s$ follows fluid elements so that the dia-surface volume flux $w^{(\dot{s})} = 0$. If the model is using a purely Lagrangian coordinate, how do we have any control over it? In general, these coordinates drift to a less useful representation of the @@ -1045,7 +1044,9 @@ processes. Even more simply, there is indeed irreversible mixing across surfaces that must be captured somehow. The method has three steps: -1. the Vertical Lagrangian step: evolve the model as above; + +1. the Vertical Lagrangian step: evolve the model with a purely Lagrangian + generalised coordinate; 2. the Vertical Regrid step: explicitly set the generalised coordinate; 3. the Vertical Remap step: ensure consistency between the ocean state and the new coordinate. @@ -1071,6 +1072,7 @@ quantities are conserved. ![Vertical Lagrangian remapping](../assets/vertical-lagrange-remap.png) There are two big advantages to using this method: + 1. There is no vertical CFL limit! As long as the remapping can handle interpolation over more than a single cell, the target grid can be arbitrary.