workbench_idemix2: IDEMIX2 - Internal Wave Energy Parameterisation for FESOM2

[patrickscholz]

IDEMIX2: Internal Wave Energy Parameterisation for FESOM2

IDEMIX2 (Internal wave Dissipation, Energy and MIXing, version 2) is a prognostic parameterisation of internal gravity wave energy and its contribution to diapycnal mixing, based on Olbers & Eden (2013) and Eden et al. (2014). It is implemented here as an extension to the existing IDEMIX1/TKE mixing scheme in FESOM2.

Concept

Unlike IDEMIX1, which tracks a single vertically integrated internal wave energy field, IDEMIX2 resolves the horizontal propagation direction of internal waves through a spectral angular dimension (nfbin directional bins, default 50 interior + 2 ghost bins covering 0–2π). This captures anisotropic wave fields near generation sites such as rough topography and coastlines, and allows wave energy to be tracked as it propagates across ocean basins.

Wave energy compartments

Two spectral wave energy fields are evolved independently:

  Surface wind forcing                 M2 tidal generation
  (NIW, near-inertial)                 (rough topography)
          │                                    │
          ▼                                    ▼
  ┌───────────────┐                  ┌─────────────────┐
  │  E_niw(φ, x)  │                  │   E_M2(φ, x)    │
  │  Near-inertial│                  │   M2 tidal IW   │
  │  waves        │                  │   (~12.4 h)     │
  └───────┬───────┘                  └────────┬────────┘
          │  ω ≈ f (lat-dependent)            │  ω = ω_M2 (fixed)
          └──────────────┬────────────────────┘
                         │  wave-wave interaction
                         ▼
               ┌──────────────────┐
               │   E_iw(z, x)     │   background IW continuum
               │   (vertically    │   (GM spectrum)
               │    resolved)     │
               └────────┬─────────┘
                        │  dissipation → diapycnal mixing
                        ▼
               ┌──────────────────┐
               │   TKE scheme     │   iw_diss added as
               │   Kv, Av         │   energy source term
               └──────────────────┘

Timestep structure

Each call to calc_cvmix_idemix2 follows this sequence:

  ┌─────────────────────────────────────────────────────────────────┐
  │ 1. Node parameters                                              │
  │    cn (baroclinic wave speed), α_c, v0, c0, τ_M2, τ_niw,        │
  │    vertical structure functions  [loop: node, OMP parallel]     │
  ├─────────────────────────────────────────────────────────────────┤
  │ 2. Element group velocities                                     │
  │    u_M2(φ), v_M2(φ), w_M2(φ)  — spectral propagation speeds     │
  │    scatter elem → node (area-weighted)                          │
  ├─────────────────────────────────────────────────────────────────┤
  │ 3. Horizontal spectral integration  [for M2, then NIW]          │
  │                                                                 │
  │   E^n  ──▶  superbee horizontal advection  ──▶  flx_uv(φ,edge)  │
  │              │                                                  │
  │              ├──▶  reflective coastal BC                        │
  │              │     (redirect toward-coast flux into             │
  │              │      mirror spectral bin at interior node)       │
  │              ▼                                                  │
  │         superbee cross-spectral advection ──▶  flx_cs(φ,node)   │
  │              │                                                  │
  │              ▼                                                  │
  │         flux → divergence  +  reflect_src injection             │
  │              │                                                  │
  │              ▼                                                  │
  │         E^(n+1) = (E^n + dt·(Edivh + Edivs + forc))             │
  │                   / (1 + dt·τ)     [AB2 or Euler]               │
  ├─────────────────────────────────────────────────────────────────┤
  │ 4. Eiw vertical diffusion + implicit dissipation                │
  │    tridiagonal solve per node  [OMP parallel]                   │
  ├─────────────────────────────────────────────────────────────────┤
  │ 5. Eiw horizontal diffusion  (optional)                         │
  ├─────────────────────────────────────────────────────────────────┤
  │ 6. Wave-wave interaction  E_M2/niw ↔ E_iw                       │
  │    [loop: node, OMP parallel]                                   │
  ├─────────────────────────────────────────────────────────────────┤
  │ 7. iw_diss → TKE (Kv, Av)                                       │
  └─────────────────────────────────────────────────────────────────┘

Reflective coastal boundary condition

Wave energy reaching a coastline is redirected into the spectrally mirrored propagation direction at the last interior node, rather than leaking into land:

  LAND │ n_coast ──── edge ──── n_int (interior node)
       │
       │  toward-coast flux in bin φ_i  →  zeroed
       │                                       │
       │                                       ▼
       │                            energy re-injected at n_int
       │                            in mirror bin φ_k = edge normal
       │                            (net energy change = 0,
       │                             spectral redistribution only)

The mirror bin φ_k for each coast edge is pre-computed once at init from the edge geometry and stored in iwe2_refl_bin(edge).

Forcing inputs

Field	Source	Role
M2 tidal forcing	Observed anisotropic tidal generation (modes 1+2)	E_M2 surface source
NIW / surface forcing	Wind-derived near-inertial flux	E_niw surface source or E_iw surface BC
Bottom tidal forcing	Near-field tidal dissipation dataset	E_iw bottom source
Topographic HRMS / λ	Seafloor roughness fields	Scattering timescale τ

[JanStreffing]

Nice work!
Should we add a CI test for IDEMIX2?

[JanStreffing]

I need some time to check this. It's quite a bit. Beginning of next week ok?

[JanStreffing]

Tested this branch on levante (pi mesh, 1 day, 32 steps/day, cvmix_TKE+cvmix_IDEMIX2).

Namelist blocker, already fixed on the branch in 7ad2944. config/namelist.cvmix had idemix2_AB_epsilon = 0.1_WP. The _WP kind suffix is Fortran source syntax and is not legal in a namelist record, so every run selecting an IDEMIX2 scheme aborted while reading the namelist, before the first timestep:

forrtl: severe (17): syntax error in NAMELIST input, unit 20,
file namelist.cvmix, line 95, position 28
  ... g_cvmix_idemix2_m -> ocean_setup_ -> fesom_module

It was the only kind-suffixed value in any shipped namelist, so IDEMIX2 could not have been run from the shipped config before this.

Could we get the IDEMIX2 forcing staged on levante? All five IDEMIX2 forcing entries point into /albedo/work/user/pscholz/... or /albedo/pool/..., so none resolve here. There are two separate cases. idemix2_niwforc_file is already present on levante at /pool/data/AWICM/FESOM2/FORCING/IDEMIX/fourier_smooth_2005_cfsr_inert_rgrid.nc under the same filename, so that one only needs the namelist path corrected, the way idemix_surforc_file a few lines above already does it. The M2, HRMS, lambda and STORMTIDE2 bottom-forcing files exist only on albedo and would need copying into /pool/data/AWICM/FESOM2/FORCING/. Once they are there the shipped namelist could point at paths that work on both machines.

Note that the NIW file is read even with idemix2_enable_niw = .false., which the error message states explicitly, so it is a hard dependency for any IDEMIX2 run.

With the NIW path pointed at the levante copy and idemix2_enable_bot = .false., IDEMIX2 runs clean, standalone on 2 ranks and alongside REcoM on 4. iwe2_E_iw starts at zero and after one day is populated over roughly 70% of wet cells with a max of 1.2e-2 m2/s2, so the E_iw evolution, vertical diffusion, dissipation and TKE coupling are all doing work.

That is as far as we can take it from here though. The bottom tidal source and the E_M2 and E_niw compartments cannot be exercised at all without the forcing files, so IDEMIX2 cannot be properly tested on levante until they are staged.

[JanStreffing]

@patrickscholz, @koldunovn Can perhaps update /pool/data/AWICM/FESOM2/FORCING/IDEMIX, or create /pool/data/AWICM/FESOM2/FORCING/IDEMIX2

[JanStreffing]

@patrickscholz: Adapted to current state of main branch. Mostly regarding single precision, and some omp ordering. Please take a look.