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Dense Darwin POSi target for diatomgraz (box scale)

⚠ SUPERSEDED FRAMING (2026-06-27). This is a point-in-time record; its data and negative results stand, but its framing is corrected by STATUS.md and docs/research_notes/2026-06-27_box_homogenization_DEFINITIVE.md. Specifically: R_PICPOC is NOT a "6/6 wall" and is NOT cluster-gated — it recovers at 1° box scale given a real calcite anchor (Daniels CP:PP / MODIS PIC) plus the RATIO_MAX=2 fix for the contaminated Southern-Ocean ratio target; the differentiable Darwin calcite port and native resolution were tested and did not help. The project is reframed as a surrogate-to-model identifiability study over 4 OBSERVABLE params {alpfe, scav_rat, diatomgraz, R_PICPOC}; the growth pair {Smallgrow, Biggrow} is unobservable by construction (excluded, not failed). The surrogate gap is dimensional (the 0-D box homogenizes spatial structure, tracer CV→1e-15), so box-vs-Darwin spatial-pattern correlations are not fidelity metrics — identifiability comes from real absolute anchors.

Date: 2026-06-11 · Status: result established. Dense POSi recovers diatomgraz (n=10 dose sweep); Eppley temperature limitation breaks the alpfe↔silica mutex and recovers the iron pair + diatomgraz together — best 3-AOI recovery in the project, reproducible at n=20.

Hypothesis

The 2026-06-11 utilization audit named dense gridded POSi (Darwin's own biogenic-silica field, TRAC16) as the cheapest laptop-feasible lever for the stuck diatomgraz parameter. Until now the only silica constraint was POSI_W, which compares the box's steady-state bsi_1 diagnostic to sparse GEOTRACES bottle bSi (typically <10 surface bins per AOI). The hypothesis: a dense, model-consistent, diatom-specific target — Darwin's own surface POSi binned to the AOI 1° grid — identifies diatomgraz where the sparse proxy and every other lever in the 856-seed sweep produced 0%.

Method

  • Tracer: POSi = TRAC16 (surface biogenic silica, mmol Si/m³, 289 monthly native LLC270 snapshots on disk). Registered in TRAC_MAPPING (src/darwindiff/llc270_loader.py), bin-averaged to 1° via the surface-level bin_native_tracer_to_1deg (aligns with the box's surface bsi_1).
  • Loss: new additive POSI_DARWIN_W lever in scripts/run_v3.0_joint_multi_aoi.py — an absolute-units MSE between the box's silica.diagnostic_bsi_steady bsi_1 and the dense Darwin POSi target, sharing the bsi_1_pred computation with the existing GEOTRACES POSI_W path (left untouched). Target cache augmented in place (bins only POSi, no re-bin of the other 5 tracers); no IC-cache or tracer-vector change.
  • Config: 3-AOI F2 Basin C — AOIS=eqpac,natlsubpolar,southernoceanpac, POSI_W=1.0, AOI_W_NATLSUBPOLAR=2.0, AOI_W_SOUTHERNOCEANPAC=2.0, CHL1_W_EXTRA=3.0, 1500 epochs. This is the canonical stuck config where diatomgraz recovery is 0% across the v3.1 856-seed sweep.
  • Design: paired seeds 0–9 (n=10) per arm; dose sweep POSI_DARWIN_W ∈ {0, 0.5, 1.0, 2.0, 5.0}. Scored vs Carroll 2022 published values (Cal-grade ≤40%, Excellent ≤10%).

Result — dose response (n=10 paired)

POSI_DARWIN_W diatomgraz alpfe Biggrow Smallgrow mean Cal-grade/6 seeds ≥4/6
0.0 (baseline) 0/10 10/10 1/10 9/10 2.00 0/10
0.5 10/10 (1 Excellent) 2/10 9/10 8/10 3.00 3/10
1.0 9/10 (2E) 2/10 5/10 7/10 2.50 2/10
2.0 8/10 (4E) 2/10 5/10 6/10 2.10 1/10
5.0 10/10 (0E) 2/10 4/10 4/10 2.10 0/10

scav_rat 0/10 and R_PICPOC 0/10 at every dose (unchanged).

Interpretation

  1. Dense POSi recovers diatomgraz — 0/10 → up to 10/10, mean |offset| 0.78 → 0.14. The audit's #1 lever is confirmed: the sparse GEOTRACES proxy never achieved this in the stuck config.
  2. A gentle dose is a genuine net gain, not a reshuffle. POSI_DARWIN_W=0.5 lifts mean recovered from 2.00 → 3.00/6 and yields 3/10 seeds at ≥4/6 (baseline 0/10) — the best 3-AOI recovery the project has produced. It recovers diatomgraz and rescues Biggrow (1→9/10).
  3. The alpfe cost is binary and dose-independent. alpfe collapses 10/10 → 2/10 at the first nonzero dose and never recovers across all doses. A new mutex analogous to the binary PIC-anchor mutex: dense-silica and iron-uptake both bind diatom biomass (iron → diatom growth → bSi), so they are mutually exclusive.
  4. The 6/6 ceiling holds. 0/10 at ≥5/6 and 0/10 at 6/6 across all doses; best single seed = 4/6. Strong doses over-constrain bSi and decay the gain (Biggrow 9→4, Smallgrow 8→4 as W rises).

Thesis refinement. "Parameter conservation" is not strict count-conservation: the effective recovered count is configuration-dependent and rises (2.0→3.0) with a better forward-model constraint that injects genuine identifying information. The hard 6/6 cap still stands, and certain parameter pairs (alpfe vs dense-silica/diatom) are mutually exclusive. This is a sixth independent line of evidence for the ceiling — and the first via a forward-model fidelity intervention rather than a loss-weight or architecture lever.

Result — forward-model fidelity levers (on POSI_DARWIN_W=0.5)

Re-reading Carroll 2020/2022 confirmed the box was missing temperature limitation of growth (Darwin uses an Eppley-style f(T); our box had growth = μ·f_Fe·1.0, LIGHT=1.0, no f(T)). Added behind two default-OFF flags: USE_EPPLEY_T (Eppley 2^((T−T_ref)/10) growth scaling in carroll6_5pft_2layer.py) and W_SINK_PIC (separate calcite sinking rate, decoupling PIC export from POC). Validated at the new best operating point.

arm (on W=0.5) alpfe scav_rat Smallgrow Biggrow diatomgraz R_PICPOC mean/6 ≥4/6 5/6
W=0.5 control (n=10) 2/10 1/10 8/10 9/10 10/10 0/10 3.00 3/10 0/10
+Eppley (n=20) 18/20 20/20 15/20 4/20 20/20 0/20 3.85 14/20 (70%) 4/20 (20%)
+wPIC only (n=10) 1/10 0/10 8/10 7/10 9/10 0/10 2.50 1/10 0/10
+Eppley+wPIC (n=10) 9/10 9/10 7/10 2/10 10/10 0/10 3.70 6/10 2/10

Recovery is real, not a scoring artifact: Eppley arm mean |offset| scav_rat 0.158 (recovered 4.7e-7 vs Carroll 6.0e-7), alpfe 0.295, diatomgraz 0.156.

Reproducible at n=20. Split-half: seeds 0–9 → mean 3.90, 7/10 ≥4/6, 2/10 at 5/6; seeds 10–19 → mean 3.80, 7/10 ≥4/6, 2/10 at 5/6. Near-identical halves — unlike the v3.1 5/6 events (1/20 flukes that vanished on retest), this 5/6 rate is stable at ~20%. (+Eppley+wPIC is n=10 only — its seeds 10–19 run was interrupted by laptop sleep at ~epoch 750; not rerun, since wPIC is inert here.)

Interpretation (updated)

  1. Eppley breaks the alpfe↔silica mutex. The dose-sweep mutex (#3) was an artifact of the missing temperature physics: without f(T), the only handle on diatom biomass is iron uptake, so pinning bSi forces alpfe. Giving diatom growth an independent SST handle lets silica be matched without commandeering the iron budget — so alpfe (2→18/20) and scav_rat (1→20/20) and diatomgraz (20/20) recover simultaneously. The v3.1.1 AOI ablation had shown the iron pair and diatomgraz were mutually exclusive across regions; the missing forward-model term, not a hard budget, was the cause.
  2. Best multi-AOI recovery in the project. mean 2.00 (baseline) → 3.85/6, 70% of seeds ≥4/6, and the first reproducible 5/6 events at 3-AOI (the v3.1 5/6 were single-seed flukes). scav_rat, previously needing the Southern Ocean and lost whenever diatomgraz recovered, now lands in 20/20.

  3. R_PICPOC is the entire 6/6 wall, and it is cluster-gated. 0/20 under Eppley, the sole miss in all four 5/6 seeds. Two box-scale attempts to crack it both fail by the same mutex:

    • Separate calcite sinking (W_SINK_PIC=0.30) alone did not move it (0/10) and slightly degraded the iron pair.
    • A PIC magnitude anchor on the Eppley config (PIC_ABS_W ∈ {0.02, 0.1}, n=10 each) does recover it (0→8/10) — so R_PICPOC is identifiable in principle — but wipes the entire iron pair (18→0/10, 20→0/10) and diatomgraz (20→1/10), even with Eppley's stabilization. Net mean drops 3.85→2.5. You get {iron pair + diatomgraz} or {R_PICPOC}, never both.

    This is the binary PIC-anchor mutex (STATUS: "any nonzero PIC_ABS_W wipes the iron pair") — and it is now shown robust even to the forward-model temperature physics that broke the other mutex. R_PICPOC under pattern-only z-loss is genuinely degenerate with the iron budget at the box scale; breaking it needs the information the box does not have (seasonal cycle, native resolution), not another laptop lever. This is the AICR case, backed by an exhaustive box-scale exclusion.

Thesis (revised). "Parameter conservation" is not a fixed effective count: forward-model fidelity injects genuine identifying information and raises the recovered count (2.0 → 3.85/6) while making 5/6 reproducible rather than a fluke. The hard cap is now sharply localized — R_PICPOC is the one parameter no laptop-scale lever (loss weight, architecture, IC, or forward-model physics) has recovered. Whether it is fundamentally unidentifiable from time-mean pattern data or needs the seasonal/native-resolution axis is the cluster-gated question (and the AICR case in the Schultz/Jon deck).

Pending follow-up

  • +Eppley+wPIC at n=20 — optional tidy-up only (seeds 10–19 interrupted by laptop sleep; n=10 already shows it tracks Eppley-alone, wPIC inert). Set powercfg /change standby-timeout-ac 0 before any rerun.
  • R_PICPOC is now characterized as cluster-gated, not a pending laptop lever: the box-scale exclusion is exhaustive (loss weight, AOI mix, architecture, IC, Eppley physics, and PIC magnitude anchor all fail by the same iron-pair mutex). The open question — fundamentally unidentifiable vs. resolvable by the seasonal/native-resolution axis — requires the cluster (AICR). This is the strongest motivation for native-resolution + seasonal fitting in the Schultz/Jon deck.

Reproduce (R_PICPOC mutex test)

# on the Eppley best config, add a PIC magnitude anchor:
DARWIN_DATA_ROOT=D:/ecco_darwin_v5 GEOTRACES_DATA_ROOT=D:/geotraces \
AOIS=eqpac,natlsubpolar,southernoceanpac POSI_W=1.0 \
AOI_W_NATLSUBPOLAR=2.0 AOI_W_SOUTHERNOCEANPAC=2.0 CHL1_W_EXTRA=3.0 \
POSI_DARWIN_W=0.5 USE_EPPLEY_T=1 PIC_ABS_W=0.02 \
NB23_SEEDS=0,1,2,3,4,5,6,7,8,9 OUTPUT_DIR=<out> \
python scripts/run_v3.0_joint_multi_aoi.py

Reproduce

DARWIN_DATA_ROOT=D:/ecco_darwin_v5 GEOTRACES_DATA_ROOT=D:/geotraces \
AOIS=eqpac,natlsubpolar,southernoceanpac POSI_W=1.0 \
AOI_W_NATLSUBPOLAR=2.0 AOI_W_SOUTHERNOCEANPAC=2.0 CHL1_W_EXTRA=3.0 \
POSI_DARWIN_W=0.5 NB23_SEEDS=0,1,2,3,4,5,6,7,8,9 \
OUTPUT_DIR=<out> python scripts/run_v3.0_joint_multi_aoi.py