Growth-pair identifiability — deep-research synthesis (next structural lever)¶
⚠ SUPERSEDED FRAMING (2026-06-27).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 theRATIO_MAX=2fix 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: 2026-06-25 · Status: LITERATURE SYNTHESIS (decision-ready). Feeds the residual wall from 2026-06-24_rpicpoc_ratio_target_fix.md: with R_PICPOC recovered, robust 6/6 is blocked by the growth pair {Smallgrow, Biggrow}, which co-vary and trade against the other params.
Provenance.
deep-researchworkflow (5 angles → 20 primary sources → 96 claims → adversarial verify). Hit the Claude.ai monthly spend cap during the synthesis step, so this writeup is hand-synthesized from the 19 adversarially-verified claims (mostly 3-0). ✅ = verified; statements without a source are my synthesis/inference.
TL;DR — verdict¶
The premise is confirmed by a peer-reviewed review: in plankton models, parameter non-identifiability is structural — data too sparse to constrain all parameters, not a tuning deficiency ✅ (Biogeosciences 14/1647/2017). So loss-tuning being exhausted is expected; only new information breaks it. The literature points to two strong, verified levers, ranked here by (gain for separating the growth pair) × (tractability in our iron-only box):
| rank | lever | evidence | cost in our box |
|---|---|---|---|
| 1 | Macronutrient (NO₃/PO₄) tracer + drawdown loss | canonical: every NPZD/PFT optimization runs with a macronutrient; a param is unconstrained when its process is structurally absent | forward-model change (add 1 tracer + loss) — but data staged (NO₃/PO₄ in v05) |
| 2 | Contrasting biome — add an oligotrophic gyre (small-phyto-dominated) | multi-PFT models separate growth structure only when forced to fit contrasting biomes with one param set | cheap — box already multi-AOI; just add the AOI + cache |
| 3 | Seasonal / time-resolved fit | bloom phase pins growth params; but seasonal biomass reflects the growth−loss balance, not rate alone | needs real seasonal forcing driving biology (currently neutralized) |
| 4 | Hessian/Fisher eigen-analysis to choose the observable | diagnostic, not a fix — we already have identifiability_sloppiness.py |
free |
| 5 | grazing / process-rate observables | claims did not survive verification (mixed) | weak evidence |
The evidence¶
Premise — structural, needs new information ✅ - "data are often too sparse to constrain all model parameters" (review, bg 14/1647/2017). - Different models reach identical model-data misfit via different element-flow pathways → a biomass/chl observable cannot uniquely constrain growth-vs-loss pathways; "need for more comprehensive data sets that uniquely constrain these pathways" ✅ (Friedrichs et al. 2007, 2006JC003852). - Biomass change = division − loss, so biomass alone cannot separate the two ✅ (PMC8422905) — exactly our box-model degeneracy.
(1) Macronutrient drawdown — strongest "root cause" support ✅ - The canonical NPZD optimization (Schartau & Oschlies 2003) runs on a nitrogen-based model (N, P, Z, D) — the field's growth-vs-loss parameter estimation relies on a macronutrient currency. Our iron-only box is the anomaly, missing the N/P constraint. - Kwon & Primeau global inverse: biological production is driven by phosphate drawdown (production restores PO₄ toward observed) — i.e. macronutrient drawdown is the production-rate constraint ✅ (escholarship 1tf9c12w). - A parameter stays unconstrained when its process is structurally absent: rN:P is poorly constrained because the model "does not explicitly simulate the nitrogen cycle"; resolving the N cycle + using N data is the fix ✅ (same) — a model-structure change, not more fitting. - Adding an independent tracer breaks parameter correlations: combining TA+DIC "greatly improves" resolving individual params, most for pairs with opposing-sign sensitivity patterns; single-tracer fits leave |r|>0.8 pairs unidentifiable ✅ (same). This is the general principle — complementary information, not reweighting. - 4D-Var practice (Friedrichs et al.) assimilates chl + nitrate + export + primary productivity jointly, not biomass alone ✅.
(2) Contrasting biome / multi-PFT — strongest "growth-pair-specific" support ✅ - A single pelagic regime is insufficient: the simplest models fit single-region data as well as multi-PFT models — one region can't separate the extra growth structure ✅. - Multi-PFT models give lower misfit only when forced to fit two contrasting biomes (eq. Pacific vs Arabian Sea) with one identical parameter set ✅ (two sources). This is the direct mechanism for separating co-varying PFT growth params. - Caveat (practical identifiability): cross-region portability improves with complexity only when few params are optimized; freeing too many degrades it ✅. And the joint optimum is a compromise vs per-site fits ✅ (Schartau 3-biome). → keep the freed-param count small; expect a worse-per-region but more-identifiable fit.
(3) Seasonal / time-resolved — real but partial ✅ - A growth-related photosynthesis param (α) was identifiable because chl constrained it and it was driven to match the initial/seasonal phase of growth ✅ — bloom onset carries growth-rate info an annual mean averages away. - Net biomass accumulation rate r = division − loss; the time-resolved trajectory (not a snapshot) gives access to r ✅. BUT: bloom onset is governed by decoupling of loss from growth, so seasonal biomass reflects the balance, not growth rate alone ✅. → seasonal helps but is not a clean growth-rate observable by itself.
(4) Sloppy-model diagnostics ✅
- Hessian/Fisher eigen-decomposition flags poorly-constrained parameter combinations
(small-eigenvalue = sloppy directions); "in practice only a few parameters of a planktonic
ecosystem model" are independently estimable ✅ (gmd 10/4881/2017). Use it to pick the
observable that breaks the specific Smallgrow↔Biggrow correlation. We already have the
machinery (scripts/identifiability_sloppiness.py).
Recommendation (highest-EV first move)¶
This partially revises my earlier "macronutrient first" bet. The evidence supports a two-step path, cheap-first:
- First (cheap): add a contrasting oligotrophic-gyre AOI where small phytoplankton dominate (subtropical Pacific/Atlantic gyre, BATS-like). We are already 3-AOI (eqpac HNLC, natl/SO bloom) and stuck — the likely gap is that none of our regions is small-phyto-dominated, so nothing separates Smallgrow from Biggrow. Adding such a biome is low-cost (box already multi-AOI; just an AOI + cache) and is the most direct verified lever for separating PFT growth params. Keep the freed-param set small.
- Then (deeper, canonical): add a macronutrient (PO₄ or NO₃) tracer + drawdown loss. This attacks the growth-vs-loss root the iron-only box structurally lacks; the field universally relies on it; data are staged (NO₃/PO₄ in v05 monthly output). Larger forward-model investment — do it if the gyre AOI doesn't suffice.
Seasonal (#85) remains valuable but is a complement (partial growth-rate signal), and is gated on giving the box real seasonal biology. Use the Fisher eigen-analysis to confirm which lever actually collapses the Smallgrow↔Biggrow eigenvector before committing.
Verified sources¶
bg.copernicus.org/articles/14/1647/2017 (review) · eprints.soton.ac.uk/12709 (Schartau & Oschlies 2003) · sciencedirect S030438000900310X & agupubs 2006JC003852 (Friedrichs et al. 2007) · escholarship 1tf9c12w (Kwon & Primeau, PO₄-drawdown inverse) · gmd 10/4881/2017 (Fisher/eigen identifiability) · agupubs 10.1002/gbc.20050 & pmc PMC8422905 (biomass = div − loss; bloom phase).