R_PICPOC (PIC:POC rain ratio) vs real-ocean observations — does ECCO-Darwin's 0.042 match?¶
Date: 2026-06-26 · Spine: D (#143) / C (#116) · Status: deep-research (11 agents,
every value source-verified). Triggered by the real-data audit (real MODIS PIC only weakly
constrains R_PICPOC) + the question "is ECCO-Darwin's calcite param actually grounded in real
data, or did we miss a discrepancy?". ECCO-Darwin value: R_PICPOC = 0.04245 (carroll6.py:75).
1. Is the rain ratio observationally constrained? YES, loosely (factor ~2)¶
Direct/inverse methods measure the production-or-export RATIO (alkalinity/nitrate drawdown), which surface MODIS PIC (a standing stock) cannot. Best real-ocean global-mean export rain ratio:
| source | method | value |
|---|---|---|
| Sarmiento 2002 (GBC 10.1029/2002GB001919) | alkalinity/nitrate inverse, 100 m | 0.06 ± 0.03 (everywhere <0.10) |
| Daniels 2018 (ESSD 10.5194/essd-10-1859-2018) | ¹⁴C CP:PP incubation, n=2751 | 0.02 geomean (production; log-normal 0.001–1) |
| Battaglia 2016 (BG 10.5194/bg-13-2823-2016) | TA*-constrained Bern3D | export → ~0.07 |
| Planchat 2023 (BG 10.5194/bg-20-1195-2023) | obs-derived | 0.14 upper; CMIP5 0.070 / CMIP6 0.083 |
| Jin 2006 (GBC 10.1029/2005GB002532) | nutrient+alk inverse | 0.09 (0.07–0.10) |
Honest band: ≈0.06 (0.03–0.09), factor-of-2 uncertainty. The legacy 0.20–0.25 (Li 1969) is a remineralization-ratio misinterpretation, not part of the modern envelope.
2. Does ECCO-Darwin's 0.042 match? Yes — consistent with real calcite; the open issue is that the constant is GLOBAL, not regional¶
- 0.042 sits inside the real-ocean uncertainty envelope (global-mean estimates span ~0.02–0.14
across methods; Daniels 2018 ¹⁴C production geomean ~0.02–0.039, Sarmiento 2002 export ~0.06±0.03).
The converged surface-calcite diagnostic (real MODIS-Aqua) is consistent with Carroll's 0.042
(optimum ~0.028; 0.042 in the acceptable low-ratio basin). The earlier "~25–30% below center / ~0.6σ
low" read was under-converged and compared only against the inverse/export estimates, which
measure a different quantity from the surface production ratio the box computes
(
dPIC = R_PICPOC·mort_total) — so do not headline a magnitude disagreement. - Carroll never tuned R_PICPOC to rain-ratio data. Carroll 2020 (10.1029/2019MS001888) optimized 6 BGC params by Green's functions against pCO2 / CO2-flux / alkalinity / nitrate / oxygen — NO rain-ratio dataset. So 0.042 is tuned for CO2/DIC closure; grading our recovery against Darwin's own PIC is circular. It is NOT disconnected from data (lands in the post-2002 consensus), but it is under-constrained and low.
3. Two discrepancies the surface-MODIS test was blind to¶
(a) Export-inversion magnitude spread (a different quantity). Surface PIC is a standing stock; it can only reject HIGH values (our flat MODIS profile over [0.005,0.05]). The direct export inversions center at 0.06–0.09 — higher than 0.042 — but they measure the EXPORT ratio, not the surface PRODUCTION ratio the box computes. Against the in-kind data (surface MODIS calcite; Daniels production ratio) Carroll's 0.042 is consistent (§2), so this is a quantity mismatch, not a model error.
(b) THE LOAD-BEARING FINDING — R_PICPOC should be REGIONAL, not a global constant. Sarmiento 2002 Table 3: rain ratio peaks EQUATORIALLY (Indian 0.099 / Pacific 0.087 / Atlantic 0.084), minimum in Southern Ocean/gyres (0.003–0.02) — >20–30× regional range, and the equatorial-max is OPPOSITE the high-latitude coccolithophore-bloom pattern. eqpac is DarwinDiff's constraining AOI, and the rain ratio is regionally variable. The export/alkalinity inversions (Sarmiento ~0.087 eqpac; Wanninkhof 0.13–0.22) imply an equatorial enhancement, but those are EXPORT-ratio inversions, not the surface PRODUCTION ratio the box computes. The Darwin-INDEPENDENT production-ratio anchor (Daniels 2018 CP:PP, PR #146) puts eqpac surface geomean at ~0.039 — about 1.6× the global ~0.025, which supports "the global constant is mis-specified / should be regional" but does not reproduce the 2–5× equatorial excess the export inversions imply (production-ratio ≠ export-ratio). So a global scalar cannot be uniquely identified against a regional AOI. This structural global-vs-regional mismatch — not a magnitude disagreement — is the real scientific result for spine D.
Non-discrepancy (don't over-read): deep sediment-trap PIC:POC of 0.5–1.7 (Wynn-Edwards 2020) is 12–40× higher but is the depth/ballast gradient (POC remineralizes, CaCO3 survives) — apples/oranges vs a surface-production ratio.
4. CO2 significance¶
The rain ratio drives dALK = -2·R_PICPOC·mort_total → air-sea CO2 (carbonate counter-pump).
Calcification leverage spans 9–285 PgC ocean uptake / 4–70 ppm atmospheric (Gangstø/Heinze
lineage) — feedback ranges, order-of-magnitude direction only, but a factor-2 rain-ratio error is
NOT carbon-neutral. Getting it right (and region-resolving it) matters for the simulated sink.
5. The test to run¶
Wire Daniels 2018 CP:PP incubations (PANGAEA 888182) as the primary, Darwin-INDEPENDENT,
per-AOI R_PICPOC anchor — the only direct surface production-ratio dataset matching the box's
dPIC = R_PICPOC·mort_total in kind; n=2751 georeferenced points → eqpac-vs-global targets,
breaking the circularity and directly testing the regional-variability hypothesis. Knowable to
~factor-2 only (log-normal); Daniels reports no clean latitudinal trend in raw incubations, so the
regional signal may be noisier than Sarmiento's inverse pattern.
Bottom line¶
ECCO-Darwin's R_PICPOC is under-constrained, but its value is consistent with real surface calcite (real MODIS-Aqua optimum ~0.028; Carroll's 0.042 in the acceptable low-ratio basin). The real result is structural, not a magnitude error — a single GLOBAL constant is mis-specified when the rain ratio is regionally variable: the Darwin-independent Daniels 2018 production-ratio anchor puts eqpac surface at ~1.6× the global mean (export inversions imply more, but production-ratio ≠ export-ratio). This is a finding ABOUT ECCO-Darwin (the field's best model still carries an under-constrained, globally-constant rain ratio), surfaced by the differentiable tool — not a failure of our recovery. Recovery = ours (works); real-world validity = ECCO-Darwin's (here it's weak + regional).