A globally-trained, IMERG-native CREST parameter set
v3: 0.508 ungauged — and physics as weak supervision

• 1,178,590 land cells (0.1°, |lat| ≤ 60°) × 15 CREST parameters, inferred from 22 globally-available covariates (climate, SoilGrids, WorldCover, MERIT);
• Dual head: CNN (two 3×3 convs — ~0.5° context) for trained continents; MLP for continental extrapolation (CNN fails catastrophically off-continent: LRO-SA −0.49);
• Dual field: yardstick-optimal (no constraint) + extrapolation-hardened (Budyko weak supervision, BUDW=100) for data-sparse continents;
• Tiered response: per-basin Gamma UH < 50,000 km²; differentiable Muskingum–Cunge river routing above (213 big-basin stations, ungauged 0.324);
• QC: 13/15 parameters <1% bound-railing; disclosed exceptions (im at zero prior outside cities; b at ×3 cap on 11% of tropical cells).

Gates: area 50–50k km² · ≥8 yr valid obs in 2003–23 · <0.1% negatives · no 60-day flatline · mask/reported area ∈ [0.5, 2]. De-dup: 2 km + 15% area, ~1,600 duplicates removed across sources (prevents double-counting and train/test leakage).

The Asia hole — ours and everyone's

Public global sets have no continental-monsoon interior: δHBV2-Globe's "Asia" is essentially Japan + South Korea (and it excludes Africa entirely via a ≥95%-completeness/41-yr gate). We keep Africa (212) and South America with an 8-yr gate instead — the other end of the coverage-vs-completeness trade-off — and harden information-poor regions with physics (slide 9). CAMELS-IND ingestion is queued: a monsoon observation set neither product has.

Split design

15% stratified holdout (region × aridity) — GRDC holdout (410 gated) is the fixed yardstick across all experiments; expansion holdout (749) reports skill on never-before-used networks. Observations of holdout stations never touch the loss; the 2003–11 window is never trained on.

Mode A: the fair ceiling

Every basin (including the 410 "holdout") gets its own freely-calibrated parameter set — same 0.1° grid, same physics, same robust loss, same optimizer, calibrated by backprop on the train window, scored on the test window. The only difference from the product is where parameters come from: per-station freedom vs a shared covariate network.

Why the gap is real information

• Train fit 0.590 ≈ ceiling 0.579 → shared network expressiveness is not the bottleneck; the cost is purely "this station was never seen";
• the same 0.07-class gap appears under MSWEP (0.650 ceiling vs 0.546 twin) — forcing-independent, so it is an information limit of regionalization, not precipitation quality;
• part of it is irreducible station-specificity (reservoir operations, karst, abstractions) that no ungauged-legal information can recover;
• remaining attack surfaces: satellite-ET multivariate calibration (B-track), CAMELS-IND, physics weak supervision (done, slide 9).

At v3 config the premium persists: MSWEP twin 0.546 vs IMERG 0.508 (+0.049, p=7.6e-9) — additive to all architecture/data gains.

The argument

Gauge assimilation is worth +0.03…+0.05 — where gauges exist. In the target deployment of a global product (ungauged, data-sparse regions) that information does not exist, and in Africa the gauge-informed product is actually worse than satellite-native. IMERG-native is therefore not a handicap we accept but the correct forcing for the question "what is achievable where only satellites exist?" — and the MSWEP twin quantifies exactly what is being given up elsewhere.

Context: δHBV2-Globe

Ji et al. 2025 (Nat. Commun.): ungauged NSE ≈0.53 with gauge-fused forcing on ≥95%-complete stations, Africa excluded, "Asia" ≈ Japan+Korea. Different question, different data philosophy; our satellite-only v3 with Africa retained: KGE 0.508 / monthly 0.603.

Why it is credible

• Ablation-clean: parameter-prior regularization = zero; novelty-gated weighting = negative (both retired) — the gain is 100% the weak-supervision term;
• monotone dose–response, replicated on two continents;
• mechanism matches diagnosis: continental extrapolation fails through β (water balance) — exactly what Budyko pins; it cannot teach timing;
• honest scope: zero-to-negative on the regime-redundant yardstick (−0.01…−0.02 price) — gains live exactly where covariate twins don't exist;
• lineage: PUB-era signature constraints (Yadav 2007, Zhang 2008), first made a gradient signal in a global differentiable framework.

Ordering follows regime redundancy — whether the training set contains climatic "twins" — not geographic distance. Budyko weak supervision claws back a third to half of the SA/AF loss (slide 9).

Architecture rule it produced

• CNN head: +0.04 in-distribution, but −0.49 when South America is left out — spatial texture is a fingerprint that does not transfer;
• MLP head: worse in-distribution, far safer off-continent;
• → dual-head product: CNN where a continent has training stations, MLP (+ Budyko hardening) where it does not — e.g. Asia.

Implication for Asia

Asia's risk profile resembles SA (regime novelty: monsoon interior) more than EU. Priority: CAMELS-IND regime anchor; until then Asia ships MLP + Budyko-hardened parameters, explicitly labeled.

Africa +0.12→+0.44 is the largest jump. Dry basins remain the hardest regime, as in every global model. β 0.98: the v1 IMERG under-catch signature (β 0.85) is fully absorbed by the robust loss + learned precip multiplier.

Blind predictions at ungauged stations, 2006–08: KGE 0.81–0.89 from Sweden/Canada snow to Brazilian tropics, 900–33,000 km².

CREST ≈ HBV — a structural tie

Tie replicated across both objectives (KGE/NSE) and both forcings (IMERG/MSWEP). The v1-era "HBV wins" verdict was an artifact of the fragile loss. With learned parameters at daily/0.1°, conceptual structure differences wash out — forcing and regionalization carry the skill. CREST keeps the product line (distributed field, EF5 deployability, sub-daily path).

Routing: UH below 50k km², Muskingum–Cunge above

• Differentiable MC on the 05′ MERIT network (1.89 M reaches, exact mass conservation, gradient-checked 6.7e-8);
• impulse physics: routing matters from ~1,000 km channel length;
• mid-tier test (<50k km²): MC loses to UH (−0.041) — UH is the right operator there;
• big tier (≥50k km², 213 stations — new coverage, excluded from every number above): MC reaches ungauged 0.324 where UH is structurally invalid.

• Asia untrained (no public monsoon-interior stations — true of all global products); ships as labeled extrapolation, Budyko-hardened;
• dry regime 0.407 — weakest mode, as everywhere;
• daily < monthly (0.508 vs 0.603): the residual error is sub-monthly timing of recessions/low flows, not volume;
• equifinality: weakly-identifiable parameters differ between independent nets; prior-regularization priced at zero — disclosed, not fixed;
• Budyko fixes β only; −0.01…−0.02 in-distribution price → two fields;
• b-multiplier rails at ×3 on 11% of cells (tropics) — box widening queued for v4.

Verified-negative results (the frontier)

• runoff gradients cannot identify snow parameters (→ needs MODIS SCA);
• ensembling ≈ 0 under the robust loss (solution is seed-unique);
• NSE loss −0.096 with α→r collapse — Gupta 2009, empirically confirmed;
• attention / UNet / capacity-alone / lake covariate: zero (multi-seed);
• novelty-adaptive constraint weighting: negative both ways.