The r ≈ 0.34 timing ceiling

Every stage lands Pearson r near 0.34 against the gauge. This is not a shortcoming of the correction - it is the predicted behaviour of any marginal correction. The pipeline's quantile mapping is strictly monotonic, so if the satellite reports more rain on day i than day j before correction, it still does after. The day-by-day pairing is fixed by the satellite; no marginal step can move rain from one day to its neighbour. You can reshape the distribution all you like - the timing does not move.

Key finding Across all three correction stages, pooled daily Pearson r moves just 0.005 - from 0.343 (LS) to 0.345 (LSEQM) to 0.348 (LSEQM+DL). The correction reshapes the distribution; it does not touch the timing.

See it on a synthetic pixel

A synthetic satellite-and-gauge day series (illustrative, as in the thesis bound schematic). Drag the quantile-mapping strength: the corrected series slides onto the gauge distribution - the distribution mismatch (KS) collapses - but its correlation with the gauge barely twitches.

Correlation with gauge

raw → corrected · essentially unchanged

Distribution mismatch (KS)

Slide λ from 0 to 1: KS falls toward 0 (the corrected distribution meets the gauge) while r holds near the whole way. Correcting the margin cannot buy timing that the satellite never measured.

The same thing on the real numbers

Pooled daily r against the 172 BMKG stations, by stage - flat by construction. The dashed line is what the same data reaches once re-aggregated to the local-day window: the real headroom is not in the correction stages, it is in the calendar-window convention.

The monthly Taylor

The bound is not a one-off pooled number. Every product's Taylor position - all six, in all twelve months - sits at the same low correlation. The correction slides the cloud along the standard-deviation axis (LS under-spread → LSEQM/LSEQM+DL on the reference circle) but never toward the correlation axis. Each grey dot is one BMKG station (all six products pooled); the coloured dots are the per-product medians. The cloud concentrates in the low-correlation wedge - a median near r ≈ 0.23, most stations below 0.5 - so the ceiling is a property of the whole network, not an artefact of pooling. A thin tail of stations reaches higher, but no product median does. Pick a month:

Headline proposition A marginal (per-cell) correction is a monotonic remap of each day's value; it cannot move rain from one day to its neighbour. So Pearson r is bounded by the raw retrieval - and on the Taylor diagram every product, every month, clusters near r ≈ 0.22. What the correction fixes is the radius: the standard-deviation ratio goes from LS 0.72 to LSEQM+DL ≈ 1.0. The cloud moves out to the reference circle, never around toward the perfect corner.

The ceiling is real but conventional, not fundamental. For a fixed UTC-day pairing the stages cannot beat ~; re-labelling to the local day lifts the same product to (see 5.2). Beyond that, closing the gap needs methods outside the marginal-correction family - the four paths.