docs(tau): final five-arm tau=9 retrain table + slice rationale (follow-up to #33)

[taddyb]

Follow-up to #33, which merged while two retrain arms were still evaluating. This PR carries the completed five-arm results table into the findings doc and skill reference, plus the doc comment on tau_trim_and_downsample explaining why the slice excludes one day (constant sample across tau values; details in the comment).

Final tau=9 retrain results (all five arms)

Full test window 1995-10..2010-09, 1,841 gauges, 30 epochs each, CPU:

arm	median NSE	median KGE
summed-q' baseline (no routing)	0.642	—
old tau (epoch-30 reference)	0.620	0.699
tau=9, aorc2f distributed	0.706	0.730
tau=9, UH retrospective	0.707	0.738
tau=9, daily LSTM	0.578	0.616
tau=9, hourly LSTM (native)	0.564	0.500
tau=9, aorc2f lumped (negative control)	0.483	0.504

The timing correction is worth +0.086 median NSE on the flagship arm and the routing now beats the summed-q' baseline by +0.064. The negative control held: the lumped store's measured optimum is about −8 on the new scale, tau=9 was predicted to hurt it, and it did (0.510 → 0.483).

Why tau = 9: UTC vs local time and inverse routing, following Bindas et al. (2024)

Bindas et al. (2024, the dMC Juniata study) handled model/observation timing with two separate corrections, and the new tau: 9 default maps onto that treatment as follows.

1. The UTC vs local-time term. In the 2024 study the forcing was UTC and the USGS hourly observations were UTC−5, corrected by a 5-hour shift of the runoff before anything else. In ddrs the same concern exists in principle (AORC/q' stores on UTC day boundaries, USGS daily values on local standard time), and the sweep campaign tested for it directly: a routing-free control (summing upstream q' with no Muskingum-Cunge and sweeping the same pooling windows) measures the net convention offset at 0 to 2 hours (docs/2026-08-06-tau-sweep-pilot-findings.md §5g). At daily resolution the store and observation day conventions net out to near-UTC-day alignment, largely because the q' generator was itself trained day-aligned against these observations, so its unit hydrograph absorbed any label offset. The 2024 paper's 5-hour term therefore contributes nothing here and no separate timezone shift is applied.

2. The inverse-routing term. The 2024 study then shifted the runoff back in time by tau = 9 hours because the LSTM, trained at basin outlets with catchment area as an input, already implicitly contained the time of concentration, and the explicit routing module simulates that concentration again. tau: 9 in ddrs is the same operation with the same sign and, empirically, the same magnitude: the q' stores were exported with each divide's runoff already routed through dHBV's learned gamma unit hydrograph (median kernel mean 1.5 days per divide, growing with upstream area), so the MC network routes water whose travel time is partly pre-applied. The measured over-delay is 6 to 9 hours at the median gauge (routed optimum at tau=20 on the legacy scale, i.e. +9 hours past day-aligned), and the signed-at-zero convention makes the correction literal: advance the routed output by 9 hours before daily scoring, exactly the paper's "shift the runoff back in time by tau hours" as a translation-only stand-in for full inverse routing (Pan & Wood, 2013).

In short: of the two timing terms in Bindas et al. (2024), the timezone term measures out to ~zero for CONUS daily scoring, and tau = 9 carries the inverse-routing term, whose root cause here is the double-carried gamma-UH travel time in the q' export (findings §5g/§5h). tau remains a compensation; the store-side fix (sub-grid-only UH) is the documented follow-up.

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