The forecast was not listening, and nothing in the code said so
The background
The project samples a simulated Atlantic from a boat, forecasts the water, and re-forecasts when the two drift apart. Somebody asked how much of the forecast came from the instruments, and reading the loop end to end showed they contributed nothing. They decided when to forecast and where the boat went; a run initialised from a copy of the simulated truth. So the forecast was always right enough and its errors shrank, exactly like learning.
The requirement
A step that moves the field toward what the instruments reported, weighting each side by how far it is worth trusting, and a field that can say cell by cell where its value came from.
The options considered
Nudging nearby cells toward each measurement is a dozen lines. Optimal interpolation won on an algebraic accident: the observation operator picks out one grid cell, so the analysed value is a weighted sum of forecast and measurements. The provenance bar is not a diagram of the calculation; it is the calculation.
Two wrong turnings. A bell curve never quite reaches zero, and never quite compounds: after four cycles the bookkeeping credited the instruments with 45% of every cell. Chopping the tail off is worse — the covariance stops being positive definite and the inversion returns nonsense — so the influence is Gaspari–Cohn, watched failing against the chopped one. And the planner's five hand-tuned numbers for a measurement's reach — a visit collapsing uncertainty by 85% where the arithmetic says 99.7% — are gone; it asks the analysis.
The demo
Choose where the value came from in the doubt control: a corridor along the track where the instruments own the value, elsewhere what was known before.