The test that isolated nothing

You measured the temperature at a spot in the ocean an hour ago. How much is that measurement worth now? In water that is churning through a sharp front, very little. In quiet water a hundred metres down, a great deal. The quantity governing that decay is the decorrelation timescale, and drogna needs it because it decides where to sample next: fast-changing water gets revisited often and quiet water gets left alone.

The obvious place to put such a number is on the thing that makes the water interesting. drogna's synthetic ocean is built by seeding four features into a background — an eddy, a front, a thermocline and one feature that drifts — so give each of them a timescale. An eddy decorrelates faster than open water; the model matches the intuition; it is trivial to record in the ground-truth manifest.

It does not survive contact with what consumes it.

Two formulations that fail

Per feature. The requirement that quiet water be left alone is a statement about the background, and per-feature authoring gives the background no timescale at all. Every location outside a feature — most of the domain — would need a value invented for it at the point of use. An invented value is not ground truth, so it cannot be scored, and drogna's rule is that every claim about recovering the environment is measured against what the generator recorded rather than asserted.

Per region. A static map over the domain, giving everywhere a timescale including the background. This closes the gap and is defensible physically. It cannot follow the drifting feature: the fast-decorrelating patch would stay where it was authored while the water it describes moved away, so the revisit cadence would be applied to the wrong water — confidently, and with no symptom.

So the timescale is a field: a value at every latitude, longitude, depth and time. Authored per feature over a domain-wide background, because that is how a person writes a scenario. Evaluated per location, because that is what every consumer needs. A moving feature carries its timescale with it.

Rates blend, timescales do not

Two features can overlap, so something has to say what happens where they do, and the rule that suggests itself — average the timescales — is wrong in a direction worth noticing. A location inside two fast features would come out slower than either of them.

The blend is therefore done in rates: one over the timescale, which is how fast memory is lost, and losses compose by adding. Each feature contributes a membership weight from its spatial kernel. Where those weights sum to one or less, the rate is the background's plus, for each feature, its weight times the difference between that feature's rate and the background's. Where they sum above one, the weights are normalised by their sum and the background drops out.

The normalisation is not tidiness. The additive form alone can drive the timescale below the shortest contributing one where two weights are both near one, which the requirement's own scenario forbids. Both branches are convex combinations and they agree exactly where the weights sum to one, so the field is continuous, equals the background where nothing overlaps, equals a feature's own authored timescale at its centre, and where features overlap lies between the shortest contributing timescale and the background. The rule is recorded in the manifest by name and version, so a different rule replaces it without a schema change.

The test that did not do what it said

The claim to be checked is that the minimum of the field sits on the drifting feature and moves with it. Testing it needs a world in which that feature is unambiguously the fastest thing present, so: give the other three the background timescale, and the drifting feature should be the only disturbance left.

It is not. Run that world and the shortest timescale sits 14.8 km from the drifting feature's centre — a long way on a domain a couple of hundred kilometres across.

Membership and timescale are separate quantities. A feature's weight at a location comes from its spatial kernel and its own geometry, and is completely unaffected by what timescale it carries. Where the weights sum above one, the blend normalises by their sum — and the background, the very value the other features were just given, drops out of the arithmetic entirely. A feature holding the background timescale still pulls the blend towards itself and still moves the argument of the minimum. Setting the value without removing the weight neutralised nothing.

The generator was right and the test was wrong, which is worth stating plainly because the reflex when a test fails is the other way round. Isolating a feature means removing its geometry, not changing its number. The eddy and the front are shrunk to a kilometre and moved to the far corner of the domain, which is as close to absent as the generator permits — it refuses a feature placed outside the domain rather than clipping it, on the ground that a clipped feature is one the manifest describes and the field does not contain. The thermocline needs no such treatment: its weight is a function of depth alone, so it dilutes the field uniformly and cannot displace a horizontal minimum.

All of that is written into the test, at length, because it is exactly the kind of thing the next reader will otherwise try again.

The check that matters most does not use the isolated world at all. In the world the generator actually writes, with all four features pulling on the field, the location of the minimum is found at two simulation times three hours apart, and the displacement between them is asserted against the drift velocity times the elapsed time, to within one grid cell. That is the property the whole decision was made for.

A refusal

One more rule earns its place. A timescale shorter than a configured multiple of the time step — twice, today — is refused when the scenario is authored, before anything is written, with the offending ratio in the message so the author can see how far under it fell. A field cannot represent decay faster than its own sampling interval, and a timescale it cannot represent does not announce itself: it quietly produces a revisit cadence that is wrong.

The values in use: three days for the background, thirty-six hours for the thermocline, eighteen for the front, twelve for the eddy, six for the drifter. All of them are recorded as ground truth, which means that recovering them later is a measurement rather than a claim.