Let a road segment be sampled at horizontal positions s1<s2<⋯<sn with elevation observations zi=h(si)+εi, where h is the true road surface profile and εi are independent, zero-mean errors with known standard deviation σz, the vertical accuracy of the elevation model. Let Δs denote horizontal distance and define the estimated grade over an interval [a,b] of the segment by g^=(z(b)−z(a))/Δs.
A detector declares a descent (a rideable downhill run) on an interval when the estimated grade clears a rideability threshold g0>0. Two families of detection floors are compared. An uncertainty-scaled floor declares a descent when g^≥g0+k⋅se(g^), where k>0 is a fixed multiplier and se(g^) is the standard error of the estimated grade under the error model. A length gate instead requires, in addition to g^≥g0, that the run length satisfy Δs≥Lmin for a fixed minimum Lmin>0.
Conjecture: for every length gate Lmin, there exists a multiplier k such that the uncertainty-scaled floor attains a false-discovery rate and recall at least as good on road networks whose elevation comes from a raster DEM with known vertical accuracy, so the length gate contributes nothing that an uncertainty-scaled floor cannot provide.