Assessing the Pisano Equations for Dry-Weather Solids Deposition in Sewer Systems: Comparative Behavior and Sensitivity Analysis

Four historical Pisano power-law equations for daily dry-weather solids deposition are audited using transparent numerical and analytical diagnostics. EQ1 is an endogenous surrogate: its slope descriptors depend on prior modeled deposition, whereas EQ4 can be evaluated from standalone network-scale inputs. An independent-uniform exploration of historical input ranges, rather than real-world occurrence probabilities, uses a common Latin hypercube sample of 200,000 combinations and gives median deposited-solids masses of 34.9, 168.0, 164.5, and 159.2 kg day−1 for EQ1–EQ4. The paired EQ1/EQ4 median log-ratio is −0.622, so EQ1 is the lower formulation. However, 19.7% of these unconstrained baseline combinations violate slope-descriptor ordering. Additional designs enforce ordering, a field-informed length-to-area envelope, and, separately, linked exponential slope quantiles. EQ1 remains distinct in these constrained tests, but its EQ4 log-ratio changes to −0.688, −0.711, and −0.422, respectively. High global rank correlations do not imply tail interchangeability: baseline EQ1/EQ4 and EQ2/EQ4 top-decile overlaps are 21.6% and 76.2%. Elasticities are invariant model properties, whereas variance shares depend on bounds and dependence: narrowing the length interval makes the EQ1 slope descriptor outweigh length. Under log-uniform marginals, output medians nearly coincide; retaining the four original flow levels also changes the induced distributions. All reported distributions and sensitivity rankings are conditional on these explicitly assumed designs. These findings support a conditional mathematical comparison of a model-dependent surrogate with standalone screening equations; they do not establish physical dominance, predictive equivalence, or design suitability.