Observation-aware reconstruction of total phosphorus release from sewer sediments: scale laws and finite-source...

In finite-volume repeated-measures experiments, each withdrawal is both an observation and a mass-removal event, so observation itself changes the state from which the next interval evolves. Using a 168 h closed-loop combined-sewer sediment record as a parameter-identification window, we applied a three-stage inference framework: exact mass-balance reconstruction of observation-induced state jumps; leave-one-condition-out (LOGO) validation of a reference-centred Buckingham-Pi scale law; and identification of the minimum finite-source structure supported by bulk total phosphorus (TP). Samples were 100 mL through 24 h and 500 mL thereafter, with equal-volume ultrapure-water replacement. At a nominal 7.0 L, preceding withdrawals would remove 59.4% of an initially conservative water-column inventory before 168 h. Reconstruction reduced declining TP intervals from 42 to 25 of 136 and eliminated corrected declines in chemical oxygen demand, total nitrogen, ammonium nitrogen and total organic carbon. The scale law separated relative Reynolds forcing, sediment availability and hydraulic exposure, with exponents of 1.548, 1.202 and 0.335 and LOGO R_log² = 0.892. A fast finite pool plus an effective continuing source predicted measured TP with LOGO R_log² = 0.926; an added return term did not improve LOGO prediction and was practically unidentifiable. The framework therefore separates measurement feedback from sediment-water dynamics and provides a mass-consistent basis for local source screening, with phase- or flux-resolved measurements reserved for mechanism-specific questions.