Dynamic grey water footprint and aggregation factor of pesticide mixtures from a periodic fugacity model: synthetic instance and numerical validation

Manuscript, supplementary material, code, numerical results and figures supporting the study of the aggregation factor of the dynamic grey water footprint of pesticide mixtures. The grey water footprint is normally reported as a single annual volume; this work derives it instead as a periodic dilution flow rate from a Level IV fugacity model with periodic thermal and hydrological forcing, and studies when the ratio of the peak of a moving average to the annual mean decays monotonically in the averaging window, what happens when it does not, and how far the failure can go. The deposit contains the dimensionless synthetic instance on which the propositions are verified numerically: the periodic cycle through the monodromy matrix, the aggregation factor over the averaging window, the unimodality test on the circle, the window of guarantee, the decreasing-rearrangement bound, and the rectangular counterexample to monotonicity. The calculation and the figure drawing are in separate scripts, so the figures can be redrawn without recomputing and the numbers recomputed without producing graphics; a third solves the application-calendar problem by exhaustive grid search and its convex relaxation to a probability measure over dates as a linear programme, and reports the gap between them; and a fourth verifies conformity, checking the dimensional homogeneity of every equation of the model in both the molar and the mass convention and closing the mass balance of one cycle numerically. Self-contained: it does not depend on the sugarcane case study, which is deposited separately.