Phosphorus load shares did not explain the 28% fall in combined river TN:TP under stationary flow normalization, 1980-1996 to 2009-2025

We tested whether changes in the contributions of two rivers explained a fall in their combined total nitrogen to total phosphorus load ratio. We used USGS release 3.0 annual loads for the Mississippi and Atchafalaya rivers. Under stationary flow normalization, the molar ratio fell from 24.986 in 1980-1996 to 18.053 in 2009-2025, a 27.75% decrease. An exact accounting method assigned -6.942 mol/mol to changes in the two river ratios and +0.009 mol/mol to changes in phosphorus load shares. The share term offset 0.14% of the fall. Generalized flow normalization and annual load estimates gave similar point results. Alternative late periods retained small share terms. A box test based on annual marginal limits retained a negative combined change. That box is not a joint confidence interval. This result tests a load-mixture explanation; it does not identify physical causes within rivers or predict coastal nutrient limitation. Joint model error, total nutrient forms, period choices and retrospective estimates limit inference. The package includes the source CSV, exact provenance, code, tables, a figure, an independent numerical audit and offline reproduction instructions.

nutrient loads · Mississippi River · Atchafalaya River · nitrogen phosphorus ratio · flow normalization · exact accounting