Annual flow changes gave no clear phosphorus-to-nitrate load response in two Gulf rivers in 1981-2025

We tested whether total phosphorus delivery responds more strongly than filtered nitrate plus nitrite delivery to annual flow changes in two Gulf rivers. We used USGS version 3.0 annual load estimates for the Mississippi and Atchafalaya rivers in 1980-2025 and 45 changes between adjacent years. The combined log-ratio response slope was -0.162, with conditional 95% three-transition block limits of -0.493 to +0.146. Separate river, time period and nutrient-form checks also had annual-change intervals that included zero. A detrended level fit gave a negative slope with limits below zero, so the conclusion depends on time representation. An exact worst-case test showed that annual log-ratio errors bounded by 0.0332 can move the primary point slope to zero. This is not a probable source-error estimate. The evidence gives no clear stronger phosphorus response at this scale. Model-derived loads, annual averaging, missing joint source errors and a short dependent record limit physical inference. Code, source hashes, annual flow inputs, load inputs, all comparisons, an independent audit and a figure are included.

nutrient loads · river flow · Mississippi · Atchafalaya · annual changes · uncertainty · null result