Annual change differences in Superior and Michigan-Huron show no clear variance decrease from 1919-1971 to 1972-2025

We tested whether annual lake-level changes in Superior and Michigan-Huron diverged less in 1972-2025 than in 1919-1971. We used coordinated v2025 monthly means and formed the difference between the two annual mean level changes. Its variance fell from 389.92 to 224.71 square centimetres. The late-to-early variance ratio was 0.576, with a conditional 95% five-year block interval of 0.338 to 1.082. Thus, this test does not resolve a decrease. All planned checks also gave intervals that include no change. The variance of the mean of the two changes had a ratio of 1.230, with limits of 0.729 to 2.164. An exact variance budget links most of the sample decrease in difference variance to a larger covariance term. This is an arithmetic result, not a physical cause. The study extends prior evidence of higher correlation with a test of absolute difference spread. Few years, dependent observations, fixed periods and source revisions limit inference. The package includes monthly inputs, source hashes, code, all block draws, a figure and an independent arithmetic audit.

Great Lakes · annual level changes · difference variance · covariance · block bootstrap · null result