A squared level term gave no clear six-month prediction gain for Michigan-Huron at 1970-2025 origins

We tested whether a squared current lake-level anomaly improves six-month predictions beyond linear local history. We used coordinated v2025 monthly means for 1918-2025. Each origin year used earlier training targets only. At 666 Michigan-Huron origins in 1970-2025, RMSE rose from 14.33 to 14.45 cm. Squared-error reduction was -1.69%, with a conditional 95% five-year block interval of -3.69% to +0.07%. Thus the primary test gave no clear added gain. The Superior test gave -0.46%, with limits of -1.74% to +0.75%. Cubic and absolute-anomaly terms also gave no clear gain. A 40-year fit gave worse quadratic predictions for Michigan-Huron. This is a narrow forecast benchmark, not proof of linear dynamics or symmetric recovery. Revised data, two related lakes, fixed terms and conditional block intervals limit inference. We provide source hashes, numeric inputs, code, all predictions, bootstrap evidence, independent numerical checks and a static figure.

Great Lakes · lake level · nonlinear response · chronological prediction · null result · Michigan-Huron