Weaker weighted phase agreement accounted for 1.82 cm of Superior's 6.56 cm mean harmonic range loss from 1948-1973 to 1974-1999

We tested whether timing variation accounts for most of the weaker mean seasonal water-level cycle on Lake Superior. We fitted annual harmonics to coordinated monthly levels, version v2025. From 1948-1973 to 1974-1999, mean harmonic range fell by 6.56 cm. An exact symmetric decomposition assigns -4.74 cm to smaller mean annual ranges and -1.82 cm to weaker amplitude-weighted phase agreement. Conditional 95% three-year block intervals are -8.77 to -0.86 cm and -3.53 to -0.20 cm. The amplitude point share is 72.3%, but the interval for phase minus amplitude contribution includes zero. Thus, the main test does not clearly rank the contributions and does not support the planned timing-majority explanation. Adding a separate linear drift in each year preserves both negative contributions and raises the amplitude share to 82.8%. Five- and seven-year block checks preserve a negative phase contribution. Removing any one year preserves the point ranking. This extends a prior campaign range comparison with a decomposition of annual strength and timing agreement. It does not identify a physical cause. Short periods, long climate cycles, amplitude weighting and fitted-model assumptions limit inference. Code, numeric source rows, hashes, bootstrap evidence and an independent numerical audit are included.

Lake Superior · seasonal cycle · phase agreement · water levels · harmonic decomposition · block bootstrap