A symmetric allocation gave precipitation 50.7% of shared monthly supply covariance in Superior and Michigan-Huron in 1950-2022

We tested how precipitation, runoff, and evaporation share the covariance of monthly net basin supply estimates for Superior and Michigan-Huron. We used L2SWBM V3.0 medians for 1950-2022. We removed each calendar month mean and split cross-component covariance terms equally between their two components. Precipitation received 50.74% of the total covariance. Its conditional 95% five-year block interval was 48.03% to 53.39%. Thus, the test did not establish a share above one half. Runoff received 25.32%, and evaporation received 23.94%. The runoff allocation was 198.11 square mm below the precipitation allocation, with an interval of 152.53 to 237.94 square mm below. This ordering held with other block lengths, trend removal, annual totals, and two model-run periods. These are arithmetic shares of covariance in model median estimates. They do not identify physical causes, explain a historical change in lake-level agreement, or include model posterior uncertainty. The package gives source hashes, monthly evidence, code, all results, primary resamples, a figure, and scalar checks.

Great Lakes · net basin supply · precipitation · runoff · evaporation · covariance · L2SWBM · conditional uncertainty