Duck Lake and Green Lake are neighboring lakes in Green Lake Township, Grand Traverse County. Bruce’s report describes Duck Lake as the headwater of the Betsie River and notes that it flows toward Green Lake through a dam that partially controls Duck Lake levels.

The report explains that the Duck Lake Dam is adjusted seasonally: levels are lowered in fall and winter to help protect Duck Lake shorelines from ice erosion, then raised for spring and summer.

That management pattern helped frame the question Bruce wanted to test. Some had hypothesized that Duck Lake dam operations were detrimental to Green Lake levels. Because Green Lake also has other water sources, Bruce wrote that the relationship was not obvious from geography alone.

Bruce says he obtained the lake-level data from the Grand Traverse County Drain Commission and applied his professional background in statistical analysis to examine whether the measured pattern looked more like one lake mechanically driving the other—or both lakes responding to influences they share.

The report describes an ongoing study beginning November 7, 2022. The supplied analysis runs through September 14, 2026 and includes 1,411 paired daily observations recorded on matching dates.

Bruce reports 4 missing Duck Lake values and 8 missing Green Lake values.

The analysis uses an XY scatter plot, Pearson correlation, Spearman rank correlation, correlation of day-to-day changes, Granger lead/lag testing, and cross-correlation of daily changes by lag.

Pearson r = 0.71 indicates a strong positive linear relationship between the measured levels. When Duck Lake is comparatively high, Green Lake also tends to be high; when one is low, both tend to be low.

Spearman ρ = 0.56 shows a moderate positive rank relationship. Bruce notes that it is lower than Pearson, suggesting the relationship is not perfectly monotonic throughout the range. His report points to a cluster of low Green Lake readings around roughly 836.8–837.0 ft where Duck Lake barely moves and is not increasing.

Correlation of day-to-day changes = 0.38. Once the focus shifts from raw levels to daily movement, the relationship weakens. Bruce interprets that difference as evidence that much of the stronger 0.71 raw-level relationship comes from the lakes trending together over longer periods—such as seasonal cycles—rather than reacting to each other tick-for-tick each day.

Bruce also used Granger causality testing. Despite the name, it asks whether earlier changes in one series improve prediction of later changes in the other; it does not by itself prove that one lake physically caused the other to move.

Duck → Green: the report says Duck Lake changes have statistically significant predictive power for Green Lake at a one-day lag, with p < 0.0001. Bruce also notes that some physical influence is intuitively plausible: changing dam level could produce at least a short-period response.

Green → Duck: this direction is also statistically significant and, in Bruce’s reported testing, shows larger F-statistics at every lag tested.

Bruce treats that two-way predictability as a key clue. If the dominant story were simply Duck Lake mechanically driving Green Lake, he argues that prediction would ordinarily be expected to run mainly in one direction. Instead, each lake helps predict the other, with Green showing the stronger statistical edge in the tested lags.

Bruce identifies possible shared influences including rainfall and snowmelt, a shared watershed or groundwater table, and coordinated water-management releases.

The cross-correlation analysis adds another clue. Bruce reports that the daily-change relationship peaks at lag 0, r = 0.38, then decays fairly symmetrically as the comparison moves backward and forward in time. He notes that this does not show the sharp “one lake leads by X days” signature one might expect from a simple direct water-transfer explanation.

The analysis does not claim the dam has no effect. In the report's final paragraph, Bruce says the twice-yearly dam changes make a small amount of physical causation plausible, but he also writes that this limited effect is not statistically significant.

Important source nuance: earlier in the report, the Duck → Green Granger predictability result is reported as statistically significant at a one-day lag (p < 0.0001). Bruce separately warns that Granger testing is statistical predictability, not proof of true physical causation. This page keeps those statements separate rather than treating the predictive result as proof that dam operations physically caused Green Lake changes.

The study supports an interpretation of the measured data; it does not establish a single physical mechanism.