With fixed area that does not increase with depth, 62 of 149 lake records allow both signs of fitted volume trends at 18°C and 5 mg/L, 1980–2017

We tested whether suitable-depth trends fix the signs of suitable-volume trends when lake basin shape is unknown. We reused 4,162 late-summer profiles from 149 lakes at 30–70° N in 1980–2017. We held the sampled depth and the year-and-date regression fixed. Main limits were temperature at most 18°C and oxygen at least 5 mg/L. We proved and implemented sharp bounds over fixed, nonnegative area profiles that do not increase with depth. A volume trend is a weighted mean of trends in all surface-to-depth columns. In 62 of 149 records, the bounds allowed both negative and positive fitted volume slopes. Fifty allowed slopes below −0.1 and above +0.1 percentage points per decade. A simple quadratic-area example reversed 17 constant-area trend signs. Mean slopes across all lakes remained negative for constant, linear and quadratic area examples: −0.99, −0.80 and −0.71 points per decade. Their 95% region bootstrap intervals excluded zero, but the paired quadratic-minus-constant mean difference of +0.28 had an interval of −0.06 to +0.82. Sign ambiguity was present in 54–62 records across five water-limit cases. The calculation concerns only the fixed sampled depth and fitted point trends. It does not estimate actual whole-lake volume, assign probabilities to basin shapes, measure fish change, or establish a cause. The package includes a proof, complete source data, provenance, code, figures, exact bounds and independent numerical checks. Basin-shape effects are established in prior work; this contribution supplies a reproducible bound and a fixed-sample application.

lake oxygen · temperature · basin shape · volume bounds · ecological change · reproducible analysis