Revisions

In response to the Reviewer comments, we made several changes that help address assumptions and limitations in the analysis:

1. In our revised manuscript, we now only consider lakes with 15 (previously 10) years of data, which improved our ability to constrain interannual variability and long-term trends. Though this change decreased our total sample size from 598 to 382 lakes, we note that we still maintain our global representation of waterbodies across 10 countries and four continents (Figure 2). We added a figure and a table (Table S1, Figure S1) to the Supplemental Information that provide additional information about data availability at each lake, including the number of years and number of data points per year. We also conducted a sensitivity analysis in lakes with greater data availability, which demonstrated that our seasonal memory metric is not strongly dependent upon the number of measurements per summer (Figure S3). Through these analyses, we confirm that our results and conclusions are robust to changing data availability among lakes.
2. We modified Figure 5 following comments from both Reviewers. The figure now presents the correlation between bottom-water temperature trends and spring/summer air temperature trends, in place of the more complicated random forest regression that was included in the previous manuscript draft. We ultimately agree with Reviewers that this simpler approach is more easily interpreted, while supporting the same conclusions as our previous analysis.
3. We re-named our memory metric to avoid using the abbreviation SEM, which is already used for Structural Equation Modeling. In the revised manuscript, we refer to this metric as cross-seasonal ecological memory throughout, and we use the abbreviation CSEM.

Ultimately, these revisions do not fundamentally alter the results or conclusions of the manuscript.