Widespread loss of safe lake ice access in response to a warming climate

2.3 Determining ice quality Ice quality is an often overlooked and understudied metric due to a paucity of data but have significant impacts on ice safety [5]. For example, the flexural strength of white ice is approxi- mately 51% lower than black ice at temperatures near 0˚C [10] and the load bearing capacity of lake ice can drop significantly when ice quality is low [9]. It is important to note that the CESM2-LE does not provide a ratio of black ice and white ice, though it does incorporate freeze-thaw cycles, snow grain evolution, and snow compression into the ice column [20,32]. Therefore, in order to make use of ice quality as a component of ice safety, we combined safety protocols from the Minnesota Department of Natural Resources (MDNR) to determine allow- able loads on black ice and white ice [5,33]. The ice quality gradients in this study focus on assumed scenarios of lake ice at 100% black ice, 100% white ice, and a 50% black ice and 50% white ice scenario. We defined the transition period from unsafe ice to safe ice thickness as the duration of time from ice first appearing at a thickness of 2 cm (i.e., ice on) to ice reaching 10 cm, 15 cm, or 20 cm, depending on the hypothetical ice quality. We chose 2 cm as ice on to elimi- nate short-lived, intermittent ice events that might occur if defining ice as >0 cm. For exam- ple, the initial skim ice that forms on a calm, cold night can break up easily from wind stress or melt from warmer temperatures during the day [7]. These periods of brief ice cover are

not typically considered as the date of ice formation in ice phenology records and are known to add uncertainty to lake ice records [34]. Using an ice thickness > 2 cm permitted us to consider the ice column of each lake within a grid to be stable. For pure black ice, a thickness of 10 cm was used to conform with the MDNR safety recommendations for a per- son walking on ice. For 50% white ice and 100% white ice, we used 15 cm and 20 cm of ice thickness, as the thickness is doubled for white ice compared to black ice for safe use [5]. Therefore, we used the equivalent thickness required for safe ice use, owing to the inability of the model to distinguish between black and white ice layers directly. We extracted the day of the year when the ice reached the specified thicknesses for a historical climate (1851– 1880), 1˚C, 2˚C, and 4˚C warming. These temperature thresholds were chosen to cohere with an established framework of indexing global temperature rise instead of a particular emission scenario since lake ice cover is strongly influenced by the global mean surface tem- perature [35]. We also excluded grids where ice cover lasted for fewer than 30 days or longer than 330 days. We then determined the phenological anomaly by subtracting the warming scenarios from the historical climatology for black ice for each individual 0.9˚-by-1.25˚ grid. From those gridded values, we then took the Northern Hemisphere average and stan- dard deviations. 2.4 Statistical analysis We tested each grouping of temperature and ice quality for normality using a Shapiro-Wilks

test (S1 Table). We then tested for significant differences in transition periods across warming scenarios within an ice quality category and across ice quality categories within the same warming scenario by using a Kruskal-Wallis test (S2 and S3 Tables). If the means differed sig- nificantly (p < 0.05) between the three groups, we used a Dunn’s test to determine which means were significantly different (S4 and S5 Tables). We verified the family-wise error rate using the Holm method [36]. Subsequently, we used a Kolmogorov-Smirnov two-sample test to determine whether distributions were significantly different, again both between warming scenarios within the same ice quality category and across ice quality categories within the same warming scenario (S6 and S7 Tables). We used the KS test to determine the absolute difference between the empirical cumulative distribution functions of the different distributions. The PLOS ONE Changing ice conditions inhibit safe use PLOS ONE | https://doi.org/10.1371/journal.pone.0313994 December 11, 2024 5 / 19