Estimated Post-Emergence Period for Denning Polar Bears of the Chukchi and Beaufort Seas

For each den, we estimated dates of den emergence and departure as the earliest occurrence of collar temperature records in the time series that surpassed thresholds defined by period-specific temperatures at that den. In our study area, ambient temperatures during denning (e.g., mean January temperature is approximately -26 degrees C in Deadhorse, Alaska and -24 degrees C in Wrangel Island, Russia; Lozhkin et al. 2001; NOAA-NCEI 2022) are markedly lower than those that typically occur in unopened dens (e.g., the temperature inside a sealed den was 21 degrees C warmer than the ambient temperature; Harington 1968). Similar to prior investigations, we anticipated that den emergence would be characterized by a marked drop in temperature on the collar when the den was opened and exposed to colder ambient air (Fischbach et al. 2007; Olson et al. 2017). We used the Kelvin scale, in which the zero point represents absolute zero, to avoid arbitrary temperature proportions and because the temperatures we considered typically spanned 0 in other common scales. A constant of 0.93 was multiplied by the mean temperature in January because it was the proportion required to reduce the mean January temperature of all bears known to have denned by 20 degrees K, the approximate difference between ambient and unopened den temperatures (Harington 1968; Olson et al. 2017). Because the opening of a den should result in consistently lower temperatures relative to those recorded before the den was opened, we required that a second record below the threshold occur within 7 days to ensure that estimates were not based on measurement errors; because we selected 7 days arbitrarily, we examined the sensitivity of emergence estimates to this choice by comparing estimates based on 7 days to those estimated with 3, 5, 9, and 11 days.

Because bears can spend >97% of their time in the den during the post-emergence period, we expected average temperatures during that time to be cooler than before emergence but characterized by large variation attributable to the recording of temperatures both inside and outside the opened den. When bears departed the den site, we anticipated that mean daily collar temperatures would decrease because bears would no longer be spending time inside dens that were warm relative to ambient conditions. Hence, we defined the date of den departure as the first day in the time series after emergence when the mean daily collar temperature decreased below a den-specific threshold and remained below that threshold for at least 7 days. This threshold temperature was defined as the mean temperature recorded during the 30 days prior to emergence multiplied by 0.98. Temperatures recorded throughout denning were relatively consistent at most dens, but for some, temperature increased or decreased systematically as denning progressed, possibly due to changes in the denning environment (e.g., changes in the depth of insulating snow). Consequently, temperatures recorded 30 days prior to emergence provided a more representative baseline of conditions prior to departure on which to base the threshold than those recorded over longer periods of time. The constant 0.98 is the proportion required to reduce the mean den temperature of bears known to have produced cubs (from subsequent observations) by 1 SD; this value was selected because it maximized congruence with GPS location-based departure estimates (described below) during preliminary analyses. We evaluated the sensitivity of den departure estimates to the choice of the requisite number of days (7) that temperatures remained below the threshold with the same approach we used for emergence estimates.

For both den emergence (E) and departure (D), estimates represent the latest date at which the event occurred (i.e., the event was estimated to have occurred by this date because temperatures had exceeded the threshold); however, it is possible that the event actually occurred between the estimated date and the previous date with temperature data, a period that could span several days if data were recorded infrequently. To account for variability in recording intervals across sensors, we refer to the dates estimated by the methods described above as the maximum date of the event (E_max and D_max for emergence and departure, respectively) and the first date with temperature data prior to the estimate as the minimum date of the event (E_min and D_min). Accordingly, we calculated the minimum duration of the post-emergence period as D_min-E_max and the maximum duration as D_max-E_min; negative duration values, which result when the range of emergence and departure estimates overlap, were treated as zeros. Midpoint duration was calculated as (Dur_min+ Dur_max)/2. For example, at a den where temperature data were recorded at a 4-day interval, if the first day in the time series with temperatures below the emergence threshold was 10 March (and assuming a second record occurred below the threshold within 7 days), then we assumed emergence occurred between 6 March (E_min) and 10 March (E_max) with a midpoint emergence estimate of 8 March. To ensure that marked gaps in time series data due to variation in recording intervals did not lead to erroneous inference about denning phenology, we considered only those dens that included temperature data on >25% of days during the period spanning 7 days prior to E_min to 7 days after D_max.