3.2 Comparison of 2- versus 3-state hidden Markov models and determination of wet state threshold values
Although 2-state HMMs have been applied in past work (Arismendi et al., 2017), we found that 2-state HMMs appeared to over- or underestimate inundation duration for several ponds or predict additional wet states when we were confident that the ponds were dry (Figure S4). Using 3-state HMMs and subsequently combining multiple wet or dry states provided more accurate and consistent state predictions between pond only and paired pond-control datasets (Tables S2, S3). Therefore, we focused our analyses on results from the 3-state HMMs, which allow for the potential for seasonal variation in daily tSDs and intermittent wet-dry states (e.g., damp) and account for potential uncertainty due to wet sediment or other factors (see Figure 3 for examples).
For the paired pond-control dataset, we used a wet state threshold of -2.0°C, meaning that the daily tSDs measured by the pond sensors were at least 2.0°C lower on average than those measured by the control sensors. This -2.0°C threshold minimized the number of false dry state predictions. It did result in a false wet prediction for T17, but this was likely due to sediment in the pond sensor housing that may have affected the reading. A more conservative threshold of -2.2°C falsely predicted T12 as dry (Table S3).
Upon fitting 3-state HMMs to the pond-only dataset, we found that a threshold between 2.9°C to 3.3°C minimized the number of false dry states for most ponds (Table S2, Table S3). This threshold is slightly lower than that proposed by Anderson et al. (2015), who determined that using daily temperature variances cutoffs between 13 and 15 (corresponding to tSDs between 3.6°C and 3.9°C) for the wet state provided the most accurate predictions of pond inundation states in their field experiments. Within our pond-only dataset, using a less conservative tSD threshold of 3.5°C decreased the accuracy leading to a false wet state prediction for pond T15U. For pond T8, the state with the highest average temperature standard deviation (~2.8°C) fell below our wet state cutoff of 3.0°C (Table S5). Because we knew that the pond was dry at two timepoints in this state (during logger deployment and logger retrieval), we decreased the wet state threshold to 2.7°C for this particular pond and considered the average tSD of 2.8°C to reflect a dry state.
To further define a “reliable” wet state prediction from our HMMs, we also required that the pond remain in a given state for a minimum of 5 consecutive days. We chose this cutoff based on site observations in early August 2018, during which ponds T17 and T20 had short predicted wet states of 7 and 5 days in July respectively and both showed evidence of prior inundation despite being dry at the time of our visit. Pond A14 also had a predicted wet state of 4 days in mid-July but showed no evidence of earlier inundation in early August (Table S2, Table S3).