2.3 Prediction of pond inundation states using hidden Markov models
We used hidden Markov models (HMMs) to detect temporal shifts in daily temperature standard deviations (tSDs) measured from the temperature sensors, which can be used to infer pond filling and drying events. The simplest HMMs partition datasets into 2 categories; in our study, the two categories represent distinct wet and dry states. However, Anderson et al. (2015) showed that seasonal fluctuation, canopy cover, pond vegetation, and water depth can influence temperature variance readings from temperature loggers placed in wetland basins, and that loggers in relatively deeper water have lower variance than those in shallower water. Use of HMMs with >2 states can help resolve this variation among dry-wet states, improving classifications. We therefore fit both 2-state and 3-state HMMs to both of our datasets, with the former modeling a simple scenario of distinct dry and wet states, and the latter factoring in the potential for additional wet, dry, or intermediate damp states.
In order to test whether a single logger (e.g., one in a pond without a control outside the pond) is sufficient to capture inundation states, we also compared two different datasets for each study site: one using temperature data from the paired pond and control loggers, calculated by subtracting the tSDs of the pond loggers from the tSDs of control loggers (wherein a value of 0 indicates no difference in daily tSD between the pond and air temperatures), and another using tSDs from pond loggers only.
We used a custom script in R v3.6.1 (R Development Core Team, 2018) to calculate tSDs measured by each temperature logger. We then used the package depmixS4 v1.4.0 (Visser & Speekenbrink, 2010) in R to fit HMMs. Because applying HMMs forces each dataset into the designated number of states, even in the absence of a true wet state, we used the HMM parameter estimates to determine appropriate tSD thresholds to designate each state as “wet” or “dry” for both datasets. We then compared the predicted states to the known states of the ponds during our four site visits (Tables S2 and S3).