A robust hierarchical model of daily stream temperature using air-water temperature synchronization, autocorrelation, and time lags

Water temperature is a primary driver of stream ecosystems and commonly forms the basis of stream classifications. Robust models of stream temperature are critical as the climate changes, but estimating daily stream temperature poses several important challenges. We developed a statistical model that accounts for many challenges that can make stream temperature estimation difficult. Our model identifies the yearly period when air and water temperature are synchronized, accommodates hysteresis, incorporates time lags, deals with missing data and autocorrelation and can include external drivers. In a small stream network, the model performed well (RMSE = 0.59 °C), identified a clear warming trend (0.063 °C · y^-1) and a widening of the synchronized period (2.9 d · y^-1). We also carefully evaluated how missing data influenced predictions. Missing data within a year had a small effect on performance (~ 0.05% average drop in RMSE with 10% fewer days with data). Missing all data for a year decreased performance (~ 0.6 °C jump in RMSE), but this decrease was moderated when data were available from other streams in the network. Straightforward incorporation of external drivers (e.g. land cover, basin size) should allow this modeling framework to be readily applied across multiple sites and at multiple spatial scales.