A hierarchical model of daily stream temperature for regional predictions

Abstract

Stream temperature is an important exogenous factor influencing populations of stream organisms such as fish, amphibians, and invertebrates. Many states regulate stream protections based on temperature. Therefore, stream temperature models are important, particularly for estimating thermal regimes in unsampled space and time. To help meet this need, we developed a hierarchical model of daily stream temperature and applied it across the eastern United States. Our model accommodates many of the key challenges associated with daily stream temperature models including the lagged response of water temperature to changes in air temperature, incomplete and widely-varying observed time series, spatial and temporal autocorrelation, and the inclusion of predictors other than air temperature. We used 248,517 daily stream temperature records from 1,352 streams to fit our model and 100,909 records were withheld for model validation. Our model had a root mean squared error of 0.61 C for the fitted data and 2.03 C for the validation data, indicating excellent fit and good predictive power for understanding regional temperature patterns. We then used our model to predict daily stream temperatures from 1980 - 2015 for all streams <200 km2 from Maine to Virginia. From these, we calculated derived stream metrics including mean July temperature, mean summer temperature, and the thermal sensitivity of each stream reach to changes in air temperature. Although generally water temperature follows similar latitudinal and altitudinal patterns as air temperature, there are considerable differences at the reach scale based on landscape and land-use factors.

Peer Review #1 of "Accurate spatiotemporal predictions of daily stream temperature from statistical models accounting for interactions between climate and landscape (v0.1)"

“…This suggests that a major driver of stream temperature is not parameterized in the covariates. For example, Hocking et al (2018) used a number of variables, interactions, random effects and an AR1 process to model stream temperature in the northeastern United States and saw an increase in RMSE from 0.59 °C for the training dataset to 2.06 °C when predicting the same sites but distinct years. While their model did attempt to account for variation in discharge and air temperature, it did not account for snowpack and depended heavily on a static AR1 process (AR1 = 0.77).…”

“…As currently constructed, models are basin specific as environmental relationships are fit relative to measurements at the specific environmental monitoring stations. Incorporating spatially explicit estimates of climate variables instead of data from point sources would potentially improve general applicability of models since environmental values would be specific to each stream segment (e.g., DayMet in Hocking et al 2018). Spatially explicit climate variables would also reduce the need to include interactions to describe variation in climate effects across space, thereby allowing for simpler models and interpretation.…”

“…Spatial modeling techniques, which utilize statistical auto-correlation to describe how upstream sites influence downstream sites, have recently become popular to predict stream temperature across entire watersheds (e.g., Peterson et al 2013, Isaak et al 2014, Jackson et al 2017. Most spatial modeling techniques require dense monitoring networks (Marsha et al 2018) and, with a few exceptions (e.g., Jackson et al 2018, Hocking et al 2018, primarily been used to predict temporally summarized metrics, such as the mean August max weekly temperature (Isaak et al 2017) or the maximum weekly mean stream temperature (Ruesch et al 2012), as opposed to continuous estimates of temperature. This is likely a consequence of spatial correlations and covariate relationships changing with climatic variability (Steel et al 2016, Jackson et al 2018.…”

“…For example, stream temperatures are likely to be more correlated across space during periods of high flows due to shorter water residency times and increased thermal inertia limiting the effect of air temperature and other influences. Consequently, models that depend on such autocorrelation techniques or other hierarchical methods may see large declines in precision when predicting into new temporal or physical spaces which are uninformed by such methods (e.g., Hocking et al 2018).…”

“…Despite clear theoretical evidence for the influence of covariates on stream temperature being conditional on other climatic and spatial influences, few statistical modeling studies have attempted to extensively utilize interactions to approximate such physical mechanism (e.g., Hocking et al 2018, Jackson et al 2018, and the utility of many interactions remains largely unexplored. Our objective was to identify and describe important interactions between climate and spatial variables and to utilize these relationships to model reach-scale spatially and temporally continuous patterns in daily mean stream temperature across complex watersheds.…”