Comparison of Statistical Approaches for Predicting Stream Temperatures Across Heterogeneous Landscapes

Estimating stream temperatures across broad spatial extents is important for regional conservation of running waters. Although statistical models can be useful in this endeavor, little information exists to aid in the selection of a particular statistical approach. Our objective was to compare the accuracy of ordinary least-squares multiple linear regression, generalized additive modeling, ordinary kriging, and linear mixed modeling (LMM) using July mean stream temperatures in Michigan and Wisconsin. Although LMM using low-rank thin-plate smoothing splines to measure the spatial autocorrelation in stream temperatures was the most accurate modeling approach; overall, there were only slight differences in prediction accuracy among the evaluated approaches. This suggests that managers and researchers can select a stream temperature modeling approach that meets their level of expertise without sacrificing substantial amounts of prediction accuracy. The most accurate models for Michigan and Wisconsin had root mean square errors of 2.0-2.3°C, suggesting that only relatively coarse predictions can be produced from landscape-based statistical models at regional scales. Explaining substantially more variability in stream temperatures likely will require the collection of finer-scale hydrologic and physiographic data, which may be cost prohibitive for monitoring and assessing stream temperatures at regional scales.