Statistical stream temperature modelling with SSN and INLA: An introduction for conservation practitioners

Statistical stream temperature models can predict the fine-scale spatial distribution of water temperatures and guide species recovery and habitat restoration efforts. However, stream temperature modelling is complicated by spatial autocorrelation arising from non-independence data collected within dendritic networks. We used data from miniature sensors deployed in Canadian Rocky Mountain streams to develop and validate two statistical stream temperature modelling techniques that account for spatial autocorrelation. The first was based on spatial steam network models (SSNs) specifically developed to account for spatial autocorrelation in dendritic stream networks. The second used integrated nested Laplace approximation (INLA) that accounts for spatial autocorrelation but was not designed to address anisotropic stream network data. We evaluated the best-fitted SSN and INLA models using leave-one-out cross validation from the data collected along the stream network. Both modelling techniques had similar RMSE and MAE (near 1oC) and r2 (> 0.6) values, and proved flexible with respect to implementation; however, the SSN models required more preprocessing steps before incorporating spatially correlated random errors. We provide practical advice and open-access data and r-script to help non-experts develop statistical stream temperature models of their own.