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

Statistical stream temperature models predicting the fine-scale spatial distribution of water temperatures (i.e., “thermalscape”) can guide aquatic species recovery and habitat restoration efforts. However, stream temperature modelling is complicated by spatial autocorrelation arising from non-independence of sampling sites within dendritic networks. We used August mean temperature data from miniature sensors deployed in Canadian Rocky Mountain streams to demonstrate two statistical stream temperature modelling techniques that account for spatial autocorrelation. The first was a spatial steam network (SSN) model specifically developed to account for spatial autocorrelation in dendritic stream networks. The second was an integrated nested Laplace approximation (INLA) model that accounts for spatial autocorrelation but was not designed to address anisotropic stream network data. We evaluated the best-fitting SSN and INLA models using leave-one-out cross-validation. Relative to INLA, SSN models had lower RMSE (1.23 vs. 1.45 C) and higher r2 (0.71 vs. 0.61); however, the SSN models required more preprocessing steps before incorporating spatially correlated random errors. We provide practical advice, an open-access r-script, and data to help non-experts develop statistical stream temperature models.