Extending geographically and temporally weighted regression to account for both spatiotemporal heterogeneity and seasonal variations in coastal seas

Space-time modelling has been successfully applied in numerous research projects and has been studied extensively in the field of geographical information science. However, the cyclical or seasonal variations in the temporal dimension of most spatiotemporal processes are rarely considered along with spatiotemporal nonstationarity. Seasonal variations are widespread and typical in marine environmental processes, and addressing both spatiotemporal heterogeneity and seasonal variations is particularly difficult in the turbid and optically complex coastal seas. By incorporating seasonal periodic effects into a geographically and temporally weighted regression (GTWR) model, we proposed a geographically and cycle-temporally weighted regression (GcTWR) model. To test its performance, modelling of chlorophyll-a, known as an important indicator of the coastal environment, is performed using the in situ data collected from 2012 to 2016 in the coastal sea of Zhejiang Province, China. GcTWR is compared with global ordinary least squares (OLS), geographically weighted regression (GWR), cycle-temporally weighted regression (cTWR), and GTWR models. In the results, the GcTWR model decreases absolute errors by 89.74%, 79.77%, 76.60% and 29.83% relative to the OLS, GWR, cTWR, and GTWR models, and presents a higher R² (0.9274) than the GWR (0.5911), cTWR (0.6465), and GTWR (0.8721) models. The estimation results further confirm that the seasonal influences in coastal areas are much more significant than the interannual effects, which accordingly demonstrates that extending the GTWR model to handle both spatiotemporal heterogeneity and seasonal variations are meaningful. In addition, a novel 3D visualization method is proposed to explore the spatiotemporal heterogeneity of the estimation results.