Modeling spatially anisotropic nonstationary processes in coastal environments based on a directional geographically neural network weighted regression

Quantifying the spatial association between ecological indicators (e.g., chlorophyll-a) and environmental parameters is crucial for explaining the ecological status in coastal ecosystems. Although global and local regression models have been widely used to estimate spatial relationships in marine environmental processes, spatial anisotropy caused by strong coastal-inland environmental gradients has not been investigated. This is very likely to result in incomprehensive characterization of the coastal ecological status. To better quantify the spatially anisotropic nonstationary relationship in coastal environments, a spatial proximity neural network (SPNN) was proposed in this paper to address the nonlinear effects of spatial anisotropy. A directional geographically neural network weighted regression (DGNNWR) model was accordingly developed by combining a geographically neural network weighted regression (GNNWR) with SPNN to incorporate anisotropic impacts into spatial nonstationarity. Modeling of chlorophyll-a in Zhejiang coastal areas of China in the spring over 2015-2017 was conducted to examine its performance. The results demonstrated that DGNNWR achieved a better fitting accuracy and a more adequate prediction ability than ordinary linear regression (OLR), geographically weighted regression (GWR), GNNWR, and anisotropic-based GWR models. Notably, compared to the best comparison model, the fitting error indicators were declined for more than 30% and the fitted R2 was considerably increased from 0.83 to 0.92 using our proposed DGNNWR. The spatial mapping of parameter estimates confirmed that DGNNWR successfully handled the anisotropic nonstationarity in coastal environments and quantified the main driven parameters of Chl-a. Based on the spatially refined relationship between Chl-a and environmental parameters, we further characterized the spatial and temporal distributions of Chl-a in Zhejiang coastal areas in the spring of 2015-2017, and then investigated the impacts of riverine discharges and ocean currents on the spatiotemporal variations of Chl-a. The findings are crucial to formulate appropriate mitigation strategies for eutrophication and are meaningful for the management of coastal ecosystems.