Spatiotemporal smoothing of water quality in a complex riverine system with physical barriers

Freshwater ecosystems offer a variety of ecosystem services, and water quality is essential information for understanding their environment, biodiversity, and functioning. Interpolation by smoothing methods is a widely used approach to obtain temporal and/or spatial patterns of water quality from sampled data. However, when these methods are applied to freshwater systems, ignoring terrestrial areas that act as physical barriers may affect the structure of spatial autocorrelation and introduce bias into the estimates. In this study, we applied stochastic partial differential equation (SPDE) smoothing methods with barriers to spatial interpolation and spatiotemporal interpolation on water quality indices (chemical oxygen demand, phosphate phosphorus, and nitrite nitrogen) in a freshwater system in Japan. Then, we compared the estimation bias and accuracy with those of conventional non-barrier models. The results showed that the estimation bias of spatial interpolations of snapshot data was improved by considering physical barriers (5.8 % for (chemical oxygen demand, 22.5 % for phosphate phosphorus, and 21.6 % for nitrite nitrogen). The prediction accuracy was comparable to that of the non-barrier model. These were consistent with the expectation that accounting for physical barriers would capture realistic spatial correlations and reduce estimation bias, but would increase the variance of the estimates due to the limited information that can be gained from the neighbourhood. On the other hand, for spatiotemporal smoothing, the barrier model was comparable to the non-barrier model in terms of both estimation bias and prediction accuracy. This may be due to the availability of information in the time direction for interpolation. These results demonstrate the advantage of considering barriers when the available data are limited, such as snapshot data. SPDE smoothing methods can be widely applied to interpolation of various environmental and biological indices in river systems and are expected to be powerful tools for studying freshwater systems spatially and temporally.