Application of interpolation methodology with dynamical constraint to the suspended particulate matter in the Liaodong Bay

Introduction Suspended Particulate Matter (SPM) influences the primary production and the distributions of pollutants in the ocean. Besides, the regulation mechanisms of SPM in the Liaodong Bay were complicated. Method To analyze the distributions and influencing factors of SPM, based on the adjoint assimilation method, an interpolation method with dynamical constraint was established in the Liaodong Bay. Result In two ideal experiments, the cost function, Mean Absolute Error (MAE) and Normalized Mean Error (NME) all had reduced by more than 90%, which proved the accuracy of the interpolation method. Based on conventional observations of SPM, the distributions of dynamically constrained, Kriging and radial basis function (RBF) interpolations in March, May, August and October of 2015 were obtained. Discussion The cross-validation was carried out to compare the dynamically constrained interpolation and the unconstrained interpolations. Among seven unconstrained interpolation methods, the averaged MAE of RBF interpolation was the lowest, which was 10.976 mg/L. The averaged MAE of dynamically constrained interpolation was 7.703 mg/L, reduced by 29.8% compared with the RBF interpolation. It was indicated that RBF interpolation was the most accurate among the seven unconstrained interpolations and dynamically constrained interpolation was more accurate than unconstrained interpolations at the observation stations. The distributions of dynamically constrained and RBF interpolations were compared with Korean Geostationary Ocean Color Imager (GOCI) satellite-derived distributions of SPM concentrations in the Liaodong Bay. Fully considering the influences of the hydrodynamic processes, the dynamically constrained interpolation provided distributions more consistent with the satellite-derived distributions. However, due to the lack of observations in some areas and ignoring the influences of currents, some high values of SPM concentration were not captured by the distributions of RBF interpolation. Moreover, in accordance with the results of dynamically constrained interpolation, it was found that the SPM concentrations in the bay were affected by the SPM discharge from the Liao River Basin.