The effects of non-local observations on the adjoint estimation of local model parameters: An example of Manning's n coefficient in a tidal model over the Bohai, Yellow, and East China Seas

Accurate parameter estimation is a key issue for enhancing the performance of hydrological models. With the rapid development of satellite technology, integrating satellite data and numerical modelling for parameter estimation has gained more prominence. The limited spatial coverage of altimeters necessitates areas without direct local observations to rely only on information from nearby non-local observations. However, the relation is far from clear between non-local observations and the estimation of local model parameters. In this study, a two-dimensional adjoint tidal model over the Bohai, Yellow, and East China Seas (BYECS) is developed, assimilating observations from TOPEX/Poseidon, Jason-1, and Jason-2 altimeters in conjunction with tide-gauge stations. In twin experiments, the feasibility and reliability of utilizing non-local observations are emphasized by varying synthetic observations. The experiments also reveal how the number and distance of non-local observations affect the ill-posedness of local parameter estimation. The estimation errors can be reduced by increasing observations within a ‘critical distance’, beyond which the accuracy does not improve further. Subsequently, the robustness of ‘critical distance’ is discussed under different prescribed parameter distributions, sizes of predefined optimized area, and random observational errors, indicating that the ‘critical distance’ is approximately 1.0°-2.0°. These results provide a positive reference for practical experiment. In BYECS, the order of Manning's n coefficient ranges from 10^-4 to 10^-1, with an average value of 0.0246 in shallow waters. The spatial distribution reveals 9 high-value areas, primarily modulated by a concurrence of sandy sediment and weak tidal currents. This study offers valuable insights into refining the adjoint model for physical parameter estimation, particularly in anticipation of the expanded spatial coverage of SWOT. Compared to only assimilating T/P series altimeters, incorporating SWOT reduces discrepancies by over 38%. Additionally, the spatial Manning's n coefficient provides guidance for enhancing tidal simulation in other models.