Tsunami Data Assimilation Using High‐Frequency Radar‐Derived Surface Currents by Considering Beam Angle‐Dependent Measurement Error Distributions

Abstract The application of high‐frequency radar as an instrument for assimilating tsunami‐induced current fields is garnering increasing interest. The performance of surface current velocity measurements depends on the azimuthal differences between the crossing radar beams at the measurement points. This study aimed to incorporate the measurement error distributions of the east‐west and north‐south velocity components into tsunami data assimilation based on an optimal interpolation method, assuming Gaussian noise with the time‐invariant and a uniform standard deviation (STD = 5 cm/s) of radial velocity measurements. Through the empirical orthogonal function (EOF) analysis of radar‐derived surface currents in the Kii Channel, Japan, the velocities reconstructed using higher modes (EOFs 16–274) were associated with measurement errors, portraying nonuniform distribution depending on the crossing beam angle of two radar beams. Based on independent fifteen‐time assimilation experiments for two different tsunami scenarios, for a uniform water depth of 500 m, we observed a significant improvement of up to 29% and 0.9% in the assimilation performance (on average) over the along‐coast stations for scenarios with 1‐ and 5‐m maximum initial sea surface heights, respectively. The measurement errors dependent on the crossing beam angle reduced the error‐induced tsunamis, resulting in stable assimilations, with lower STDs in the fifteen‐time assimilation performances. When the STD of Gaussian noise varies with time, it is important to consider the temporal change in the radial velocity measurement errors and/or noise‐filtering techniques, to maintain a certain level of noise intensity.