Sea Level Time Series Reconstruction of the California Coast Using Neural Network Residual Imputation and ERA5 Data

This work proposes a methodology for sea level time series imputation based on separating the observed signal into an astronomical tidal component (via harmonic analysis using T-TIDE) and a residual non-tidal component, which is then modeled using a multilayer perceptron (MLP) with meteorological variables (wind, pressure, sea surface temperature) from ERA5 and cyclical temporal features (sine/cosine encoding). The main contribution consists in separating the observed signal into two physically meaningful components: (i) the tidal astronomical component, obtained through classical harmonic analysis, and (ii) the residual component, which captures non-tidal variability. Subsequently, the residual component is modeled using a multilayer perceptron (MLP) with meteorological variables from ERA5 and time data as the feature vector. The method is evaluated at four NOAA tide gauge stations along the California coast (San Diego, La Jolla, Los Angeles, and San Francisco), using hourly records spanning from 1 January 1950 to 30 June 2025, with station-dependent missing data fractions. The harmonic plus MLP approach achieves a coefficient of determination (R2) of 0.9955 and a root mean square error (RMSE) of 0.03475 across the four stations, representing an average reduction of 52% in the RMSE compared to classical harmonic analysis alone.