A continuous implicit neural representation framework with gradient regularization for sea surface height reconstruction from satellite altimetry

Satellite altimetry provides valuable measurements of sea surface height (SSH) but is characterized by irregular spatiotemporal sampling and substantial data gaps arising from orbital configurations, sensor limitations, and environmental conditions. These sampling properties pose challenges for constructing continuous and dynamically consistent SSH fields. In this study, we develop a reconstruction framework based on implicit neural representations (INRs), in which SSH is represented as a continuous function of space and time. The framework uses a sinusoidal representation network (SIREN)-based coordinate network to learn a continuous space–time representation of SSH from sparse along-track observations, and includes total-variation (TV)-based spatial-gradient regularization to discourage unsupported local variations. The combination of a continuous, differentiable INR formulation with gradient-based regularization provides a compact and flexible approach for SSH reconstruction. We evaluate the proposed framework using both multi-mission satellite altimetry observations and high-resolution numerical simulations. Experiments conducted indicate that the proposed SIREN–TV framework can reconstruct the broad SSH variability and dominant mesoscale patterns while reducing some localized reconstruction artifacts. The method maintains a level of global accuracy comparable to existing interpolation and data-assimilation approaches and provides improved effective feature resolution under the adopted benchmark protocol. In addition, the continuous and fully differentiable representation enables direct computation of spatial derivatives, facilitating higher-order oceanographic diagnostics. These results suggest that INR-based formulations offer a promising complementary avenue for SSH interpolation under sparse and irregular sampling configurations.