A Continuous Implicit Neural Representation Framework with Gradient Regularization for Sea Surface Height Reconstruction From Satellite Altimetry

Abstract. 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 an interpolation framework based on implicit neural representations (INRs), in which SSH is represented as a continuous function of space and time. The framework employs sinusoidal representation networks (SIREN) to enable smooth gradients and efficient spectral representation. To improve reconstruction in regions with sharp spatial transitions, such as fronts and eddy boundaries, we incorporate a total variation (TV) regularization term, allowing the model to preserve abrupt features while maintaining global smoothness. 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 recover fine-scale and locally sharp structures while preserving the large-scale variability of the SSH field. The method maintains a level of global accuracy comparable to existing interpolation and data-assimilation approaches, but provides enhanced spatial detail in regions affected by strong gradients, fronts, or mesoscale activity. 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.