FourierBGC 1.0: Fourier feature encoding of spatiotemporal inputs for biogeochemical Argo profile reconstruction

Abstract. Reconstructing biogeochemical Argo profiles is essential to bridge the severe spatiotemporal coverage gaps between abundant physical observations and scarce biogeochemical data, providing the continuous ocean-state representations required for climate models and global carbon budget analyses. A recent convolutional method for profile reconstruction, PPCon, encodes day-of-year, year, latitude, and longitude through four independently learned multilayer perceptrons. These learned encoders add substantial parameter overhead and may yield sub-optimal spatiotemporal representations for the variables being reconstructed. To address this, we introduce FourierBGC, which replaces PPCon's learned encoders with a fixed Fourier-feature encoding of day-of-year, latitude, and longitude, combined with a lightweight learned projection, cutting encoder parameters by 88 %. By directly embedding periodic annual cycles and smooth spatial continuity into input space, this encoding provides strong multifrequency coordinate representations that facilitate lightweight yet highly expressive spatiotemporal representations. Through a controlled ablation holding PPCon's convolutional backbone fixed, FourierBGC outperforms PPCon on all three reconstructed variables (nitrate, chlorophyll-a, and bbp700), and the Fourier encoding achieves the lowest reconstruction error in every sub-basin and season. Disentangling the sources of error reduction reveals that beyond an optimized training procedure, the Fourier encoding yields a consistent, highly parameter-efficient performance boost across all variables. Furthermore, the learned projection's role exhibits variable- and season-specific behavior tied to upper-ocean physics: it is dispensable on nitrate, essential for capturing the complex profile of chlorophyll-a, and on bbp700 helps under summer stratification while costing accuracy in winter, a pattern consistent with the projection expressing vertical water-column structure only when it is present. Overall, FourierBGC demonstrates that structuring spatiotemporal inputs with explicit frequency priors offers a parameter-efficient strategy for reconstructing sparse geophysical and environmental fields.