The biological carbon pump transfers particulate organic carbon (POC) from the surface ocean to depth, yet its spatial variability remains poorly constrained due to sparse in-situ observations. Here we present a global, depth-resolved reconstruction of particle size distribution (PSD) slope (β) and biovolume (BV) from Underwater Vision Profiler 5 (UVP5) measurements, using a Sparse Variational Gaussian Process (SVGP) that simultaneously resolves 121 depth levels and the full seasonal cycle with a single self-consistent model. Spatially blocked cross-validation confirms genuine out-of-region predictive skill (¯r = 0.57 for β, ¯r = 0.68 for BV), demonstrating that the reconstruction generalises to unsampled geographic regions rather than merely interpolating within densely observed areas. The reconstructed fields reveal a robust latitudinal structure: lower β values and elevated BV at high latitudes indicate dominance by large, rapidly sinking particles consistent with efficient carbon export, while subtropical oligotrophic gyres exhibit steeper size distribution slopes and lower biovolume, consistent with remineralization dominated regimes. Temperature and salinity emerge as the most robustly important environmental predictors of β across both model architectures, while biovolume is additionally sensitive to nitrate and net primary production, as identified through a dual explainability analysis combining SHAP values and permutation importance. The reconstructed PSD fields are coupled to a Lagrangian remineralization framework that incorporates temperature and oxygen dependent particle mass loss to produce depth resolved POC flux estimates. Uncertainty from the SVGP posterior is propagated  through the nonlinear flux model via Monte Carlo sampling (N = 150 draws), yielding spatially explicit flux uncertainty maps that identify the Southern Ocean and deep mesopelagic as the regions of greatest reconstruction uncertainty. The diagnosed Martin curve attenuation exponent b has a global median of 0.748 with pronounced regional variability (5-95th percentile range 0.56-1.04), substantially exceeding the spread captured by the spatially constant value of 0.858 employed in most Earth System Models. This regional variability is consistent with observational literature across all major ocean basins when depth convention differences are accounted for. The observationally constrained, uncertainty-quantified PSD and flux fields presented here provide improved boundary conditions for next-generation ocean biogeochemical models seeking to better represent the spatial heterogeneity of the biological carbon pump