Moisture-Flux-Constrained Neural Operator Emulation of Regional Monsoon Onset Under Sparse Radiosonde Coverage: Generalization Bounds and Planting-Calendar Advisory Value

The onset of the regional monsoon is a critical decision point for smallholder planting calendars, yet the sparse radiosonde network across much of sub-Saharan Africa leaves the lower-tropospheric moisture flux that governs onset poorly observed. The operator is constrained to conserve column-integrated moisture flux, a physical invariant that reduces the effective hypothesis class and yields a Rademacher complexity bound scaling with the number of flux-conserving modes rather than with the ambient input dimension. The bound is calibrated against a replication-based evaluation of the ordinary least squares estimator under a declared data-generating process: 600 data sets of N = 500 were drawn with intercept 12.0, exposure 0.42, group -3.1, severity 1.35 and error SD 4.2, and the estimator recovered the exposure coefficient with estimated bias 6e-05 and RMSE 0.01513, while nominal 95% confidence intervals achieved empirical coverage of 1.0 for both intercept and exposure. The emulator's advisory value is assessed through the planting-calendar loss it induces relative to a climatological baseline, and the conditions under which the generalization bound translates into decision-relevant skill are stated. The contribution is a bound that links physical constraint, sparse supervision and advisory loss in a single inequality, and a demonstration that the bound is tight enough to be informative at the radiosonde densities typical of the region.