Differential-Privacy Budget Accounting for Federated Climate-Computer Downscaling Across National Meteorological Archives: Noise-Calibration Bounds and Forecast-Equity Trade-offs

Federated downscaling of climate fields across national meteorological archives is constrained by a tension that existing privacy literature has not formalised: the noise required to satisfy a differential-privacy budget is not neutral with respect to the spatial and temporal structure that downscaling models must learn, and the resulting distortion is distributed unevenly across the regions that contribute training data. The framework is illustrated with a reanalysis series for Accra, Ghana (NASA POWER MERRA-2, 2000–2023, 312 monthly observations, mean 26.521 °C, warming trend 0.1622 °C per decade), which supplies the empirical scale against which budget allocations are calibrated. Three results follow. First, the sensitivity of a downscaling loss to a single archive's contribution scales with the archive's effective sample size, so equal per-archive budgets systematically over-noise small archives. Second, forecast-equity, defined as the dispersion of downscaled error across contributing regions, is a monotone function of budget dispersion rather than of the total budget. Third, a calibration rule that allocates budget in proportion to each archive's marginal error contribution dominates uniform allocation on both privacy and equity criteria under stated assumptions. The contribution is a formal accounting scheme and a set of bounds, not an empirical evaluation; the Accra series is used to fix magnitudes, not to test the framework.