Differential-Privacy Budgets for Artificial Intelligence Climate Analytics on Smallholder Survey Microdata: Utility Bounds and Statistical Disparity in Adaptation Targeting

Smallholder survey microdata underpin climate adaptation targeting, yet releasing them for artificial intelligence training risks re-identification of respondents. Differential privacy offers a formal release guarantee, but the budget allocated to a release determines both the utility of downstream analytics and the distribution of that utility across subgroups. The framework is derived from a sensitivity analysis of the empirical risk under bounded privacy mechanisms, combined with a group-wise decomposition of the excess-risk functional. The analysis yields a closed-form expression for the utility bound as a function of the budget, the number of queries, the Lipschitz constant of the loss, and the calibration of the underlying score. A second result shows that the disparity bound is not monotone in the budget: at very tight budgets, noise dominates and disparities shrink toward zero, while at intermediate budgets the disparity can exceed the non-private baseline because the larger group's signal survives noise more readily. The framework is illustrated with a reanalysis of public reanalysis temperature data for Accra, Ghana, which supplies the climate signal that adaptation targeting would consume; the data comprise 312 monthly observations from 2000 to 2023, with a mean of 26.521 C and a warming trend of 0.1622 C per decade. Privacy-budget selection is a distributive choice, not only a technical one, and that reporting a single budget without subgroup utility diagnostics conceals the disparity it creates.