Active-learning acquisition for sparse hydroclimatic sensor placement: a climate-analytics evaluation of reconstruction-error and monitoring-equity trade-offs across national networks

Sparse hydroclimatic sensor networks face a design conflict that standard active-learning formulations do not represent: the acquisition rule that minimises reconstruction error over a target field is not the rule that distributes monitoring benefit equitably across the administrative units a national network is meant to serve. The framework is used to characterise the conditions under which the two objectives diverge, to derive a bound on the equity cost of pure error-minimising acquisition, and to specify a constrained acquisition rule that trades reconstruction accuracy against a max-min coverage criterion. The analysis is methodological and comparative rather than empirical: no sensor network is deployed and no reconstruction experiment is executed. The contribution is a formal statement of the trade-off, a set of propositions identifying when it is severe, and a design protocol that makes the trade-off explicit at the acquisition stage rather than after the network is built. The framework is illustrated with reference to the temperature record at Accra, Ghana (2000–2023), which provides a concrete setting for the reconstruction and equity quantities the framework defines.