Climate models depend on dynamics across many spatial and temporal scales. It is infeasible to resolve all of these scales. Instead, the physics at the smallest scales is represented by parameterization schemes that link what is unresolvable to variables resolved on the grid scale. A large source of uncertainty in climate predictions comes from the calibration of empirical parameters in such parameterization schemes, and these uncertainties are generally not quantified. The uncertainties can be reduced and quantified with data that may have limited availability in space and time, for example, data from field campaigns or from targeted high-resolution simulations in limited areas. But the sensitivity of simulated climate statistics, such as precipitation rates, to parameterizations varies in space and time, raising the question of where and when to acquire additional data so as to optimize the information gain from the data. We construct an automated algorithm that finds optimal regions and time periods for such data acquisition, to maximize the information the data provides about uncertain parameters. We use a Bayesian framework to characterize the uncertainty and apply the new Calibrate-Emulate-Sample (CES) methodology to accelerate its calculation. The combined algorithm is parallelizable, and is efficient with respect to evaluations of the model. In proof-of-concept simulations with an idealized global atmosphere model, we show that our algorithm can successfully identify informative regions and times, even in cases where physics-based intuition may lead to sub-optimal choices.