Extending Data Worth Analyses to Select Multiple Observations Targeting Multiple Forecasts

Hydrological models are often set up to provide specific forecasts of interest. Owing to the inherent uncertainty in data used to derive model structure and used to constrain parameter variations, the model forecasts will be uncertain. Additional data collection is often performed to minimize this forecast uncertainty. Given our common financial restrictions, it is critical that we identify data with maximal information content with respect to forecast of interest. In practice, this often devolves to qualitative decisions based on expert opinion. However, there is no assurance that this will lead to optimal design, especially for complex hydrogeological problems. Specifically, these complexities include considerations of multiple forecasts, shared information among potential observations, information content of existing data, and the assumptions and simplifications underlying model construction. In the present study, we extend previous data worth analyses to include: simultaneous selection of multiple new measurements and consideration of multiple forecasts of interest. We show how the suggested approach can be used to optimize data collection. This can be used in a manner that suggests specific measurement sets or that produces probability maps indicating areas likely to be informative for specific forecasts. Moreover, we provide examples documenting that sequential measurement election approaches often lead to suboptimal designs and that estimates of data covariance should be included when selecting future measurement sets.