Technical Note: The divide and measure nonconformity - how metrics can mislead when we evaluate on different data partitions

The evaluation of model performance is an essential part of hydrological modeling. However, leveraging the full information that performance criteria provide requires a deep understanding of their properties. This Technical Note focuses on a rather counterintuitive aspect of the perhaps most widely used hydrological metric, the Nash-Sutcliffe efficiency (NSE). Specifically, we demonstrate that the overall NSE of a dataset is not bounded by the NSEs of all its partitions. We term this phenomenon the "divide and measure nonconformity". It follows naturally from the definition of the NSE, yet because modelers often subdivide datasets in a non-random way, the resulting behavior can have unintended consequences in practice. In this note we therefore discuss the implications of the divide and measure nonconformity, examine its empirical and theoretical properties, and provide recommendations for modelers to avoid drawing misleading conclusions.