Metrics that matter: objective functions and their impact on signature representation in conceptual hydrological models

Abstract. Although objective functions (OFs) are widely discussed in the literature, many modelling studies still default to a few common metrics, without much consideration of their relative strengths and weaknesses. This paper systematically investigates the impact of OF choice on the representation of various streamflow characteristics across 47 conceptual models and 10 hydro-climatically diverse catchments selected from the CARAVAN dataset. We use eight different OFs for calibration, including the Kling–Gupta efficiency (KGE), Nash–Sutcliffe efficiency (NSE), and their respective logarithmic variants, as well as four more recently proposed metrics. We evaluate the representation of 15 hydrological signatures that capture a relevant selection of streamflow characteristics to determine generalizable strengths and weaknesses of individual OFs across different models and catchments. Results show that the choice of OF can significantly affect a model's capability to simulate different hydrological signatures such as runoff ratios, extreme flow percentiles, and certain baseflow characteristics. While certain signatures, particularly those related to flow variability, are relatively insensitive to OF choice, others exhibit large performance shifts across different OFs. Generally, no single OF simultaneously achieved high performance across all tested signatures, highlighting that a single-objective calibration is unlikely to lead to an all-purpose model. Our results reinforce calls to choose objective functions deliberately and in line with the objectives of a study. They also provide initial guidance on which metrics highlight particular facets of streamflow behaviour.