Runoff prediction is a crucial aspect of water resource management and risk mitigation. Despite hydrological modelling plays a vital role in accurately representing catchment behaviour, calibration still poses a significant challenge. This study explores the use of knowable moments (KMoments), a category of high -order statistical moments, as part of the core of objective functions in hydrological model calibration. Traditional objective functions, such as Nash -Sutcliffe Efficiency (NSE) and Kling -Gupta Efficiency (KGE), often make assumptions about data distribution and are sensitive to outliers. KMoments offer a promising alternative by enabling reliable estimation and effective description of high -order statistics from typical hydrological samples and therefore, reducing uncertainty in their estimation and computation of the objective functions in question. Three daily lumped hydrological models (GR4J, VIC, and HYMOD) were employed to test the performance of different calibration strategies using KMoments-based objective functions and compare them with conventional approaches. The hydrological consistency of the simulations was also assessed through 27 hydrological signatures. Our findings highlight the advantages of using KMoments, including improved performance metrics and enhanced hydrological signature reproduction. The findings contribute to advancing hydrological modelling techniques and provide valuable insights for researchers and practitioners seeking to enhance simulation accuracy and reliability.