Most hydrological models require a calibration process, performed usually using objective functions that measure the differences between observed and simulated data. Objective functions are typically based on statistical metrics, such as the mean squared error (MSE), which penalizes extreme values in statistics, or mean absolute error (MAE), which assigns equal weight to each measure. Although the MSE is effective in capturing model prediction bias or variability, the calibration results with MSE-based objective functions tend to focus on high flow events at the expense of low flow errors. As different objective functions may emphasize different model response aspects, an appropriate objective function is critical to successful model calibration for model application suitability to a given task. The primary aim of this study is not to directly compare the MSE and MAE to determine which is more relevant to model performance. Instead, as an extended formulation for the Kling–Gupta efficiency (KGE), the new objective functions were designed to incorporate performance metrics based on both the MSE and MAE to evaluate model performance more comprehensively across different flow regimes. The case study has investigated the influence of the proposed objective functions on long-term daily streamflow simulations from a land surface model (LSM) over four study watersheds in the Republic of Korea. The proposed objective functions can help simulate streamflow for the specific purpose of model applications through trade-offs between the MSE- and MAE-based variability metrics in the constituent components. The proposed calibration method allows for a more balanced consideration of various flow regime aspects, compared with the results obtained using traditional objective functions.