We investigated the potential impact of observation error on the calibration performance of an integrated watershed model. A three-dimensional integrated model was constructed using HydroGeoSphere and applied to the Sabgyo watershed in South Korea to assess the groundwater–surface water interaction process. During the model calibration, three different weighting schemes that consider observation error variances were applied to the parameter estimation tool (PEST). The applied weighting schemes were compared with the results from stochastic models, in which observation errors from surface discharges were considered a random variable. Based on the calibrated model, the interactions between groundwater and surface water were predicted under different climate change scenarios (RCP). Comparisons of calibration performance between the different models showed that the observation-error-based weighting schemes contributed to an improvement in the model parameterization. Analysis of the exchange flux between groundwater and surface water highlighted the significance of groundwater in delaying the hydrological response of integrated water systems. Predictions based on different RCP scenarios suggested the increasing role of groundwater in watershed dynamics. We concluded that the comparison of different weighting schemes for the determination of error covariance could contribute to an improved characterization of watershed processes and reduce the model uncertainty arising from observation errors.