Abstract: Existing studies on the channel storage increment during freeze-up periods in cold-region rivers have rarely addressed its differentiation under non-overbank and overbank conditions. Based on the self-regulation and delayed-response theory of river systems, and employing the Muskingum method while considering the phase transitions (liquid to ice) of channel storage, a delayed-response model for the channel storage increment (including liquid water and ice volume) during the freeze-up period is developed in this study. By statistically analyzing the different influencing factors and variation patterns of model parameters under non-overbank and overbank conditions, the differentiation mechanism of the channel storage increment is revealed. Taking the Inner Mongolia reach of the Yellow River as a case study, through the model parameters calibration, the variation process of the channel storage increment during the freeze-up period is simulated. The simulation results are found to be in good agreement with the measured data, with the coefficient of determination and the Nash-Sutcliffe efficiency coefficient reaching 0.99 and 0.96, respectively. The analysis of model parameter variations reveals a significant positive correlation between the liquid water storage coefficient and the ratio of initial channel storage to bank-full discharge, reflecting the effect of increased flow resistance under overbank conditions. Under non-overbank conditions, the comprehensive ice volume coefficient exhibits a negative correlation with the liquid water storage coefficient, reflecting the effects of reduced main channel velocity and decreased frazil ice accumulation thickness. Under overbank conditions, the comprehensive ice volume coefficient can be decomposed into a river ice area growth coefficient and an ice thickness growth coefficient. The former shows a positive correlation with the ratio of average discharge during freeze-up to bank-full discharge, indicating the effect of the increased overbank extent, while the latter is positively correlated with bank-full discharge, reflecting enhanced main flow velocity and increased frazil ice accumulation thickness. In the Inner Mongolia reach of the Yellow River, channel shrinkage and reduced bank-full discharge increase the likelihood of overbank flow during the freeze-up period. An increase in the liquid water storage coefficient contributes to greater liquid channel storage, while an expansion of the river ice area promotes an increase in ice volume. In contrast, a decrease in the ice thickness growth coefficient tends to reduce ice volume. The differing variation patterns and combined effects of these three factors result in complex changes to the channel storage increment.