The Heilongjiang River is a transboundary river between China and Russia, which often experiences ice dams that can trigger spring floods and significant damages in the region. Owing to insufficient data, no river ice model is applicable for the Heilongjiang River. Therefore, a river ice thickness model based on continuous meteorological data and river ice data at the Mohe Station located in the upper reach of the Heilongjiang River was proposed. Specifically, the proposed model was based on physical river ice processes and the Russian empirical theory. System dynamic models were applied to assess the proposed model. The performance of the river ice model was evaluated using root-mean-square error (RMSE), coefficient of determination (R2), and Nash–Sutcliffe efficiency (NSE). Subsequently, sensitivity analyses of the model parameters through Latin hypercube sampling and uncertainty analyses of input variables were conducted. Results show that the formation of ice starts 10 days after the air temperature reaches below 0 °C. The maximum ice thickness occurs 10 days after the atmospheric temperature reaches the minimum. Ice starts to melt after the highest temperature is greater than 0 °C. The R2 of ice thickness in the middle of river (ITMR) and ice thickness at the riverside (ITRS) are 0.67 and 0.69, respectively; the RMSEs of ITMR and ITRS are 6.50 and 6.84, respectively; and the NSEs of ITMR and ITRS are 0.72 and 0.70, respectively. Sensitivity analyses show that ice growth and ice melt are sensitive to the air temperature characterizing the thermal state. Uncertainty analyses show temperature has the greatest effect on river ice.


  • This study is the first to consider and confirm the lag days between river ice and temperature.

  • This study builds a river ice model including growth and melt upstream of the Heilongjiang River.

  • This study is the first to apply system dynamic models to a river ice model.

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