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The seepage of the dam is an important representation of the operation characteristics of the dam, and there are many factors affecting the seepage with a certain lag. It is still difficult to predict its change and sensitivity because of complex operating conditions. At present, the lag-sensitivity of influence factors of the dam seepage has not been studied. The time series influence factors of seepage are determined by HTRT (hydrostatic-thermal-rainfall-time) model in this paper. To avoid the pseudo fitting of conventional methods, HTRT model nested random forest algorithm is used to establish the predicting model of the dam seepage. And MIC algorithm is used to achieve the dual purposes of time lag and sensitivity analysis. Firstly, the time lag of relationship between seepage and its influencing factors is characterized, and the most appropriate lag time of the HTRT model factors is determined. Secondly, independent correlation analysis on all influencing factors is carried out and the sensitivity of each factor is analyzed by MIC. Meanwhile, the sensitivity of the factors to seepage is quantitatively analyzed by the two parameters of %IncMSE and IncNodePurity of RF algorithm. The sensitivity of influencing factors is analyzed by comparing MIC results with RF results. Combined with the case, taking the error of fitting prediction as the evaluation index of seepage prediction, the prediction accuracy of MIC-RF model, RF model and MIC-BPNN (Back Propagation neural network) model is calculated and compared. Case study showed that MIC- RF monitoring model has high prediction accuracy, strong adaptability and high robustness in dam seepage, and the sensitivity and time lag of influencing factors can be quantitatively analyzed. The water pressure and rainfall of the lag time are 14 days and 16 days respectively. The sensitivity study of the time series influencing factors of seepage showed that the water pressure component is the main controlling factor of seepage, and rainfall component is more sensitive to later stage. The MIC-RF model can be used as a new dam seepage safety monitoring model.