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The stationarity of observed hydrological series has been broken or destroyed in many areas worldwide due to changing environments, causing hydrologic designs under stationarity assumption to be questioned and placing designed projects under threat. This paper proposed a data expansion approach-namely, the cross-reconstruction (CR) method-for frequency analysis for a step-changed runoff series combined with the empirical mode decomposition (EMD) method. The purpose is to expand the small data on each step to meet the requirements of data capacity for frequency analysis and to provide more reliable statistics within a stepped runoff series. Taking runoff records at three gauges in western China as examples, the results showed that the cross-reconstruction method has the advantage of data expansion of the small sample runoff data, and the expanded runoff data at steps can meet the data capacity requirements for frequency analysis. In addition, the comparison of the expanded and measured data at steps indicated that the expanded data can demonstrate the statistics closer to the potential data population, rather than just reflecting the measured data. Therefore, it is considered that the CR method ought to be available in frequency analysis for step-changed records, can be used as a tool to construct the hydrological probability distribution under different levels of changing environments (at different steps) through data expansion, and can further assist policy-making in water resources management in the future.

A Cross-Reconstruction Method for Step-Changed Runoff Series to Implement Frequency Analysis under Changing Environment