Use Cross-validation and Markov Chain to Assess the Reliability of Annual Runoff Classification for Wet and Dry Years Calculated by Different Methods

Abstract

【Objective】 Various methods have been proposed to classify changes in runoff in catchments, but how to assess their reliability remains a challenge. In this paper, we present a method to assess the reliability of the annual runoff classification for wet and dry years calculated by different methods. Its effectiveness was tested against data measured from a watershed. 【Method】 The reliability of the methods for classifying annual runoff for wet and dry years is analyzed based on their stability and predictability. The assessment is based on the cross-validation method and Markov chain method. We evaluate the stability and predictability of the classified results obtained by the mean-standard deviation method (MSD), gray relational analysis (GRA), and set-pair analysis (SPA). The difference in the classification and the transfer probability of the indices is established to evaluate the stability and predictability of the classified results. The proposed model is tested against annual runoff measured from 1956—2021 at the Tangnaihai Hydrological Station in the upper reaches of the Yellow River basin. 【Result】 ①Analysis using the cross-validation method and Markov chain showed that the results calculated by different classification methods vary, indicating that the stability and predictability of different methods are different. ②The classification difference index indicates that the GRA method is most stable and the MSD method is least stable. The transfer probability differences indicates that the GRA method has the best predictability and the MSD has the worst. ③Considering stability and predictability, the GRA method is most reliable for classifying annual runoff abundance and depletion, and the MSD method is the least. 【Conclusion】 The reliability of different methods for classifying annual runoff for wet and dry years varies for the same watershed. The method we developed from the cross-validation method and Markov chain can effectively assess the reliability of the results calculated by different classification methods.

Keywords

• reliability of wet-dry classification
• cross validation
• markov chain
• gray relational analysis
• set pair analysis