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• 1. The lag degree of hydrological drought is studied by changing the time scale. • 2. Multi-scale standardized indicators can explore the strongest correlation. • 3. According to the synchronization, relevance, correlation to calculate the results. • 4.The scale time with the strongest correlation is the propagation time. To study the propagation law of meteorological droughts to hydrological droughts under variable time scales, and to reveal the synchronisation gap and lag time of hydrological droughts compared to meteorological droughts, and the lag degree of hydrological drought is quantitatively studied. In this paper, the Yellow River Water Supply Area in Henan is taken as the research area, and the propagation time of meteorological drought to hydrological drought under variable time scale is mainly studied. The calculation of drought propagation time is set as two states: interval scale and continuous scale. The Standardized Precipitation Index (SPI) sequence and Standardized Runoff Index (SRI) sequence (1)with interval and continuous scales were obtained by multi-scale standardization of precipitation and runoff, which were used to characterize meteorological drought and hydrological drought respectively. The Mann-Kendall (M−K) test method was used to analyze the evolution of SPI sequence and SRI sequence at monthly scale, and to study the lag time of hydrological drought in four seasons compared with meteorological drought. Combining the Grey Correlation Method and Pearson correlation coefficient methods, the time interval for the propagation of meteorological droughts to hydrological droughts was determined based on the strongest correlation of different combinations of sequences. Finally, the propagation time series is divided into sliding windows to analyse the M−K dynamic trend of propagation time from a seasonal scale perspective. It provides a strong basis for the study of drought propagation based on multi-scale. [ABSTRACT FROM AUTHOR]

• Drought loss models of wheat are built using two different statistical models. • The important SPEI variables recognized by two methods are different. • The random forest-derived model outperforms the stepwise regression model. Agricultural drought loss models provide services for the rapid risk assessment of agricultural disasters, and regional disaster prevention and mitigation efforts. This paper takes wheat as an example, and chooses counties dominated by rain-fed farmland in Henan Province as the study area. Counties dominated by rain-fed farmland are determined by setting a rain-fed threshold that is related to the proportion of the effective irrigation area to the cultivated land area. Modeling samples are screened by considering both drought occurrence time and wheat yield reductions. Under different thresholds (30%, 40%, 50% and 60%), we use the yield loss ratio as the dependent variable and 24 standardized precipitation evapotranspiration index parameters as independent variables to build drought loss models using both a multivariate stepwise regression model and a random forest model. Yield loss ratio from 1990 to 2015 is calculated by decomposing historical wheat yield time series. 24 standardized precipitation evapotranspiration index variables are 1–3 months' time scale standardized precipitation evapotranspiration index during the growth period (from October to May of the following year) of winter wheat in Henan Province. The results show that the random forest-derived model outperforms the stepwise regression model in all tests. The accuracy of all the models increases with an increase of the proportion of the rain-fed threshold. When the rain-fed threshold is 60%, the R2 values of the random forest model and the multivariate stepwise regression equation are 0.720 and 0.523, respectively. The validation results show that the mean absolute error and the root mean square error of the multivariate stepwise regression are 1.38 times and 1.31 times larger than the mean absolute error and the root mean square error from the random forests model. Moreover, both models identify that standardized precipitation evapotranspiration indices in October (sowing/planting stage) and February (overwintering stage) are important variables. However, the multivariate stepwise regression model fails to recognize the importance of standardized precipitation evapotranspiration indices during April–May (filling stage). [ABSTRACT FROM AUTHOR]