The consistency of runoff sequences is often broken due to meteorological changes and human activities

and a direct study of non-consistent hydrological sequences becomes necessary. This paper presents a new method for estimating the design annual runoff and peak flood flow of non-stationary series for the Jialu River basin in the loess plateau based on Generalized Additive Model for Location

Scale and Shape (GAMLSS)

using the average design life level method (ADLL) and equivalent reliability method (ER)

and selecting air temperature

precipitation and the controlling river basin area of the reservoir and dam as covariates in simulation analysis. The results show that the two hydrological sequences are non-consistent

the developed multi-covariate annual runoff model gives good fitting to the low and high quantile curves

and the flood peak model has achieved satisfactory simulation results. Application of GAMLSS and the corresponding ADLL and ER methods provides higher accuracy of design peak flood and design annual runoff in a specific return period or probability interval

and thus the method better estimates the influence of the hydrological sequence trend on the design values.