Abstract: The hydrological process within the upper catchment of the Red River Basin (URRB) significantly influenced by mountainous climates and human activities,leading to pronounced temporal and spatial heterogeneity.Over the past half-century,the patterns of runoff in this basin have progressively become more intricate,highlighting the growing prominence of transboundary water security risks.This study utilized monthly hydrological and meteorological data spanning 1961 to 2015 and employed Generalized Additive Models for Location,Scale,and Shape (GAMLSS) with time and climate factors as covariates.This methodology was employed to systematically analyze the non-stationary patterns in runoff series within this basin in China under various environmental influences and uncover their responses to climate change.Additionally,the Expected Number of Exceedances (ENE) method was used within a non-stationary framework to calculate the designed annual runoff,shedding light on the potential consequences of non-stationarity on water resource management.Key findings include:(1) runoff in URRB exhibits significant non-stationary characteristic,with the Yuanjiang River showing a tendency towards abrupt changes and a notable inflection point in 2002,while the Lixian River displays a pronounced decreasing trend after a change point in 1986;(2) the GAMLSS models with climate factors as covariates,conforming to gamma and log-normal distributions respectively,provide an optimal fit for the runoff series,effectively capturing the impact of climate change on the runoff of both the Yuanjiang River and Lixian River;(3) in comparison to conventional stationary models,the time-varying moment model offers a more scientifically robust method for calculating designed annual runoff in changing environments.Under selected emission scenarios,the designed annual runoff values for the Yuanjiang River and Lixian River,derived from the time-varying moment model,exhibit variations of -15.12% to 25.46% and -17.29% to 22.24%,respectively,compared to stationary models.The variations in the designed annual runoff values have substantial implications for water resource development and management.This research contributes a novel scientific basis for the rational utilization and coordinated management of transboundary water resources in the URRB.