Evaluation Of Different Improved Budyko-Type Equations Under Non-Steady State In The Yellow River Basin

Water cycle is an important natural and physical process on earth.Water balance equation reveals the basic law of water cycle evolution.Quantifying each component of water balance is helpful to understand water resource allocation in water cycle.The Budyko framework,which takes both water and energy balances into account,is a widely proven and effective tool for assessing water balance components.When the Budyko framework is applied on a short time scale,the assumptions of Budyko framework are no longer valid because the changes of terrestrial water storage cannot be ignored.Several studies have proposed different measures to expand the application of Budyko framework.Improvements give rise to equations with various forms,which makes researchers confused to choose the optimal equation for their own research area.Taking the Yellow River Basin as the research area,this study first verified the unstable state of the Yellow River Basin on the short time scale,and analyzed the changes of terrestrial water reserves in the Yellow River Basin.On this basis,six parametric equations under the original Budyko framework,two transformation relationship equations and four improved equations under the extended framework were selected to calculate the efficiency coefficients of evaporation estimation on 35 river basins for further comparison.The applicability of Budyko framework in the Yellow River Basin was comprehensively evaluated on different time scales of multi-years,years and months.The effect of equation form and seasonal classification method on the applicability is analyzed.The main contents and conclusions of this paper are as follows.1.The reliability of an interpolated,extended and reconstructed terrestrial water reserve data set(LT-TWSA)has been verified.In this study,two satellite data post-processing products(GFZ-TWS and COSTG-TWS)were selected.By calculating the Spearman rank correlation coefficient of LT-TWSA data series,GFZ-TWS and COSTG-TWS data series at the same period,the correlation degree between data sets was analyzed.The correlation coefficients between LT-TWSA,GFZ-TWS and COSTG-TWS are all close to 0.9,which proves the reliability of LT-TWSA in the Yellow River Basin.2.The variation of terrestrial water reserves in the Yellow River Basin has been analyzed from the perspective of space and time.The series of terrestrial water reserves in the Yellow River Basin was divided into two parts(before and after the 21 st century).The standard deviations of 460 grids of terrestrial water reserves in the basin were calculated,and the dynamic changes of terrestrial water reserves in the Yellow River Basin were compared and analyzed from the perspective of space and time.There is a general dynamic change of terrestrial water reserves in the Yellow River Basin before and after the 21 st century,and the dynamic change is the most obvious in the downstream regions.After the 21 st century,the dynamic change was weakened,especially in the downstream region.The Yellow River Basin was divided into upstream,midstream and downstream regions.The classical Mann-Kendall test and seasonal Mann-Kendall test were used to evaluate the variation trend of terrestrial water reserves in different regions of the Yellow River Basin after the 21 st century,and the Theil-Sen slope of terrestrial water reserve series was calculated.The terrestrial water reserves of the whole Yellow River Basin show a decreasing trend after the 21 st century,and the decreasing trend is more obvious after excluding the influence of seasonal factors.The decrease rate is the highest in the downstream regions,followed by the midstream regions and the whole basin.The decline in terrestrial water reserves is most gradual in the upstream regions.3.The drought characteristics of the sub-basins in the Yellow River Basin have been identified.Thirty-five sub-basins of the Yellow River Basin were selected as research area,and the characteristic drought index of each sub-basin was calculated.According to the generalized climate classification scheme provided by the United Nations Environment Program(UNEP),drought characteristics of each basin were divided.Among the 35 basins,28 belong to arid area and only 7belong to humid area which are all concentrated in the Guanzhong plain.4.The applicability of the Budyko framework on different time scales in the Yellow River Basin has been evaluated.In this study,GLDAS2.2 data set was used to fit equations under the Budyko framework on different time scales on 35 subbasins,and the efficiency coefficient between basin evaporation and fitting results was calculated to evaluate the applicability of the Budyko framework in the Yellow River Basin.This study verifies that the Budyko framework can well describe the long-term water and energy balance relationship in the Yellow River Basin.On a short-term scale,taking the change of terrestrial water reserves into consideration is a necessary way to extend the Budyko framework in the arid region.In this study,parametric equations,transformation equations,and seasonal classification methods were evaluated on different time scales,so as to provide reference for the subsequent application of Budyko framework in the Yellow River Basin.This study is helpful for the subsequent study which aims to evaluate the applicability of Budyko framework in other regions.