基于 Budyko 框架及径流变化情势指标同气象因子的拟合关系，拓展 Budyko 方程并得到微分方程。选择汉 江上游安康和白河水文站的年均径流、汛期平均径流和非汛期平均径流资料系列，开展径流情势变化及归因研究。 结果表明：所有径流指标均发生变异且明显减小；多元对数线性回归模型拟合的相关系数大于 0.90，能够较好预 估径流变化情势指标，并捕捉到径流变化情势指标同气象参数之间的非线性关系；基于 Budyko 假设的互补关系 法性能优于全微分法，气候（流域下垫面）变化对安康站年均径流量、汛期平均径流量和非汛期平均径流量贡献的 绝对值分别为 35.89%?(64.11%)、34.58%?(65.42%) 和 71.12%(28.88%)，对白河站年均径流量、汛期平均径流量和非 汛期平均径流量贡献的绝对值分别为 34.82%(65.18%)、26.29?%(73.71%) 和 35.11%(64.89%)。

Under?the?combined?effect?of?global?warming?and?human?activities,?the?terrestrial?energy?budget?and?the hydrological ?cycle ?have ?undergone ?great ?changes. ?These ?changes ?have ?aggravated ?the ?uneven ?spatiotemporal distribution?of?water?resources,?resulting?in?significant?alteration?in?flow?regimes.?The?analysis?of?runoff?evolution and?their?attribution?under?changing?environment?has?become?a?hot?topic.?The?upper?Han?River?basin?is?the?water source ?of ?the ?Middle ?Route ?of ?South-North ?Water ?Transfers ?Project ?and ?the ?pilot ?basin ?of ?the ?strictest ?water resources?management?system?in?China.?The?attribution?study?of?runoff?evolution?in?the?upper?Han?River?basin?can help?strengthen?water?resources?protection?and?integrated?management. ??????The?Mann-Kendall?test?was?used?to?detect?the?abrupt?change?points?of?three?runoff?signatures,?i.e.,?annual?mean runoff,?mean?stream?flows?in?the?wet?and?dry?seasons,?at?the?Ankang?and?Baihe?hydrological?stations?based?on?the hydrometeorological?data?including?temperature,?precipitation?and?runoff?from?1961?to?2020.?The?multiple?log- transformed ?linear ?regression ?models ?(MLLR) ?were ?built ?for ?investigating ?the ?relationships ?between ?runoff signatures, ?annual ?runoff ?and ?climate ?metrics ?and ?the ?differential ?equation ?was ?derived. ?Then ?an ?integrated framework?involving?extended?Budyko?equation?was?developed?and?differential?equation?was?derived?to?distinguish the?individual?impact?of?climate?change?and?catchment?change?on?multiple?runoff?signatures?for?interpreting?their evolution.?Meanwhile,?the?proposed?methodology?is?validated?with?the?observed?and?simulated?values?based?on hydrological?models. ??????The?abrupt?year?of?the?mean?runoff?in?dry?seasons?at?Ankang?station?was?1972,?and?the?breakpoints?of?both?mean annual?runoff,?mean?runoff?in?wet?seasons?occurred?in?1990.?The?results?of?Baihe?station?detected?by?change-point detection?technique?was?consistent?with?that?of?Ankang?station.?To?maintain?the?consistency?of?the?pre-?and?post- periods?of?each?station,?the?abrupt?years?are?obtained?by?averaging?the?abrupt?years?of?the?individual?signature?series. Therefore,?the?average?abrupt?year?of?both?stations?was?1984.?After?the?variation,?the?mean?annual?runoff?at?each station ?decreased ?significantly ?by ?23.39%?and ?23.18%?respectively. ?The ?precipitation ?decreased ?by ?7.07%?and 6.17%?respectively.?There?was?a?slight?decrease?in?potential?evapotranspiration.?The?mean?runoff?in?wet?and?dry seasons?decreased?26.43%?and?26.04%?respectively. ??????The?multi-correlation?coefficients?of?runoff?signatures?in?wet?and?dry?seasons?were?0.99?and?0.93?at?Ankang station?and?0.99?and?0.92?at?Baihe?station?respectively,?and?the?average?multi-correlation?coefficients?were?0.96?for both?stations.?The?relative?bias?of?all?runoff?signatures?was?within?±1%,?indicating?that?the?nonlinear?relationships between?runoff?signatures?and?climate?parameters?were?well?captured?by?the?MLLR?model?and?it?demonstrated robust?performance?in?estimating?the?runoff?signatures.?Both?forward?and?backward?approximations,?the?generally used ?total ?differential ?methods ?within ?Budyko's ?theory, ?usually ?lead ?to ?some ?unaccounted ?difference ?in ?the estimation?of?the?change?in?the?mean?runoff,?while?the?complementary?relationship?method?can?accurately?partition the?effects?of?climate?change?and?catchment?changes?on?runoff?signatures.?The?contribution?to?runoff?signatures?from climate?change?at?Ankang?station?ranged?from??71.12%?to??34.58%,?and?that?of?Baihe?station?ranged?from??35.11% to??26.29%.?The?average?absolute?values?of?the?contribution?to?runoff?signatures?from?climate?change?were?35.36%, 30.43%?and?53.11%?for?each?station?respectively.?The?Kling-Gupta?efficiency?equals?0.86?and?0.94?in?the?ABCD model?calibration?and?validation?periods?respectively,?which?shows?that?it?can?simulate?monthly?runoff?in?the?upper Han?River?basin?well.?The?observed?and?simulated?values?based?on?ABCD?model?for?partitioning?the?contributions of?climate?change?and?catchment?change?are?close?to?that?derived?by?the?extended?Budyko?method.