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Summary The Budyko-type equations have begun to be widely adopted to separate the contributions of climate change and human activities to the variation of runoff over long-term periods by using the multi-year averages of hydrological variables. In this study, a two-step framework based on four single-parameter Budyko-type equations is proposed to separate the impacts of climate change and human activities on runoff. First, the relationship of the parameter w in each Budyko-type equation with climatic and human factors is built to reveal the time-variation process of w by using an 11-year moving window. Second, the impacts of climate change and human activities on runoff are separated by using both the decomposition method and the sensitivity method. This separating framework is applied to analyze the variation of the runoff during 1960–2009 in the Weihe River. It is found that the parameter w in each Budyko-type equation is significantly related to both factors of climate and human activities. The results from both the decomposition method and the sensitivity method show that climate change is the main driving factor to the decline in runoff of the Weihe River, while human activities are another important factor. In general, climate change affects runoff not only by changing the hydrological inputs (precipitation and potential evaporation) but also by altering the watershed characteristics as represented by the parameter w ; while the impacts of human activities on runoff are exerted mainly through the alteration of the watershed characteristics. [ABSTRACT FROM AUTHOR]

• An improved Budyko complementary relationship (IBCR) is developed. • The IBCR incorporates effects of both climate change and human activities on basin characteristics. • The IBCR is more flexible than the original relation in separating runoff change. Numerous efforts have been made to separate effects of climate change and human activities on long-term runoff change, including a commonly used method based on the Budyko complementary relationship (BCR) to deal with the non-closure problems often encountered in separating the observed runoff change into its contributed components. The BCR was derived by assuming the change of the Budyko parameter reflecting basin characteristics is related to human activities alone. However, some studies show that basin characteristics are related to both climate change and human activities in certain basins, where applying the BCR method could lead to wrong results. In the study, a more flexible form of the BCR, the improved Budyko complementary relationship (IBCR), is developed under the situation that basin characteristics may relate to climate change. A separation method based on the IBCR is also developed. In this IBCR method, the relationship of the basin characteristics parameter to climate and/or human factors is estimated by using a multi-year moving window. To identify the flexibility of the IBCR method relative to the BCR method, both methods were applied to the Weihe basin of China, whose basin characteristics have been found to be affected by both climate change and human activities. Compared with the IBCR method, the BCR method overestimates the climate effect, while underestimates the human effect on the runoff change in the Weihe basin. It is found that whether or not to incorporate the climate effect into the basin characteristics parameter has a significant impact on the runoff change separation results in Weihe basin. Overall, the IBCR method is more reasonable and flexible for separating the long-term runoff change into different components. [ABSTRACT FROM AUTHOR]