Separating runoff change by the improved Budyko complementary relationship considering effects of both climate change and human activities on basin characteristics

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.