A line-integral-based method to partition climate and catchment effects on runoff.

It is a common task to partition the synergistic impacts of drivers in the environmental sciences. However, there is no mathematically precise solution to this partition task. Here I present a line-integral-based method, which addresses the sensitivity to the drivers throughout the drivers' evolutionary paths so as to ensure a precise partition. The method reveals that the partition depends on both the change magnitude and pathway (timing of the change) but not on the magnitude alone unless used for a linear system. To illustrate this method, I applied the Budyko framework to partition the effects of climatic and catchment conditions on the temporal change in the runoff for 19 catchments from Australia and China. The proposed method reduces to the decomposition method when assuming a path in which climate change occurs first, followed by an abrupt change in catchment properties. The proposed method re-defines the widely used sensitivity at a point as the path-averaged sensitivity. The total-differential and the complementary methods simply concern the sensitivity at the initial and/or the terminal state, so they cannot give precise results. Although the path-averaged sensitivities varied greatly among the catchments, they can be readily predicted within the Budyko framework. As a mathematically accurate solution, the proposed method provides a generic tool for conducting quantitative attribution analyses. [ABSTRACT FROM AUTHOR]