Derivation of climate elasticity of runoff to assess the effects of climate change on annual runoff

Abstract

[1] Climate elasticity of runoff is an important indicator for evaluating the effects of climate change on runoff. Consequently, this paper proposes an analytical derivation of climate elasticity. Based on the mean annual water-energy balance equation, two dimensionless numbers (the elasticities of runoff to precipitation and potential evaporation) were derived. Combining the first-order differential of the Penman equation, the elasticities of runoff to precipitation, net radiation, air temperature, wind speed, and relative humidity were derived to separate the contributions of different climatic variables. The case study was carried out in the Futuo River catchment in the Hai River basin, as well as in 89 catchments of the Hai River and the Yellow River basins of China. Based on the mean annual of climatic variables, the climate elasticity in the Futuo River basin was estimated as follows: precipitation elasticity " P ¼ 2:4, net radiation elasticity " Rn ¼ À0:8, air temperature elasticity " T ¼ À0:05 C À1 , wind speed elasticity " U ¼ À0:3, and relative humidity elasticity " RH ¼ 0:8. In this catchment, precipitation decrease was mainly responsible for runoff decline, and wind speed decline had the second greatest effect on runoff. In the 89 catchments of the Hai River and the Yellow River basins of China, climate elasticity was estimated as follows: " P ranging from 1.6 to 3.9, " Rn ranging from À1.9 to À0.3, " T ranging from À0.11 to À0.02 C À1 , " U ranging from À0.8 to À0.1, and " RH ranging from 0.2 to 1.9. Additional analysis shows that climate elasticity was sensitive to catchment characteristics.

Quantifying the effects of climate change and human activities on runoff in the water source area of Beijing, China

“…The climate change effects include the impacts of precipitation, solar radiation, temperature, wind speed and vapour pressure. However, we do not yet know how many climatic variables need to be considered when assessing climate change effects on runoff, or which variables are dominant (Yang and Yang 2011). From the results obtained, the precipitation and temperature changes are the main two factors of climate change that caused decline in runoff, while the changes in solar radiation, wind speed and vapour pressure had a positive effect on the runoff change.…”

“…The available estimation methods can be classified into five categories: calibrating a conceptual watershed model, analytical derivation, fitting multivariate regional hydrological models, empirical estimation and use of multivariate statistical methods (Sankarasubramanian et al 2001). Among these methods, the analytical derivation method based on Budyko's hypothesis is clear in its theory and requires less input data (Yang and Yang 2011). The method has been widely used in previous studies and is useful for evaluating the impacts of climate change and human activities (Dooge et al 1999, Arora 2002, Zheng et al 2009, Li et al 2012.…”

“…Most previous studies separating the effects of climate change and human activities only evaluate the impact of precipitation and potential evapotranspiration changes or temperature on water. Other climate variables, such as solar radiation and wind speed, which are also generally important driving forces of change in potential evapotranspiration (Liu et al 2004, Yang and Yang 2011, have not been widely investigated. By analysing the impacts of climate variables on the water cycle, it should be possible to determine the dominant climate variables, which is useful for understanding the complex relationships between climate and runoff.…”

“…The climate elasticity method proposed by Schaake (1990) is an effective approach to investigate the impacts of climate variability on hydrological processes (Vogel et al 1999, Sankarasubramanian et al 2001, Chiew 2006, Fu et al 2007, Yang and Yang 2011. It is also a useful method for quantifying and separating the relative contributions of climate change and human activities on runoff changes (Zhang et al 2011a, Li et al 2012, Wang et al 2012.…”

The response of agricultural drought to meteorological drought and the influencing factors: A case study in the Wei River Basin, China

“…The Budyko hypothesis is an effective tool for investigating the interaction between climate, hydrological cycle, and vegetation (Roderick and Farquhar, 2011;Yang and Yang, 2011). According to Fu (1981), the relationship between the long-term average annual ET, PET, and P can be expressed as follows:…”