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

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 epsilon(P) = 2: 4, net radiation elasticity epsilon(Rn) = -0.8, air temperature elasticity epsilon(T) = -0.05 degrees C-1, wind speed elasticity epsilon(U) = -0.3, and relative humidity elasticity epsilon(RH) = 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: epsilon(P) ranging from 1.6 to 3.9, epsilon(Rn) ranging from -1.9 to -0.3, epsilon(T) ranging from -0.11 to -0.02 degrees C-1, epsilon(U) ranging from -0.8 to -0.1, and epsilon(RH) ranging from 0.2 to 1.9. Additional analysis shows that climate elasticity was sensitive to catchment characteristics.