Regional variation in climate elasticity and climate contribution to runoff across China:
according to the Budyko hypothesis
Hanbo YANG* and Dawen Yang
State key Laboratory of Hydro-Science and Engineering & Department of Hydraulic Engineering, Tsinghua University, Beijing, China
*E-mail: yanghanbo@tsinghua.edu.cn
1. Introduction
Climate change has an increasing impact on water resources.
One basic question is how much runoff change occurs due to a 10%
change precipitation. The climate elasticity was proposed to answer
this question.
Based on the Mezentsev-Choudhury-Yang equation (with n
representing catchments characteristics):
E0 P
E
n
n 1/ n
 P  E0 
207 catchments were chose for this study, except 3 inland river
catchments of the 210 catchments. Based on mean annual precipitation,
potential evaporation and runoff, we calibrated n and then calculated ε1
and ε2. The change trends in P and E0 were detected as the linear slope
of annual series from 1961 to 2010. Potential evaporation was estimated
according to Penman equation. In addition, two small catchments were
chosen for method validation.
and water balance equation R = P ─ E, Yang et al. [2011] derived
climate elasticity of runoff to precipitation and potential
evaporation as
dE0
dR
dP
 1 
 2 
R
P
E0
1  f

1 
P  P
PE
4. Climate elasticity and climate contribution
The precipitation elasticity
has a large regional variation.
The largest values appear in the
Hai River basin, the Liao River
basin, the Huai River basin, and
the Yellow River basin.
Fig.4 Precipitation elasticity to runoff of the 207 catchments
3. The parameter n
f E0  E0
2  
PE
where R, P, E0 are runoff, precipitation, and potential
evaporation; f represents the function R=f(P, E0, n); and ε1 and ε2
are the climate elasticity of runoff to precipitation and potential
evaporation.
Both the climate and catchment characteristics have large
spatial variations in China, which will lead to a spatial variation
in climate elasticity. Therefore, we divide China into 210
catchments, calibrate n for each catchment, and estimate the
climate elasticity to further understand its spatial variation and
reveal the impacts of climate change on hydrology.
The parameter has a large
regional variation. It has a
significant correlation with
catchment slope and a relative
weaker correlation with
vegetation. The vegetation
coverage was estimated as
Fig.5 Contribution of (A ) precipitation and (B) potential evaporation to runoff during 1961-2010
The largest positive
contributions of climate change
to runoff occur in the Northwest,
ranging from 1.1–3.1%/a, while
largest negative contributions
occur in the middle reach of the
Yellow River basin, ranging
from −1.3%/a to −1.0%/a.
M   NDVI  NDVImin   NDVImax  NDVImin 
Fig.2 The parameter n of the 207 catchments
2. Data and Method
Fig.1 210 catchments across China and two catchments
for validating the climate elasticity method
Climatic variables were
collected from 735
meteorological stations
across China during 19612010. Potential evaporation
was estimated according to
Penman equation. The
catchment slope (S) was
estimated according to
DEM, and the vegetation
coverage (M) was estimated
from NDVI.
Fig.5 Climate contribution to runoff during 1961-20100
Fig.3 Relationship of the parameter n with (A) catchment slope (S) and (B) vegetation
coverage (M) in the 207 catchments
Reference
Yang, H. B., and D. W. Yang (2011), Derivation of climate elasticity of runoff to
assess the effects of climate change on annual runoff, Water Resour. Res., 47,
W07526, doi:10.1029/2010WR009287.
Yang, H. B., J. Qi, X. Y. Xu, and D. W. Yang (2014), The regional variation in
climate elasticity and climate contribution to runoff across China. J. Hydrol. 517:
607-615.