Supplementary Materials for
Variability of Modeled Runoff over China and
its links to climate change
Li Mingxing, Ma Zhuguo, Lv Meixia
RCE-TEA, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing
100029, China
This file includes:
Supplementary text
Methodology
S1 Statistical analyses
S1.1 Estimating multiple rates of change
S1.2 Correlation, curve fitting, and envelope methods
S2 Links assessment between runoff and climatic covariates
Fig3. S1–S9
Tab. S1
References
Methodology
S1 Statistical analysis
S1.1 Estimating multiple rates of change
Runoff time series are often characterized by unequal variations owing to the complex
feedback from the determinants, i.e., precipitation, vegetation cover, and
geomorphology. Estimating multiple rates of change (slopes) provides a more complete
picture of the runoff evolution and its interaction with climatic covariates. In this study,
we adopt the quantile regression (QR) method to estimate the functional relations
between runoff and climate variables (precipitation and temperature) for all portions of
a probability distribution rather than the mean. QR is a collection of statistical methods
for estimating and drawing inferences about conditional quantile functions. Compared
with the widely used ordinary least squares regression (OLS), it is more suitable to
model the heterogeneous variance of nonstationary change rates in heterogeneous data.
Since its introduction by Koenker and Bassett (1978), QR has been used extensively in
economics (Alagidede and Panagiotidis, 2012), ecology (Cozzoli et al., 2013), climate
change (Barbosa et al., 2011; Bremnes, 2004; Hirschi et al., 2011; Meng and Shen,
2014), and so on. In this study, we used the sparsity method to compute the confidence
intervals of the regression slopes.
S1.2 Correlation, curve fitting, and envelope methods
We used the Pearson correlation coefficient and the Student’s t-test to estimate its
significance. The variation trends in the time series expressed as linear slopes were
estimated using least squares, with significance tested by Student’s t-test. The
correlation coefficient R between simulations (r) and observations (f) is defined as
1
𝑅=𝑁
∑𝑁
𝑛=1(𝑓𝑛 −𝑓)(𝑟𝑛 −𝑟)
𝜎𝑓 𝜎𝑟
,
(1)
where N is the sample size, 𝑓 and 𝑟 are means of the simulated and observed series,
respectively, and σf and σr are the standard deviations of the simulated and observed
series, respectively.
Curve fitting was performed using polynomials of the form
y  c  ax  bx 2 .
(2)
The envelope calculations were performed by using the local maximum method
combined with cubic spline interpolation and smoothed by the two-point adjacent
averaging (Adler 1978).
S2 Link assessment between runoff and climatic covariates
The links between runoff and covariates are complex owing to the land–atmosphere
and ocean–atmosphere interactions in variable spatiotemporal scales. Understanding
the mechanisms behind them is beyond the scope of this study. Building on the
observations of precipitation and temperature herein, we provide the relation patterns
for runoff and covariates (precipitation and temperature) for the in-depth understanding
of the nature of runoff variability. For simplicity, the relations are quantified using the
correlation coefficient (eq. 1) and the Student’s t-test for its significance. The annual
correlation is derived from 12-month averaged time series with sample size of 48
(1961–2008). Similarly, the summertime correlation is calculated from three-month
(JJA) averaged values. The spatial structures of the links between runoff and climatic
covariates are described by the correlation coefficients for each grid cell. The sensitivity
of the runoff to covariates is represented by nonparametric regression, the quantile
slopes, and the 0.1 and 0.9 quantiles for lower and upper end responses, respectively
(see section 1). The slope significance is assessed with the standard errors of the
quantile slopes by local estimates of sparsity.
Fig S1 Comparison of normalized model monthly terrestrial water storage with those
of GRACE over China from February 2004 to December 2008, a monthly time series,
b averaged annual variations, c time series without annual variations.
Fig S2 Spatial patterns for ratios (%) of annual and summer mean runoff to
precipitation over 1961–2008
Figure S2 shows that high ratios cover the humid southeast and gradually decrease to
the arid northwest, with maxima over 90% and minima close to zero across China.
Summer runoff ratios likewise are characterized by the southeast–northwest gradient,
although high-end percentages extend notably over southeastern China. The spatial
structure of runoff ratio across China is largely related to that of soil moisture and
precipitation (Li et al. 2011). Generally, in the humid regions with high soil moisture
contents, saturation excess runoff model dominants runoff generation and leads to great
runoff ratio; in the arid regions, infiltration excess runoff is the major model of runoff.
The runoff ratios decline with precipitation drops and soil dryness. However, the
mechanisms for runoff–precipitation interaction are complex, especially in the areas of
plateau, mountain, glacial, permafrost (Huntington and Billmire 2014; Xu 2015).
Fig S3 Spatial patterns for means of surface runoff and subsurface runoff (mm mo−1)
across China over 1951–2008, and linear trends patterns (mm mo−1). The black lines
indicate significance at the 0.05 level.
Fig S4 Spatial patterns for runoff trends (mm mo−1) at quantiles 0.1, 0.3, 0.5 0.7, and
0.9, respectively, over 1951–2008. The black lines denote significance at the 0.05
level.
Figure S4 shows that the spatial patterns of runoff trends for quantiles from 0.1 to 0.9
are characterized by the generally similar spatial gradient: significant increasing trends
in the humid south, large-area decreasing trends in the wet–dry transition zone, and
non-significant and mixed trends in the arid northwest. Moreover, the upper quantile
trends are generally much steeper than those at lower quantiles. Discrepancies in trends
from lower to upper quantiles manifest mainly over parts of northeastern China,
northwestern high latitudes, and the Tibetan Plateau, where the trends tend to be upward
at upper quantiles, but downward or slightly upward at lower quantiles. The changes in
quantile trends of runoff imply generally intensified runoff variability from 1951 to
2008, which is associated with increased extreme precipitation (Zhai et al., 2005),
groundwater level variations, and climate-warming introduced thawing/melting of
glacial and permafrost (Chen et al. 2012; Xu 2015).
Fig S5 Evolutions of runoff in the regions with significant ling-term trends.
Fig S6 The time series of summer (JJA) runoff, precipitation, and temperature for the
two critical regions in 1961-2008. The runoff is modeled by CLM driven with
observation-based forcing. Precipitation (Prec-CMA) and temperature (Temp-CMA)
series are taken from gridded observations by CMA, along with the precipitation from
GPCP (Prec-GPCP) for 1979–2008.
Fig S7 Quantile regression slopes at the 0.1–0.9 quantiles for the summer (JJA)
monthly runoff versus monthly precipitation (a, c) and temperature (b, d) for two
critical regions, along with 95% confidence interval of the estimated slopes shown as
shadings. The horizontal lines indicate a slope of 0 (no trends). Red lines indicate
regression slopes by the ordinary least squares regression with 95% confidence
intervals (red dash lines).
Fig S8 Spatial patterns of correlation coefficients for annual runoff versus a
precipitation and b temperature in 1961-2008.
Figure S8 shows that the spatial patterns of correlation between annual runoff and
precipitation and temperature over 1961–2008 are similar to the spatial structure of
precipitation climate (not show the figure). The positive correlation locates over the
humid regions, the negative (or weak positive) correlation over the arid regions, and
the transition zone mostly covered by weak correlation, largely analogous to that in
Interim ECMWF (European Centre for Medium-Range Weather Forecasts) ReAnalysis [ERA-Interim (Dee et al. 2011), not show the figures]. The negative
correlation over arid and mountainous regions and plateaus is associated with relatively
less proportion contributed from local precipitation but increasing effects of lateral
groundwater transport, glacial melt (Gao et al. 2012). With respect to temperature, the
spatial characteristics resemble that for runoff versus precipitation, with negative
correlation over arid regions but the positive over humid regions. In the humid regions,
the runoff-temperature correlation is remarkably less than those between runoff and
precipitation. The relation of temperature to runoff showed a more mixed spatial
structure, with significantly negative correlation over the South China, North China,
and most of arid regions, but positive relation over the most part of Tibetan Plateau,
Sichuan Basin, and northern coastal areas. Such correlation changes reflect the evident
regional characteristics of the interactions between runoff and climate covariates.
Fig S9 Spatial patterns of quantile slopes for summer (JJA) runoff versus precipitation
and runoff versus temperature at quantile 0.1.
Table S1 Quantile slopes (mm mo-1) of runoff and corresponding standard errors for
Fig 3
Domains
Region A
Region B
0.1
-0.61
(0.22)
0.48
(0.22)
0.3
-0.56
(0.09)
0.69
(0.18)
Quantile
0.5
0.7
-0.44
-0.54
(0.14)
(0.06)
0.69
0.74
(0.14)
(0.13)
0.9
-0.24
(0.26)
1.08
(0.25)
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