Auxiliary material
Journal of Geophysical Research – Atmosphere
Supporting Information for
A multivariate conditional model for streamflow prediction and spatial
precipitation refinement
Zhiyong Liu1, Ping Zhou2, Xiuzhi Chen3, Yinghui Guan4,5
1
Institute of Geography, Heidelberg University, Heidelberg 69120, Germany
2
Department of Forest Ecology, Guangdong Academy of Forestry, Guangzhou 510520, China
3
South China Botanical Garden, Chinese Academy of Sciences, Guangzhou 510650, China
4
College of Resources and Environment, State Key Laboratory of Soil Erosion and Dryland Farming on the Loess
Plateau, Northwest A&F University, Yangling, 712100,China
5
Institute of Soil and Water Conservation, Chinese Academy of Sciences & Ministry of Water Resources, Yangling,
712100, China
Contents of this file
Text S1 to S2
Tables S1
Figures S1 to S2
Introduction
This Auxiliary Material includes the Supporting Information (SI) for the architectures and
parameters of ANFIS and SVR used in this study.
Text S1. Architecture and parameters of ANFIS
The ANFIS used in the study is a Sugeno-type fuzzy inference model consisting of both an
ANN and fuzzy system [Jang, 1993]. We used the ANFIS tool in MATLAB to produce streamflow
predictions. The optimal parameters and structure of ANFIS were obtained using random trial-anderror [Nourani et al., 2011; Huang et al., 2015]. Table S1 presents the optimal ANFIS parameters,
and Figure S1 shows the ANFIS structure used in this study.
Text S2. Architecture and parameters of SVR
We implemented the SVR model for streamflow prediction based on the LIBSVM program
developed by Chang and Lin [2001]. Figure S2 shows the structure of SVR. There are three
parameters to be determined: gamma (  ), epsilon (  ), and cost (C). The SVR parameters were
optimized using the two-step grid search method described by Yu et al. [2006] and Hsu et al.
[2010], which is included in the LIBSVM program. In this study, the optimal SVR parameters (C,
 ,  ) = (0.25, 0.1251, 1) were obtained using LIBSVM program.
References
Chang, C.C., and C. J. Lin (2001), LIBSVM: a library for support vector machines. <
http://www.csie.ntu.edu.tw/~cjlin/libsvm/ >.
Hsu, C.W., Chang, C.C., and C.J. Lin (2010), A Practical Guide to Support Vector Classification,
available at: <http://www.csie.ntu.edu.tw/~cjlin/papers/guide/guide.pdf>.
Huang, C.L., Hsu, N.S., Wei, C.C., and C.W. Lo (2015), Using Artificial Intelligence to Retrieve
the Optimal Parameters and Structures of Adaptive Network-Based Fuzzy Inference System for
Typhoon Precipitation Forecast Modeling, Adv Meteorol., doi:10.1155/2015/472523.
Jang, J.S.R. (1993), ANFIS: adaptive-network-based fuzzy inference system, IEEE Transactions
System Management and Cybernetics, 23(3), 665–685, doi: 10.1109/21.256541.
Nourani, V., O. Kisi, and M. Komasi (2011), Two hybrid artificial intelligence approaches for
modeling
rainfall–runoff
process,
J.
Hydrol.,
402(1–2),
41–59,
doi:
10.1016/j.jhydrol.2011.03.002.
Vapnik, V. (1995), The Nature of Statistical Learning Theory, Springer Verlag, New York, USA.
Yu, P. S., S. T. Chen, and I. F. Chang (2006), Support vector regression for real-time flood stage
forecasting, J. Hydrol., 328(3–4),704–716, doi:10.1016/j.jhydrol.2006.01.021.
Table S1. ANFIS parameters used in this study.
Parameter
Value
Number of inputs
6
Number of input membership functions
5
Type of input membership function
Gaussian
Number of rules
5
Type of output membership function
Linear
Number of output membership functions
5
Figure S1. ANFIS structure. Layer-1 represents inputs, layer-2 is the input membership function,
layer-3 contains the rules, layer-4 is the output membership function, layer-5 gives the weighted
output, and layer-6 is the final output.
Figure S2. SVR structure, where K(xi, x) is the output of the ith hidden node with respect to the
input vector x [Vapnik, 1995].