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 . 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.  and Hsu et al. , 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].