The impacts of climate change on the water environment have aroused widespread concern. With global warming, mountainous basins are facing serious water supply situations. However, there are limited meteorological stations on mountains, which thus creates a challenge in terms of accurate simulation of streamflow and water resources. To solve this problem, this study developed a method to model streamflow in data-scarce mountainous basins. Selecting the two head waters originating in the Tienshan mountains, Aksu and Kaidu Rivers, we firstly reconstructed precipitation and temperature dynamics based on Earth system data products, and then integrated the radial basis function artificial neural network and complete ensemble empirical mode decomposition with adaptive noise to model streamflow. Comparison with the observed streamflow according to hydrological stations indicated that the proposed approach was highly accurate. The modeling results showed that the El-Niño Southern Oscillation, temperature, precipitation, and the North Atlantic Oscillation are the main factors driving streamflow, and the streamflow decreased in both the Aksu River and Kaidu River between 2000 and 2017.