The recent advances in sensing technology and machine learning have offered new opportunities in hydro-climate research with tremendous data and highly complex, nonlinear models. However, a model tends to lose interpretability when it becomes complex, which can degrade its transferability under out-of-sample conditions. Therefore, the tradeoff between model complexity (accuracy) and interpretability must be considered. In this dissertation, I implement some interpretable data-driven approaches through a typical chain of uncertainty propagation in three major sectors of climate, hydrology, and water resource management. My research serves as an early effort to quantify uncertainty from two major sources, climate forcing and hydrological responses, and to incorporate them into water resource management. I first examine the feasibility of a regularized regression model in uncovering teleconnections between regional precipitation and large-scale climates from both physical and statistical perspectives. Next, we explore the potential of a Bayesian estimation method as a cheap surveillance tool for monitoring dynamics of rainfall-runoff responses for small watersheds. Finally, we adopt the evolutionary multi-objective direct policy search framework to quantitatively compare how forcing data of different resolutions can alter water system optimization. Based on these projects, we figure that 1) data-driven approaches can guide exploration of physical knowledge and 2) computational costs can be reduced by using physical constraints.