In this paper we develop a positive calibrated approach to stochastic dynamic programming. Risk aversion, discount rate, and intertemporal substitution preferences of the decision-maker are calibrated by a procedure that minimizes the mean squared error from data on past decisions. We apply this framework to managing stochastic water supplies from Oroville Reservoir, located in Northern California. The calibrated positive SDP closely reproduces the historical storage and releases from the dam and shows sensitivity of optimal decisions to a decision-maker's risk aversion and intertemporal preferences. The calibrated model has average prediction errors that are substantially lower than those from the model with an expected net present value objective.