Many Earth‐surface processes are studied using field, experimental, or numerical modeling datasets that represent a small subset of possible outcomes observed in nature. Based on these data, deterministic models can be built that describe the average evolution of a system. However, these models commonly cannot account for the complex variability of many processes or present a quantitative statement of uncertainty. To assess such uncertainty, stochastic models are needed that can mimic spatial as well as temporal variability. A common limitation for applying stochastic models to Earth surface processes is a lack of data and methods that allow constraining the full spatio‐temporal variability of these models. In this paper, we propose a Bayesian framework for calibrating input parameters to stochastic models of morpho‐ dynamic systems using time‐series of image data from the field, or from numerical and laboratory experiments. The framework consists of generating synthetic time‐series of images using the stochastic model, and rejecting those time‐series that do not reproduce key morphodynamic statistics of the available datasets. The calibrated stochastic model allows us to quantify both the spatial and temporal uncertainty about the evolution of the morphodynamic systems of interest. For demonstration purposes, we apply the framework to a single flume experiment of braided river channels evolving under steady water and sediment discharges, but it can be used more generally to quantify spatio‐temporal uncertainty for any time‐series of morphodynamic data for which key statistics can be defined.