||Flow modeling in open channels is essential in planning, design, operation and maintenance of the flow-related hydro-infrastructural systems, such as bridges, dams, levees, storm sewers, pipelines, and coastal/offshore structures. Uncertainty exists in flow modeling arising from model inputs and parameters, such as the initial conditions, boundary conditions and roughness coefficient, due to the naturally inherent variability, which leads to uncertainty in predicting or estimating flow. The stochastic model of unsteady open channel flow is developed by the perturbative expansion-based moment equation (PEME) method to provide a framework of quantifying flood prediction uncertainty resulting from inherent randomness of model inputs/parameters and assessing their impacts on flow system performance. The stochastic moment equations are derived by fully considering and characterizing the temporal and/or spatial variability of the random input functions and solved through numerical finite difference method. The effects of level of variability and persistence of spatio-temporal correlations of input/parameter random functions are evaluated and their relative importances are investigated. Uncertainties associated with the hydraulic unsteady open channel flow model due to random inputs are further incorporated into the reliability assessment and failure consequence analysis of an example flood defense system to demonstrate its usefulness for a more rational planning, design, and decision making. The performance of the proposed PEME model on solving stochastic unsteady open channel flow under random initial conditions, boundary conditions and Manning's roughness coefficient is examined through numerical experiments. The study also developed a second-order correction procedure which shows that it could provide desirable improvement of model prediction accuracy. The PEME model is found to be capable of providing accurate estimations on flow statistics and revealing more physical insights as compared with the MCS approach under small to moderate variability in random inputs and parameters. The computational efficiency of the PEME model depends on the domain size, level of spatial-temporal variability and the types of flow. Under the condition of identical spatial-temporal discretization of the flow domain for the PEME and MCS approaches, the former is computationally superior to latter when the flow is steady or uniform, or one is interested in information for sub-region rather than the entirety, of flow computation domain. This makes the PEME method potentially quite useful in practical engineering applications. In addition, the PEME method shows good potentials for improving computational efficiency through using coarser spatial-temporal discretization of the flow computation domain than that in MCS for the same problem since flow statistics sought by the moment equations are themselves the averaged quantities, which are much smoother. The probabilistic modeling of unsteady open channel flow in the present study provides a viable way to understand the physical mechanisms of uncertainty propagation through quantitative analysis. It demonstrates good potentials for practical implementations of stochastic modeling of more complex flow systems. The probabilistic analysis presented herein could be also extended to real-time forecast and updating system through the development of adaptive updating schemes and/or Bayesian approaches based on observations. Such modeling exercises provide engineers with useful information and insights for improving flood prediction precision and assessing system reliability for risk-based decision-making.