||A geomorphologic instantaneous unit hydrograph (GIUH) provides physical link between the hydrologic response and geomorphology of a watershed. It can be represented as the sum of weighted probability density functions of the rainwater travel time for all plausible flow paths within the watershed. Using the kinematic-wave routing procedure, the rainwater travel time for each overland and channel components is derived as function of random channel length, slope and roughness coefficient due to their spatial variability. However, limited samples for random surface roughness and slope result in sampling errors which render the determination of statistical moments of component travel time uncertain. Hence, the resulting kinematic-wave based GIUH is inevitably subject to uncertainty, which will further be transmitted into the design flow hydrograph. This study uses the modified Harr probabilistic point estimation method, along with the normal transform techniques, to assess the uncertainty of the kinematic-wave based GIUH as well as that of the GIUH-based flow hydrograph. The uncertainty features associated with the flow hydrograph are incorporated for reliability analysis of hydraulic structures. Constrained Gaussian simulation with hydrologic routing is used to evaluate the overtopping risk of a hypothetical flood detention reservoir. A unique aspect of the study is concerned with the techniques in uncertainty analysis. The probabilistic point estimation (PPE) methods developed thus far, in general, could provide reasonable accuracy only for estimating the first two statistical moments of model output. This study develops two new PPE schemes to enhance the accuracy in higher-order statistical moments estimation for model output. Performance evaluation indicates the advantages and limitations for each proposed method.