Mixing Probabilistic Meteorology Outlooks in Operational Hydrology

There are now several kinds of probabilistic meteorology outlooks available to the water resource engineer or hydrologist. These outlooks are defined over different time periods at different lag times, and they forecast either event probabilities or only most-probable events. An existing operational hydrology approach (for making hydrology outlooks) builds a set of hydrological possibilities from past meteorology to match forecast event probabilities, but it does not consider most-probable event forecasts. This approach is extended to mix both types of probabilistic meteorology outlooks in determining weights to apply to the set of hydrological possibilities to make hydrological outlooks. Boundary condition equations for the weights are constructed corresponding to forecast event probabilities, and boundary condition inequalities are constructed corresponding to forecast most-probable events. The inequalities are converted to equivalent equations through the introduction of additional variables. The resulting set of all boundary condition equations is solved for physically relevant values. The solution is an optimization problem for the general case, similar to earlier consideration of only forecast event probabilities. An example illustrates the concepts and methods.