Reliable probabilistic forecasts from an ensemble reservoir inflow forecasting system

This paper describes a probabilistic reservoir inflow forecasting system that explicitly attempts to sample from major sources of uncertainty in the modeling chain. Uncertainty in hydrologic forecasts arises due to errors in the hydrologic models themselves, their parameterizations, and in the initial and boundary conditions (e.g., meteorological observations or forecasts) used to drive the forecasts. The Member-to-Member (M2M) ensemble presented herein uses individual members of a numerical weather model ensemble to drive two different distributed hydrologic models, each of which is calibrated using three different objective functions. An ensemble of deterministic hydrologic states is generated by spinning up the daily simulated state using each model and parameterization. To produce probabilistic forecasts, uncertainty models are used to fit probability distribution functions (PDF) to the bias-corrected ensemble. The parameters of the distribution are estimated based on statistical properties of the ensemble and past verifying observations. The uncertainty model is able to produce reliable probability forecasts by matching the shape of the PDF to the shape of the empirical distribution of forecast errors. This shape is found to vary seasonally in the case-study watershed. We present an intelligent adaptation to a Probability Integral Transform (PIT)-based probability calibration scheme that relabels raw cumulative probabilities into calibrated cumulative probabilities based on recent past forecast performance. As expected, the intelligent scheme, which applies calibration corrections only when probability forecasts are deemed sufficiently unreliable, improves reliability without the inflation of ignorance exhibited in certain cases by the original PIT-based scheme.