Bayesian theory of probabilistic forecasting via deterministic hydrologic model

Rational decision making (for flood warning, navigation, or reservoir systems) requires that the total uncertainty about a hydrologic predictand (such as river stage, discharge, or runoff volume) be quantified in terms of a probability distribution, conditional on all available information and knowledge. Hydrologic knowledge is typically embodied in a deterministic catchment model. Fundamentals are presented of a Bayesian forecasting system (BFS) for producing a probabilistic forecast of a hydrologic predictand via any deterministic catchment model. The BFS decomposes the total uncertainty into input uncertainty and hydrologic uncertainty, which are quantified independently and then integrated into a predictive (Bayes) distribution. This distribution results from a revision of a prior (climatic) distribution, is well calibrated, and has a nonnegative ex ante economic value. The BFS is compared with Monte Carlo simulation and “ensemble forecasting” technique, none of which can alone produce a probabilistic forecast that meets requirements of rational decision making, but each can serve as a component of the BFS.

[1]  Norman W. Junker,et al.  Evaluation of 33 Years of Quantitative Precipitation Forecasting at the NMC , 1995 .

[2]  George E. P. Box,et al.  Empirical Model‐Building and Response Surfaces , 1988 .

[3]  A. H. Murphy,et al.  Probabilities, Odds, and Forecasts of Rare Events , 1991 .

[4]  Roman Krzysztofowicz,et al.  Calibration of Probabilistic Quantitative Precipitation Forecasts , 1999 .

[5]  Roman Krzysztofowicz.  Markovian Forecast Processes , 1987 .

[6]  A. Tversky,et al.  Judgment under Uncertainty: Heuristics and Biases , 1974, Science.

[7]  Roman Krzysztofowicz.  Bayesian Correlation Score: A Utilitarian Measure of Forecast Skill , 1992 .

[8]  Roman Krzysztofowicz,et al.  Probability distributions for flood warning systems , 1994 .

[9]  Eugenia Kalnay,et al.  Operational Ensemble Prediction at the National Meteorological Center: Practical Aspects , 1993 .

[10]  Konstantine P. Georgakakos,et al.  Impacts of climate variability on the operational forecast and management of the Upper Des Moines River Basin , 1998 .

[11]  Roman Krzysztofowicz,et al.  Stochastic Model of Seasonal Runoff Forecasts , 1986 .

[12]  Eugenia Kalnay,et al.  Ensemble Forecasting at NMC: The Generation of Perturbations , 1993 .

[13]  Roman Krzysztofowicz,et al.  Probabilistic Hydrometeorological Forecasts: Toward a New Era in Operational Forecasting , 1998 .

[14]  Roman Krzysztofowicz,et al.  BAYESIAN MODELS OF FORECASTED TIME SERIES , 1985 .

[15]  Averill M. Law,et al.  Simulation Modeling and Analysis , 1982 .

[16]  M. Degroot.  Optimal Statistical Decisions , 1970 .

[17]  Roman Krzysztofowicz.  Why should a forecaster and a decision maker use Bayes Theorem , 1983 .

[18]  A. H. Murphy,et al.  Credible Interval Temperature Forecasting: Some Experimental Results , 1974 .

[19]  Roman Krzysztofowicz,et al.  Bayesian analyses of seasonal runoff forecasts , 1991 .

[20]  Roman Krzysztofowicz,et al.  Probabilistic Quantitative Precipitation Forecasts for River Basins , 1993, Weather and Forecasting.

[21]  J. Berger.  Statistical Decision Theory and Bayesian Analysis , 1988 .

[22]  H. Raiffa,et al.  Judgment under uncertainty: A progress report on the training of probability assessors , 1982 .

[23]  Gerald N. Day,et al.  Extended Streamflow Forecasting Using NWSRFS , 1985 .