Successful Hydrologic Forecasting for California Using an Information Theoretic Model

R. A. Christensen Entropy Limited, South Great Road, Lincoln, MA 01773

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R. F. Eilbert Entropy Limited, South Great Road, Lincoln, MA 01773

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O. H. Lindgren Entropy Limited, South Great Road, Lincoln, MA 01773

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L. L. Rans Entropy Limited, South Great Road, Lincoln, MA 01773

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Abstract

The Entropy Minimax technique from information theory has been applied to long-range, hydrologic forecasting in California. Based on 1852–1977 records, the technique exhibits a limited, but statistically significant, success for predictions one year ahead. A seven-station precipitation index having a 126 water-year base period was chosen as the dependent variable to represent the area's hydrologic status. Random division of the water years into training (model building) and test (reserved for verification only) halves was strictly enforced and a “one-try-only” constraint was placed on predictive runs. Predictions were formulated by an analog selection procedure based on patterns found in a 42-dimensional space of independent variables. These had been extracted by selection, compression and filtering from a data base containing over 100 000 time series. Wet/dry predictions (above or below median), validated on the test water years, demonstrated a 63% accuracy with a 94% confidence that this success is not due to chance. The accuracy rose to 78% when borderline SSPI years were omitted from the validation set, a result significant at the 0.4% level. By comparison, a predictor based on persistence alone is essentially random.

Abstract

The Entropy Minimax technique from information theory has been applied to long-range, hydrologic forecasting in California. Based on 1852–1977 records, the technique exhibits a limited, but statistically significant, success for predictions one year ahead. A seven-station precipitation index having a 126 water-year base period was chosen as the dependent variable to represent the area's hydrologic status. Random division of the water years into training (model building) and test (reserved for verification only) halves was strictly enforced and a “one-try-only” constraint was placed on predictive runs. Predictions were formulated by an analog selection procedure based on patterns found in a 42-dimensional space of independent variables. These had been extracted by selection, compression and filtering from a data base containing over 100 000 time series. Wet/dry predictions (above or below median), validated on the test water years, demonstrated a 63% accuracy with a 94% confidence that this success is not due to chance. The accuracy rose to 78% when borderline SSPI years were omitted from the validation set, a result significant at the 0.4% level. By comparison, a predictor based on persistence alone is essentially random.

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