Estimation of Flood Forecasting Errors and Flow-Duration Joint Probabilities of Exceedance

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Abstract
The conceptual analogy between the impulse response function and the unit hydrograph is applied for the identification of a transfer function model for real-time flood forecasting. The real-time corrections of flood forecasts are obtained from probability distributions of observed and forecasted (without real-time corrections) flows approximated by exponential distributions. The method adds considerable smoothing to error terms. The flood event is defined as the amount of total flow in excess of an alarm level of the flood over its duration. The correlation between the flood flow and its duration is considered to estimate the joint probabilities of exceedance (JPE) of designed flood flow over specified duration using the joint distribution of the flow and duration, given by the Gumbel's bivariate exponential distribution (second type). It is discussed that the univariate analysis (i.e., flow alone) underestimates the exceedance probability of flood flow. The study shows that the JPE increases with the increase of correlation between the flood flow and its duration. The radar-derived rainfall data in the Irwell basin, U.K., are applied in a case study. The method of JPE can be extended to link flood forecasting and flow-duration profile for effective management of flood risk areas.

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