Role of a 'combination rule' in hybrid short-term prediction of hydrological events

Data-driven hydrological predictions based on supervised classification have recently gained momentum.This technique supports the classification of waterbodies and flood events that occur at different watersheds, predictions of a class of a hydrological event, e.g., 'high-' or 'low-flow', as opposed to forecasting magnitudes of streamflow characteristics generated by ANNs, regression models or other modelling tools.Flood management teams declare a state of emergency and/or take mitigation measures based on a set of business rules reflecting water level exceedance of an established threshold.Therefore, predicting a class of a hydrological event, e.g.'flood' or 'no-flood', carries even more important information for operational flood managers than projected magnitudes of streamflow characteristics.When predictions of a class of an event are obtained based on data available in real-time, they can be easily deployed in flood management.Scientific literature has demonstrated the usefulness of various classification algorithms (inducers) in applied hydrology.The performance of these inducers, however, deviated notably on different data sets.To alleviate these deviations and generate forecasts with reduced generalization error, an ensemble of classifier can be constructed.One of the important steps in developing an ensemble of classifiers is identifying the approach to aggregate individual predictions into a final judgement.The current study investigates the effect of various weighting schemes on the accuracy of the generated forecasts of hydrological events.The predictors were developed using C4.5, CART, REPTree, NBTree, Ridor, JRip, and Random Forest inducers trained on data collected by stream and rain gauges located on a small highly urbanized watershed during two hydrologically distinct years.The data sets were first transformed into time series of various granularity from 15 minutes to 60 minutes.Time series of the same granularity and corresponding to the same year were converted to an augmented phase space providing datasets for training and testing developed predictors.Ensembles were constructed using five combination rules: majority vote, maximum probability, minimum probability, average probability, and product of probabilities.The ensemble's generalization error was estimated using two measures: recall and Fscore.Combining the results of predictors constructed via training of individual inducers allows to develop a more robust model generating reliable predictions.However, the estimates of the ensemble's generalization error vary up to 28% depending on the combination rule used to aggregate individual predictions into the final judgement.The issue of selecting a combination rule which is the most suitable for an application domain has both theoretical importance and practical significance.Computational experiments revealed that the classifier constructed with the minimum probability combination rule outperformed the others.It consistently delivered the most accurate results for all investigated data sets and all lead time intervals.The performance of classifiers utilizing the maximum probability rule on all data sets was the weakest, contrasting to its interpretation as a rule which identifies a classifier with the highest estimated confidence.Although the results of data-driven analysis are site-specific, they suggest further investigation of this rule, including theoretical considerations and application of the rule to data sets from other watersheds.Another combination rule which should not be easily discarded for the given problem domain, is the majority vote.

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