Abstract
The support vector machine is used as a data mining technique to extract informative hydrologic data on the basis of a strong relationship between error tolerance and the number of support vectors. Hydrologic data of flash flood events in the Lan-Yang River basin in Taiwan were used for the case study. Various percentages (from 50% to 10%) of hydrologic data, including those for flood stage and rainfall data, were mined and used as informative data to characterize a flood hydrograph. Information on these mined hydrologic data sets was quantified using entropy indices, namely marginal entropy, joint entropy, transinformation, and conditional entropy. Analytical results obtained using the entropy indices proved that the mined informative data could be hydrologically interpreted and have a meaningful explanation based on information entropy. Estimates of marginal and joint entropies showed that, in view of flood forecasting, the flood stage was a more informative variable than rainfall. In addition, hydrologic models with variables containing more total information were preferable to variables containing less total information. Analysis results of transinformation explained that approximately 30% of information on the flood stage could be derived from the upstream flood stage and 10% to 20% from the rainfall. Elucidating the mined hydrologic data by applying information theory enabled using the entropy indices to interpret various hydrologic processes.
Highlights
The support vector machine (SVM), proposed by Vapnik [1,2], is a commonly used method for solving classification and regression problems
The SVM has been proven to be a robust method for hydrologic modeling and forecasting, with various applications in hydrology that include runoff forecasting [3,4,5,6,7,8,9], flood stage forecasting [10,11,12,13,14,15], rainfall forecasting [16,17,18], typhoon rainfall forecasting [19,20,21], modeling and correction of radar rainfall estimates [22,23], and statistical downscaling [24,25,26,27]
These results prove that informative data that characterized the flood hydrograph were mined as support vectors (SVs), and that SVs obtained using the proposed support vector regression (SVR) model represent informative hydrologic data
Summary
The support vector machine (SVM), proposed by Vapnik [1,2], is a commonly used method for solving classification and regression problems. Chen and Yu [13] applied support vector regression (SVR) to flood forecasting and demonstrated that pruning SVs reduced network complexity, but did not degrade forecasting ability. They [13] showed that SVs are informative hydrologic data, and that the SVs that were informative in characterizing floods were preserved in the networks during the pruning process. The present study applied information entropy to quantify the amount of information of hydrologic data mined using an SVR flood forecasting model [13]. Analytical results obtained using the entropy indices proved that the mined informative data had hydrologic implications for the flood process and contained meaningful information measures that could be hydrologically explained using entropy theory
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