Wavelet Analysis and the Information Cost Function Index for Selection of Calibration Events for Flood Simulation

Abstract

Globally, floods are a prevalent type of natural disaster. Simulating floods is a critical component in the successful implementation of flood management and mitigation strategies within a river basin or catchment area. Selecting appropriate calibration data to establish a reliable hydrological model is of great importance for flood simulation. Usually, hydrologists select the number of flood events used for calibration depending on the catchment size. Currently, there is no numerical index to help hydrologists quantitatively select flood events for calibrating the hydrological models. The question is, what is the necessary and sufficient amount (e.g., 10 events) of calibration flood events that must be selected? This study analyses the spectral characteristics of flood data in Sequences before model calibration. The absolute best set of calibration data is selected using an entropy-like function called the information cost function (ICF), which is calculated from the discrete wavelet transform (DWT) decomposition results. Given that the validation flood events have already been identified, we presume that the greater the similarity between the calibration dataset and the validation dataset, the higher the performance of the hydrological model should be after calibration. The calibration datasets for the Tunxi catchment in southeast China were derived from 21 hourly flood events, and the calibration datasets were generated by arranging 14 flood events in sequences from 3 to 14 (i.e., a Sequence of 3 with 12 sets (set 1 = flood events 1, 2, 3; set 2 = flood events 2, 3, 4, …, and so on)), resulting in a total of 12 sequences and 78 sets. With a predetermined validation set of 7 flood events and the hydrological model chosen as the Hydrologic Engineering Center (HEC–HMS) model, the absolute best calibration flood set was selected. The best set from the Sequence of 10 (set 4 = S10′) was found to be the absolute best calibration set of flood events. The potential of the percentile energy entropy was also analyzed for the best calibration sets, but the ICF was the most consistent index to reveal the ranking based on similarity with model performance. The proposed ICF index in this study is helpful for hydrologists to use data efficiently with more hydrological data obtained in the new era of big data. This study also demonstrates the possibility of improving the effectiveness of utilizing calibration data, particularly in catchments with limited data.