Identifying causes of errors between two wave-related data using performance metrics

Recently, numerous prediction methods of time-series data of wave-related phenomena have been developed. Quantitative evaluation of an error of a predicted result against a reference result is important to improve prediction accuracy. Many performance metrics are engaged to evaluate their accuracy. However, it is difficult for them to identify the error causes because all errors, no matter what the cause, are combined together. This paper presents new representations of performance metrics to separate errors by causes. Performances are evaluated in a frequency domain instead of a time domain. A frequency domain’s amplitude and phase are respectively evaluated using performance metrics. In addition, to detect errors due to instantaneous phenomena and changes in an error trend over time, mean errors are defined by three-time intervals. The original metric uses all time-series data. On the other hand, a finite interval mean error at the present time is calculated by the mean of the preceding data. In addition, cumulative mean error at the present time is calculated by the mean of the data up to the present time. These new representations of performance metrics could help to identify error causes. Benchmark tests are carried out to demonstrate the validity of the proposed representations. • Quantitative evaluation of time-series data using performance metrics is important. • New representations of performance metrics are proposed to identify causes of errors. • Benchmark tests are demonstrated to validate the proposed representations.