Energy-based wavelet de-noising of hydrologic time series

PLoS One. 2014 Oct 31;9(10):e110733. doi: 10.1371/journal.pone.0110733. eCollection 2014.

Abstract

De-noising is a substantial issue in hydrologic time series analysis, but it is a difficult task due to the defect of methods. In this paper an energy-based wavelet de-noising method was proposed. It is to remove noise by comparing energy distribution of series with the background energy distribution, which is established from Monte-Carlo test. Differing from wavelet threshold de-noising (WTD) method with the basis of wavelet coefficient thresholding, the proposed method is based on energy distribution of series. It can distinguish noise from deterministic components in series, and uncertainty of de-noising result can be quantitatively estimated using proper confidence interval, but WTD method cannot do this. Analysis of both synthetic and observed series verified the comparable power of the proposed method and WTD, but de-noising process by the former is more easily operable. The results also indicate the influences of three key factors (wavelet choice, decomposition level choice and noise content) on wavelet de-noising. Wavelet should be carefully chosen when using the proposed method. The suitable decomposition level for wavelet de-noising should correspond to series' deterministic sub-signal which has the smallest temporal scale. If too much noise is included in a series, accurate de-noising result cannot be obtained by the proposed method or WTD, but the series would show pure random but not autocorrelation characters, so de-noising is no longer needed.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Hydrology*
  • Monte Carlo Method
  • Signal Processing, Computer-Assisted*
  • Signal-To-Noise Ratio
  • Statistics as Topic / methods*
  • Time Factors

Grants and funding

The Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDB03030202), the National Natural Science Foundation of China (NSFC) (No. 41201036 and 41330529), and the Opening Fund of Key Laboratory of Land Surface Process and Climate Change in Cold and Arid Regions (No. LPCC201203) provided funding for this work. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.