Sang Yan-Fang, Liu Changming, Wang Zhonggen, Wen Jun, Shang Lunyu
Key Laboratory of Water Cycle & Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing, China; Key Laboratory of Land Surface Process and Climate Change in Cold and Arid Regions, Chinese Academy of Sciences, Lanzhou, China.
Key Laboratory of Water Cycle & Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing, China.
PLoS One. 2014 Oct 31;9(10):e110733. doi: 10.1371/journal.pone.0110733. eCollection 2014.
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.
去噪是水文时间序列分析中的一个重要问题，但由于方法的缺陷，这是一项艰巨的任务。本文提出了一种基于能量的小波去噪方法。它通过将序列的能量分布与通过蒙特卡罗试验建立的背景能量分布进行比较来去除噪声。与基于小波系数阈值化的小波阈值去噪（WTD）方法不同，该方法基于序列的能量分布。它可以区分序列中的噪声和确定性成分，并且可以使用适当的置信区间对去噪结果的不确定性进行定量估计，但WTD方法无法做到这一点。对合成序列和实测序列的分析验证了该方法与WTD方法具有相当的能力，但前者的去噪过程更易于操作。结果还表明了三个关键因素（小波选择、分解层数选择和噪声含量）对小波去噪的影响。使用该方法时应仔细选择小波。小波去噪的合适分解层数应与具有最小时间尺度的序列确定性子信号相对应。如果序列中包含过多噪声，则该方法或WTD方法无法获得准确的去噪结果，但该序列将呈现纯随机而非自相关特征，因此不再需要去噪。
