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Energy-based wavelet de-noising of hydrologic time series.

Sang YF, Liu C, Wang Z, Wen J, Shang L - PLoS ONE (2014)

Bottom Line: 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.The results also indicate the influences of three key factors (wavelet choice, decomposition level choice and noise content) on wavelet de-noising.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.

View Article: PubMed Central - PubMed

Affiliation: 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.

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.

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De-noising results of RS1 (a) and RS2 (b) series by the energy-based wavelet de-noising method (the new method) and the wavelet threshold de-noising (WTD) method.
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pone-0110733-g005: De-noising results of RS1 (a) and RS2 (b) series by the energy-based wavelet de-noising method (the new method) and the wavelet threshold de-noising (WTD) method.

Mentions: The two observed series are analyzed by the proposed method using five wavelets (“db3”, “db8”, “sym7”, “coif4”, and “bior4.4”). Results in Fig. 4 clearly indicate that energy distributions of series vary with the wavelets used. Energies of RS1 series' sub-signals under L3, L4, L5, L7, L8, L9, L10, L11, and L12 obtained by any of the five wavelets overstep 95% confidence interval, so their sum is the de-noised RS1 series. The sub-signals of RS2 series under L2, L3, L4, L5, L6 and L9 have the energies overstepping 95% confidence interval, and their sum is the de-noised RS2 series. Results in Table 6 indicate that de-noising results of RS1 series by five wavelets are similar, but de-noising results of RS2 series by five wavelets show big difference. It is due to more complex variation of RS2 series as shown in Fig. 5. As a result, the “db8” wavelet is chosen for de-noising of RS1 and RS2 series.


Energy-based wavelet de-noising of hydrologic time series.

Sang YF, Liu C, Wang Z, Wen J, Shang L - PLoS ONE (2014)

De-noising results of RS1 (a) and RS2 (b) series by the energy-based wavelet de-noising method (the new method) and the wavelet threshold de-noising (WTD) method.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4215914&req=5

pone-0110733-g005: De-noising results of RS1 (a) and RS2 (b) series by the energy-based wavelet de-noising method (the new method) and the wavelet threshold de-noising (WTD) method.
Mentions: The two observed series are analyzed by the proposed method using five wavelets (“db3”, “db8”, “sym7”, “coif4”, and “bior4.4”). Results in Fig. 4 clearly indicate that energy distributions of series vary with the wavelets used. Energies of RS1 series' sub-signals under L3, L4, L5, L7, L8, L9, L10, L11, and L12 obtained by any of the five wavelets overstep 95% confidence interval, so their sum is the de-noised RS1 series. The sub-signals of RS2 series under L2, L3, L4, L5, L6 and L9 have the energies overstepping 95% confidence interval, and their sum is the de-noised RS2 series. Results in Table 6 indicate that de-noising results of RS1 series by five wavelets are similar, but de-noising results of RS2 series by five wavelets show big difference. It is due to more complex variation of RS2 series as shown in Fig. 5. As a result, the “db8” wavelet is chosen for de-noising of RS1 and RS2 series.

Bottom Line: 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.The results also indicate the influences of three key factors (wavelet choice, decomposition level choice and noise content) on wavelet de-noising.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.

View Article: PubMed Central - PubMed

Affiliation: 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.

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.

Show MeSH