07 Dec 2018
07 Dec 2018
Technical note: Decomposing a time series into independent trend, seasonal and random components
- 1Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia
- 2Australian Research Council Centre of Excellence for Climate System Science, Canberra, Australia
- 3Australian Research Council Centre of Excellence for Climate Extremes, Canberra, Australia
- 1Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia
- 2Australian Research Council Centre of Excellence for Climate System Science, Canberra, Australia
- 3Australian Research Council Centre of Excellence for Climate Extremes, Canberra, Australia
Abstract. Many time series observations in hydrology and climate show large seasonal variations and it has long been common practice to separate the original data into trend, seasonal and random components. We were interested in using that decomposition approach as a basis for understanding variability in hydro-climatic time series. For that purpose, it is desirable that the trend, seasonal and random components are independent so that the variance of the original time series equals the sum of the variances of the three components. We show that the resulting decomposition with the trend component traditionally estimated either as a linear trend or a moving average does not produce components that are independent. Instead we introduce the rarely adopted two-way ANOVA model into studies of hydro-climatic variability and define the trend as equal to the annual anomaly. This traditional approach produces a decomposition with three independent components. We then use global land precipitation data to demonstrate a simple application showing how this decomposition method can be used as a basis for comparing hydro-climatic variability. We anticipate that the three-part decomposition based on the two-way ANOVA approach will prove useful for future applications that seek to understand the space-time dimensions of hydro-climatic variability.
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Dongqin Yin et al.


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RC1: 'Review HESS-2018-601', Anonymous Referee #1, 30 Dec 2018
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AC1: 'Reply to Anonymous Referee #1', Dongqin Yin, 18 Jan 2019
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AC1: 'Reply to Anonymous Referee #1', Dongqin Yin, 18 Jan 2019
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RC2: 'Review report for Yin et al, HESS-2018-601', Sandhya Patidar, 11 Jan 2019
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AC2: 'Reply to Dr. Patidar', Dongqin Yin, 18 Jan 2019
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RC3: 'Eq 24', Sandhya Patidar, 18 Jan 2019
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AC3: 'Reply to Dr. Patidar about Eq. A24', Dongqin Yin, 22 Jan 2019
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RC4: 'Eq 24', Sandhya Patidar, 22 Jan 2019
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AC4: 'Reply to Dr. Patidar about Eq. A24', Dongqin Yin, 04 Feb 2019
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AC4: 'Reply to Dr. Patidar about Eq. A24', Dongqin Yin, 04 Feb 2019
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RC4: 'Eq 24', Sandhya Patidar, 22 Jan 2019
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AC3: 'Reply to Dr. Patidar about Eq. A24', Dongqin Yin, 22 Jan 2019
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RC3: 'Eq 24', Sandhya Patidar, 18 Jan 2019
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AC2: 'Reply to Dr. Patidar', Dongqin Yin, 18 Jan 2019


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RC1: 'Review HESS-2018-601', Anonymous Referee #1, 30 Dec 2018
-
AC1: 'Reply to Anonymous Referee #1', Dongqin Yin, 18 Jan 2019
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AC1: 'Reply to Anonymous Referee #1', Dongqin Yin, 18 Jan 2019
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RC2: 'Review report for Yin et al, HESS-2018-601', Sandhya Patidar, 11 Jan 2019
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AC2: 'Reply to Dr. Patidar', Dongqin Yin, 18 Jan 2019
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RC3: 'Eq 24', Sandhya Patidar, 18 Jan 2019
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AC3: 'Reply to Dr. Patidar about Eq. A24', Dongqin Yin, 22 Jan 2019
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RC4: 'Eq 24', Sandhya Patidar, 22 Jan 2019
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AC4: 'Reply to Dr. Patidar about Eq. A24', Dongqin Yin, 04 Feb 2019
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AC4: 'Reply to Dr. Patidar about Eq. A24', Dongqin Yin, 04 Feb 2019
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RC4: 'Eq 24', Sandhya Patidar, 22 Jan 2019
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AC3: 'Reply to Dr. Patidar about Eq. A24', Dongqin Yin, 22 Jan 2019
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RC3: 'Eq 24', Sandhya Patidar, 18 Jan 2019
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AC2: 'Reply to Dr. Patidar', Dongqin Yin, 18 Jan 2019
Dongqin Yin et al.
Data sets
Updated high-resolution grids of monthly climatic observations–the CRU TS3. 10 Dataset I. Harris, P. D. Jones, T. J. Osborn, and D. H. Lister https://doi.org/10.1002/joc.3711
Dongqin Yin et al.
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