An Enhanced Innovative Triangular Trend Analysis of Rainfall Based on a Spectral Approach
Abstract
:1. Introduction
2. Materials and Methods
- Pretreatment of the input rainfall signal X(t).
- Using filter bank includes high pass filter (A) and low pass filter (D) for signal filtering.
- The outputs of A and D are downsampled by the DWT scale coefficient (factor of 2).
- Choosing the adequate sub-band signal or the scale of decomposition for downsampling based on the time series length.
- Selecting the mother- and daughter-wavelet, e.g., Daubechies mother-wavelet (db20).
- After step 5, the wavelet coefficients are obtained.
- From the wavelet coefficients (approximations and details), 24 models were proposed (Table 2), assessed, and analyzed using correlation and spectral analyses for assessing the periodicity and to perform the filtering
- The 24 proposed models were used as input time series into the ITTA.
2.1. Triangular Trend Analysis Methodology
- To exploit the entire available time series.
- To always stay within the original methodology (same template) and for comparative purposes.
- To extract and detect long-term and significant partial trends.
2.2. Discrete Wavelet Transform
2.3. Correlation and Spectral Analysis
2.4. Study Area and Collected Data
3. Results and Discussion
3.1. Triangular Trend Analysis Methodology
3.2. Combining Triangular Trend Analysis Methodology with Discrete Wavelet Transform
- A partial trend toward drier conditions occurred between 1920 and 1950.
- A partial trend toward humid conditions occurred from 1950 to 1975.
- A partial negative trend extended in northern Algeria from the years 1975.
- A partial trend with a non−significant increase occurred from the end of the 1990s.
- The short and medium-term processes, and less than decadal periodicity, dominate the high variability of rainfall. This masks the partial trend and change points presented in the rainfall series and makes it hard to identify. In southwestern Europe, between 1850 and 2018, the authors in [21] linked the lack of substantially declining or growing patterns to the long-term rainfall series, to the predominance of inter-annual variability, making trend identification difficult. Thus, spectral analysis as a time–frequency-based method, and a first assessment tool to diagnose and characterize climatic series’ high variability before inserting in trend method analyses, is indispensable.
4. Conclusions
- According to the analysis, the ITTA−DWT successfully detected the partial patterns in the studied rainfall time series.
- The analysis revealed the alternate long-term dry and wet periods, where most components of wet periods occurred between 1950 and 1975, with a non−significant increase in rainy episodes observed from the end of the 1990s. The dry periods were observed from 1975 to the end of the 1990s.
- The analysis indicated an increase in the occurrence of heavy rainfalls compared to low and medium intensity rainfalls, in the study area, which can infer the risk of occurrence of torrential rainfalls, which can generate floods.
- The analysis proved DWT’s efficiency as a coupling method that can improve ITTA accuracy for partial trend component identification.
- The analysis proved the effectiveness of DWT as a filtering and denoising method for climatic time series.
- The inter-annual to multiannual of the short to medium processes dominate the high variability of rainfall, masking the partial trend components existing in the rainfall series, making it hard for identification.
- Before inducing the climatic time series in the trend analysis methods, the diagnosis of its behavior, and removing some components, can improve the accuracy of the analysis.
- The obtained results indicated that combining ITA, D–ITA, T–ITA, ITTA, and some input combination models resulting from the DWT is very promising, relative to those of the initial rainfall sequence. Those results corroborate the results obtained by [14]. The ITA–DWT, D–ITA–DWT, T–ITA–DWT, ITTA–DWT methods outperformed the ITA, D–ITA, T–ITA, ITTA methods for partial trend identification.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Sub-Series | 1st | 2nd | 3rd | 4th | (n/t)th |
---|---|---|---|---|---|
1st | 1 | 1st–2nd | 1st–3rd | 1st–4th…. | 1th–(n/t)th |
2nd | 1 | 2nd–3rd | 2nd–4th…. | 2nd–(n/t)th | |
3rd | Meaningless | 1 | 3rd–4th…. | 3rd–(n/t)th | |
4th | 1 | 4th–(n/t)th | |||
(n/t)th | 1 |
Oued Taria Station X = 274.4 km Y = 176.4 km Z = 1000 m | Azazga Station X = 649.6 km Y = 383.9 km Z = 430 m | Ain Beida Station X = 924.15 km Y = 288 km Z = 1004 m | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Model (M) | Combination | R12 | Min | Max | CTV (%) | R22 | Min | Max | CTV (%) | R32 | Min | Max | CTV (%) |
OS | - | 1.00 | 72 | 754 | 100 | 1.00 | 521 | 1577 | 100 | 1.00 | 155 | 631 | 100 |
M 1 | D1 | 0.30 | −169 | 195 | 30.6 | 0.43 | −398 | 360 | 43.1 | 0.42 | −154 | 152 | 41.4 |
M 2 | D2 | 0.22 | −124 | 139 | 20.7 | 0.28 | −364 | 288 | 29.8 | 0.32 | −94 | 89 | 30.3 |
M 3 | D3 | 0.05 | −51 | 55 | 5.6 | 0.07 | −149 | 165 | 11.2 | 0.06 | −61 | 64 | 7.0 |
M 4 | D4 | 0.09 | −68 | 66 | 9.5 | 0.06 | −118 | 126 | 6.3 | 0.09 | −64 | 40 | 10.6 |
M 5 | D5 | 0.08 | −68 | 82 | 13.7 | 0.10 | −113 | 134 | 11.0 | 0.05 | −16 | 10 | 0.8 |
M 6 | A5 | 0.20 | 278 | 423 | 24.5 | 0.01 | 945 | 1036 | 1.2 | 0.09 | 350 | 437 | 7.6 |
M 7 | D1+A5 | 0.50 | 179 | 618 | 54.9 | 0.44 | 585 | 1363 | 44.4 | 0.51 | 242 | 546 | 49.2 |
M 8 | D2+A5 | 0.40 | 174 | 561 | 45.5 | 0.29 | 642 | 1291 | 31.1 | 0.40 | 256 | 494 | 38.1 |
M 9 | D3+A5 | 0.25 | 228 | 451 | 30.4 | 0.09 | 799 | 1110 | 12.1 | 0.16 | 332 | 461 | 14.0 |
M10 | D4+A5 | 0.29 | 220 | 445 | 34.2 | 0.07 | 849 | 1092 | 7.7 | 0.19 | 287 | 465 | 17.3 |
M 11 | D5+A5 | 0.33 | 213 | 417 | 32.9 | 0.12 | 835 | 1104 | 12.4 | 0.10 | 339 | 443 | 11.4 |
M 12 | D1+D2+A5 | 0.71 | 140 | 732 | 76.1 | 0.72 | 591 | 1650 | 74.3 | 0.81 | 223 | 617 | 80.0 |
M 13 | D1+D2+D3+A5 | 0.76 | 100 | 753 | 81.9 | 0.82 | 530 | 1602 | 82.9 | 0.88 | 210 | 616 | 87.0 |
M 14 | D1+D2+D3+D4+A5 | 0.86 | 54 | 769 | 91.7 | 0.88 | 530 | 1627 | 89.0 | 0.99 | 163 | 625 | 96.3 |
M 15 | D1+D2+D3+D5+A5 | 0.90 | 119 | 738 | 90.2 | 0.93 | 519 | 1594 | 93.9 | 0.89 | 198 | 622 | 90.7 |
M 16 | D1+D3+D4+D5+A5 | 0.79 | 149 | 640 | 78.9 | 0.70 | 482 | 1434 | 71.9 | 0.69 | 194 | 560 | 68.9 |
M 17 | D1+D3+D4+A5 | 0.65 | 130 | 655 | 70.6 | 0.61 | 512 | 1480 | 62.2 | 0.68 | 187 | 554 | 65.1 |
M 18 | D1+D4+D5+A5 | 0.74 | 175 | 619 | 73.1 | 0.71 | 512 | 1480 | 62.2 | 0.62 | 227 | 561 | 62.7 |
M 19 | D2+D4+D5+A5 | 0.63 | 80 | 571 | 63.7 | 0.45 | 644 | 1374 | 49.3 | 0.51 | 190 | 525 | 51.4 |
M 20 | D3+D4+D5+A5 | 0.48 | 178 | 472 | 48.3 | 0.27 | 729 | 1253 | 28.6 | 0.27 | 276 | 480 | 27.2 |
M 21 | D4+D5+A5 | 0.43 | 192 | 451 | 42.6 | 0.18 | 826 | 1226 | 18.9 | 0.20 | 276 | 469 | 21.1 |
M 22 | D3+D5+A5 | 0.39 | 187 | 432 | 38.7 | 0.20 | 686 | 1165 | 22.7 | 0.17 | 337 | 471 | 17.8 |
M 23 | D2+D5+A5 | 0.54 | 132 | 549 | 53.9 | 0.20 | 605 | 1328 | 42.6 | 0.41 | 248 | 500 | 41.8 |
M 24 | D1+D5+A5 | 0.64 | 158 | 603 | 63.3 | 0.55 | 558 | 1356 | 55.6 | 0.51 | 226 | 551 | 53.0 |
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Zerouali, B.; Al-Ansari, N.; Chettih, M.; Mohamed, M.; Abda, Z.; Santos, C.A.G.; Zerouali, B.; Elbeltagi, A. An Enhanced Innovative Triangular Trend Analysis of Rainfall Based on a Spectral Approach. Water 2021, 13, 727. https://doi.org/10.3390/w13050727
Zerouali B, Al-Ansari N, Chettih M, Mohamed M, Abda Z, Santos CAG, Zerouali B, Elbeltagi A. An Enhanced Innovative Triangular Trend Analysis of Rainfall Based on a Spectral Approach. Water. 2021; 13(5):727. https://doi.org/10.3390/w13050727
Chicago/Turabian StyleZerouali, Bilel, Nadhir Al-Ansari, Mohamed Chettih, Mesbah Mohamed, Zaki Abda, Celso Augusto Guimarães Santos, Bilal Zerouali, and Ahmed Elbeltagi. 2021. "An Enhanced Innovative Triangular Trend Analysis of Rainfall Based on a Spectral Approach" Water 13, no. 5: 727. https://doi.org/10.3390/w13050727