Wavelet-ANN versus ANN-Based Model for Hydrometeorological Drought Forecasting
<p>Neural network structure.</p> "> Figure 2
<p>Schematic diagram of wavelet-based artificial neural network (W-ANN) model development.</p> "> Figure 3
<p>Langat River Basin.</p> "> Figure 4
<p>Monthly rainfall distribution at station 2, estimated using data from 1986 to 2016.</p> "> Figure 5
<p>Water level data for 30 years at station 1 (1986–2016).</p> "> Figure 6
<p>Standard Index of Annual Precipitation (SIAP) values for 30 years at station 2.</p> "> Figure 7
<p>Distribution of SIAP values into classes (station 2).</p> "> Figure 8
<p>Neural network training regression for input model 1.</p> "> Figure 9
<p>Error histogram of input model number 1.</p> "> Figure 10
<p>Comparison of observed and forecasted SIAP at station 2 of input model number 1.</p> "> Figure 11
<p>Standardized Water Storage Index (SWSI) values for station 1 for 30 years (360 months).</p> "> Figure 12
<p>SWSI observed and forecasted values (360 months) of station 1 for input model number 3.</p> "> Figure 13
<p>Error histogram for SWSI input model number 3.</p> "> Figure 14
<p>Correlation coefficient for SWSI at station 1 for input model number 3.</p> "> Figure 15
<p>Scatter plot comparing observed and forecasted hydrological drought using W-ANN models.</p> "> Figure 16
<p>Scatter plot comparing observed and forecasted meteorological drought using W-ANN models.</p> ">
Abstract
:1. Introduction
2. Materials and Methods
2.1. Standard Index of Annual Precipitation (SIAP)
2.2. Standardized Water Storage Index (SWSI)
2.3. Development of Forecasting Model Using ANN
2.4. Discrete Wavelet
2.5. W-ANN Model
- Decompose the original time series for each input into subseries components (details and approximations) by DWT.
- Select the most important and effective of each subseries component for each input by the correlation coefficient.
- Construct a W-ANN model using the new summed series obtained by adding the significant components of details sub-time series and approximations sub-time series for each input as the new input to the ANN, and the original output time series as the output of the ANN. Figure 2 shows a schematic representation of the model.
2.6. Study Area and Data Collection
2.6.1. Langat River Basin
2.6.2. Data Collection
2.6.3. Distribution of Rainfall and Water Level
3. Results and Discussion
3.1. Assessment Using Standard Index of Annual Precipitation (SIAP)
Artificial Neural Network (ANN) Model
3.2. Assessment Using SWSI for Hydrological Drought
Artificial Neural Network Model for Hydrological Drought
3.3. W-ANN Model
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Classes of Drought Intensity | SIAP Values |
---|---|
Extremely wet | 0.84 or more |
Wet | 0.52 to 0.84 |
Normal | −0.52 to 0.52 |
Drought | −0.52 to −0.84 |
Extreme drought | −0.84 or less |
SWSI Values | Classification |
---|---|
2.0 or more | Extremely wet |
1.5 to 1.99 | Very wet |
1.0 to 1.49 | Moderately wet |
−0.99 to 0.99 | Near normal |
−1.49 to −1.00 | Moderate drought |
−1.99 to −1.5 | Severe drought |
−2 or less | Extreme drought |
Station | Station Name | Station No. | Coordinates | Data Availability (Years) | Missing Data (%) | |
---|---|---|---|---|---|---|
Latitude (N) | Longitude (E) | |||||
1 | Sg. Semenyih di Sg. Rincing | WL 2918401 | 02°54′55″ | 101°49′25″ | 1986–2016 | 5.4% |
2 | Ldg. Dominion | RF 3018107 | 03°00′13″ | 101°52′55″ | 6.5% |
Category | Number of Months | Percentage (%) |
---|---|---|
Extremely wet | 62 | 17 |
Wet | 25 | 7 |
Normal | 140 | 39 |
Drought | 61 | 17 |
Very severe drought | 72 | 20 |
Total | 360 | 100 |
Input Model Number | Number of Neurons | R | |||
---|---|---|---|---|---|
Training | Validation | Testing | Overall | ||
1 | 10 | 0.907 | 0.865 | 0.908 | 0.899 |
1 | 15 | 0.803 | 0.845 | 0.758 | 0.800 |
1 | 12 | 0.796 | 0.765 | 0.801 | 0.783 |
2 | 8 | 0.712 | 0.813 | 0.705 | 0.741 |
2 | 9 | 0.737 | 0.799 | 0.782 | 0.770 |
2 | 10 | 0.882 | 0.875 | 0.851 | 0.868 |
Drought Classification | Condition | Number of Months | Percentage (%) |
---|---|---|---|
Extremely wet | >2 | 12 | 3.33 |
Very wet | 1.5 to −2 | 16 | 4.44 |
Moderately wet | 1.0 to 1.5 | 35 | 9.72 |
Near normal | −1.0 to 1.0 | 240 | 66.67 |
Moderate drought | −1.5 to −1.0 | 37 | 10.28 |
Severe drought | −2.0 to −1.5 | 9 | 2.50 |
Extreme drought | <−2 | 11 | 3.06 |
Input Model Number | Number of Neurons | R | |||
---|---|---|---|---|---|
Training | Validation | Testing | Overall | ||
3 | 10 | 0.968 | 0.967 | 0.969 | 0.968 |
3 | 11 | 0.898 | 0.908 | 0.951 | 0.918 |
3 | 7 | 0.767 | 0.801 | 0.822 | 0.796 |
4 | 15 | 0.901 | 0.855 | 0.835 | 0.865 |
4 | 10 | 0.911 | 0.899 | 0.853 | 0.888 |
4 | 6 | 0.751 | 0.772 | 0.811 | 0.779 |
Discrete Wavelet Components (db3) | Correlation between Detailed Sub-Time Series and Observed Drought Index/Rainfall/Water Level Data | ||||
---|---|---|---|---|---|
SIAP | SWSI | Rainfall | Water Level * | Dominant | |
D1 | 0.5291 | 0.1996 | 0.5291 | 0.1335 | √ |
D2 | 0.5732 | 0.2221 | 0.5732 | 0.1522 | √ |
D3 | 0.3645 | 0.1900 | 0.3645 | 0.1409 | √ |
D4 | 0.2130 | 0.1322 | 0.2130 | 0.1120 | x |
D5 | 0.1616 | 0.1519 | 0.1616 | 0.1333 | x |
D6 | 0.2576 | 0.1885 | 0.2576 | 0.0694 | x |
D7 | 0.2015 | 0.0820 | 0.2015 | 0.3151 * | |
D8 | 0.3201 | 0.3923 | 0.3201 | 0.4303 * | √ |
Average | 0.3274 | 0.1948 | 0.3274 | 0.1858 |
Input Model (After Wavelet Decomposition) | RMSE (Validation) | R (Overall) | Hidden Neurons |
---|---|---|---|
1 (Rt-1, Rt-2, Rt-3) | 0.38 | 0.932 | 8 |
1 (Rt-1, Rt-2, Rt-3) | 0.41 | 0.931 | 10 |
1 (Rt-1, Rt-2, Rt-3) | 0.38 | 0.901 | 15 |
2 (SIt-1, SIt-2, SIt-3) | 0.40 | 0.922 | 8 |
2 (SIt-1, SIt-2, SIt-3) | 0.42 | 0.931 | 10 |
2 (SIt-1, SIt-2, SIt-3) | 0.39 | 0.940 | 15 |
3 (Wt-1, Wt-2, Wt-3) | 0.40 | 0.902 | 8 |
3 (Wt-1, Wt-2, Wt-3) | 0.43 | 0.901 | 10 |
3 (Wt-1, Wt-2, Wt-3) | 0.38 | 0.910 | 15 |
4 (SWt-1, SWt-2, SWt-3) | 0.19 | 0.971 | 10 |
4 (SWt-1, SWt-2, SWt-3) | 0.17 | 0.972 | 13 |
4 (SWt-1, SWt-2, SWt-3) | 0.21 | 0.973 | 15 |
Input Model | R (With Wavelet Decomposition) | R (Without Wavelet Decomposition) | Performance Improvement (%) |
---|---|---|---|
1 (Rt-1, Rt-2, Rt-3) | 0.932 | 0.899 | +3.67 |
2 (SIt-1, SIt-2, SIt-3) | 0.940 | 0.868 | +8.29 |
3 (Wt-1, Wt-2, Wt-3) | 0.910 | 0.968 | −5.99 |
4 (SWt-1, SWt-2, SWt-3) | 0.973 | 0.888 | +9.57 |
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Khan, M.M.H.; Muhammad, N.S.; El-Shafie, A. Wavelet-ANN versus ANN-Based Model for Hydrometeorological Drought Forecasting. Water 2018, 10, 998. https://doi.org/10.3390/w10080998
Khan MMH, Muhammad NS, El-Shafie A. Wavelet-ANN versus ANN-Based Model for Hydrometeorological Drought Forecasting. Water. 2018; 10(8):998. https://doi.org/10.3390/w10080998
Chicago/Turabian StyleKhan, Md Munir H., Nur Shazwani Muhammad, and Ahmed El-Shafie. 2018. "Wavelet-ANN versus ANN-Based Model for Hydrometeorological Drought Forecasting" Water 10, no. 8: 998. https://doi.org/10.3390/w10080998