Performance Evaluation of Deep Learning-Based Gated Recurrent Units (GRUs) and Tree-Based Models for Estimating ETo by Using Limited Meteorological Variables
Abstract
:1. Introduction
2. Material and Methods
2.1. ETo Calculation
2.2. Tree Models
2.3. M5 Decision Tree (M5T)
2.4. Reduces Error Pruning (REP) Tree Classifier
2.5. The Random Tree
2.6. The Random Forest
2.7. Gated Recurrent Units (GRU)
2.8. Weka and Python
3. Results and Discussion
3.1. M5P Model
3.2. The Random Forest
3.3. The Random Tree
3.4. REPtree
3.5. GRU
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Variable | Minimum | Maximum | Mean | Std. Deviation |
---|---|---|---|---|
Tmin (°C) | −11.50 | 26.20 | 10.96 | 7.18 |
Tmax (°C) | −7.20 | 40.20 | 18.58 | 8.15 |
Wind speed - U2 (m/s) | 0.10 | 10.60 | 2.54 | 1.07 |
Tdew (°C) | −13.15 | 27.07 | 10.79 | 6.92 |
Sunshine duration - n (hr) | 0.00 | 11.00 | 5.85 | 2.81 |
Min RH (%) | 1.00 | 100.00 | 65.88 | 16.39 |
Max RH (%) | 37.00 | 100.00 | 88.49 | 8.74 |
ETo-PM (mm/day) | 0.22 | 8.17 | 2.69 | 1.74 |
Variables | MTI | tmin | tmax | u2 | tdew | n | Min RH | Max RH | ETo-PM |
---|---|---|---|---|---|---|---|---|---|
MTI ** | 1 | 0.307 | 0.281 | 0.029 | 0.308 | 0.023 | −0.038 | −0.044 | 0.058 |
tmin | 0.307 | 1 | 0.952 | 0.028 | 0.960 | 0.746 | −0.336 | −0.210 | 0.843 |
tmax | 0.281 | 0.952 | 1 | 0.000 | 0.928 | 0.776 | −0.455 | −0.262 | 0.870 |
u2 | 0.029 | 0.028 | 0.000 | 1 | −0.048 | −0.032 | −0.231 | −0.156 | 0.101 |
tdew | 0.308 | 0.960 | 0.928 | −0.048 | 1 | 0.699 | −0.171 | −0.008 | 0.752 |
n | 0.023 | 0.746 | 0.776 | −0.032 | 0.699 | 1 | −0.385 | −0.355 | 0.904 |
Min RH | −0.038 | −0.336 | −0.455 | −0.231 | −0.171 | −0.385 | 1 | 0.548 | −0.550 |
Max RH | −0.044 | −0.210 | −0.262 | −0.156 | −0.008 | −0.355 | 0.548 | 1 | −0.460 |
ETo-PM | 0.058 | 0.843 | 0.870 | 0.101 | 0.752 | 0.904 | −0.550 | −0.460 | 1 |
Scenarios | Inputs | Number of Input Parameters | |||||||
---|---|---|---|---|---|---|---|---|---|
MTI | Tmin | Tmax | U2 | Tdev | n | MinRH | MaxRH | ||
1 | * | * | * | * | * | * | * | * | 8 |
2 | * | * | * | * | * | * | * | 7 | |
3 | * | * | * | * | * | * | 6 | ||
4 | * | * | * | * | * | 5 | |||
5 | * | * | * | * | 4 | ||||
6 | * | * | * | 3 | |||||
7 | * | * | 2 | ||||||
8 | * | 1 | |||||||
9 | * | 1 | |||||||
10 | * | * | 2 | ||||||
11 | * | 1 | |||||||
12 | * | * | 2 | ||||||
13 | * | * | * | * | 4 | ||||
14 | * | * | * | 3 | |||||
15 | * | * | 2 |
Scenarios | Evaluation Metrics | Number of Input Parameters | ||||
---|---|---|---|---|---|---|
R | MAE (mm/day) | RMSE (mm/day) | LM No | Run Time (s) | ||
1 | 0.9925 | 0.1566 | 0.2135 | 63 | 0.18 | 8 |
2 | 0.9917 | 0.1617 | 0.2236 | 62 | 0.58 | 7 |
3 | 0.9795 | 0.2595 | 0.3506 | 64 | 0.59 | 6 |
4 | 0.9771 | 0.2745 | 0.3704 | 45 | 0.56 | 5 |
5 | 0.9692 | 0.3215 | 0.4289 | 45 | 0.56 | 4 |
6 | 0.9063 | 0.5856 | 0.7360 | 4 | 0.53 | 3 |
7 | 0.9027 | 0.5977 | 0.7493 | 7 | 0.49 | 2 |
8 | 0.9012 | 0.6013 | 0.7548 | 5 | 0.12 | 1 |
9 | 0.8742 | 0.6690 | 0.8455 | 5 | 0.13 | 1 |
10 | 0.9051 | 0.5892 | 0.7404 | 4 | 0.45 | 2 |
11 | 0.9334 | 0.4611 | 0.6250 | 37 | 0.09 | 1 |
12 | 0.9629 | 0.3509 | 0.4698 | 45 | 0.44 | 2 |
13 | 0.9763 | 0.2812 | 0.3768 | 21 | 0.55 | 4 |
14 | 0.9223 | 0.5375 | 0.6731 | 6 | 0.53 | 3 |
15 | 0.9694 | 0.3190 | 0.4277 | 20 | 0.28 | 2 |
Scenarios | Evaluation Metrics | Number of Input Parameters | |||
---|---|---|---|---|---|
R | MAE (mm/day) | RMSE (mm/day) | Run Time (s) | ||
1 | 0.9926 | 0.1533 | 0.2122 | 3.54 | 8 |
2 | 0.9925 | 0.1531 | 0.2136 | 2.60 | 7 |
3 | 0.9826 | 0.2363 | 0.3235 | 2.47 | 6 |
4 | 0.9799 | 0.2554 | 0.3480 | 3.07 | 5 |
5 | 0.9715 | 0.3045 | 0.4126 | 2.71 | 4 |
6 | 0.8947 | 0.6079 | 0.7789 | 2.07 | 3 |
7 | 0.8729 | 0.6611 | 0.8560 | 2.62 | 2 |
8 | 0.8971 | 0.6116 | 0.7697 | 0.59 | 1 |
9 | 0.8709 | 0.6753 | 0.8561 | 0.55 | 1 |
10 | 0.8746 | 0.6551 | 0.8507 | 2.63 | 2 |
11 | 0.9362 | 0.4488 | 0.6122 | 0.43 | 1 |
12 | 0.9586 | 0.3640 | 0.4969 | 2.17 | 2 |
13 | 0.8068 | 3.8546 | 5.1657 | 3.43 | 4 |
14 | 0.9129 | 0.5556 | 0.7113 | 2.37 | 3 |
15 | 0.963 | 0.3486 | 0.4697 | 1.45 | 2 |
Scenarios | Evaluation Metrics | Number of Input Parameters | |||
---|---|---|---|---|---|
R | MAE (mm/day) | RMSE (mm/day) | Run Time (s) | ||
1 | 0.9798 | 0.2472 | 0.3502 | 0.05 | 8 |
2 | 0.9790 | 0.2502 | 0.3567 | 0.22 | 7 |
3 | 0.9623 | 0.3355 | 0.4768 | 0.03 | 6 |
4 | 0.9580 | 0.3599 | 0.5045 | 0.04 | 5 |
5 | 0.9459 | 0.4149 | 0.5739 | 0.04 | 4 |
6 | 0.8205 | 0.7909 | 1.0435 | 0.05 | 3 |
7 | 0.8215 | 0.7909 | 1.0368 | 0.03 | 2 |
8 | 0.8968 | 0.6122 | 0.7706 | 0 | 1 |
9 | 0.8708 | 0.6755 | 0.8563 | 0 | 1 |
10 | 0.8365 | 0.7485 | 0.9867 | 0.02 | 2 |
11 | 0.9362 | 0.4488 | 0.6120 | 0 | 1 |
12 | 0.9419 | 0.4285 | 0.5920 | 0.03 | 2 |
13 | 0.9557 | 0.3721 | 0.5168 | 0.05 | 4 |
14 | 0.8509 | 0.7103 | 0.9495 | 0.03 | 3 |
15 | 0.9599 | 0.3591 | 0.4895 | 0.01 | 2 |
Scenarios | Evaluation Metrics | Number of Input Parameters | |||
---|---|---|---|---|---|
R | MAE (mm/day) | RMSE (mm/day) | Run Time (s) | ||
1 | 0.9820 | 0.2366 | 0.3288 | 0.04 | 8 |
2 | 0.9820 | 0.2373 | 0.3293 | 0.21 | 7 |
3 | 0.9703 | 0.3052 | 0.4219 | 0.05 | 6 |
4 | 0.9697 | 0.3085 | 0.4256 | 0.03 | 5 |
5 | 0.9676 | 0.3218 | 0.4400 | 0.03 | 4 |
6 | 0.9000 | 0.5990 | 0.7594 | 0.02 | 3 |
7 | 0.8977 | 0.6079 | 0.7676 | 0.01 | 2 |
8 | 0.8993 | 0.6061 | 0.7615 | 0 | 1 |
9 | 0.8721 | 0.6729 | 0.8523 | 0 | 1 |
10 | 0.8972 | 0.6063 | 0.7693 | 0.02 | 2 |
11 | 0.9356 | 0.4514 | 0.6147 | 0 | 1 |
12 | 0.9620 | 0.3509 | 0.4756 | 0.02 | 2 |
13 | 0.9668 | 0.3273 | 0.4454 | 0.03 | 4 |
14 | 0.9079 | 0.5700 | 0.7313 | 0.03 | 3 |
15 | 0.9670 | 0.3284 | 0.4435 | 0.02 | 2 |
Scenarios | Evaluation Metrics | Number of Input Parameters | |||
---|---|---|---|---|---|
R | MAE (mm/day) | RMSE (mm/day) | Run Time (m) | ||
1 | 0.9931 | 0.1953 | 0.2556 | 3.15 | 8 |
2 | 0.9918 | 0.1747 | 0.2424 | 3.28 | 7 |
3 | 0.9747 | 0.3214 | 0.4171 | 3.01 | 6 |
4 | 0.9731 | 0.3304 | 0.4295 | 1.20 | 5 |
5 | 0.9632 | 0.4103 | 0.5252 | 1.42 | 4 |
6 | 0.9176 | 0.5768 | 0.7261 | 1.25 | 3 |
7 | 0.9131 | 0.5868 | 0.7426 | 2.05 | 2 |
8 | 0.9110 | 0.6193 | 0.7721 | 1.26 | 1 |
9 | 0.9100 | 0.6200 | 0.7661 | 3.22 | 1 |
10 | 0.9169 | 0.5811 | 0.7299 | 1.53 | 2 |
11 | 0.9851 | 0.2402 | 0.3193 | 1.36 | 1 |
12 | 0.9543 | 0.4481 | 0.5882 | 3.14 | 2 |
13 | 0.9708 | 0.3552 | 0.4719 | 3.24 | 4 |
14 | 0.9327 | 0.5350 | 0.6598 | 2.52 | 3 |
15 | 0.9837 | 0.2433 | 0.3292 | 3.43 | 2 |
Method | Scenario | Minimum | Maximum | Mean | Std. Deviation |
---|---|---|---|---|---|
M5P | 1 | 0.174 | 7.556 | 2.686 | 1.726 |
15 | 0.510 | 6.701 | 2.689 | 1.685 | |
RF | 1 | 0.316 | 6.855 | 2.687 | 1.709 |
15 | 0.272 | 7.579 | 2.688 | 1.699 | |
RF | 1 | 0.291 | 8.169 | 2.690 | 1.740 |
15 | 0.223 | 8.169 | 2.688 | 1.705 | |
REP Tree | 1 | 0.292 | 7.616 | 2.690 | 1.718 |
15 | 0.291 | 7.320 | 2.688 | 1.691 | |
GRU | 1 | 0.190 | 7.128 | 2.685 | 1.623 |
15 | 0.382 | 7.319 | 2.679 | 1.687 | |
ETo-PM (mm/day) | 0.223 | 8.169 | 2.687 | 1.742 |
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Sattari, M.T.; Apaydin, H.; Shamshirband, S. Performance Evaluation of Deep Learning-Based Gated Recurrent Units (GRUs) and Tree-Based Models for Estimating ETo by Using Limited Meteorological Variables. Mathematics 2020, 8, 972. https://doi.org/10.3390/math8060972
Sattari MT, Apaydin H, Shamshirband S. Performance Evaluation of Deep Learning-Based Gated Recurrent Units (GRUs) and Tree-Based Models for Estimating ETo by Using Limited Meteorological Variables. Mathematics. 2020; 8(6):972. https://doi.org/10.3390/math8060972
Chicago/Turabian StyleSattari, Mohammad Taghi, Halit Apaydin, and Shahaboddin Shamshirband. 2020. "Performance Evaluation of Deep Learning-Based Gated Recurrent Units (GRUs) and Tree-Based Models for Estimating ETo by Using Limited Meteorological Variables" Mathematics 8, no. 6: 972. https://doi.org/10.3390/math8060972
APA StyleSattari, M. T., Apaydin, H., & Shamshirband, S. (2020). Performance Evaluation of Deep Learning-Based Gated Recurrent Units (GRUs) and Tree-Based Models for Estimating ETo by Using Limited Meteorological Variables. Mathematics, 8(6), 972. https://doi.org/10.3390/math8060972