Reference Evapotranspiration Variation Analysis and Its Approaches Evaluation of 13 Empirical Models in Sub-Humid and Humid Regions: A Case Study of the Huai River Basin, Eastern China
Abstract
:1. Introduction
2. Materials and Methods
2.1. Study Area and Datasets
2.2. Penman–Monteith FAO-56 Model (PMF-56 Model)
2.3. Empirical Models
2.4. Performance Evaluation Approaches
2.5. Calibration and Validation of the Empirical Models
2.6. Trend Test
3. Results and Discussion
3.1. Monthly Variations of the ETPMF
3.2. Performance Evaluation of the 13 Empirical Models in the HRB
3.3. Calibration of the Empirical Models
3.4. Validation of the Calibrated Empirical Models
4. Conclusions
- (1)
- The ETPMF increased initially and then decreased on a monthly timescale, with the peak value appearing in June and the lowest value appearing in January. The ETPMF exhibited significant decreasing trends in January, June, July, and August; however, in March and April, the ETPMF demonstrated slightly non-significant increasing trends.
- (2)
- On a daily timescale, before the calibration, the VA3 model could be regarded as the best alternative model for estimating reference evapotranspiration in the HRB. However, the PEN, WMO, TRA, and JH models could not be considered appropriate alternative models, because of large errors in their estimations. In particular, the PEN model performed the worst with values of the RRMSE, the MAE, and the NS at 0.580, 1.301, and −0.006, respectively.
- (3)
- During the calibration, the determination coefficients of the temperature-based, radiation-based, and combined models presented change trends that increased primarily and then decreased from January to December. High determination coefficients of these models mainly existed between April and October. On the contrary, the mass transfer-based models revealed opposite change trends from January to December. Despite the fact that the mass transfer-based models showed poor performances in daily scatter plots, the performances of these models in January and December were better, with the determination coefficients of the WMO and TRA models at greater than 0.9 and also greater than that of the VA3 model.
- (4)
- After the calibration, the reference evapotranspiration calculated by each of the 13 empirical models on monthly and annual timescales were very close to that estimated by the PMF-56 model, except for the PEN model, which overestimated the reference evapotranspiration from March to October and also on an annual timescale.
- (5)
- If the comprehensive meteorological datasets were available, the VA3 model would be the best alternative empirical model for the PMF-56 model, because it had an easy computation procedure and generated fewer errors compared to the other 12 empirical models, and it was also highly correlated with the PMF-56 model. After accurate validation for the VA3 model using Equation (5), the calibrated parameters of a and b for each site in the HRB were obtained. Based on data availability, the temperature-based, radiation-based, VA1, and VA2 models are recommended during April–October if corresponding input parameters in Table 2 are accessible in the HRB and other similar regions, whereas the mass transfer-based models are preferable in other months.
Acknowledgments
Author Contributions
Conflicts of Interest
Appendix A
WMO Number | Stations | Lon. (°E) | Lat. (°N) | H (m) | WMO Number | Stations | Lon. (°E) | Lat. (°N) | H (m) |
---|---|---|---|---|---|---|---|---|---|
54836 | Yiyuan | 118.15 | 36.18 | 301.6 | 58011 | Shanxian | 116.07 | 34.80 | 44.3 |
54906 | Heze | 115.43 | 35.25 | 50.8 | 58012 | Fengxian | 116.58 | 34.68 | 40.6 |
54908 | Dongming | 115.08 | 35.28 | 59.5 | 58013 | Peixian | 116.92 | 34.72 | 36.7 |
54910 | Liangshan | 116.08 | 35.80 | 40.8 | 58015 | Dangshan | 116.33 | 34.42 | 50.9 |
54913 | Ningyang | 116.80 | 35.75 | 61.2 | 58016 | Xiaoxian | 116.97 | 34.18 | 39.2 |
54914 | Juye | 116.10 | 35.42 | 41.1 | 58017 | Xiayi | 116.13 | 34.25 | 41 |
54915 | Jining | 116.58 | 35.43 | 45.2 | 58020 | Weishan | 117.13 | 34.85 | 40.5 |
54916 | Yanzhou | 116.85 | 35.57 | 53 | 58024 | Zaozhuang | 117.58 | 34.87 | 74.8 |
54917 | Jinxiang | 116.30 | 35.10 | 41.3 | 58026 | Pizhou | 117.85 | 34.30 | 24 |
54919 | Zoucheng | 117.00 | 35.42 | 78.9 | 58027 | Xuzhou | 117.15 | 34.28 | 41.9 |
54920 | Sishui | 117.27 | 35.65 | 110.4 | 58034 | Tancheng | 118.37 | 34.62 | 38.4 |
54923 | Mengyin | 117.92 | 35.72 | 202.9 | 58035 | Xinyi | 118.35 | 34.35 | 29.4 |
54925 | Pingyi | 117.62 | 35.50 | 167 | 58036 | Donghai | 118.73 | 34.52 | 35.2 |
54927 | Tengzhou | 117.13 | 35.12 | 65.9 | 58038 | Shuyang | 118.75 | 34.10 | 8.8 |
54929 | Feixian | 117.95 | 35.25 | 120.5 | 58040 | Ganyu | 119.12 | 34.83 | 9.8 |
54932 | Yishui | 118.67 | 35.80 | 160.6 | 58044 | Lianyungang | 119.17 | 34.58 | 4.1 |
54936 | Juxian | 118.83 | 35.58 | 108.6 | 58047 | Guanyun | 119.23 | 34.30 | 5 |
54938 | Linyi | 118.35 | 35.05 | 86.5 | 58048 | Guannan | 119.35 | 34.10 | 6 |
54939 | Junan | 118.83 | 35.25 | 113.1 | 58049 | Binhai | 119.82 | 34.03 | 4.5 |
54945 | Rizhao | 119.53 | 35.38 | 22.8 | 58100 | Dancheng | 115.18 | 33.63 | 42.4 |
57075 | Ruzhou | 112.83 | 34.18 | 214.2 | 58101 | Luyi | 115.48 | 33.88 | 41.2 |
57078 | Ruyang | 112.47 | 34.15 | 307.8 | 58102 | Bozhou | 115.77 | 33.87 | 41.8 |
57081 | Xingyang | 113.43 | 34.80 | 140.5 | 58104 | Shenqiu | 115.07 | 33.40 | 42 |
57083 | Zhengzhou | 113.65 | 34.72 | 111.3 | 58107 | Linquan | 115.38 | 33.07 | 36.5 |
57085 | Xinmi | 113.37 | 34.52 | 289.3 | 58108 | Jieshou | 115.35 | 33.27 | 38.7 |
57086 | Xinzheng | 113.73 | 34.40 | 111.9 | 58111 | Yongcheng | 116.38 | 33.93 | 32.7 |
57087 | Changge | 113.80 | 34.20 | 88.5 | 58114 | Guoyang | 116.20 | 33.50 | 31.2 |
57088 | Yuzhou | 113.50 | 34.15 | 117.2 | 58118 | Mengcheng | 116.53 | 33.28 | 27.5 |
57089 | Xuchang | 113.85 | 34.02 | 67.7 | 58122 | Suzhou | 116.98 | 33.63 | 36.7 |
57090 | Zhongmu | 114.02 | 34.72 | 82.1 | 58125 | Lingbi | 117.55 | 33.55 | 28.1 |
57091 | Kaifeng | 114.38 | 34.77 | 73.7 | 58126 | Sixian | 117.87 | 33.47 | 20.6 |
57093 | Lankao | 114.82 | 34.85 | 72.2 | 58129 | Wuhe | 117.88 | 33.13 | 21 |
57094 | Weishi | 114.20 | 34.40 | 67.5 | 58130 | Suining | 117.92 | 33.88 | 23.5 |
57095 | Yanling | 114.20 | 34.08 | 60.4 | 58131 | Suyu | 118.23 | 33.95 | 28.1 |
57096 | Qixian | 114.78 | 34.53 | 60.7 | 58132 | Siyang | 118.72 | 33.70 | 15.6 |
57098 | Fugou | 114.40 | 34.08 | 59.3 | 58135 | Sihong | 118.22 | 33.45 | 17 |
57099 | Taikang | 114.85 | 34.07 | 53.6 | 58138 | Xuyi | 118.52 | 32.98 | 36.3 |
57173 | Lushan | 112.88 | 33.75 | 146.9 | 58139 | Hongze | 118.85 | 33.30 | 19.6 |
57179 | Fangcheng | 113.00 | 33.28 | 161.5 | 58140 | Lianshui | 119.27 | 33.78 | 10.2 |
57180 | Jiaxian | 113.20 | 33.98 | 118.6 | 58143 | Funing | 119.80 | 33.80 | 3.1 |
57181 | Baofeng | 113.05 | 33.88 | 137.5 | 58145 | Chuzhou | 119.17 | 33.53 | 8.3 |
57182 | Xiangcheng | 113.50 | 33.85 | 81.4 | 58146 | Jianhu | 119.82 | 33.48 | 3.4 |
57183 | Linying | 113.92 | 33.80 | 60.8 | 58147 | Jinhu | 119.03 | 33.03 | 10.9 |
57184 | Yexian | 113.65 | 33.60 | 86.7 | 58148 | Baoying | 119.30 | 33.23 | 8.4 |
57185 | Wuyang | 113.58 | 33.45 | 92.3 | 58150 | Sheyang | 120.25 | 33.77 | 6.7 |
57186 | Luohe | 114.00 | 33.58 | 62.1 | 58158 | Dafeng | 120.48 | 33.20 | 7.3 |
57188 | Xiping | 114.00 | 33.38 | 60.6 | 58202 | Funan | 115.58 | 32.63 | 35.7 |
57192 | Huaiyang | 114.85 | 33.73 | 46.3 | 58203 | Fuyang | 115.82 | 32.92 | 38.6 |
57193 | Xihua | 114.52 | 33.78 | 53.5 | 58207 | Huangchuan | 115.03 | 32.15 | 42.9 |
57194 | Shangcai | 114.27 | 33.28 | 60.8 | 58208 | Gushi | 115.67 | 32.17 | 57.9 |
57195 | Chuanhuiqu | 114.62 | 33.62 | 47.6 | 58210 | Yingshang | 116.22 | 32.57 | 25.5 |
57196 | Xiangcheng | 114.88 | 33.45 | 44.4 | 58214 | Huoqiu | 116.28 | 32.33 | 36.9 |
57285 | Tongbai | 113.42 | 32.38 | 149.1 | 58215 | Shouxian | 116.78 | 32.55 | 23.5 |
57290 | Zhumadian | 114.02 | 33.00 | 83.3 | 58221 | Bengbu | 117.38 | 32.95 | 26 |
57292 | Pingyu | 114.63 | 32.95 | 44 | 58222 | Fengyang | 117.55 | 32.87 | 28 |
57293 | Xincai | 114.98 | 32.73 | 39.1 | 58223 | Mingguang | 117.98 | 32.78 | 35.6 |
57295 | Zhengyang | 114.35 | 32.62 | 79.7 | 58225 | Dingyuan | 117.67 | 32.53 | 76.7 |
57296 | Xixian | 114.73 | 32.35 | 50.1 | 58240 | Tianchang | 119.02 | 32.68 | 21 |
57297 | Xinyang | 114.05 | 32.13 | 115.1 | 58243 | Xinghua | 119.83 | 32.93 | 7.3 |
57298 | Luoshan | 114.55 | 32.22 | 56.1 | 58244 | Jiangdu | 119.57 | 32.45 | 10.3 |
57299 | Guangshan | 114.90 | 32.02 | 50.6 | 58245 | Yangzhou | 119.42 | 32.42 | 9.9 |
57390 | Jigongshan | 114.07 | 31.80 | 733.5 | 58251 | Dongtai | 120.32 | 32.87 | 5.1 |
57396 | Xinxian | 114.85 | 31.63 | 130.8 | 58254 | Haian | 120.45 | 32.53 | 5.2 |
58001 | Suixian | 115.10 | 34.43 | 57.1 | 58264 | Rudong | 121.18 | 32.33 | 3.4 |
58002 | Caoxian | 115.55 | 34.82 | 50 | 58301 | Shangcheng | 115.38 | 31.80 | 79.1 |
58004 | Minquan | 115.15 | 34.65 | 61 | 58306 | Jinzhai | 115.88 | 31.68 | 94 |
58005 | Shangqiu | 115.67 | 34.45 | 51 | 58311 | Luan | 116.50 | 31.75 | 60.4 |
58006 | Yucheng | 115.88 | 34.38 | 47.2 |
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Region | T (°C) | Tmax (°C) | Tmin (°C) | RH (%) | u2 (m·s−1) | Rs (MJ·m−2·d—1) | Pr (mm·a—1) | ET0 (mm·a—1) |
---|---|---|---|---|---|---|---|---|
Sub-humid (I) | 14.45 | 19.93 | 9.84 | 70.29 | 1.86 | 15.08 | 783.05 | 981.23 |
Humid (II) | 15.03 | 19.88 | 11.12 | 75.96 | 1.95 | 14.85 | 1049.63 | 936.89 |
Whole | 14.60 | 19.92 | 10.18 | 71.78 | 1.88 | 15.02 | 853.10 | 969.57 |
NO. | Models | Models Input | Equations | References |
---|---|---|---|---|
Temperature-based | ||||
1 | Hargreaves–Samani | T, Tmax, Tmin | [32] | |
Mass transfer-based | ||||
2 | Penman | u2, es − ea | [33] | |
3 | WMO | u2, es − ea | [34] | |
4 | Trabert | u2, es − ea | [35] | |
Radiation-based | ||||
5 | Makkink | Rs, T | [36] | |
6 | Priestley–Taylor | Rn, T | [37] | |
7 | Jensen–Haise | Rs, T | [38] | |
8 | Abtew | Rs, Tmax | [39] | |
9 | Irmak | Rs, T | [40] | |
10 | Tabari | Rs, Tmax, Tmin | [24] | |
Combined | ||||
11 | Valiantzas1 | Rs, T, RH | [41,42] | |
12 | Valiantzas2 | Rs, T, Tmin | [41,42] | |
13 | Valiantzas3 | Rs, T, RH, u2 | [41,42] |
Parameters | Jan | Feby | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec |
---|---|---|---|---|---|---|---|---|---|---|---|---|
β | −0.108 * | −0.075 | 0.022 | 0.030 | −0.252 | −0.628 *** | −0.330 ** | −0.460 *** | −0.155 | −0.081 | −0.082 | −0.089 |
Z | −2.074 | −1.015 | 0.149 | 0.269 | −1.701 | −4.148 | −2.716 | −4.252 | −1.925 | −0.985 | −1.343 | −1.641 |
Parameters | ETHS | ETPEN | ETWMO | ETTRA | ETMAK | ETPT | ETJH | ETABT | ETIRM | ETTAB | ETVA1 | ETVA2 | ETVA3 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
RRMSE | 0.222 | 0.580 | 0.500 | 0.364 | 0.217 | 0.195 | 0.417 | 0.195 | 0.161 | 0.190 | 0.147 | 0.160 | 0.126 |
MAE | 0.475 | 1.301 | 1.079 | 0.723 | 0.440 | 0.411 | 0.870 | 0.427 | 0.347 | 0.350 | 0.309 | 0.340 | 0.267 |
NS | 0.853 | −0.006 | 0.250 | 0.604 | 0.859 | 0.886 | 0.479 | 0.886 | 0.923 | 0.892 | 0.935 | 0.924 | 0.953 |
Month | Parameters | ETHS | ETPEN | ETWMO | ETTRA | ETMAK | ETPT | ETJH | ETABT | ETIRM | ETTAB | ETVA1 | ETVA2 | ETVA3 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
January | a | 0.671 | 1.188 | 0.783 | 0.639 | 0.709 | 0.868 | 0.477 | 0.562 | 0.467 | 0.562 | 0.606 | 0.506 | 0.613 |
b | 0.316 | 0.329 | 0.443 | 0.410 | 0.376 | 0.334 | 0.804 | 0.727 | 0.578 | 0.588 | 0.370 | 0.627 | 0.364 | |
R2 | 0.350 | 0.814 | 0.943 | 0.958 | 0.428 | 0.114 | 0.207 | 0.354 | 0.430 | 0.394 | 0.703 | 0.402 | 0.899 | |
February | a | 0.825 | 1.311 | 0.851 | 0.685 | 0.908 | 1.244 | 0.712 | 0.721 | 0.648 | 0.772 | 0.680 | 0.665 | 0.664 |
b | 0.181 | 0.478 | 0.626 | 0.589 | 0.274 | −0.149 | 0.834 | 0.797 | 0.466 | 0.455 | 0.381 | 0.614 | 0.394 | |
R2 | 0.658 | 0.871 | 0.891 | 0.913 | 0.665 | 0.570 | 0.578 | 0.661 | 0.677 | 0.620 | 0.861 | 0.696 | 0.954 | |
March | a | 0.902 | 1.443 | 0.826 | 0.687 | 0.995 | 1.098 | 0.763 | 0.785 | 0.830 | 0.983 | 0.761 | 0.748 | 0.721 |
b | 0.000 | 0.747 | 1.034 | 0.953 | 0.301 | −0.175 | 0.786 | 0.878 | 0.270 | 0.234 | 0.380 | 0.621 | 0.409 | |
R2 | 0.743 | 0.880 | 0.834 | 0.868 | 0.779 | 0.723 | 0.779 | 0.795 | 0.783 | 0.754 | 0.911 | 0.796 | 0.975 | |
April | a | 0.946 | 1.338 | 0.763 | 0.636 | 1.014 | 0.964 | 0.663 | 0.756 | 0.987 | 1.144 | 0.792 | 0.770 | 0.770 |
b | −0.269 | 1.276 | 1.677 | 1.556 | 0.435 | −0.035 | 0.915 | 1.026 | −0.051 | −0.065 | 0.480 | 0.701 | 0.465 | |
R2 | 0.757 | 0.846 | 0.745 | 0.794 | 0.824 | 0.773 | 0.823 | 0.843 | 0.826 | 0.799 | 0.930 | 0.837 | 0.977 | |
May | a | 1.072 | 1.113 | 0.710 | 0.567 | 1.129 | 1.045 | 0.694 | 0.798 | 1.213 | 1.398 | 0.828 | 0.855 | 0.806 |
b | −1.007 | 1.846 | 2.241 | 2.146 | 0.254 | −0.484 | 0.627 | 0.883 | −0.810 | −0.819 | 0.508 | 0.496 | 0.561 | |
R2 | 0.837 | 0.847 | 0.782 | 0.811 | 0.875 | 0.837 | 0.897 | 0.905 | 0.885 | 0.854 | 0.955 | 0.897 | 0.985 | |
June | a | 1.278 | 0.985 | 0.622 | 0.496 | 1.212 | 1.080 | 0.710 | 0.850 | 1.403 | 1.557 | 0.864 | 0.931 | 0.827 |
b | −2.062 | 2.129 | 2.622 | 2.510 | 0.192 | −0.669 | 0.402 | 0.693 | −1.557 | −1.383 | 0.534 | 0.318 | 0.671 | |
R2 | 0.855 | 0.827 | 0.796 | 0.817 | 0.888 | 0.835 | 0.910 | 0.920 | 0.901 | 0.867 | 0.958 | 0.915 | 0.991 | |
July | a | 1.417 | 1.265 | 0.750 | 0.607 | 1.151 | 0.920 | 0.628 | 0.807 | 1.330 | 1.431 | 0.885 | 0.902 | 0.864 |
b | −2.517 | 2.018 | 2.680 | 2.556 | 0.175 | −0.369 | 0.452 | 0.608 | −1.598 | −1.340 | 0.477 | 0.228 | 0.584 | |
R2 | 0.814 | 0.785 | 0.676 | 0.707 | 0.942 | 0.942 | 0.965 | 0.965 | 0.955 | 0.947 | 0.977 | 0.958 | 0.993 | |
August | a | 1.365 | 1.377 | 0.925 | 0.713 | 1.069 | 0.864 | 0.596 | 0.759 | 1.225 | 1.322 | 0.836 | 0.842 | 0.850 |
b | −2.009 | 1.771 | 2.342 | 2.293 | 0.293 | −0.144 | 0.524 | 0.672 | −1.289 | −1.061 | 0.542 | 0.337 | 0.556 | |
R2 | 0.853 | 0.769 | 0.612 | 0.634 | 0.958 | 0.963 | 0.980 | 0.976 | 0.970 | 0.958 | 0.977 | 0.968 | 0.988 | |
September | a | 0.997 | 1.086 | 0.774 | 0.605 | 0.892 | 0.830 | 0.564 | 0.663 | 0.969 | 1.090 | 0.700 | 0.697 | 0.746 |
b | −0.531 | 1.398 | 1.768 | 1.719 | 0.628 | 0.208 | 0.722 | 0.901 | −0.342 | −0.240 | 0.703 | 0.682 | 0.633 | |
R2 | 0.825 | 0.657 | 0.503 | 0.528 | 0.909 | 0.871 | 0.923 | 0.919 | 0.921 | 0.905 | 0.933 | 0.915 | 0.965 | |
October | a | 0.797 | 0.984 | 0.736 | 0.572 | 0.806 | 0.888 | 0.573 | 0.613 | 0.796 | 0.952 | 0.623 | 0.612 | 0.667 |
b | 0.107 | 0.913 | 1.119 | 1.091 | 0.552 | 0.251 | 0.658 | 0.819 | 0.061 | 0.076 | 0.558 | 0.651 | 0.508 | |
R2 | 0.708 | 0.757 | 0.720 | 0.739 | 0.773 | 0.684 | 0.794 | 0.776 | 0.788 | 0.780 | 0.857 | 0.775 | 0.936 | |
November | a | 0.625 | 0.960 | 0.712 | 0.563 | 0.692 | 0.802 | 0.510 | 0.531 | 0.551 | 0.683 | 0.567 | 0.498 | 0.623 |
b | 0.386 | 0.551 | 0.641 | 0.615 | 0.500 | 0.469 | 0.718 | 0.760 | 0.473 | 0.483 | 0.429 | 0.649 | 0.354 | |
R2 | 0.451 | 0.801 | 0.882 | 0.898 | 0.526 | 0.288 | 0.489 | 0.503 | 0.522 | 0.506 | 0.736 | 0.520 | 0.905 | |
December | a | 0.589 | 1.078 | 0.740 | 0.595 | 0.667 | 0.477 | 0.466 | 0.499 | 0.453 | 0.579 | 0.575 | 0.449 | 0.606 |
b | 0.376 | 0.320 | 0.421 | 0.394 | 0.406 | 0.661 | 0.734 | 0.698 | 0.557 | 0.561 | 0.343 | 0.617 | 0.314 | |
R2 | 0.277 | 0.803 | 0.981 | 0.984 | 0.363 | 0.020 | 0.234 | 0.305 | 0.360 | 0.338 | 0.647 | 0.338 | 0.882 |
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Li, M.; Chu, R.; Islam, A.R.M.T.; Shen, S. Reference Evapotranspiration Variation Analysis and Its Approaches Evaluation of 13 Empirical Models in Sub-Humid and Humid Regions: A Case Study of the Huai River Basin, Eastern China. Water 2018, 10, 493. https://doi.org/10.3390/w10040493
Li M, Chu R, Islam ARMT, Shen S. Reference Evapotranspiration Variation Analysis and Its Approaches Evaluation of 13 Empirical Models in Sub-Humid and Humid Regions: A Case Study of the Huai River Basin, Eastern China. Water. 2018; 10(4):493. https://doi.org/10.3390/w10040493
Chicago/Turabian StyleLi, Meng, Ronghao Chu, Abu Reza Md. Towfiqul Islam, and Shuanghe Shen. 2018. "Reference Evapotranspiration Variation Analysis and Its Approaches Evaluation of 13 Empirical Models in Sub-Humid and Humid Regions: A Case Study of the Huai River Basin, Eastern China" Water 10, no. 4: 493. https://doi.org/10.3390/w10040493