1. Introduction
In recent years, climate changes and increasing water demand have caused problems in the sustainable management of water resources in the country [ 1 ]. This is especially important in the case of drinking water supply, and sometimes it has caused a tendency to supply different water needs from underground water sources and an excessive drop in the level of some aquifers in the country [ 2 , 3 ]. On the other hand, every year, millions of cubic meters of fresh water stored behind the dams, which are built and maintained at huge costs, evaporate and are wasted [ 4 ].
Accurate and timely estimation of evaporation has a significant and vital impact on preserving water resources and agriculture and hydrology, which is used to estimate the water required by crops for irrigation planning and drought management [ 5 ]. Evaporation is a critical phenomenon in hydrological studies which understanding its amount is vital for management of irrigation systems and water resources [ 6 - 8 ]. One method of estimating evaporation is using evaporation pans [ 9 - 14 ], which is well-known as a means of measuring evaporation from the free surface of water globally [ 15 , 16 ]. Given the importance of evaporation and its high impact on climate change and the amount of freshwater resources that lead to negative effects on water resources, accurate prediction of evaporation is essential in the hydrological cycle [ 17 ]. Many parameters affect the rate of evaporation, including relative humidity, temperature, wind speed, and sunshine hours [ 18 - 22 ]. Another method of predicting the rate of evaporation is the use of intelligent methods [ 23 - 26 ]. Intelligent methods have been welcomed due to the reduction of computation time, as well as the reduction of trial and error process [ 27 , 28 ].
In recent years, many intelligent models have been proposed to estimate the rate of evaporation, including the MLP model [ 12 , 13 , 29 - 31 ], SVR model [ 14 , 25 , 32 - 34 ], M5tree model [ 35 - 38 ], GEP model [ 35 , 39 , 40 ], ANFIS model [ 40 - 43 ]. Also, various hybrid models in evaporation simulation have been presented [ 12 , 23 , 30 , 41 , 44 - 46 ]. Table 1 provided some studies in connection with research on estimating the rate of evaporation by intelligent methods.
Due to the fact that very few studies have been conducted to estimate evaporation using deep learning methods, the purpose of this study was to compare the performance of two models of artificial neural network and Long- Short Term Memory (LSTM) to estimate evaporation from the pan in Semnan and Garmsar cities from Semnan province of Iran. Considering that the mentioned cities are in hot and dry weather conditions, in this research we seek to investigate the efficiency of LSTM model in predicting evaporation in dry areas. Also, the results of the LSTM model of the current research were compared with the results of other researches that estimate evaporation from the pan with soft computing model. Meteorological parameters of T_{min}, T_{max}, WS, SH, PA, RH and EP were examined as input data. The present study also answers the question whether the two ANN and LSTM models are suitable methods for estimating evaporation in the cities of Semnan and Garmsar?
Previous work | Number of years study | Station | Methods | R^{2} | Input variables | |
---|---|---|---|---|---|---|
Kisi, 2015 [49] | 20 | Mersin | LLSVM | 0.88 | AT^{1}, SR^{2}, WS, RH, EP | |
M5 Tree | 0.76 | |||||
MARS | 0.86 | |||||
20 | Antalya | LLSVM | 0.93 | |||
M5 Tree | 0.92 | |||||
MARS | 0.88 | |||||
Wang et al., 2017 [38] | 39 | Yangtze River Basin IDs 57461 | ANFIS-GP | 0.93 | AT, SR, PA, WS | |
0.93 | FG | |||||
0.91 | M5Tree | |||||
39 | Yangtze River Basin IDs 57494 | ANFIS-GP | 0.89 | |||
FG | 0.90 | |||||
M5Tree | 0.90 | |||||
39 | Yangtze River Basin IDs 57516 | ANFIS-GP | 0.96 | |||
FG | 0.97 | |||||
M5Tree | 0.95 | |||||
39 | Yangtze River Basin IDs 58238 | ANFIS-GP | 0.95 | |||
FG | 0.95 | |||||
M5Tree | 0.92 | |||||
39 | Yangtze River Basin IDs 58321 | ANFIS-GP | 0.92 | |||
FG | 0.90 | |||||
M5Tree | 0.90 | |||||
39 | Yangtze River Basin IDs 58362 | ANFIS-GP | 0.95 | |||
FG | 0.95 | |||||
M5Tree | 0.92 | |||||
Malik et al., 2017 [50] | 4 | Himalayas, | Uttarakhand | RBNN | 0.87 | T_{min}, T_{max}, RH_{morning}, RH_{afternoon}, WS, SH, EP |
SOMNN | 0.83 | |||||
MLR | 0.81 | |||||
Eray et al., 2018 [51] | 27 | Antakya | MGGP | 0.92 | T_{min}, T_{max}, RA, RH, WS, EP | |
GP | 0.94 | |||||
DENFIS | 0.94 | |||||
39 | Antalya | MGGP | 0.95 | |||
GP | 0.95 | |||||
DENFIS | 0.93 | |||||
Moazenzadeh et al., 2018 [33] | 10 | Lahijan | SVR | 0.78 | T_{min}, T_{max}, RA, RH, WS, EP, P^{3}, SH | |
SVR-FA | 0.79 | |||||
10 | Rasht | SVR | 0.74 | |||
SVR-FA | 0.81 | |||||
Majhi et al., 2019 [52] | 34 | Raipur | Deep-LSTM | 0.91 | T_{min}, T_{max}, RH_{morning}, RH_{afternoon}, WS, SH, EP | |
MLANN | 0.88 | |||||
24 | Jagdalpur | Deep-LSTM | 0.76 | |||
MLANN | 0.76 | |||||
16 | Ambikapur | Deep-LSTM | 0.71 | |||
MLANN | 0.70 | |||||
Karami et al., 2021 [53] | 9 | Garmsar | GMDH-NN | 0.84 | T_{min}, T_{max}, WS, RH, PA, SH | |
Shahi et al., 2021 [54] | 16 | Dameghan | ANN | 0.80 | T_{min}, T_{max}, RH, WS,SH | |
Abed et al., 2021 [55] | 19 | Alor Setar | LSTM | 0.97 | T_{min}, T_{max}, RH, WS,, RA, SH | |
Kota Bharu | LSTM | 0.98 | ||||
^{1}Air Temperature | ||||||
^{2}Solar Radiation | ||||||
^{3}Precipitation |
2. Data and studied areas
Semnan province locates in northeastern of Iran (Figure 1), where its center is Semnan city [ 47 ]. The area of this province is 97491 Km^{2} [ 48 ]. The cities of Semnan and Garmsar have arid and semi-arid climatic conditions. In this study, 19 consecutive years of daily meteorological data of synoptic stations of Semnan and Garmsar between 2000 and 2018 were considered. The data is equivalent to 6935 data, including minimum and maximum temperature, sunny hours, wind speed, air pressure, relative humidity and evaporation.
The daily evaporation rate of the pan was modeled as a dependent variable and other parameters were modeled as independent variables. 70% of the data were used for training and 30% for data. 30% of the data is completely random and selected by the algorithm itself. This makes the inherited characteristic not transmitted by the time series and the ability to check the machine learning towards the reality. Table 2 provides the abbreviations of the six input data and one output data used in this study. Also the statistical specifications of input and output data [ 56 ]. For better data performance in both models, the input and output data were normalized using Equation (1). Thus, all data are formed between 0.1 and 0.9 and then used in relationship development [ 31 , 53 ].
Station | Dataset | Climatic data | Mean | Minimum | Maximum | Standard deviation |
---|---|---|---|---|---|---|
Semnan | Tmax(̊c) | Maximum temperature | 29.51 | 3.8 | 43.8 | 8.37 |
Tmin(̊c) | Minimum temperature | 17.64 | -1.6 | 33 | 7.55 | |
SH(Hours) | Sunshine hours | 9.36 | 0.00 | 14.2 | 2.98 | |
WS(m/s) | Wind speed | 6.49 | 0.00 | 22 | 3.03 | |
PA(hPa) | Air pressure | 886.62 | 872.53 | 902.70 | 4.58 | |
RH (%) | Relative humidity | 31.16 | 6.50 | 91.5 | 15.59 | |
EP (mm) | Evaporation | 9.11 | 0.00 | 25 | 4.92 | |
Garmsar | Tmax(̊c) | Maximum temperature | 26.31 | -1.6 | 47 | 9.71 |
Tmin(̊c) | Minimum temperature | 13.08 | -1.2 | 35 | 11.08 | |
SH(Hours) | Sunshine hours | 8.79 | 0.00 | 13.8 | 3.27 | |
WS(m/s) | Wind speed | 7.27 | 0.00 | 35 | 3.99 | |
PA(hPa) | Air pressure | 914.71 | 887.8 | 936.98 | 12.58 | |
RH (%) | Relative humidity | 37.13 | 4.5 | 97.6 | 19.34 | |
EP (mm) | Evaporation | 7.37 | 0.00 | 39.1 | 6.69 |
$\begin{array}{cc}{\mathrm{Parameter}}_{\mathrm{Scaled}}=\left[\right(\mathrm{0.9}-\mathrm{0.1}\left)\right(\frac{\mathrm{Parameter}-{\mathrm{Parameter}}_{\mathrm{min}}}{{\mathrm{Parameter}}_{\mathrm{max}}-{\mathrm{Parameter}}_{\mathrm{min}}}\left)\right]+\mathrm{0.1}& \mathrm{(1)}\end{array}$
One method for measuring evaporation is using different evaporation pans. One of the most common types of pans is used in synoptic and meteorological stations is the Class A pan. In Semnan and Garmsar synoptic stations, evaporation data were collected using this type of pan. Evaporation pans are made of galvanized iron or stainless steel with a thickness of 1.5 mm in a circle shape with a standard diameter (48 inches) and a height of 25.4 cm (10 inches). The bottom of the pan is integrated and its upper edges have a resistant fold. The water depth is 20 cm. Class A pans are usually placed on pedestals made of wood. The height of these bases is 15 cm from the ground. Figure 2 shows a graphical view of a standard Class A evaporator.
3. Multilayer perceptron network (MLP)
The Multilayer Perceptron network [ 57 , 58 ] is a forward neural network that consists of input (first layer), hidden (second layer) and output (third layer)[ 59 ]. The purpose of training this network is to achieve generalizability and learning, this means that the network is able to correctly identify patterns that it has not seen in the training phase, as well as correctly identify training patterns [ 60 ]. The training of this network is done in two stages, forward and backward which means that the data moves toward the output layer and after calculation of the error, the error comes back to the input layer [ 61 ]. The structure of this network is shown in Figure 3. In this study, the number of input data was 3, 4, 5 and 6. The number of neurons in the secretory and output layers are 5 and 1, respectively. Hyperbolic tangent (tanh) was used as the activation function.
4. Long short term memory (LSTM)
LSTM is a recursive neural network architecture designed to store and access information better than the traditional version. The unit of LSTM was first introduced by Hochreiter and Schmidhuber (1997). The LSTM network uses a Ct memory at time t. ht is expressed as the output or activation of the LSTM unit. Γ_0 is the output gateway that controls the amount of content delivered through memory [ 63 ]. σ is the Softmax activation function. W0 is also an hermitian matrix. The Ct memory cell is also the current memory with relative forgetfulness. New memory content is obtained with the expression C [ 63 ]. The amount of current memory to be forgotten is controlled by the bf forgetfulness gateway, and the amount of new memory to be added to the memory cell is updated by the gateway. Improved versions, such as LSTM, show that this capability is provided to the network by imposing restrictions on the freedom of parameters (by inserting new gateways) in the optimization process. Figure 4 shows an LSTM network. Equations 2 to 7 are provided for the network. In this study, LSTM layer nodes, Dense layer-1 nodes, Dense layer-2 nodes, Batch size and Epoch were considered 32, 20, 20, 72 and 300, respectively.
$\begin{array}{cc}\stackrel{\u02c6}{C}=\mathrm{tanh}({W}_{C}.[{h}_{\mathrm{t-1}}{X}_{t}]+{b}_{c})& \mathrm{(2)}\end{array}$
$\begin{array}{cc}{C}_{t}={\Gamma}_{f}=\sigma ({W}_{f}.[{h}_{\mathrm{t-1}}{X}_{t}]+{b}_{f})& \mathrm{(3)}\end{array}$
$\begin{array}{cc}{\Gamma}_{f}=\sigma ({W}_{f}.[{h}_{\mathrm{t-1}}{X}_{t}]+{b}_{f})& \mathrm{(4)}\end{array}$
$\begin{array}{cc}{\Gamma}_{u}=\sigma ({W}_{u}.[{h}_{\mathrm{t-1}}{X}_{t}]+{b}_{u})& \mathrm{(5)}\end{array}$
$\begin{array}{cc}{\Gamma}_{o}=\sigma ({W}_{o}.[{h}_{\mathrm{t-1}}{X}_{t}]+{b}_{o})& \mathrm{(6)}\end{array}$
$\begin{array}{cc}{h}_{t}={\Gamma}_{o}.\mathrm{tanh}\left({C}_{t}\right)& \mathrm{(7)}\end{array}$
5. Evaluation criteria
Explanation coefficient (R^{2})[ 64 , 65 ], root mean square error (RMSE)[ 66 ] and mean absolute error (MAE)[ 67 ] were used to evaluate the performance of the models [ 68 ]. Equations 8 to 10 represent R^{2}, RMSE, and MAE, respectively. The closer the R^{2} is to one, the higher the correspondence between the observational data and the modeling data. The closer the MAE and RMSE indices are to zero, the better the matching of the observed and simulated data.
$\begin{array}{cc}{R}^{2}=\left[\frac{\sum _{\mathrm{i=1}}^{n}({x}_{i}-\stackrel{-}{x})({y}_{i}-\stackrel{-}{y})}{\sum _{\mathrm{i=1}}^{n}{({x}_{i}-\stackrel{-}{x})}^{2}\sum _{\mathrm{i=1}}^{n}{({y}_{i}-\stackrel{-}{y})}^{2}}\right]& \mathrm{(8)}\end{array}$
$\begin{array}{cc}\mathrm{RMSE}=\sqrt{\frac{\sum _{\mathrm{i=1}}^{n}{({y}_{i}-{x}_{i})}^{2}}{N}}& \mathrm{(9)}\end{array}$
$\begin{array}{cc}\mathrm{MAE}=\frac{1}{N}\sum _{\mathrm{i=1}}^{n}|{y}_{i}-{x}_{i}|& \mathrm{(10)}\end{array}$
In equations 8 to 10, x_{i} is the observational evaporation value at the station, y_{i} is the simulated evaporation value, $\stackrel{-}{x}$ is the mean observational evaporation value at the station, and $\stackrel{-}{y}$ is the equivalent average for the simulated values.
6. Result and discussion
To estimate daily evaporation, LSTM and MLP models are simulated in Python. Different input combinations for the two models are shown in Table 3. The lowest input is for the first combination. Which contains only three parameters of minimum temperature, maximum temperature, and relative humidity. In input combination No. 4, all data is used as input for modeling. The different combinations of input parameters are to check the effectiveness and efficiency of each meteorological data on evaporation in the study areas. In fact, by considering different combinations of input data and removing one or more parameters in a combination, the effect of that parameter on evaporation can be identified. Also, this method can show whether more accurate simulation results are obtained by having more input data.
Scenario | Models | Input combination | Number of input |
---|---|---|---|
1 | LSTM1 & MLP1 | T_{max}, T_{min}, RH | 3 |
2 | LSTM2 & MLP2 | T_{max}, T_{min}, RH, WS | 4 |
3 | LSTM3 & MLP3 | T_{max}, T_{min}, RH, WS, SH | 5 |
4 | LSTM4 & MLP4 | T_{max}, T_{min}, RH, WS, SH , PA | 6 |
The performance of the proposed models based on the evaluation criteria is shown in Table 4. Overally, scenario 4 was superior for both stations and for both LSTM and MLP models. The best model for both stations is the LSTM4 model. Considering the performance of LSTM4 for Semnan station, the values of R^{2}, RMSE and MAE were estimated 0.9451, 1.8345, 0.5437 respectively, where their values for Garmsar station are 0.9255, 1.7920 and 1.3513, respectively. In total, the value of R^{2} for all inputs in both models is higher than 0.9, which indicates the proper performance of both models. Comparing the LSTM and MLP models in pairs, the results show that LSTM has a better performance than MLP in both stations. This obtained result is consistent with Majhi et al. [ 52 ]. The best prediction accuracy was obtained with models that used the complete meteorological data set for both stations. This showed that the prediction accuracy of the model increases with having more input parameters, which is consistent with the studies of Wang et al. [ 69 ] and Fan et al. [ 70 ].
Station | Models | R^{2} | RMSE | MAE |
---|---|---|---|---|
Semnan | LSTM1 | 0.9315 | 1.8923 | 1.059 |
MLP1 | 0.9004 | 2.1036 | 1.0395 | |
LSTM2 | 0.9320 | 1.8887 | 1.0845 | |
MLP2 | 0.9272 | 1.9227 | 1.0641 | |
LSTM3 | 0.9359 | 1.8605 | 1.1202 | |
MLP3 | 0.9348 | 1.8613 | 1.1230 | |
LSTM4 | 0.9451 | 1.8345 | 0.5437 | |
MLP4 | 0.9395 | 1.8544 | 1.1329 | |
Garmsar | LSTM1 | 0.9080 | 1.9291 | 1.2402 |
MLP1 | 0.9078 | 1.9301 | 1.2671 | |
LSTM2 | 0.9115 | 1.9018 | 1.2524 | |
MLP2 | 0.9100 | 1.9133 | 1.2530 | |
LSTM3 | 0.9170 | 1.8564 | 1.3420 | |
MLP3 | 0.9111 | 1.9055 | 1.3312 | |
LSTM4 | 0.9255 | 1.7920 | 1.3513 | |
MLP4 | 0.9204 | 1.8323 | 1.3531 |
Abed et al. [ 55 ] used minimum temperature, maximum temperature, average temperature, wind speed, relative humidity and solar radiation data as input to estimate the evaporation rate using XGB, Elastic Net LR and LSTM models. Also Majhi et al. [ 52 ] have used minimum and maximum temperature, morning and afternoon relative humidity, wind speed and solar radiation data as input for LSTM and MLP models. Best results for both above research are obtained when all the input data were considered into the estimation process. The results of Qasem et al. [ 14 ] also showed that the higher the number and types of inputs, the higher the accuracy of the results by ANN, WANN, SVR and WSVR models. Alsumaiei [ 71 ] used the ANN for the dry area of Kuwait International Airport (KIA) to model the evaporation rate, the results of which are consistent with the obtained results in current study. Figures 5 and 6 show the time series of the observed and simulated data of daily evaporation from the pan for Semnan and Garmsar stations, respectively. In other words, these figures are a comparison of total observational and simulated data for LSTM and MLP models. The more the simulated values correspond to the measured values, the more accurate and less error the model will have. In LSTM4 and MLP4 there is less visual difference between the observed and simulated data. Also, this difference for Garmsar station is less than Semnan station. The scattering curve of the estimated values against the observed values for both training and testing and for both Semnan and Garmsar stations can be seen in Figures 7 and 8, respectively. In Singh et al. [ 21 ] a comparison between machine learning and ANN and statistical technique versus MLR to predict pan evaporation found that the correlation coefficient of SVR and ANN was higher than the MLR model for calibration and validation.
In Alsumaiei [ 71 ], it was stated that the MLP model can have a relatively good performance in predicting evaporation in arid and very arid regions, which is confirmed by the results obtained in the present study. Majhi et al. [ 52 ] and Abed et al. [ 55 ] show that the LSTM model can have high efficiency in estimating and modeling the rate of evaporation from the pan in humid and very humid climates. The current study showed that the DEEP-LSTM model for hot and dry areas has a good performance in estimating evaporation from the pan, which is in line with the results of Majhi et al. [ 52 ] and Abed et al. [ 55 ].
A radar chart is a graph that shows the status of various required variables by displaying one or more polygons. By looking at the radar chart, the degree of proximity and similarity of the same variables will be understood. One of the main applications of radar charts is to compare observational status with predicted status considering some criteria. Figure 9 shows the radar diagrams of LSTM and MLP models for different scenarios in Semnan and Garmsar stations. Based on these graphs, both models performed well in both stations in terms of R^{2}, RMSE and MAE evaluation criteria, and the LSTM4 performed better for both stations. These results are in good agreement with the research of Yin et al. [ 72 ] and Ferreira and Da Cuna [ 73 ].
The box diagram of the results obtained in the test phase for Semnan and Garmsar stations are shown in Figures 10 and 11. The middle line shows the difference between the average observed values and the estimated average daily evaporation values in millimeters. The first line and the last line of the boxes show the 25th and 75th percentiles respectively, and the line in the middle of the box shows the average.
Considering LSTM and MLP, Taylor Diagram [ 58 ] was drawn to investigate and analyze the values of RMSE, R^{2} and standard deviation between the observed evaporation data of Semnan and Garmsar stations with data modeled by LSTM and MLP models (Figure 12). This figure shows that the LSTM4 model is the most accurate prediction model for both studied cities. Also, by comparing the combinations of the MLP model together, the MLP4 model performed better for both cities. It should be noted that this diagram is presented in two forms, semicircle and quadrilateral (only to show positive correlations). In both types, the values of R^{2} are plotted as the radius of a circle on its arc, the values of standard deviation are plotted as concentric circles relative to the center of the circle, and the RMSE values are plotted as concentric circles relative to the reference point (solid circle). The results show that the performance of both models is close to each other and acceptable for all scenarios. Gao et al. [ 74 ], indicating the better performance of the proposed LSTM model. Chia et al [ 75 ], who reported minimum MAE and RMSE values of 0.444 mm/d and 0.543 mm/d, respectively. These results are relatively close to the results of the present study.
7. Conclusions
Soft computational models and statistical techniques are useful frameworks for predicting complex climate indicators, such as pan evaporation. This study was performed to evaluate the potential of Deep-LSTM structure and compare it with MLP to estimate daily evaporation under hot and dry climates with the use of meteorological data. Meteorological parameters used in this research were Minimum and maximum air temperature (Tmax, Tmin), wind speed (WS), sunshine hours (SH), air pressure (PA), relative humidity (RH). In this study 4 input combinations were considered for the two models. Prediction models were tested and trained using daily evaporation data from the existing pan from 2000 to 2018. The accuracy of the models was compared by calculating the statistical criteria of standard R^{2}, RMSE and MAE.
The following results were obtained in this study:
-LSTM and MLP models can perform well in daily EP simulations.
-The LSTM model performed better in all scenarios than the MLP model.
-Simultaneous consideration of all inputs, in both LSTM and MLP models and for both Semnan and Garmsar stations showed the best performance.
-Due to the availability of methodological data, LSTM can be used as a suitable model for estimating the daily evaporation rate in stations where direct evaporation measurement is not performed.
-Other neural network structures based on deep learning can also be used to predict the process of evaporation from the pan and reference evapotranspiration.
For future research, it is suggested to investigate the LSTM model for different weather conditions. For multi-stage evaporation prediction, LSTM model and other deep learning models such as CNN, Bi LSTM, etc. should be investigated.
Funding
This research received no external funding.
Conflicts of interest
The authors declare no conflict of interest.
Authors contribution statement
AS1, YD: Conceptualization; HG, HK: Data curation; AS1, AS2: Formal analysis; HK, HA, YD: Investigation; AS1, HA, AS2: Methodology; HK, HR: Project administration; AS1, YD, HA: Resources; AS1, HG, AS2: Software; HK: Supervision; HK, HG, SA1, YD, SA2: Validation; AS1, HK: Visualization; HG, AS, YD, HK, AS: Roles/Writing - original draft; HK, AS1, HG, AS2, YD: Writing - review & editing.
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