ANN-based PCA to predict evapotranspiration: a case study in India

ANN

artificial neural network

ASCE

American Society of Civil Engineers

ET

evapotranspiration

PCA

principal component analysis

RH

relative humidity

SD

standard deviation

SEE

standard error of estimate

ET₀

potential evapotranspiration (mm/day)

I_m

moisture index, mm

n/N

ratio of actual to maximum possible duration of sunshine hours

R²

coefficient of determination

R_n

net radiation at the crop surface (MJm⁻²day⁻¹)

s

the water surplus, mm

d

the water deficit, mm

T_mean

average temperature (°C)

T_max

maximum temperature (°C)

T_min

minimum temperature (°C)

U

wind velocity (km day⁻¹)

efficiency

standard deviation

Computation of evapotranspiration (ET) for various agro-climatic regions is essential for efficient water management. ET is the combined loss of water to the atmosphere due to evaporation from the soil, water surface, and plant transpiration. If water is unlimited, the amount of water lost is determined by atmospheric conditions, and this evaporation power of the atmosphere is described as potential evapotranspiration (ET₀). It is challenging to quantify and predict ET, a key factor in models of terrestrial water balance (Joshua et al. 2005). Direct measurement of ET is costly and laborious. Simple prediction techniques like Blany–Criddle and complicated prediction techniques like the Penman method have both been developed during the past few decades (Allen et al.1986). Penman's method made use of variables like surface aerodynamics, net radiation intensity, and evaporation dynamics. Later, Montieth enhanced this approach by taking into account the plant's daily resistance and created the Penman–Montieth (P–M) equation (Allen et al. 1998). The Food and Agricultural Organization (FAO) considers ET calculated using the P–M method as the standard and recommends it for all climate zones (Allen et al. 1998). Different ET models were developed and evaluated using the P–M approach as a reference (Kisi 2007; Landeras et al. 2008). The optimal ET model is chosen based on factors such as data availability, location, season, climate, purpose, and time period (Samani 2000). Actual ET, according to Kumar et al. (2002), is a complicated and nonlinear phenomenon that depends on the interplay of various environmental factors, including crop type and development stage, wind speed, air humidity, and temperature. Lysimeters can be used to measure reference ET, however, this approach is very expensive and difficult to use (Valipour 2014). The heat produced by the earth and the solar radiation that is absorbed by the atmosphere raises the temperature of the air. The rate of ET is controlled by the sensible heat of the surrounding air, which transmits energy to the crop. This variability is more in drier climates (Doorenbos & Pruitt 1977). ET₀ values estimated by the Hargreaves method were 22% higher than the P–M method in the warm climate of Southern Europe (Trajkovic 2007). The variation in temperature and relative humidity (RH) values is primarily responsible for the differentiation. Similar results were reported by Sentelhas et al. (2010) and Kaya et al. (2017). Strong spatial and temporal variability of climatic conditions are characteristic of semi-arid environments (Leduc et al. 2007).

The artificial neural network (ANN) technology is widely used to solve complex nonlinear interactions in various sciences and has provided many promising results in the field of hydrology and water resources engineering (Ghazvinian et al. 2020). The ability to identify a relationship from sufficient data pairs makes it possible for ANNs to solve large-scale complex problems such as pattern recognition and nonlinear modeling (ASCE 2000).

Soft computing models are extensively used in various fields of water resources, such as streamflow simulation, where ANN models performed better than the Hydrologic Engineering Centre – Hydrologic Modeling System (HEC-HMS) (Loyeh & Jamnani 2017); infiltration process, where random forest regression models performed better than an ANN, multi-linear regression, and M5P tree models (Singh et al. 2021). Suspended sediment load prediction of a Ganga river stretch with up to 95% accuracy was found possible with the ANN model, with the performance tested by normalized root mean square error, correlation coefficient and Theil's U statistics (Gaur et al. 2021a). Groundwater levels were modeled using wavelet support vector machine (SVM) and ANN algorithms, and the performance was evaluated using correlation coefficient and Nash–Sutcliffe efficiency index. Wavelet decomposition-based SVR was observed to be superior (Gaur et al. 2021b). Podeh et al. (2023) carried out calibration of infiltration models using particle swarm optimization. Kia et al. (2012) developed a flood model with flood causing factors using ANN to model and simulate flood-prone areas in the southern part of Peninsular Malaysia.

The PCA-based Adaptive Neuro Fuzzy Inference System (ANFIS) developed by Parsaie et al. (2018) was designed to estimate the longitudinal dispersion coefficient (D_L) in rivers and the performance of the developed model was found suitable to predict the D_L.

The piezometric head in the core and the seepage discharge through the body of the earth dam were predicted using soft computing models, including the multi-layer perceptron neural network (MLPNN), SVM, multivariate adaptive regression splines (MARS), genetic programming (GP), M5 algorithm, and group method of data handling (GMDH). The results revealed that all models had a tolerable level of accuracy in predicting the piezometric heads, although the MARS model performed the best and the M5 method performed the worst Parsaie et al. (2021).

Nezaratian et al. (2021) approximated the transverse mixing coefficient (TMC) in streams using SVM based on genetic algorithm (GA) and found that efficient TMC estimate by GA-SVM can reduce the complexity by minimizing the number of input parameters.

The effect of climate change on ET was studied by Chakraborty et al. (2018) and Li et al. (2020). Balmat et al. (2019) computed reference crop evapotranspiration (ET₀) in a greenhouse based on an adaptive-network-based fuzzy inference system, to estimate ET₀ with less information than the standard methods. Ramírez et al. (2005) explored the use of ANN in precipitation forecasting for a Brazilian watershed and discovered that predictions were accurate. Dahamsheh & Aksoy (2009) used ANN to forecast monthly precipitation in Jordan's dry regions, and found that ANN performed better than multivariate regression.

The P–M approach is the most effective physical method, while the ANN model is an accurate empirical method (Adamala & Srivastava 2018). The findings of the factor analysis were very helpful in revealing the relative significance of meteorological variables in explaining the variations in ET estimation (Lakshman & Kovoor 2006). Many researchers have used ANN for modeling the complex process of ET with minimum climatological data (Kim & Kim 2008; Traore et al. 2010; Diamantopoulou et al. 2011). Sudheer et al. (2003) adopted three options for input data to estimate ET₀, and in the more simplified option, ET₀ was estimated as a function of average air temperature only. Zanetti et al. (2007) obtained satisfactory estimates of reference ET, by ANN, using only the maximum and minimum air temperatures as input for a province in Rio de Janeiro. Salami & Ehteshami (2016) used the ANN model to show the average rate of temperature variation. Genaidy (2020) found satisfactory performance for the ANN model with four inputs such as T_max, T_min, dew point data, and wind speed, with P–M ET as the target for a station in the province of Nubaria. Deshmukh (2016) used multiple input combinations to create ANN models for ET estimation in the Nagpur region of India, which has a hot and humid climate, and found that they performed well. For hot climatic conditions, ANN models were created using pan evaporation data by a few researchers (Keskin & Terzi 2006; Khoob 2008).

Since agriculture is the largest consumer of water, developing irrigation systems and managing water supplies depend on accurately estimating the ET process. Underestimation of ET results in plant moisture stress and a reduction in agricultural production, while over estimation wastes water, damages crops and contaminates groundwater and soil. Given the complexity of agricultural systems, which deal with many factors, a nonlinear method is needed to interpret the relationships, which is possible with ANN (Gunathilake et al. 2021).

The P–M model's accurate prediction of ET has limited applicability because many of the parameters are not available for several stations. Hence, less data-intensive computational tools, such as ANN models, are highly valuable in precisely estimating ET₀ for effective agricultural water management, and the climatic parameters for a region should be chosen based on the sensitivity of the parameter for the region. Hence, simpler ANN models can be employed, as they are accurate as the classic P–M model, though they do not require as many parameters.

The P–M approach was used as the target in the current investigation to compute ET₀. ANN models were developed for ET₀ estimation with all the climatic variables and with the crucial climatic variables identified by PCA.

The meteorological data were obtained from the India Meteorological Department (IMD), Government of India for all the stations for a period of five years. For each station, the daily climatic data collected included maximum air temperature in °C (T_max), minimum air temperature in °C (T_min), maximum relative humidity in % (RH_max), minimum relative humidity in % (RH_min), actual sunshine hours, 24-h wind speed, rainfall, and pan evaporation depth. Site details such as latitude and longitude of the stations, altitude above mean sea level, and wind speed measurement height were also obtained from the IMD, Pune.

Principal component analysis (PCA) is a statistical process for converting a large number of potentially linked variables into a smaller number of uncorrelated variables known as principal components. PCA is a technique used in statistics to simplify a dataset by reducing multidimensional datasets to fewer dimensions for analysis. The first principal component accounts for as much variety as feasible in the data, and each subsequent component accounts for as much variability as possible. Eigen analysis is the mathematical approach utilized in PCA. A square symmetric matrix containing a sum of squares and cross products has its eigen values and eigen vectors solved. The eigen vector associated with the largest eigen value has the same direction as the first principal component. The eigen vector associated with the second largest eigen value determines the direction of the second principal component. PCA can be used for dimensionality reduction in a dataset while retaining those characteristics of the dataset that contribute most to its variance.

Sensitivity analysis identifies the parameter(s) that have the biggest influence on the model's output (Omar et al. 2021). A sensitivity analysis is the process of varying model input parameters over a reasonable range and observing the relative change in model response. Sensitivity analysis was carried out to find which climatic variables are more sensitive in the ET equation. Sensitivity can be considered as the absolute change in ET₀ results for a positive or negative change in different variables individually. Each of the climatic variables was varied in turn over a specified range while keeping the other variables constant and its impact on ET₀ estimate was assessed. Percentage changes in ET₀ with percentage changes in different variables were plotted to identify the more sensitive parameters. The relative importance of variables on ET₀ and the impact of estimation errors due to individual variables are also analyzed. The results of sensitivity analysis will also be highly beneficial for determining the direction of future data collection activities.

ANN can be successfully utilized to predict the complex process of ET using minimal climatological data. The neural network learns naturally and incrementally in the course of processing. The learning process is carried out by a learning algorithm, by modifying the weights of interconnections of the network with known inputs and outputs. Later these weights are used to produce the desired output for a given input pattern.

The ANN toolbox in MATLAB (The MathWorks Inc. 2003) was used for the study. The neural network procedure used in the present study was a feed forward network type backpropagation algorithm in which the flow of information is from input layer to output layer. Mean square error regression analysis was used to test the agreement between P–M ET₀ and ANN ET_0. Training was done by varying the number of neurons until a good agreement was obtained. After training was over the network was frozen and the validation data were fed into the system to make predictions. The performance of the network during validation was analyzed using various statistical procedures to assess the generalization properties of the trained network.

The performance of the developed models was evaluated using statistics like the coefficient of determination (R²), standard error of estimate (SEE), standard deviation (SD), and efficiency values (%⁠). The statistical test of significance used for the study was z-test.

R² measures the degree to which two variables are linearly related and a value of R² close to unity indicates a high degree of association between the two variables.

Model efficiency (%⁠): The difference between the ET estimated by the P–M method and each of the other methods is calculated. If the difference is less than 0.5 mm/day, the estimate is good. The number of occasions on which the difference is less than 0.5 mm/day, expressed as a percentage of the total number of populations, will give the model efficiency (Mohan 1988).

Test for significance: The z-test was used to test whether there is a significant difference between ET₀ values estimated by the P–M method and the ET₀ values estimated by the ANN model. The assumptions used in this test include: samples are independent and random in nature; populations are normally distributed or if not normal, can be approximated by a normal distribution (n₁ ≥ 30 and n₂ ≥ 30).

The availability of climatic data is an important criterion in selecting an appropriate method. Depending on the method, different datasets are required, ranging from the Pan method, which just requires information on pan evaporation, to the P–M method, which requires a large number of meteorological data. A suitable method that results in a fairly accurate estimation ET₀ should be found under a data-short environment.

The daily values of ET₀ were calculated by the P–M method for each of the 10 stations. The average value of estimates, obtained by averaging ET₀ values across the period of record, varied from a low value of 3.09 mm/day at the coastal area of Anakapalle to a high of 4.58 mm/day at the semi-arid location of Bellary. The annual average ET₀ values also showed similar trends with a maximum value of ET₀ for Bellary (1,680 mm) and a minimum value for Anakapalle (1,136 mm) as per P–M estimate.

A study on PCA was performed in order to gain a deeper insight into the relative influence of different meteorological variables on ET₀ under different climatic conditions and to find the most critical climatic variables for each station considered. Daily data on net radiation (R_n, MJ m⁻² day⁻¹), maximum temperature (T_max, °C), minimum temperature (T_min, °C), average RH (%), wind velocity (U, km day⁻¹), and ratio of sunshine hours (n/N) were considered for PCA. Rotated factor loadings were examined to provide useful quantitative information. In the analysis, the principal components were first identified and then the factors were derived using varimax rotation using SPSS software (Shaffer et al. 1999). From the PCA carried out, it was observed that radiation is the most important climatic variable for ET₀ estimation, followed by RH/temperature and wind speed, as evident from Table 2.

Sensitivity analysis was carried out to assess the influence of climatic variables on the ET equation and the percentage changes in ET₀ for a 25% change in various climatic variables. The results indicated that the relationship between daily ET₀ and climatic variables is generally linear, except for the relationship with temperature where slight non-linearity was observed in a few cases.

The spatial analysis showed that R_n and RH_mean are dominating for the per-humid Pattambi station. The two variables, namely RH_mean and T_max, are found to be dominating variables for ET₀ estimates in the humid Dharwad station with high influence during the monsoon season. For the moist sub-humid station Bangalore, R_n and RH_mean were found to be most influential followed by T_max. In the dry sub-humid station, R_n was the single most important climatic variable. T_max was observed as the most influential weather factor for the coastal Rajahmundry station whereas R_n was found to be dominating in the other coastal station, Anakapalle. T_max and RH_mean were found to be the sensitive variables for Annamalainagar and Kovilpatti stations. The variation in T_max was found to be highly sensitive to the changes in the estimates of ET₀ for the semi-arid stations of Bellary, Hyderabad, and Sholapur. The net radiation at the reference surface is the energy source that drives away moisture as ET_0, and at the same time, it affects other climatic variables also. ET₀ is sensitive to temperature, where it is positively correlated, and RH_mean, where it is negatively correlated. Wind speed is also important when R_n is high and the air is relatively dry.

The sensitivity is expressed quantitatively in Table 3 as percentage change in ET₀ for 25% increase in the climatic variables. The overall average changes in ET₀ values for 25% change in the climatic variables were 18, 16, 14, 7, 5, and 4% for T_max, RH_mean,R_n, wind speed, T_min and sunshine hours, respectively. Overall, ET₀ was found to be sensitive to radiation (R_n) for all seasons. Mean relative humidity (RH_mean) has a high influence but there were seasonal fluctuations. T_max was also found to be sensitive to seasonal variations followed by wind speed. The results are similar to the results of the sensitivity analysis of Meyer et al. (1989) using the original Penman equation as a target, in which RH and R_n were found to have profound effects on the calculated ET₀ value, whereas wind speed was less critical.

One of the multivariate statistical techniques that can be used to simplify the complexity of the input variables is PCA. Most of the variability is contained in the principal components. Although the P–M model is the best, if all climatic data are available, the ANN with principal components offers an alternative for locations where full climatic data are not accessible. The ANN with all variables is the ANN model with all the eight climatic variables used for the computation of ET₀. ANN with PCA variables is the ANN model wherein only the climatic variables identified by PCA for the respective station are used for the computation of ET₀.

ET₀ values were ranked based on R², SEE, %⁠, and z-test values in comparison to P–M estimate of ET₀. Tables 5 and 6 show the applicability of the developed ANN models for different agro-climatic regions based on the calibration and validation statistics. The optimum number of neurons for ET₀ estimation for each climatic station with their performance indices with all variables and with PCA variables is also given in Tables 5 and 6. It was observed that increasing the number of neurons has increased the efficiency of the model in terms of coefficient of determination (R²) and error reduction including root mean square error and standard error of the estimate.

Table 5

Evaluation statistics for the ANN model with all climatic variables

Sl. no. .	Station name .	No. of neurons .	Calibration .					Validation .
			R2 .	SEE .	SD .	% .	z .	R2 .	SEE .	SD .	% .	z .
1	Pattambi	20	0.999	0.02	0.71	100	0.01	0.988	0.36	0.77	0.96	−1.33
2	Dharwad	20	0.999	0.03	1.26	100	0.004	0.998	0.16	1.29	100	0.54
3	Bangalore	20	0.996	0.07	0.86	100	0.06	0.985	0.34	0.92	81	−1.64
4	Kovilpatti	15	0.999	0.04	1.36	100	0.01	0.993	0.29	1.05	94	1.02
5	Rajahmundry	15	0.998	0.05	0.98	100	0.02	0.99	0.39	0.82	92	1.6
6	Anakapalle	15	0.998	0.04	0.81	100	0.02	0.99	0.13	0.84	100	0.04
7	Annamalainagar	15	0.996	0.11	1.13	100	0.11	0.994	0.23	1.09	98	0.92
8	Sholapur	10	0.988	0.22	1.42	96	0.07	0.987	0.48	1.15	80	1.69
9	Bellary	15	0.996	0.14	1.54	99	0.02	0.988	0.71	1.20	38	2.26*
10	Hyderabad	25	0.999	0.06	1.61	100	0.02	0.96	0.67	1.78	52	1.31

Sl. no. .	Station name .	No. of neurons .	Calibration .					Validation .
			R2 .	SEE .	SD .	% .	z .	R2 .	SEE .	SD .	% .	z .
1	Pattambi	20	0.999	0.02	0.71	100	0.01	0.988	0.36	0.77	0.96	−1.33
2	Dharwad	20	0.999	0.03	1.26	100	0.004	0.998	0.16	1.29	100	0.54
3	Bangalore	20	0.996	0.07	0.86	100	0.06	0.985	0.34	0.92	81	−1.64
4	Kovilpatti	15	0.999	0.04	1.36	100	0.01	0.993	0.29	1.05	94	1.02
5	Rajahmundry	15	0.998	0.05	0.98	100	0.02	0.99	0.39	0.82	92	1.6
6	Anakapalle	15	0.998	0.04	0.81	100	0.02	0.99	0.13	0.84	100	0.04
7	Annamalainagar	15	0.996	0.11	1.13	100	0.11	0.994	0.23	1.09	98	0.92
8	Sholapur	10	0.988	0.22	1.42	96	0.07	0.987	0.48	1.15	80	1.69
9	Bellary	15	0.996	0.14	1.54	99	0.02	0.988	0.71	1.20	38	2.26*
10	Hyderabad	25	0.999	0.06	1.61	100	0.02	0.96	0.67	1.78	52	1.31

*Significant at 0.05 level.

View Large

Table 6

Evaluation statistics for the ANN model with PCA variables

Sl. no. .	Station name .	No. of neurons .	Calibration .					Validation .
			R2 .	SEE .	SD .	% .	z .	R2 .	SEE .	SD .	% .	z .
1	Pattambi	10	0.982	0.13	0.72	99	−0.03	0.977	0.37	0.63	96	−1.43
2	Dharwad	10	0.982	0.24	1.23	95	0.02	0.965	0.36	1.34	75	0.46
3	Bangalore	10	0.984	0.16	0.82	100	0.22	0.978	0.17	0.83	100	0.00
4	Kovilpatti	5	0.978	0.28	1.29	90	0.09	0.97	0.39	1.03	73	1.09
5	Rajahmundry	5	0.989	0.15	0.96	100	0.07	0.99	0.48	0.75	67	1.9
6	Anakapalle	6	0.99	0.10	0.79	100	0.10	0.989	0.19	0.81	100	0.91
7	Annamalainagar	9	0.996	0.10	1.16	100	0.01	0.992	0.36	1.0	87	1.56
8	Sholapur	5	0.988	0.22	1.41	96	0.05	0.98	0.57	1.18	50	2.00*
9	Bellary	7	0.993	0.17	1.53	99	0.01	0.98	0.97	1.25	8	3.32*
10	Hyderabad	10	0.988	0.25	1.57	0.94	0.03	0.97	0.83	1.44	33	2.37*

Sl. no. .	Station name .	No. of neurons .	Calibration .					Validation .
			R2 .	SEE .	SD .	% .	z .	R2 .	SEE .	SD .	% .	z .
1	Pattambi	10	0.982	0.13	0.72	99	−0.03	0.977	0.37	0.63	96	−1.43
2	Dharwad	10	0.982	0.24	1.23	95	0.02	0.965	0.36	1.34	75	0.46
3	Bangalore	10	0.984	0.16	0.82	100	0.22	0.978	0.17	0.83	100	0.00
4	Kovilpatti	5	0.978	0.28	1.29	90	0.09	0.97	0.39	1.03	73	1.09
5	Rajahmundry	5	0.989	0.15	0.96	100	0.07	0.99	0.48	0.75	67	1.9
6	Anakapalle	6	0.99	0.10	0.79	100	0.10	0.989	0.19	0.81	100	0.91
7	Annamalainagar	9	0.996	0.10	1.16	100	0.01	0.992	0.36	1.0	87	1.56
8	Sholapur	5	0.988	0.22	1.41	96	0.05	0.98	0.57	1.18	50	2.00*
9	Bellary	7	0.993	0.17	1.53	99	0.01	0.98	0.97	1.25	8	3.32*
10	Hyderabad	10	0.988	0.25	1.57	0.94	0.03	0.97	0.83	1.44	33	2.37*

*Significant at 0.05 level.

View Large

The ANN model showed good performance in most of the stations except in the semi-arid climatic conditions. The performance of all the models in training was better than testing. For coastal, per-humid and humid climatic stations the models resulted in high performance both during the training period and testing period. The poor performance during the testing period in the case of semi-arid climatic stations indicated the complexity of ET models and questions the applicability of these models for the climate. In dry climatic regions, the fluctuations in climatic variables within a day are much higher than in humid regions. So the daily weather data may not be able to account for the hourly fluctuations accurately. It can be the reason for the poor performance of the ET equations in semi-arid climatic regions. A similar observation was made by Lakshman & Kovoor (2006).

The performance of ET₀ obtained from the ANN model was compared with the standard P–M model for different agro-climatic regions based on the linguistic notations shown in Table 7, such as very good, good, low and poor, respectively. Performance decreased as it moved from coastal, humid to semi-arid regions. ET₀ estimates showed poor performance in drier regions compared to humid regions. In dry climatic regions, the fluctuations in climatic variables within a day are much higher than in humid regions and the daily weather data may not be able to account for the hourly fluctuations accurately. This leads to the poor performance of the simplified ET equations in drier climatic regions.

Table 7

Criteria for the selection of linguistic variables

Sl. No. .	Criteria, values .	VG .	G .	L .	P .
1	R2	0.95	0.95–0.60	0.60–0.50	0.50
2	SEE	0.30	0.30–0.50	0.50–0.70	0.70
3	%	95%	95–70%	70–50%	50%
4	z-test (95% confidence interval)	Not significant	Not significant	Not significant	Significant

Sl. No. .	Criteria, values .	VG .	G .	L .	P .
1	R2	0.95	0.95–0.60	0.60–0.50	0.50
2	SEE	0.30	0.30–0.50	0.50–0.70	0.70
3	%	95%	95–70%	70–50%	50%
4	z-test (95% confidence interval)	Not significant	Not significant	Not significant	Significant

VG, very good; G, good; L, low; P, poor.

View Large

According to the criteria, the ANN with all variables had very good performance, and ANN with PCA variables had good performance for coastal, per-humid, and humid climatic conditions. For moist sub-humid climates, both ANN models had good performance, whereas dry sub-humid climates had low and semi-arid climates had poor performance for both the ANN models (Table 8).

The poor performance during the testing period in the semi-arid climatic stations indicates the complexity of ET models for these stations. Statistical analysis showed that ET₀ estimates in Bellary station showed a significant difference between the P–M model and the ANN model with all climatic variables in the validation period, but there was no significant difference in the calibration phase. Similarly semi-arid stations Sholapur, Bellary, and Hyderabad showed significant differences between ET estimate by P–M model and ANN model with PCA variables in the validation period, but there was no significant difference in the calibration phase. The variation in climatic variables within a day is significantly bigger in dry climate regions than it is in humid climate regions. As a result, the developed ET equations perform poorly in places with drier climates. A similar observation was made by Lakshman & Kovoor (2006). Gallego-Elvira et al. (2012) and McJannet et al. (2013) also state that the P–M method which takes into account heat storage and aerodynamic resistance is preferred in semi-arid climatic regions.

The ANN model with all the climatic variables performed better than the ANN model with variables resulting from PCA. ET estimates by the ANN model with PCA variables produced good results, but the performance during validation was poor for semi-arid stations due to the hourly fluctuations in weather in the drier climates. The study demonstrates the applicability of ANN models for various agro-climatic areas under limited data conditions.

ET is a complex process involving several meteorological parameters. The choice of an ET estimation method is determined by the local climate and the availability of meteorological data. Though ET estimation by the data-intensive P–M model is accurate, its applicability is limited due to the unavailability of many of the parameters for several Indian stations. So, less data-intensive computation techniques such as ANN models are found to be very useful in accurately predicting ET₀ for efficient agricultural water management. PCA was used to identify the important climatic factors for various regions, and these important climatic variables were used to build ANN-ET. Based on the study for Indian climate T_max, RH_mean, and R_n are found to be the most sensitive parameters for ET computation.

Statistical analysis proved that ANN models performed very well in coastal, per-humid, and humid climate regions and can be very effectively used for the estimation of ET₀, but the model performance was slightly poor in warmer regions. Accurate estimation of ET is a challenge in drier climates due to hourly variations in weather conditions. In dry climate regions, daily variations in meteorological factors are substantially higher than in humid climate regions, and the hourly variations may not be fully accounted for by daily weather data. An hourly model will be able to address the issue in arid regions. Although the P–M model is the best if all climatic data are available, ANN with principle components offers an alternative for locations where full climatic data are not accessible. Hence, less complex ANN models can be employed, as they are reasonably accurate as the classic P–M model, though they do not require as many parameters.

Future research can focus on the assessment of the ET accounting hourly performance of ANN models for agro-climatic zones. Also, other soft computing techniques can be tried for the estimation of ET.

The authors are thankful to the Indian Institute of Technology Madras, for providing the laboratory facilities for doing the research work.

No funds, grants, or other support were received.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.