Estimation of onion crop evapotranspiration and crop coefficients using weighing lysimeters and machine learning models in semi-arid region

Abstract

Water scarcity is a significant challenge in Iran’s agricultural sector, particularly for onion (Allium cepa L.) cultivation, which is a vital crop for the country’s economy and diet. However, there is a lack of standardized data on onion evapotranspiration (ET_c) in semi-arid conditions, making precise irrigation management difficult. To address this gap, a two-year field experiment was conducted at the Kooshkak Agricultural Research Station, Shiraz University, Iran to measure ET_c using digital weighing lysimeters based on the water balance method and to develop predictive models using machine learning algorithms. The ET_c of onion in the first and second years were 447.1 mm and 432.2 mm, respectively. Soil evaporation accounted for 36.6% and 32.8% of the total ET_c in the first and second years, respectively. The average of single crop coefficient values for the initial, mid, and late growth stages across both years were 0.41, 0.68, and 0.51, respectively. Additionally, the basal crop coefficient values for the initial, mid, and late growth stages were 0.10, 0.51, and 0.37, respectively. To estimate using easily accessible parameters, five machine learning algorithms were developed: Artificial Neural Network, Support Vector Machine, Decision Tree, Random Forest, and Lasso Regression. These models utilized meteorological variables (temperature, relative humidity, wind speed, net radiation) and crop parameters (leaf area index and plant height) as input features and measured was utilized as target outputs for calibrating and validating the model. Among the algorithms, the RF and DT achieved the highest predictive accuracy (R² = 0.98, NRMSE = 0.04), followed by ANN (R² = 0.97, NRMSE = 0.07), SVR (R² = 0.97, NRMSE = 0.08), and LASSO (R² = 0.85, NRMSE = 0.18). Using lysimeter measurements as reliable reference data to evaluate machine-learning models provides a dependable framework for optimizing irrigation scheduling and enhancing water-use efficiency in onion cultivation under semi-arid conditions.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-43887-w.

Introduction

Iran is predominantly arid and semi-arid¹, with an annual mean precipitation of only about 235.2 mm, which is well below the global average^2,3. Agriculture is the largest consumer of the country’s water resources⁴, emphasizing the critical need for efficient water management to ensure water security. Proper management and efficient use of agricultural water are therefore essential to sustainable production under water-scarce conditions^5,6. Accurate measurement of crop evapotranspiration (ET_c) is a critical factor in optimizing irrigation strategies and increasing water use efficiency⁷. The ET_c represents the total water loss via soil evaporation and crop transpiration under non-stressed field conditions, and is influenced by climatic (i.e., grass reference evapotranspiration, ET_o), crop, soil, and management factors^8,9. The ET_c is determined using direct and indirect methods⁸. Weighing lysimeters (the most accurate method) have been widely used to measure using the water balance principle^10,11. However, these systems are expensive to install and maintain, and their applicability is restricted in terms of spatial coverage¹². In this regard, studies have been conducted on many crops such as onion using weighing lysimeters¹³, maize with four weighing lysimeters¹⁴, wheat and maize with two weighing lysimeters¹⁵, and barley with two weighing lysimeters¹⁶. To indirectly estimate the , it is necessary to calculate the grass reference crop evapotranspiration () and crop coefficient () that vary widely across crops and environments. These methodological challenges are particularly pronounced in semi-arid regions like Iran, where environmental heterogeneity and data scarcity hinder the development of region-specific standard ET_c. The Penman-Monteith method is a widely recommended indirect and common method to calculate , although, it requires a significant amount of climatic data, including temperature, humidity, wind speed, and solar radiation⁸ in comparison with other methods such as Hargreaves-Samani¹⁷, Blaney-Criddle¹⁸, and etc. The crop coefficient () is a variable parameter that changes throughout the crop growth cycle and is influenced by factors such as crop type and management, growth stage, planting date, weather conditions, and soil properties⁸. The is defined as the ratio of to and can be applied using either a single or dual crop coefficient approach. The single crop coefficient () combines crop transpiration and soil evaporation. In contrast, the dual crop coefficient method separately considers transpiration () and soil evaporation (). The represents plant transpiration under optimal conditions without additional soil wetting, while reflects soil surface evaporation¹⁵.

In a study¹⁹, found that the water requirements for onions in a semi-arid region (Spain) for optimum yield (75 t ) were 662.3 mm when using drip irrigation and plant density of 35 plant m⁻². In a study conducted by²⁰ in Albacete, Central Spain, the seasonal evapotranspiration of onions measured in the lysimeter was 893.4 mm with plant density of 40 plant m⁻² in a continental climate with moderate humidity and sprinkler irrigation system. It was reported by Abyaneh et al.²¹ that the garlic water requirements in a semi-arid area of Iran, where cooler temperatures and partial rainfall contributed to lower water use, were 546.5 mm and 519.2 mm in 2008 and 2009, respectively. In a semi-arid region in Punjab, India²², reported onion evapotranspiration as 346.5 mm in 2004 and 323.1 mm in 2005 under full irrigation irrigated with micro-sprinkler irrigation system and limited seasonal rainfall (27–36 mm). The wide range of ETc values (323–893 mm) reported in the literature highlights the sensitivity of crop water requirements to environmental and management factors. This diversity underscores the current lack of standardized ET_c data for onion cultivation under semi-arid Iranian conditions, which this study aims to address.

Onion (Allium cepa) belongs to the Alliaceae family, which is grown as an annual crop for bulb production and as a biennial crop for seed production²³. Onion originated in Iran and its neighboring countries²⁴. In the 2022–2023, the cultivated area of onion in Iran was 51,499 ha, with a total onion production of 2,422,637 tons. Onion is rich in vitamins such as ascorbic acid, thiamine, niacin and A, as well as antioxidants, proteins, and minerals like riboflavin, phosphorus, potassium, sulfur, and iodine²⁵. Despite being recognized as a water-sensitive crop and a staple in Iranian diets^23–25, no comprehensive, standardized ET_c and K_c dataset currently exists for onion under Iran’s semi-arid conditions. This lack of reliable data limits the calibration of irrigation scheduling and model-based water management systems.

Evapotranspiration is a highly nonlinear process influenced by meteorological, soil, and crop-related factors²⁶, and its estimation accuracy strongly depends on both the quality and the diversity of available input data²⁷. A cross-study comparison reveals several consistent patterns in ML model performance. Ensemble tree-based methods—such as Random Forest, Bagging, Gradient Boosting, and XGBoost—tend to achieve strong results when high-dimensional meteorological or multisource datasets are available, as demonstrated in studies on sugar beet²⁸, sugarcane²⁹, and ET_o estimation under drought conditions³⁰. Support vector-based models (SVM, LSSVR) often perform best in data-limited contexts due to their strong generalization ability, with notable success reported for sugar beet²⁸ and ET_o estimation³¹. Deep architectures such as DNN outperform traditional ML models when soil water content or crop parameters (LAI, SWC) are included, as shown for maize transpiration in semi-arid regions of China³². In contrast, regression-based methods such as MNLR or M5P offer simpler and faster computation and may exceed neural networks when input-output relationships are more linear, as reported for potato ET³³ and ET_o estimation^30,31. ANN-based models have shown strong performance in semi-arid barley systems due to lower data requirements, although they remain sensitive to parameterization and lack physical interpretability¹⁶.

Despite these advances, most prior studies exhibit recurring limitations: reliance on coarse resolution meteorological data rather than high-precision reference ET (e.g., lysimeter-based) measurements; evaluation across limited stations or single crops; and a lack of systematic comparison of multiple ML models under unified conditions. These shortcomings underscore the need for studies that integrate high-resolution ground-truth ET measurements and assess multiple ML approaches across diverse input scenarios in semi-arid environments—gaps that the present study directly addressed. Due to the dietary importance of onion and the limited availability of standardized ET_c data for this crop under semi-arid conditions, this study was conducted. This study aims (1) to determine onion evapotranspiration (), the single crop coefficient (), and the basal crop coefficient () in a semi-arid region of Iran; (2) to analyze and compare five top used machine learning algorithms [(ANN, SVM, RF, DT (Decision Tree), and LASSO (Least Absolute Shrinkage and Selection Operator) Regression)] covering both linear and nonlinear modeling approaches for onion ET_c simulation; and (3) to evaluate the relative contributions of meteorological vs. crop growth parameters in ET_c estimation. The novelty of this research lies in using high-resolution lysimeter measurements as reliable reference data for evaluating multiple machine-learning approaches for onion production under semi-arid conditions, providing the first standardized ET_c and K_c values for the region. This work not only identifies the most reliable predictive model but also enhances data-driven irrigation management for data-scarce environments.

Materials and methods

Experimental site description

A two-year experiment was conducted at the Kooshkak Agricultural Research Station, School of Agriculture, Shiraz University, situated in the Fars province, southwest; Iran with latitude of 30°4′45′′ N, longitude of 52°35′14′′ E, and 1620 m above mean sea level (Fig. 1). Kooshkak Agricultural Research Station is administratively affiliated with the School of Agriculture, Shiraz University, under the same institutional authority. The local climate of the study region is classified as semi-arid³⁴. Climate data, including maximum and minimum temperature, relative humidity, wind speed, sunshine hours, and rainfall depth, were recorded daily in the weather station close to the experimental field during 2021–2022 and 2022–2023. The meteorological data are shown as monthly averages in Table 1, and the daily variations of temperature, relative humidity, wind speed, and grass reference evapotranspiration () are shown in Fig. 2. The soil physical characteristics used in the lysimeters are provided in Table 2.

Fig. 1.

The geographical location of the study area (A) (The map generated from QGIS 3.24; QGIS Development Team. QGIS Geographic Information System. https://qgis.org), and schematic of weighing lysimeter (left) and onion near harvest (right) (B).

Table 1.

Monthly climatic characteristics for the experimental years.

Years	Months	Tmax (°C)*	Tmin (°C)	Tavg (°C)	RHmax (%)	RHmin (%)	RHavg (%)	Sunshine (hr)
2021–2022	November	20.5	3.6	12.0	96.3	28.4	62.4	7.8	0.72
	December	17.4	1.1	9.3	97.5	32.6	65.1	7.1	0.67
	January	12.2	-2.4	4.9	100	27.7	63.8	6.5	1.1
	February	17.1	-0.82	8.1	99.8	27.5	63.6	8.4	0.98
	March	21.7	3.5	12.6	87.6	21.5	54.5	8.2	1.7
	April	27.3	8.4	17.8	88.9	23.8	56.3	8.9	1.3
	May	30.7	10.4	20.6	67.9	14.3	41.1	10.7	1.6
	June	35.2	13.2	24.2	31.3	10.5	20.9	11.5	0.87
2022–2023	November	18.3	4.1	11.2	93.9	29.2	61.5	7.1	0.71
	December	11.6	-1.2	5.2	97.1	47.7	72.4	5.8	0.55
	January	9.3	-2.1	3.6	96.6	43.5	70.0	5.9	0.84
	February	14.2	-0.92	6.6	82.7	28.7	55.7	6.1	1.5
	March	18.1	-0.51	8.8	90.7	24.7	57.7	8.1	0.95
	April	22.6	3.3	12.9	83.3	21.3	52.3	9.7	0.91
	May	29.2	8.1	18.6	61.6	17.7	39.7	10.5	0.98
	June	33.5	13.2	23.4	56.6	19.4	38.0	12.3	1.0

* denote maximum air temperature (°C), minimum air temperature (°C), average air temperature (°C), maximum air relative humidity (%), minimum air relative humidity (%) and wind speed, respectively.

Fig. 2.

Variations of mean daily temperature (a), mean daily relative humidity (b), daily grass reference evapotranspiration (c) and mean daily wind speed (d) in first (2021–2022) and second (2022–2023) year.

Table 2.

Physical characteristics of the soil in lysimeters and surrounding field.

Depth (cm)	Soil Texture	Clay (%)	Silt (%)	Sand (%)	)	PWP (%)	FC (%)
0–15	Silty clay loam	36	48	16	1.45	21.3	39
15–30	Silty clay loam	35	45	18	1.50	21.3	39
30–60	Silty clay loam	34	46	20	1.41	18.1	42

*BD: Bulk density, PWP: Soil volumetric water content at permanent wilting point, FC: Soil volumetric water content at field capacity.

Crop evapotranspiration measurement

Onion seeds (cv. Armaghan G.) were sown on 10 and 9 November 2021 and 2020 (following a typical practice of farmers that cultivate onion seeds in late autumn), respectively, in two large-scale weighing circular lysimeters (Fig. 1) and surrounding area. The onion seeds were obtained from local farmers. Each lysimeter had a surface area of 7.07 m² and they were located centrally in a 1600 m² experimental field (40 × 40 m) to minimize the side effects. Two lysimeters (with a resolution of measured daily of 0.28 mm (15-minute measuring intervals), 15-minute measuring intervals, a diameter of 3 m, and depth of 1.7 m), contained 11 rows of onion plants, with a row spacing of 30 cm and a plant spacing of 5 cm within each row. Prior to the experiment, both lysimeters were calibrated using step-loading methods to validate measurement precision under dynamic loading conditions³⁵. Similar planting practices were also followed in the surrounding field. Prior to sowing, 150 kg ha⁻¹ phosphorus fertilizer (in the form of triple superphosphate) was applied to soil in both years. Also, 150 kg ha⁻¹ nitrogen fertilizer (in the form of urea) was applied to soil in two stages in both years.

Irrigation water was applied after sowing to ensure uniform germination. A surface (flood) irrigation method was used on a flat lysimeter surface to uniformly distributed the irrigation water over the lysimeter surface and measured the volume of irrigation water with volumetric flow meter to ensure precision. Differences between lysimeter weights after each irrigation event and before the next irrigation were used to determine the amount of irrigation water. The soil water measurements indicated that soil water content before irrigation events were higher than the critical soil water content for many field crops (i.e., 0.3 cm³ cm⁻³⁸, ensuring the non-stress ET_c condition. The irrigation interval was 7 days. However, the lysimeter weight was monitored daily to ensure that the soil water content is higher than the readily available water. The lysimeters and the surrounding field were maintained in non-stressed conditions throughout the entire experiment.

The daily crop evapotranspiration () values for two lysimeters were computed by weighing the changes over 24 h while accounting for precipitation, irrigation, and drainage. The for the onion was calculated as the average of from two lysimeters. The daily evapotranspiration of the onion was calculated using a water balance principle, as follows:

1

where is the daily crop evapotranspiration (mm), I is the irrigation water depth (mm), P is the precipitation (mm), D is the drainage water (mm), and is the daily change in weight of the lysimeter (mm). Drainage water was calculated by weighing the amount of drained water from the bottom of the lysimeters (there is a tank beneath the lysimeters to collect the free drained water, Fig. 1).

Crop coefficient

The single crop coefficient () was calculated by dividing , measured using lysimeters, by the daily grass reference evapotranspiration () as follows:

2

The was calculated based on modified Penman-Montieth equation³⁶ and FAO-56 manual⁸.

The dual crop coefficient () was determined to separate the crop transpiration and soil evaporation. The soil surface evaporation (E) was measured using PVC micro-lysimeters with an inner diameter of 10.5 cm and a depth of 20 cm. The micro-lysimeters were installed inside the weighing lysimeters between two crop rows and filled with field soil at its natural bulk density to ensure the soil surface inside was level with the surrounding ground. Each micro-lysimeter had a perforated plate at the bottom to allow excess water to drain freely. They were irrigated simultaneously with the main lysimeters during each irrigation event. The micro-lysimeters were weighed daily, using a precision balance. The difference in weight between the two measurements represented the daily soil evaporation, and transpiration (T) was calculated as the difference between soil evaporation and the crop’s daily evapotranspiration. The basal crop coefficient () is the ratio of T to , while evaporation coefficient () is the ratio of E to , as explained in the FAO-56 manual⁸. These two variables combined to provide dual crop coefficient (k_c−dual) as follows:

3

Crop height and leaf area index

Three plants were selected in each lysimeter to measure the height of the onion at the main crop growth stages throughout the growing seasons (10 times). The leaf area of selected plants was measured by the WinDias image analysis system (Delta-T Devices, Cambridge, UK) 12 times during the main crop growth stages. Thereafter, the leaf area index of each plant was calculated by dividing the leaf area of a plant by the area occupied by that plant (product of the row spacing and the plant spacing on each row). As the leaf of onion is similar to cone, the leaf length and leaf diameter in the middle of each leaf was measured during the first and second year to calculate the lateral surface area of onion leaf³⁷.

Machine learning methods

In this research, five machine learning algorithms were used to represent a range of linear and non-linear modeling approaches with different levels of complexity and interpretability. This diversity allowed us to identify which modeling structure best captures the relationship between input variables (Table 3) and the daily evapotranspiration of onion (A total of 400 data in two growing seasons).

Table 3.

Different machine learning scenarios, input variables and output variable.

Scenarios	Input variables	Output variable
First Scenario	Tmin, Tmax, Tavg, RHmin, RHmax, RHavg	Measured daily
Second Scenario	Tmin, Tmax, Tavg, RHmin, RHmax, RHavg, U2, Rn
Third Scenario	Tmin, Tmax, Tavg, RHmin, RHmax, RHavg, U2, n
Fourth Scenario	Tmin, Tmax, Tavg, RHmin, RHmax, RHavg, Ra
Fifth Scenario	Crop Height, LAI, Crop Height×LAI
Sixth Scenario	Tmin, Tmax, Tavg, RHmin, RHmax, RHavg, Crop Height, LAI, Crop Height×LAI
Seventh Scenario	Tmin, Tmax, Tavg, RHmin, RHmax, RHavg, U2, Rn, Crop Height, LAI, Crop Height×LAI

*T_max, T_min, T_avg, RH_max, RH_min, RH_avg, , Rn, n, Ra, LAI, and denote maximum daily air temperature (^oC), minimum daily air temperature (^oC), average daily air temperature (^oC), maximum daily air relative humidity (%), minimum daily air relative humidity (%), average daily air relative humidity (%), wind speed (m s⁻¹), net radiation (Mj m⁻² d⁻¹), sunshine hours (hr), extraterritorial radiation (Mj m⁻² d⁻¹), leaf area index (cm² cm⁻²), and daily onion evapotranspiration, respectively.

Artificial neural network

An artificial neural network (ANN) is a massively parallel computational system designed to mimic the functioning of the human brain. It consists of many simple processing units where the connections are described by assigned weights³⁸. A multilayer network is classified as a type of feedforward artificial neural network that consists of at least three layers: input, hidden, and output. In this artificial neural network, the outputs of the first layer are used as the inputs of the next layer. This process continues in the same manner, and the outputs of the last hidden layer are used as the inputs of the output layer. For the ANN model, a feed-forward multilayer perceptron structure was used with one or two hidden layers. The optimal number of neurons in each hidden layer was determined through a trial-and-error approach to minimize the testing error. For more detailed explanations, please refer to³⁹.

Support vector regression

Support Vector Machine (SVM) is one of the supervised machine learning algorithms that is widely used for classification problems. In regression problems, the model allows small errors within a certain range to be ignored, defined by ε, and only focus on larger deviations. This makes SVM effective for regression tasks, specifically referred to as Support Vector Regression (SVR)⁴⁰. The goal of SVR is to find a function that estimates the relationship between the input variables and the output variable while minimizing the prediction error. The SVR models were tested with different kernel functions, including the radial basis function (RBF) and polynomial kernels of degrees 2 and 3. The RBF kernel yielded the best performance and was selected for the final modeling. After selecting the kernel, the main hyperparameters—cost (C), kernel scale (γ), and the insensitive loss function width (ε)—were optimized automatically using the OptimizeHyperparameters function in MATLAB. Find more detailed explanations in⁴¹.

Decision tree

A decision tree (DT) is a flowchart-based predictive model that links observations of an item to conclusions about its target variable. The DT is commonly referred as the Classification and Regression Tree (CART)⁴². Various algorithms like CART, C4.5, CHAID, and QUEST are used to build decision trees but CART analysis has been popularized as an umbrella term for any decision tree learning method⁴³. The DT is made up of different nodes. The root node is the starting point of the decision tree, which usually contains all the data for the problem. The leaf nodes are the end points of each branch of the tree, or the final output of a set of decisions⁴². The objective of constructing a regression tree is to minimize the sum of squared errors through a recursive process that generates a binary tree, identifying optimal feature selections and split points⁴⁴. The tree structure can be adjusted to align with the characteristics of the data being modeled. However, when the tree grows excessively, it may lead to issues such as overfitting. The main parameters, MaxNumSplits, MinLeafSize, and NumVariablesToSample, were tuned using the OptimizeHyperparameters function to minimize the validation error. For further details, please refer to⁴⁵.

Random forest

Random forests (RF), an ensemble method for classification and regression, are multiple decision trees in agreement with a small variation of trees instead of a single tree. The RF uses majority voting for classification, while the average of the tree outputs forms the basis for regression tasks and makes the RF one of the most reliable algorithms for predictive analysis⁴⁶. RF constructs an ensemble of unpruned decision trees using bootstrap sampling which means that instead of training on all the observations, each tree of RF is trained on a subset of the observations. The chosen subset is called the bag, and the remaining are called Out of Bag (OOB) samples⁴⁷. At each split, the best feature is selected from a random subset of features, promoting diversity among trees. This approach enhances model robustness and enables efficient OOB-based estimation of generalization error, strength, and correlation without needing a validation set. The combination of bootstrap sampling and random feature selection reduces overfitting and improves predictive performance⁴⁸. The Random Forest model was built as an ensemble of decision trees using bootstrap aggregation (bagging). The optimal MinLeafSize value was determined using the OOBPrediction (Out-of-Bag) option, which estimates the prediction error on unseen data. After fixing the optimal leaf size, the number of trees (NumTrees) was adjusted through trial-and-error to balance model accuracy and computational cost. For more detailed explanation, please refer to⁴⁷.

LASSO regression

Lasso, also known as Least Absolute Shrinkage and Selection Operator, is a regression technique widely used in statistics and machine learning⁴⁹. It combines variable selection and regularization to improve the predictive performance and interpretability of statistical models. This method operates under the assumption that the coefficients of the linear model are sparse, meaning only a small number of them are non-zero⁵⁰. LASSO regression was used to provide a regularized linear baseline and to perform embedded feature selection among the candidate predictors. Prior to fitting the LASSO model, all input variables were normalized to the zero and one range to ensure comparable scaling across predictors and to match the preprocessing applied to the other machine learning methods. We fitted LASSO with 10-fold cross-validation to select the regularization parameter λ that minimized the cross-validated mean squared error (MSE). The final model was chosen at LambdaMinMSE, and the corresponding coefficient vector (with many coefficients shrunken exactly to zero) was used for test predictions and model interpretation.

Data set

All machine learning algorithms take numerical inputs and produce numerical outputs, so all datasets were normalized to improve the performance of the model. In this study the following equation⁵¹ was used:

4

where x is the observed data, is the normalized data, and are the lowest and highest observed data, respectively.

In this study MATLAB R 2023b was used to implement the machine learning algorithms. The dataset, consisting of two years of data, was combined and split into two portions: 70% for training the models and 30% for testing. The dataset was partitioned into 10 subsets (k), and the models were trained and tested iteratively, utilizing different portions of the data in each cycle. This method ensured that each data point was used as part of the validation set exactly once and appeared in the training set k − 1 times. To improve the robustness of the results, the data distribution across the training and validation subsets was randomized.

Considering the effective parameters, several scenarios with different structures and input parameters were tested to estimate onion evapotranspiration (Table 3). Also, due to the lack of access to all meteorological and crop parameters across different regions, different options were considered as network inputs. Moreover, the scenarios were designed to separately test meteorological-only (Scenarios 1–4), crop-only (scenario 5), and integrated inputs (scenarios 6–7 to evaluate the contribution of each category. The reason for considering sunshine hour (n) and extraterrestrial radiation (R_a) separately in scenarios was due to the fact that they represent different concepts with distinct measurement characteristics and availability. Sunshine hours measure actual sunlight duration received at the surface, reflecting local atmospheric conditions, cloud cover, and immediate solar energy availability influencing evapotranspiration. Extraterrestrial radiation, on the other hand, represents the maximum potential solar radiation received at the top of the atmosphere based on location, date, and time, independent of local weather conditions. Testing them separately allows analyzing their relative importance and predictive value in the ML models because R_a is a theoretical, constant upper boundary of solar input, while n is an observed variable that captures local variability. Statistical indicators were used to evaluate the effect of scenarios on ET_c prediction. The impact of meteorological and crop variables on model performance was assessed by comparing seven different input scenarios using statistical index.

Statistical analysis

Statistical analysis is an essential tool for evaluating the accuracy of different machine learning algorithms and selecting the best ones. In this study, statistical parameters were calculated to assess the model’s accuracy as follows:

(i) Mean squared error (MSE)

5

where is the simulated crop evapotranspiration by the machine learning algorithms, is the observed crop evapotranspiration (measured by a lysimeter), and n is the number of observations.

(ii) Root mean square error (RMSE)

6

(iii) Normalized root mean square error (NRMSE)

7

where is the average of observed crop evapotranspiration values.

(iv) Mean Absolute Error (MAE)

8

(v) Index of agreement (d)

9

(vi) Coefficient of determination (R²)

10

MSE, RMSE, NRMSE and MAE with smaller values, and d and with higher values indicates higher precision and accuracy of the model.

Results

Leaf area index and crop height

The variations of the leaf area index (LAI) during the first and second growing seasons are presented in Fig. 3a, c. In both years, early crop height was limited by cold temperatures, which delayed LAI measurements. In the first year, significant growth began 116 days after planting, with the highest LAI of 0.32 at 158 DAS, corresponding to the maximum vegetative cover. In contrast, temperatures were colder in the second year experienced with an average decrease of 2.3 C, which delayed plant growth and shifted the onion growth.

Fig. 3.

Variations of leaf area index and height during 2021–2022 (a,b) and 2022–2023 (c,d) growing season, respectively. Y is the measured value and x is days after sowing (DAS). Solid curves and lines represent third- and first-degree regression lines.

In the second year, the crop growth started 157 days after sowing (DAS) and the maximum LAI of 0.27 was reached at 192 DAS. After the peak value of LAI, it decreased as the leaves turned yellow and dried. Since the onions were harvested before flowering and full leaf senescence, the LAI on the day of the harvest was not zero. Third-degree polynomial equations (followed by^52,53) fitted to show the variations of LAI throughout both growing seasons (Fig. 3a, c).

The variations of crop height during the first and second growing seasons are presented in Fig. 3b,d. In the first year, plant growth was minimal during the first 50 days after sowing due to cold weather. In the first year, the first crop height measurement was taken at 90 days after sowing, and the maximum crop height of 55.4 cm was recorded at 209 days after sowing, just before harvest. In the second year, a colder winter delayed growth by about 40 days compared to the first year. Crop height measurements began at 130 days after sowing, and the maximum height of 51.6 cm was recorded at 214 days after sowing. In both years, onions were harvested before flowering, so the crop height showed no decline (Fig. 3).

Crop evapotranspiration

Crop evapotranspiration () of onion was measured using two weighing lysimeters and the water balance method. The results are presented as the average between consecutive irrigation or rainfall events. Specifically, the average of was calculated from the day of irrigation until the next irrigation or rainfall. Additionally, the average values of irrigation water, rainfall, drainage, and for the two growing seasons of 2021–2022 and 2022–2023 are provided in Table 4. The difference between the input (Irrigation water depth +Rainfall) and output (drainage water + onion evapotranspiration) of water balance (Table 4) is due storage changes in the lysimeter system.

Table 4.

The average values of irrigation water depth (I), rainfall (R), drainage (D), and onion evapotranspiration () during the growing seasons of 2021–2022 and 2022–2023.

Growing season	(mm)	D (mm)	R (mm)	I (mm)
2021–2022	447.1	335.2	174.0	1022.2
2022–2023	432.2	411.2	291.5	1200.6

Figure 4a, d show the variations of onion during the growing seasons. In the first year, data for the first 50 days after sowing was unavailable due to lysimeter malfunctions and issues with rapid drainage after irrigation. The rates were low at the start of the season, increased steadily during mid-growth, peaked as 5.5 mm d⁻¹ at 158 days after sowing, and then declined after bulb formation. The total for the first growing season was 447 mm. In the second growing season (2022–2023), the maximum was 4.4 mm d⁻¹ at 185 days after sowing, with a total of 432 mm. The maximum rate in the second year was about 20% lower than in the first year due to lower temperatures. To describe the onion as a function of days after sowing, third degree polynomial regression curves were fitted to the measured data for both growing seasons. Figure 4b, e shows the variations in soil evaporation during the growing seasons. During the first growing season, soil evaporation peaked at 1.4 mm d⁻¹ at the 197 days after sowing, totaling 163.5 mm for the season. The soil evaporation decreased as air temperatures dropped and the soil was frozen during winter, but rose again with increasing air temperatures. The onion crop was harvested before flowering, so the evaporation curve did not decline. During the second growing season, maximum soil evaporation rate reached 1.15 mm d⁻¹ at the 178 days after sowing, totaling 141.5 mm for the season.

Fig. 4.

Variations of onion evapotranspiration, evaporation and transpiration during 2021–2022 (a–c) and 2022–2023 (d–f) growing season, respectively. Y is the measured value and x is days after sowing (DAS). Solid curve is the regression line.

The evaporation trend was similar to the previous year, but colder temperatures led to lower maximum evaporation compared to the first year. Onion transpiration rate can be calculated by subtracting soil evaporation from the . The results are shown in Fig. 4c, f. During the first growing season, onion transpiration peaked as 4.4 mm d⁻¹ at the 158 days after sowing, with a total of 284.6 mm for the season. During the second growing season, the maximum transpiration occurred on the 185th day after sowing, totaling 261.9 mm, and it was decreased by 8.0% in comparison with that in the previous year. Despite differences in total transpiration, onion transpiration trends closely followed overall patterns in both seasons. Variations can be attributed to climatic conditions, especially lower temperatures in the second year. Third-degree polynomial curves were fitted to the transpiration data for both years, showing the relationship between transpiration intensity and days after sowing (R² > 0.7).

Moreover, the average of E/ET_c was 0.5, 0.3, and 0.37 for initial, mid, and end stage, respectively and the average of T/ET_c was 0.37, 0.66, and 0.60 for initial, mid, and end stage, respectively, over two growing seasons.

Single and dual crop coefficient

In this study, the average of both growing seasons for onion was considered from mid-November to mid-June, lasting as 199 days. The average length of initial, crop development, mid-season and late-season stage is provided in Table 5.

Table 5.

Average the length of different onion growth stages.

Years	Initial (days)	Crop development (days)	Mid-season (days)	Late-season (days)	Total (days)
2021–2023	64	71	40	24	199

The average variations of single and dual crop coefficients are shown in Fig. 5. According to Fig. 5a, onion single crop coefficient () in the two growing seasons generally varied from 0.41 to 0.72. The average single crop coefficient values for initial, mid-season and late-season of onion were determined as 0.41, 0.68, and 0.51, respectively. Figure 5b shows the variation of average of soil evaporation coefficient during the growing season. The average values for for initial, mid- season and late-season stages were 0.31, 0.17, and 0.14, respectively. The average values of the basal crop coefficient for initial, mid-season and late-season were 0.10, 0.51, and 0.37, respectively (Fig. 5c). Third-degree polynomial and linear curves were fitted to the average K_c, K_e and K_cb for both years, showing the relationship between single and dual crop coefficient and days after sowing.

Fig. 5.

Variation of average single crop coefficient (), surface evaporation coefficient (), and basal crop coefficient (). DAS represents days after sowing. Solid lines represent different mean onion growth stages.

Machine learning method

This study evaluates the performance of various algorithms in simulating ET_c using different combinations of meteorological data and crop parameters. Five machine learning algorithms were utilized to train and test subsets across seven scenarios. The modeling performance results are summarized using statistical indicators in Tables 6, 7, 8, 9 and 10 for ANN, SVR, DT, RF, and LASSO regression models, respectively. A comparison of measured and the best simulated onion ET_c is shown in Fig. 6 for ANN, SVR, DT, RF, and LASSO algorithms, respectively, based on regression analysis forced through the origin.

Table 6.

Optimal results of artificial neural network algorithm with one and two hidden layers for simulated onion evapotranspiration.

Hidden layers	Method	Training algorithm	Activation function	Number of neurons	Training MSE	Testing
						MSE	RMSE	NRMSE	MAE	R2	d
One	ANN1	Lm	Logsig	5	0.269	0.422	0.620	0.254	0.482	0.663	0.900
	ANN2	Lm	Logsig	7	0.050	0.144	0.380	0.161	0.251	0.873	0.966
	ANN3	Br	Tansig	5	0.123	0.208	0.456	0.195	0.319	0.823	0.952
	ANN4	Lm	Logsig	3	0.174	0.177	0.421	0.165	0.318	0.857	0.961
	ANN5	Lm	Tansig	8	0.037	0.063	0.251	0.110	0.177	0.949	0.986
	ANN6	Lm *	Tansig	4	0.017	0.026	0.161	0.071	0.129	0.971	0.992
	ANN7	Lm	Tansig	4	0.006	0.048	0.219	0.099	0.119	0.954	0.988
Two	ANN1	Br	Log-Tan	3–3	0.293	0.330	0.574	0.252	0.460	0.713	0.909
	ANN2	Br	Tan-Log	7 − 2	0.025	0.229	0.479	0.199	0.307	0.797	0.941
	ANN3	Br	Tan-Log	2–9	0.153	0.209	0.457	0.192	0.333	0.806	0.943
	ANN4	Br	Tan-Log	3–3	0.132	0.153	0.392	0.174	0.278	0.876	0.966
	ANN5	Lm	Tan-Log	3–4	0.038	0.048	0.220	0.096	0.142	0.953	0.988
	ANN6	Lm *	Log-Tan	4–4	0.002	0.017	0.132	0.056	0.061	0.986	0.996
	ANN7	Lm	Tan-Log	4–8	0.002	0.122	0.350	0.147	0.125	0.883	0.971

*The best selections for each scenario are shown in italic. Lm, Br, Logsig, Tansig, MSE, RMSE, NRMSE, MAE, R², and d represent Levenberg-Marquardt, Bayesian Regularization, logistic sigmoid, tangent sigmoid, mean squared error (mm ), root mean squared error (mm ), normalized root mean squared error, mean absolute error (mm ), coefficient of determination, and index of agreement, respectively.

Table 7.

Optimal results of support vector machine algorithm for simulating onion evapotranspiration.

Method	Kernel function	Hyperparameters			Training MSE*	Testing
		Cost	Gamma	Epsilon		MSE	RMSE	NRMSE	MAE	R2	d
SVR1	RBF	1.213	0.457	0.003	0.265	0.366	0.605	0.270	0.472	0.688	0.905
SVR2		0.473	0.632	0.043	0.076	0.088	0.297	0.132	0.211	0.924	0.979
SVR3		0.267	0.664	0.006	0.133	0.169	0.412	0.184	0.289	0.855	0.958
SVR4		546.92	1.774	0.045	0.181	0.234	0.484	0.216	0.355	0.800	0.940
SVR5		19.253	0.073	0.0007	0.063	0.065	0.255	0.114	0.135	0.944	0.984
SVR6		20.21	1.339	0.0003	0.048	0.093	0.306	0.136	0.183	0.920	0.978
SVR7*		841.45	2.697	0.001	0.009	0.031	0.177	0.079	0.097	0.973	0.993

*The best selections for each scenario are shown in italic. MSE, RMSE, NRMSE, MAE, R², and d represent mean squared error (mm ), root mean squared error (mm ), normalized root mean squared error, mean absolute error (mm ), coefficient of determination, and index of agreement, respectively.

Table 8.

Optimal results of decision tree algorithm for simulating onion evapotranspiration.

Method	Hyperparameters		Training MSE*	Testing
	Min Leaf Size	Max Num Splits		MSE	RMSE	NRMSE	MAE	R 2	d
DT1	6	63	0.209	0.415	0.644	0.204	0.482	0.646	0.887
DT2	4	34	0.047	0.122	0.350	0.097	0.246	0.895	0.972
DT3	2	48	0.042	0.215	0.464	0.092	0.314	0.816	0.950
DT4	5	32	0.114	0.219	0.468	0.151	0.310	0.813	0.943
DT5	7	37	0.044	0.073	0.271	0.093	0.211	0.937	0.983
DT6*	4	51	0.009	0.023	0.153	0.043	0.102	0.980	0.995
DT7	4	33	0.009	0.023	0.153	0.043	0.103	0.980	0.995

*The best selections for each scenario are shown in italic. MSE, RMSE, NRMSE, MAE, R², and d represent mean squared error (mm ), root mean squared error (mm ), normalized root mean squared error, mean absolute error (mm ), coefficient of determination, and index of agreement, respectively.

Table 9.

Optimal results of random forest algorithm for simulating onion evapotranspiration.

Method	Hyperparameters		Training MSE*	Testing
	Min Leaf Size	Num Tree		MSE	RMSE	NRMSE	MAE	R 2	d
RF1	2	300	0.108	0.311	0.557	0.147	0.476	0.735	0.906
RF2	2	150	0.037	0.116	0.341	0.086	0.262	0.901	0.970
RF3	2	50	0.049	0.135	0.368	0.099	0.278	0.884	0.964
RF4	3	300	0.079	0.154	0.392	0.125	0.328	0.868	0.957
RF5	2	300	0.066	0.077	0.278	0.115	0.183	0.934	0.981
RF6	2	200	0.008	0.026	0.164	0.040	0.121	0.977	0.993
RF7*	2	50	0.007	0.019	0.139	0.037	0.100	0.983	0.995

*The best selections for each scenario are shown in italic. MSE, RMSE, NRMSE, MAE, R², and d represent mean squared error (mm ), root mean squared error (mm ), normalized root mean squared error, mean absolute error (mm ), coefficient of determination, and index of agreement, respectively.

Table 10.

Optimal results of LASSO regression algorithm for simulating onion evapotranspiration.

Method	Hyperparameter	Training MSE	Testing
	λ		MSE	RMSE	NRMSE	MAE	R 2	d
LR1	0.0006	0.640	0.726	0.852	0.357	0.702	0.381	0.750
LR2	0.0031	0.463	0.480	0.692	0.304	0.538	0.591	0.858
LR3	0.0006	0.528	0.600	0.774	0.324	0.648	0.488	0.812
LR4	0.0008	0.625	0.676	0.822	0.353	0.676	0.424	0.770
LR5	0.0002	0.241	0.276	0.525	0.219	0.409	0.765	0.927
LR6	0.0001	0.193	0.225	0.475	0.196	0.397	0.807	0.943
LR7*	0.0008	0.161	0.175	0.418	0.179	0.341	0.851	0.957

*The best selections for each scenario are shown in italic. MSE, RMSE, NRMSE, MAE, R², and d represent mean squared error (mm ), root mean squared error (mm ), normalized root mean squared error, mean absolute error (mm ), coefficient of determination, and index of agreement, respectively.

Fig. 6.

Relationship between the measured and the best simulated onion of machine learning algorithms during testing period. Dash line indicates 1:1 line.

Performance of ANN method

The performance of the ANN algorithm in simulating values was evaluated using one and two hidden layers, and the results are presented in Table 6 and supplementary Table S1. Seven different scenarios were tested to assess the model’s effectiveness. Determining the optimal number of neurons in the hidden layer lacks a definitive methodology; therefore, the selection was conducted through a trial-and-error approach to identify the most suitable configuration. The results of the artificial neural network with two hidden layers showed that adding an extra hidden layer to the model did not significantly improve the accuracy of the model. For both ANN models with one and two hidden layers, ANN6 exhibited the best performance (Fig. 6a, d). Numbers after machine learning algorithms indicate the number of the scenarios presented in Table 3. According to Fig. 6a, the slope of regression indicates that the ANN model with one hidden layer has accurately simulated values, as it is close to 1.0. The coefficient of determination (R² = 0.97) signifies a strong correlation and the index of agreement (d = 0.99), and NRMSE equal to 0.07 further confirms the high accuracy of the model. The ANN6 model, which incorporates meteorological factors (temperature and humidity) along with crop parameters, showed superior simulation accuracy. It was configured with four neurons per one hidden layer, trained using the Levenberg-Marquardt algorithm, and utilized a tangent sigmoid activation function. Adding one more hidden layer slightly improved the simulated onion ET_c, as the statistical indicators for ANN2 with two hidden layers were d = 0.99, R² =0.99 and NRMSE = 0.06 (Table 6; Fig. 6d).

Performance of SVR method

The results demonstrate that hyperparameter selection is crucial in determining the simulation accuracy of SVR models. The cost parameter (C), gamma (γ), and epsilon (ε) significantly impact the model’s ability to capture complex data patterns while avoiding overfitting. The details of statistical index for training test of SVR algorithms is provided in Table S2. SVR7 exhibited the best performance (Fig. 6b), the slope indicates that the model has effectively simulated the value, as it closely aligns with a slope of 1.0 and the high (0.97) and d (0.99) values. Despite two outlier points, the overall slope of the line remains very close to the 1:1 line. Also, SVR7 model achieved the lowest testing MSE (0.03 mm ), RMSE (0.18 mm ), NRMSE (0.08), and MAE (0.1 mm ). According to Table 7, SVR5 also performed well, with relatively low testing MSE (0.07 mm ), RMSE (0.26 mm ), and high (0.94). In contrast, SVR1 and SVR4 showed weaker performance compared to the top models. SVR1, despite a moderate cost parameter (C = 1.21), exhibited relatively high testing RMSE (0.61 mm ) and NRMSE (0.27), indicating poor generalization. Similarly, SVR4 with excessively high cost (546.9) and high gamma (1.77), displayed suboptimal performance with testing (0.80) and RMSE (0.48 mm ). This highlights that an overly large cost value combined with high gamma can lead to overfitting, diminishing the model’s generalization ability to new data.

Performance of DT method

Table 8 and S3 shows the result of decision tree performance in simulating . The DT6 and DT7 achieved the best performance, with the lowest testing MSE (0.02 mm ), RMSE (0.15 mm ), NRMSE (0.04), and MAE (0.10 mm ). These models also showed the highest (0.98) and d (0.995) values, indicating a strong correlation between the simulated and actual values (Fig. 6e). The regression slope suggests that the model has accurately simulated the value, as it closely aligns with a slope of 1.0. DT5 performed well with testing MSE (0.07 mm ) and RMSE (0.27 mm ), showing a high value of 0.94 and d of 0.98. It was nearly as effective as DT6 and DT7, but the slightly larger min leaf size of 7 may have caused minor under fitting. DT2 showed balanced performance with a moderately low testing MSE (0.12 mm ) and RMSE (0.35 mm ). Its value of 0.90 and d of 0.97 indicate good simulation capability. DT1 with the largest min leaf size of 6 and max num splits of 63 had weakest performance with highest MSE = 0.41 mm , NRMSE = 0.2, and lowest (0.65) value, indicating poor generalization due to an overly complex tree.

Performance of RF method

Among the models, RF7 (min leaf size = 2, num tree = 50) exhibited the best performance with the lowest testing MSE (0.02 mm ), RMSE (0.14 mm ), NRMSE (0.04), and MAE (0.10 mm ), indicating strong simulation capability with minimal error (Fig. 6c). Among RF models, RF7 exhibited the best performance (Table 9 and S4). The linear regression fitted between measured and simulated onion ET_c with RF7 showed that model accurately and effectively simulated the with the slope of 1.0, of 0.98, and d of 0.99. RF6 (min leaf size = 2, num tree = 200) showed similar accuracy with testing MSE (0.03 mm ), R² (0.98), and d (0.99). Interestingly, increasing the number of trees beyond 50 did not consistently improve performance. For example, RF5 (num tree = 300) had higher testing MSE (0.08 mm ) and lower R² (0.93) compared to RF6 and RF7, suggesting a point of diminishing returns in model complexity. RF1 (min leaf size = 2, num tree = 300) had a high testing RMSE (0.56 mm ) and the lowest (0.91). Also, RF4, with higher min leaf size (3), demonstrated lower performance, with an MSE (0.15 mm ), and R² (0.87), indicating potential under-fitting due to reduced model flexibility.

Performance of LASSO regression method

In LASSO model, several meteorological predictors were driven to zero and the model therefore performed predictions without them. In scenarios 1 and 4, LASSO eliminated RH_ave, in scenarios 2 and 3, it excluded T_min together with RH_min, in scenario 6, it excluded T_avg and RH_avg; in scenario 7 it excluded RH_min, and in scenario 5 no meteorological variables were zeroed (all were retained). The results of LASSO regression for simulating onion evapotranspiration show the significant impact of the hyperparameter (λ) on model performance. Among the models tested, LR7 with λ = 0.0008 had the lowest testing MSE (0.17 mm ), RMSE (0.42 mm ), and MAE (0.34 mm ), with the highest R² (0.85) and d (0.96) values. LR7 achieved the optimal trade-off between complexity and generalization, making it the most reliable model for simulation. According to Fig. 6f, the slope of 0.96, slightly less than 1.0, indicated that the LASSO model tends to slightly underestimate values. The regression line closely follows the 1:1 line with slight deviation, especially at lower values, where some points are more scattered. This variability in prediction accuracy for smaller values indicates that the LASSO model may have limitations in certain scenarios. According to Table 10 and S5, it is indicated that LR6 (λ = 0.0001) and LR5 (λ = 0.0002) also performed well, with low MSE values (0.22 and 0.28 mm , respectively) and high R² values (0.81 and 0.77, respectively), indicating that mild regularization enhances accuracy while preventing overfitting. LR1 (λ = 0.0006) and LR4 (λ = 0.0008) had higher testing MSE values (0.73 and 0.68 mm , respectively) and lower R² values (0.0.38 and 0.42). LR2 (λ = 0.0031) achieved a moderate balance between bias and variance but performed worse than models with smaller λ values. Smaller λ values tend to perform better by retaining essential predictors without unnecessary complexity. However, excessively small λ values can lead to overfitting, emphasizing the importance of selecting an optimal λ value.

Comparative result of different machine learning

Across all scenarios, ANN, SVR, RF, and DT demonstrated higher predictive accuracy than LASSO regression. Scenarios six and seven, which incorporated both meteorological and crop parameters, produced the best performance for most algorithms. In contrast, scenarios relying solely on meteorological variables generally resulted in lower accuracy.

Among scenarios one to four, the SVR model in scenario two yielded the best performance across the tested algorithms. The optimal cost (C) parameter for the SVR model varied among scenarios, reflecting differences in input dimensionality and data characteristics. The RF model achieved the highest overall accuracy, with RF7 identified as the best-performing model–scenario combination (Fig. 6c). The DT model showed improved performance when crop parameters were included, although it consistently ranked below the RF model. For the ANN models, configurations with two hidden layers outperformed those with a single hidden layer under the sixth scenario (Fig. 6a and d). However, the difference in performance between one and two hidden layers was relatively small. The ANN with two hidden layers and the SVR model produced similar accuracy levels under comparable input scenarios.

The relative importance of predictor variables was assessed for the RF7 model using the PredictorImportance function in MATLAB, based on reductions in mean squared error (MSE) across all trees. The importance values were as follows: T_min (0.34), T_max (0.62), T_avg (0.49), RH_min (0.08), RH_max (0.67), RH_avg (0.38), wind speed (0.95), net radiation (0.92), plant height (1.03), leaf area index (1.29), and the interaction term (plant height × leaf area index) (0.85). Scenarios including net received radiation, particularly scenario seven, resulted in improved performance for RF, SVR, and LASSO regression compared to scenarios excluding this variable.

Discussion

Plant height and Leaf area index

Leaf area index (LAI) and crop height (H) are key indicators of vegetation structure^54,55. Efficient estimating these parameters is crucial for enhancing crop growth monitoring, assessing plant health, and predicting yield⁵⁶. The maximum LAI achieved in our study was 0.32 and 0.27 , with corresponding maximum H of 55.4 and 51.6 cm in the first and second year, respectively. Onion exhibited a lower early relative growth rate, which was attributed to the crop canopy’s limited light interception ability and the low initial radiation use efficiency³⁷. Also, onion due to its upright and vertical leaves, typically exhibits low LAI and even lower fractional ground cover compared to other row crops⁵⁷. In a study⁵⁸, showed that the maximum LAI of transplanting Behbahan onion was 2.5 . The higher LAI observed in the latter study compared to the current study is attributed to the plants spending the first 85 days of growth under controlled conditions before being transplanted into the field, where the onions experienced warmer temperature during rapid growth stage. Also²³, demonstrated that transplanting onion (cv. kharif) in Punjab, India, with varying rainfall ranging from 900 to 1100 mm, using a spacing of 15 × 10 cm, led to significantly increased plant height (30.87 cm) and number of leaves per plant (12.20) compared to 10 × 7.5 cm spacing. The differences between our LAI and H with other studies may be attributed to variations in planting density, onion cultivars, precipitation levels and environmental conditions.

Evapotranspiration of onion

In the arid and semi-arid climates, accurate estimation of can help calculate crop water requirements and provide a scientific basis for developing irrigation schedules that can increase crop production⁵⁹. In our study, the amount of , transpiration and surface evaporation slightly decreased in the second year by 3.3%, 7.9% and 13.4% compared to the first year. This decrease was attributed to lower temperature and higher relative humidity (Fig. 2). The seasonal onion for non-deficit irrigation treatment in Turky’s arid region was the highest as 680.7 mm and the lowest as 190.0 mm in the non-irrigation treatment⁶⁰. Also²⁰, reported the seasonal for onion measured in the lysimeter as 893.3 mm under semi-arid conditions in Spain. Additionally⁶¹, reported that the accumulated onion in the Winter Garden region of Texas, with rainfall of 80 mm and 166 mm and irrigation water of 238 mm and 215 mm in 2002 and 2004, respectively, was 362 and 438 mm in first and second growing years, respectively. Our results fall within the range of water requirements (350 to 550 mm) for optimal onion yield (35,000 to 45,000 kg ha⁻¹) as described by⁶². However, the differences between our and other studies may be attributed to variations in onion cultivars, precipitation levels and environmental conditions.

Single and dual crop coefficient

The maximum K_c and K_cb was 0.68 and 0.51 obtained at mid stage, respectively. The starts at a high value (0.31) in the early growing season and gradually decreases as the season progresses. This trend is expected as the evaporation rate from the soil is initially high when the onion is first planted and has limited vegetation cover. As the plant grows and the vegetation cover on the soil increases, the evaporation rate decreases until the end of the growing season (Fig. 5b). The existing literature shows various values depending on the onion cultivar, planting density, cropping techniques, local climatic conditions, and irrigation system⁹. The lower values of single and double crop coefficient observed in the current study compared to that presented in FAO-56 manual^8,63, and⁹ were due to application of different cultivars, plant density (as farmers use in the study) and irrigation method (sprinkler and sub-surface drip irrigation). It was explained that canopy development of onion (Armaghan G. cultivar) was lower than other cultivars as having maximum LAI of only 0.32 cm² m⁻² and height of 55 cm. Although the planting density was within the normal range for the region, the sparse canopy limited radiation interception and transpiration. Cold winter conditions also delayed growth and shortened the effective growing season. Therefore, the lower Kc and Kcb values observed here primarily reflect the canopy architecture and environmental conditions. In a study⁶⁴, determined the values of 0.4, 1.1, and 0.87 for the initial, mid and late growth stages of onion (cv. Giza 61) irrigated by flood irrigation system in Egypt, with a semi-arid region. In a similar study in Spain²⁰, reported onion (A. cepa L., cv. Granero) values of 0.65, 1.20, and 0.75 for the initial, mid, and late stages using sprinkler irrigation. Additionally⁶¹, determined growth stage-specific values for onion (cv. Texas Legend) as 0.40 at emergence, 0.90 at bulb development, and 0.70 at dry leaf stage using sub-surface drip irrigation.

Simulation of by different algorithms of machine learning

The results of our study indicate that all the models used (ANN, SVR, RF, and DT) except LASSO regression, can effectively capture nonlinear relationships between weather and crop parameters to simulate . The selection of input variables significantly influences the accuracy of estimation using machine learning models²⁷. Comparing machine learning algorithm results revealed that scenarios six and seven, incorporating both meteorological and crop parameters, outperformed other scenarios. In situations where measuring all meteorological data is not practical, machine learning algorithms offer a viable alternative for estimating directly crop evapotranspiration because it can provide reliable, accurate estimates by learning from available data and capturing complex variable relationships⁶⁵. Moreover, the machine learning models trained on local canopy and environmental data can adapt to site-specific conditions, giving more precise ET_c estimates than generalized FAO-56 coefficients⁶⁶. The strong performance of the Random Forest model can be attributed to its ensemble learning framework, which reduces overfitting and improves generalization by aggregating multiple decision trees. This structure allows RF to remain robust in the presence of noisy inputs and collinearity among meteorological variables, making it particularly effective for agricultural applications where environmental data often exhibit high variability^67,68. Following the RF, the DT algorithm also showed improved results. The RF outperformed the decision tree due to its use of multiple decision trees for simulation, preventing overfitting issues⁶⁸. Artificial Neural Networks and Support Vector Regression exhibited comparable predictive behavior, suggesting that both methods can effectively learn nonlinear relationships between input variables and ET_c⁶⁹. Increasing ANN model complexity through additional hidden layers resulted in only marginal performance gains, indicating that evapotranspiration dynamics can be captured without excessive network depth when relevant input variables are provided⁶⁸. Similarly, variations in SVR performance across input scenarios reflect its sensitivity to kernel configuration and regularization, underscoring the importance of appropriate parameter tuning⁶⁹. The LASSO regression performs poorer than other algorithms due to the nonlinear relationship between input and output parameters. LASSO applies linear shrinkage, the removal of these RH and T parameters (which often act nonlinearly and interactively with other drivers of evapotranspiration) likely led to loss of important explanatory information and contributed to its lower predictive accuracy compared with nonlinear algorithms^70,71.

The seventh scenario in RF, SVR, and LASSO regression algorithms show better performance possibly due to the net received radiation parameter being a significant input, indicating a stronger influence on onion evapotranspiration compared to other parameters⁷². Canopy-related parameters such as LAI and plant height, along with net radiation and wind speed, were the most influential predictors of onion evapotranspiration^73,74. This finding highlights the crucial role of both plant structural and energy-related variables in accurately estimating ET_c⁶⁸. Variables such as leaf area index and plant height influence aerodynamic resistance, radiation interception, and transpiration efficiency, thereby strengthening the physical linkage between crop growth dynamics and water fluxes⁷². This finding confirms that models trained with combined meteorological and crop information are better able to represent site-specific evapotranspiration behavior than those relying on atmospheric data alone. In contrast, humidity parameters, especially RH_min, exhibited relatively lower importance, suggesting that aerodynamic and air moisture-related factors had a smaller influence under the semi-arid conditions of the study area⁷¹. In a study by⁷⁵, six machine learning algorithms (linear regression, ridge regression, lasso regression, K-nearest neighbors, random forest, and XGBoost) were compared. After training and testing all algorithms, the XGBoost model demonstrated superior performance in predicting maize grain yield and evapotranspiration. This was confirmed by higher values and lower RMSE and NRMSE compared to the other regression models. Additionally⁷⁶, found that support vector machine (SVM) and ANN optimized by genetic algorithm (GANN) accurately estimated maize using meteorological and crop data. Also³³, showed that multivariate nonlinear regression (MNLR) method had the highest accuracy in predicting potato compared to ANN and neural network–genetic algorithm (NNGA) methods. In a study²⁷, compared k-Nearest Neighbour (kNN), ANN and Adaptive Boosting (AdaBoost) models to predict daily potato using different sets of meteorological data. The kNN model showed the best performance when meteorological data is limited. Therefore, the kNN model is recommended estimating with limited meteorological data, while the ANN model is suitable when all parameters are available. Others studies have reported the best machine learning model for simulating ^16,77–79.

Advantages and limitations of the study

This study offers significant advantages in experimental and modeling approaches. It provides precise and continuous lysimetric measurements of onion evapotranspiration (ET_c) and crop coefficients (K_c and K_cb) under semi-arid field conditions, which are scarce in the literature, especially for the Arghavan onion cultivar in Iran. The high-precision digital weighing lysimeters used in this study allowed for daily monitoring ET_c with minimal measurement uncertainty, capturing fine-scale temporal dynamics and supporting accurate estimation of crop coefficients. This capability is valuable for calibrating and validating crop water requirements and irrigation scheduling in water-limited environments. Moreover, this study integrated crop growth parameters and meteorological variables into five machine learning frameworks with distinct structures to estimate ET_c.

Limitations include the restriction of the experiment to a single research station and soil type, limiting the generalizability of the results. Variability in soil texture, fertility, and microclimatic conditions in other regions may affect ET_c and model accuracy. Lysimeter-based measurements, while obtaining precise results, are costly, labor-intensive, and spatially limited, reducing large-scale replication feasibility. The machine learning models were trained on a relatively small dataset, potentially limiting generalization to unseen conditions. Key variables influencing ET_c, such as soil water content and canopy temperature, were not included in the input features, potentially affecting model performance under extreme stress conditions. Future research should focus on validating the models across multiple locations and seasons, incorporating additional physiological indicators to improve ET_c prediction and develop scalable irrigation tools for semi- arid and arid environments.

Conclusions

The crop evapotranspiration () of onions was measured using weighing lysimeters in a semi-arid region. The major contribution of this study can be summarized as follows:

1. The highest rate was 5.5 (mm ) in the first growing season and 4.4 (mm ) in the second growing season, with seasonal totals of 447.1 mm and 432.2 mm, respectively. This result can help adjust cropping patterns based on water availability and refine deficit irrigation strategies for effective and sustainable water management. Also, the and values for onion in the study region were determined, and can be used for calculation of the onion in the study region.

2. This study assessed the performance of five machine learning techniques in seven scenarios with varying meteorological and crop parameters. The findings indicate that RF7 modeling, incorporating key variables like temperature, humidity, wind speed, net radiation, leaf area index, and crop height, can be a practical alternative to more intricate algorithms. In situations where plant parameters are unavailable, SVR model with the second scenario yielded the best performance for simulating onion evapotranspiration using machine learning.

3. Canopy-related parameters such as LAI and plant height, net radiation, and wind speed, were the most influential predictors of onion evapotranspiration. This finding highlights the crucial role of both plant structural and energy-related variables in accurately estimating ET_c.

To improve simulation accuracy, additional studies should evaluate the performance of the five used machine learning models under different environmental conditions and data availability levels.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

Saba Hashempour: The conception and design of the study, acquisition of data, analysis, interpretation of data, and writing the first draft of manuscript; Fatemeh Razzaghi: The conception and design of the study, acquisition of data, analysis and interpretation of data, supervising, and revising the article critically; Ali Reza Sepaskhah: The conception and design of the study, and revising the article critically.

Funding

This research was funded by Shiraz University under Grant no. 2GCB1M222407. Second author has received research support.

Data availability

Data will be available upon reasonable request from the corresponding author.

Declarations

Competing interests

The authors declare no competing interests.