Towards an explainable irrigation scheduling approach by predicting soil moisture and evapotranspiration via multi-target regression

Abstract

Significant population growth and ongoing socioeconomic development have increased reliance on irrigated agriculture and agricultural intensification. However, accurately predicting crop water demand is problematic since it is affected by several factors such as weather, soil, and water properties. Many studies have shown that a hybrid irrigation system based on two irrigation strategies (i.e., evapotranspiration and soil-based irrigation) can provide a credible and reliable irrigation system. The latter can also alert farmers and other experts to phenomena such as noise, erroneous sensor signals, numerous correlated input and target variables, and incomplete or missing data, especially when the two irrigation strategies produce inconsistent results. Hence, we propose Multi-Target soil moisture and evapotranspiration prediction (MTR-SMET) for estimating soil moisture and evapotranspiration. These predictions are then used to compute water needs based on Food and Agriculture Organization (FAO) and soil-based methods. Besides, we propose an explainable MTR-SMET (xMTR-SMET) that explains the ML-based irrigation to the farmers/users using several explainable AI to provide simple visual explanations for the given predictions. It is the first attempt that explains and offers meaningful insights into the output of a machine learning-based irrigation approach. The conducted experiments showed that the proposed MTR-SMET model achieves low error rates (i.e., MSE = 0.00015, RMSE = 0.0039, MAE = 0.002) and high $R^{2}$ score (i.e., 0.9676).

Keywords

Evapotranspiration soil moisture irrigation scheduling Multi-Target Regression XAI

1. Introduction

In recent decades, significant population expansion, combined with ongoing socio-economic development, has increased reliance on irrigated agriculture and agricultural intensification to meet rising food demand [17]. As a result, a substantial strain on water supplies has emerged in recent years, particularly in water-stressed arid regions [42]. Climate change increases this strain and poses future water governance issues due to rising air temperatures and altering drought and rainfall patterns. According to FAO [15], owing to projected climate change, approximately 51% of people in arid countries would live in highly water-stressed areas by 2050. Irrigated agriculture and agricultural intensification can impact the quantity of water resources [17]. Several studies [2,6,29,35] have revealed that inefficient irrigation water usage, improper soil management, and unsuitable crop type choices are all causing a continuous decline in the quantity of water resources. However, forecasting water demand precisely is a highly complex task since it depends on many factors such as weather,soil, and water properties [17].

Nowadays, the latest sensors and weather stations allow the collection of a large amount of historical data that was unavailable in the past. According to [16], big data and artificial intelligence are the best tools for handling this amount of data, thanks to their capability to extract useful information and give additional value and usefulness to systems installed in the field. For this reason, many machine learning and IoT-based studies are proposed in the field of smart irrigation. According to [17], the existing irrigation methods are categorized into four types: evapotranspiration and water balance (ET-WB), soil moisture measurement, plant growth parameters, and process-based agricultural models. To give adequate irrigation, all of these categories need to be properly operated. An effective irrigation method should strike a balance between practicability, accuracy, and universalizability.

The first category is based on the evapotranspiration to forecast water demand. In fact, the two phenomena of evaporation and transpiration are combined under the umbrella term “evapotranspiration” (ET). The phenomenon of water transitioning from a liquid state to a vapor state is known as evaporation. Some examples are the surface of the soil, a pond or lake, or the surface of water. Whereas, the transpiration is the process of water being evaporated by trees through their stomata. The amount of water a tree needs to reach maturity is called the tree’s water requirement. For a tree to create one kilogram of dry matter, 400–1000 kg of water are needed [10]. The ET-WB based methods are often used in the field of irrigation, thanks to the availability of weather data since soil data is not necessary for this category. Generally, this type of method follows the guidelines provided by FAO-56 [4]. However, this method is not very accurate when used in site-specific circumstances, particularly when the error of daily soil moisture prediction accumulates [40]. As for soil moisture-based methods, they require sensors that measure the soil water status, which is a paramount task in modulating the water requirements of the crops. The main variables that should be captured in real-time are soil water status and elevation. Also, monitoring other variables, such as hydrodynamic soil factors or water drainage, might increase the chances of the irrigation predicted by the models being properly used by the plants [23]. The main challenge with the soil moisture-based methods is that their accuracy depends on the values returned by the sensors. If the sensors fail to transmit correct signals – due to sensing malfunctions or field noises like animals or rainfall – the scheduling may fail. Hence, one of the major problems of smart irrigation and wireless sensor networks is the sudden failure of physical nodes. Sometimes it is impossible to determine whether the physical nodes are transmitting accurate sensor values or if they are degrading with time. Physical nodes that are not functioning correctly can only be found manually, which is a time-consuming task. Any real-time system is severely impacted by the faulty sensor node [34].

Combining climate and soil variables has the potential to properly manage irrigation in a more efficient way than other traditional approaches. The study in [41] demonstrated that precision irrigation should consider both soil moisture and evapotranspiration since soil moisture is connected to atmospheric moisture through direct evaporation and vegetation transpiration. They also illustrated that soil moisture is affected by evapotranspiration and thus it always moves upward in the surface soil. When the evapotranspiration is large, the amount of water transport increases, and it suggests that the use of soil moisture fluctuation signals can be used to reflect evapotranspiration. Hence, these two parameters should be jointly and correlatively predicted to optimally schedule the daily water needs.

A hybrid irrigation system that relies on two irrigation strategies: ET-based irrigation and soil-based irrigation, could provide a credible and reliable irrigation system and also alert farmers and other experts from being subject to phenomena like noise, erroneous sensor signals, numerous correlated input and target variables, and incomplete or missing data [34] especially when the two irrigation strategies give inconsistent outputs.

According to this, we propose a Multi-Target Regression (MTR) model, a well-established technique in the fields of applied statistics and machine learning [8], to estimate both ET and soil moisture, denoted as VWC (Volumetric Water Content). To the best of our knowledge, this is the first attempt in the field of smart irrigation that uses MTR to estimate both parameters. Indeed, our objective in this context is to analyse and compare multi-target regression models as a new approach to estimating ET and VWC, and to select subsequently the best regression that will be used to calculate the quantity of water needed for each using the two irrigation strategies.

However, machine learning-based irrigation is always considered “black-box” and uninterpretable by humans. Indeed, the farmers/users could not understand the irrigation decision because of the inconsistency between the two irrigation strategies. In this regard, one of the most critical requirements in the majority of fields for understanding the motivations behind any particular choice is explainable AI [13]. It eliminates the outdated notion of machine learning as a “black box” and helps users comprehend the underlying causes of the discovered solution [33]. In the field of smart agriculture, a recent study [36] highlighted the necessity of using explainable artificial intelligence to monitor crop growth and disease control, policy standardization, and other technological and deployment advancements. To sum up, the main contributions of this study are:

A Multi-Target soil moisture and evapotranspiration prediction (MTR-SMET) for estimating both the soil moisture and evapotranspiration. MTR-SMET helps detecting inconsistent outputs due to erroneous sensor signals.

The use of two well known irrigation methods in the agriculture field to calculate water needs based on the MTR-SMET to provide an accurate and robust daily amount of water for irrigation.

An explainable MTR-SMET (xMTR-SMET) that explains the ML-based irrigation to the farmers/users using several explainable AI to provide simple visual explanations for the given predictions. It should be noted that this is the first attempt that explains and gives meaningful insights into the output of a machine learning-based irrigation approach.

2. Related work

We present in this section some relevant works that discuss machine learning-based approaches in the field of irrigation management. In particular, we present both evapotranspiration based irrigation scheduling and soil moisture prediction approaches.

2.1. Evapotranspiration based irrigation scheduling

The evapotranspiration referred as $ET$ represents the evapotranspiration from an actively growing virtual vegetated surface that is 0.12 m tall, with a completely shaded ground and adequate water supply, and without pests or diseases. At present, $ET$ has become a fundamental parameter in the fields of regional water resource management and irrigation scheduling. The most widely accepted $ET$ estimating method is the FAO-56 Penman–Monteith method (P-M), which has been proposed as a standard method for validating other methods because of its global applicability and simplicity since it doesn’t require any calibration parameters [4].

In 2011, Jahanbani and El-Shafie [21] employed an artificial neural network (ANN) for predicting monthly $ET$ at Rasht city located northern part of Iran using minimum and maximum daily temperatures collected from 1975 to 1988 of the region. To predict $ET$ , the authors considered the climatic data, including Tmax, Tmin and SD as input variables for ANN model. The findings proved the ANN reliability for predicting the $ET$ for the same month or for the next month.

To predict $ET$ , Mosavi and Edalatifar [28] used a hybrid algorithm of adaptive neuro-fuzzy inference system (ANFIS), particle swarm optimization (PSO) and principle component analysis (PCA). The data set for the training model includes ea, sh, U, Tmin, Tmax that are gathered from two cities of Iran, at two meteorological stations of Tehran and Zanjan for the period of 1981–2011. The PCA was used to transfer the data into an uncorrelated space and extract the key characteristics from it. With the PCA, the data’s dimensions were decreased. Then, the output of PCA was used to train the ANFIS, whose parameter values are determined by the use of PSO.

Han et al. [19] evaluated the capability of coupling a Bat algorithm with the XGBoost method (i.e., the BAXGB model) for estimating monthly $ET$ in the arid and semiarid regions of China. Results indicated that BAXGB models were more accurate than either MARS or GPR for estimating $ET$ .

Aghelpour and Norooz-Valashedi [3] evaluated the performances of stochastic models, including autoregressive moving average (ARMA), and autoregressive integrated moving average (ARIMA) and machine learning models, including least square support vector machine (LSSVM), adaptive neuro-fuzzy inference system (ANFIS), and generalized regression neural network (GRNN), in predicting $ET$ for Mazandaran province in Iran. The studied data belong to 5 synoptic stations in Mazandaran province and include Tmean, Tmax, Tmin, RHmin, RHmax, RHmean, U, and SD. These data are received on a daily basis from the Iranian Meteorological Organization during the period 2003–2018. This study used the FAO-56 Penman-Monteith model to calculate daily $ET$ rates. They revealed that stochastic models, such as the time series models ARMA and ARIMA, outperform machine learning methods, such as LSSVM, in most circumstances in most cases.

2.2. Soil moisture prediction

The advantage of soil moisture-based methods is the ease of practice and automation with some commercially available systems. Major drawbacks of the soil moisture sensor–based scheduling method are the spatial soil moisture heterogeneity, errors in sensor installation, the difficulty in the representation of the entire root zone, the need for sensor calibration, and the inaccuracy of measurements when gravel exists [34]. However, ET-based irrigation methods strongly rely on the estimation of local climatic data. ET-based irrigation methods also depend on local-specific crop coefficients and may be inaccurate. Cumulative errors may occur with calculated ET-based scheduling approaches, so field-based measurements are generally needed to correct or reset ET-based irrigation.

Table 1
Comparisons of related literature. ea: actual vapor pressure, sh: sunshine hours, T: air temperature, Tmean: mean air temperature, Tmax: maximum air temperature, Tmin: minimum air temperature, U: wind speed, Umean: mean daily wind speed, RH: relative humidity, Rs: solar radiation, RHmin: minimum relative humidity, RHmax: maximum relative humidity, RHmean: mean relative humidity, SD: sunshine duration, DPT: dew point temperature, RD: Root Depth (cm), R: rainfall, ST: soil temperature, VWC: soil moisture, $ET$ : evapotranspiration

Reference Model Location Time scale Input Target

[21] ANN Iran Monthly Tmax, Tmin, SD $ET$

[28] ANFIS, PSO, PCA Iran Monthly ea, sh, Tmin, Tmax $ET$

[19] XGBoost China Month Tmean, Tmax, Tmin, U, RH, and Rs $ET$

[3] ARMA, ARIMA, ANFIS, GRNN, LSSVM Iran Daily Tmean, Tmax, Tmin, RHmin, RHmax, RHmean, U, and SD $ET$

[18] MLP United States (Colorado) Daily Tmean, RH, Rs, U, RD, R VWC of seven layers VWC

[11] ANN-MFPA Canada Hourly ST, Tmean, RH VWC

[39] LightGBM, LR, DT, RF, MLP, LSTM, STEMGNN Brazil Daily U, Rs, T, RH, VWC ${VWC}_{min}$ , ${VWC}_{max}$

Reference	Model	Location	Time scale	Input	Target
[21]	ANN	Iran	Monthly	Tmax, Tmin, SD	$ET$
[28]	ANFIS, PSO, PCA	Iran	Monthly	ea, sh, Tmin, Tmax	$ET$
[19]	XGBoost	China	Month	Tmean, Tmax, Tmin, U, RH, and Rs	$ET$
[3]	ARMA, ARIMA, ANFIS, GRNN, LSSVM	Iran	Daily	Tmean, Tmax, Tmin, RHmin, RHmax, RHmean, U, and SD	$ET$
[18]	MLP	United States (Colorado)	Daily	Tmean, RH, Rs, U, RD, R VWC of seven layers	VWC
[11]	ANN-MFPA	Canada	Hourly	ST, Tmean, RH	VWC
[39]	LightGBM, LR, DT, RF, MLP, LSTM, STEMGNN	Brazil	Daily	U, Rs, T, RH, VWC	${VWC}_{min}$ , ${VWC}_{max}$

Gu et al. [18] proposed a method for irrigation scheduling based on neural network (NN) model. As shown in Table 1, the NN model was trained using weather data, root depth and soil moisture of seven soil layers. The latter was predicted using the Root Zone Water Quality Model (RZWQM2) which is a comprehensive simulation model designed to predict the hydrologic response, including potential for ground water contamination, of alternative crop-management systems [34]. The output of the NN model was the soil moisture of the root zone and the seven layers. Thereafter, the predicted root zone soil moisture was used in the irrigation scheduling method to compute the irrigation quantity based on the field capacity.

Chatterjee et al. [11] proposed a hybrid modified flower pollination algorithm supported ANN (NN-MFPA) model to predict the soil moisture quantity. The MFPA is used to find the optimal weight vector for the ANN by using soil temperature, air temperature, and relative humidity as input features recorded hourly. The NN-MFPA model was compared with PSO (Particle Swarm Optimization) supported ANN, Cuckoo Search (CS) supported ANN, and multilayer perceptron feed-forward network (MLP-FFN).

The authors in [39] developed a guideline for soil moisture prediction using machine learning. In order to accomplish this, they tested several algorithms: LightGBM, linear regression, decision tree, random forest, multilayer perceptron, LSTM, and StemGNN. As input, they considered air temperature, solar radiation, relative humidity, wind speed, precipitation and soil moisture. As a goal, they predicted the lowest and highest soil moisture levels. The different ML algorithms are trained and tested in a real case analysis comprehending eight crop types in twelve fields from four farms distributed over diverse climatic scenarios in Brazil. The findings revealed that soil moisture prediction reaches its maximum performance when using only past soil moisture, a context-aware index, and the precipitation. Moreover, experiments find out that LightGBM outperforms other ML algorithms.

2.3. Discussion

In order to predict evapotranspiration or soil moisture of the root zone for irrigation management, the studies discussed above proposed ML-based models, particularly regression methods, in the field of irrigation management. These models can run complex mathematical algorithms in real-time at low cost [17], to predict evapotranspiration or soil moisture of the root zone for the purpose of irrigation management. Each study considered different features related to weather data, soil data, and crop. They used different supervised algorithms to predict either ET or VWC in different locations. Although the relevance of these studies in the field of smart irrigation, the main limitations and the ignored challenges are presented as follow:

The majority of studies are limited to predicting the parameters (ET or VWC) that interfere in the irrigation process without completing this later by proposing decision support systems for the purpose of real-time operation based on the predicted parameters. Only the work of Gu et al. [18] that proposed NN-based irrigation scheduling method based on soil moisture parameters. In this regard, we offer a comprehensive system that begins with the prediction of the required parameters, the quantity of water required, and ends with the explanation of the irrigation decision.

The second limitation of the existing studies is that the performance is based on the accuracy value returned by the sensors. Our proposed approach is based on two irrigation strategies by predicting both ET and VWC and using two irrigation methods. This aims to provide an optimal water requirement quantity for the crop and also to verify the proper functioning of the sensors to alert farmers/users if an inconsistency is detected.

Another challenge neglected in the existing studies is the complex decisions by ML-based systems since they are considered as black-box predictions that cannot readily be explained to farmers. This could decrease the transparency and reliability of the irrigation system [36]. As a result, while we recognize the need of involving farmers and other users in the irrigation management process, we provide an explainable AI to supplement the ET and VWC predictions with information on the irrigation decision explanation.

3. Material and dataset description

3.1. Multi-target regression models & time series analysis

Multi-Target Regression (MTR), also known as multivariate or multi-output regression, is related to the problems with multiple continuous outputs [8] by considering not only the relationships between features and targets but also the relationships between target variables [8].

The most common categorization of MTR methods is divided into Problem Transformation (PT), Algorithm Adaptation (AA) and Ensemble methods. PT methods transform the Multi-Target Regression problem into a series of more specific single-target problems for each target. Among PT methods, Binary Relevance (BR) is the most frequently used method [32], in which the target variables are estimated independently, and any potential inter-correlation between them is ignored. In contrast, the AA methods are based on single regression models to handle multi-target problems directly by exploiting the potential correlation between the multiple targets. To do so, existing single-target algorithms are adjusted to support the multi-target problems. The most popular models on which MTR are built include Predictive Clustering Trees (PCTs) [7], ADABOOST.MR and BP-MLL [26].

The ensemble methods for multi-target learning are developed on top of the common PT or AA methods. For instance, the regressor chain (RC) method is an extension of BR that aims to consider interdependencies among targets. RC was proposed by Spyromitros-Xioufis et al. [37] based on the idea of chaining single-target models. In this method, the single-target regressors are linked along a chain (given by a random permutation of the set of target variables). The feature space of each link in the chain is augmented with the values of previous targets in the chain. The main concern with the RC method is that it is sensitive to the selected chain order [8]. As a solution, Spyromitros-xioufis et al. [37] proposed the Ensemble of Regressor Chains (ERC) method that combines several chains. This method has had great success in the MTR field and is widely used in many domains [8]. The ERC algorithm uses L Regressor Chains ${RC}_{1}, {RC}_{2}, \dots, {RC}_{L}$ , wherein each ${RC}_{k}$ , a random chain is performed using a random sequence of targets. For the multi-target regression of a new instance, the decisions of all regressor chains are gathered and combined. On the other hand, Kocev et al. [22] proposed a random forest method that aggregates PCTs trees (RF-PCT) to enhance and accelerate MTR prediction problems. Several studies recommend RF-PCT since it achieves significant results in many fields [26,43].

Moreover, the present study supports also time series analysis. A time series is a sequence of historical measurements of an observable variable at equal time intervals. Time series analysis is a cutting-edge scientific issue since it is able to quantitatively describe the relationship between a sequence of observations. Time series analysis has emerged as a paramount technique in the irrigation field for presenting sequential irrigation due to the recent tremendous increase in interest in the scientific understanding of climate change. According to this, the present study aims to combine the different regression algorithms with a sliding window time series analysis technique [20].

3.2. Explainable artificial intelligence tools

Explainable Artificial Intelligence (XAI) is a developing topic of study thanks to the growing use of artificial intelligence and machine learning and the current reliance on these technologies. XAI refers to systems that try to explain how a black-box AI model produces its outcomes. XAI methods can be divided into two broad categories: model-based and post-hoc methods [13]. Model-based methods reflect how the ML model produces its outputs. This type of XAI refers to applying interpretation methods during model training, which may impact their overall performance. The main challenge for these methods is developing a trade-off between model accuracy and explainability [27]. As for the post-hoc XAI methods, they approximate the behavior of a black-box by extracting relationships between feature values and the predictions [27]. In particular, they use information from an ML model to identify the features most responsible for an outcome for a given input. The post-hoc explanatory refers to applying interpretation methods after the model training. Post-hoc XAI methods can be further divided into global and local methods. Global explanations try to figure out how a black-box model works as a whole, while local explanations try to find correlations between the values of a record’s features and its results. Moreover, the output of post-hoc XAI methods varies among text, visual explanations, and feature relevance/feature importance. The current work focuses on post-hoc explanation, specifically visual explanations, by relying on two well-known tools used in the literature [13]: LIME [33] and SHAP [25].

3.2.1. Local Interpretable Model-agnostic Explanations (LIME)

Local Interpretable Model-agnostic Explanations are a tool for comprehending and interpreting the underlying machine learning model while remaining model-neutral. LIME approximates the machine learning model with an understandable model [33]. It is carried out locally since complex machine learning models may be simpler to comprehend and approximate broadly. Users will be able to understand and analyze the model thanks to the explanations offered by LIME.

3.2.2. Shapley additive explanations (SHAP)

The SHAP is a game theory-based XAI method that aims to compute Shapely values to explain the contribution of each feature to the prediction [25]. SHAP is based on coalitional game theory to identify how well each group (or coalition) of agents can do for itself. To compute the shapely values, SHAP makes only some feature values present, and some are not. The main purpose is to identify the contribution of each feature to the prediction.

Lundberg and Lee [25] developed a Python package that can calculate the SHAP for various technologies, including LightGBM, XGBoost, GBoost, CatBoost Scikit-learn, and tree models. This implementation is considered by enormous researchers that rely on SHAP to interpret different AI models [13].

The main difference between SHAP and LIME is that LIME uses the distance between vectors as the influence, whereas SHAP uses the Shapley value as the influence.

Moreover, Lundberg et al. [24] proposed an extension of SHAP, namely the SHAP tree explainer. The latter suggests that the exact evaluation of SHAP values can be done in polynomial time exclusively for tree-based models (including RF but not models like SVM and NNs) by exploiting the information stored in the tree structure. Note that the SHAP tree explainer does not assume feature independence since feature interactions are already captured in the underlying trees.

3.3. Data from COSMOS-UK

The COSMOS-UK project consists of a soil moisture monitoring station that collects long-term soil moisture measurements at about 50 sites [12]. Figure 1 plots the site locations. An innovative cosmic ray neutron sensor (CRNS) instrument is used to generate soil moisture observations for each site over an area of up to 120 000 $m^{2}$ (∼30 acres). In this study, we have used daily average soil moisture data from 10 COSMOS-UK sites as observations. The sites were selected based on the completeness of soil moisture, evapotranspiration, and meteorological data over six years from 2014–2019. A summary of the different variables considered in the study is presented in Table 2. The evapotranspiration variable (ET) data are derived from the hydrometeorological data at the end of the day according to the Penman-Monteith method [4]. Soil volumetric water content (VWC) data are derived from 30-minute hydrometeorological data and data from the cosmic-ray sensing every hour. The data were calculated using the method described in the study of Evans et al. [14].

Fig. 1.

Map of COSMOS-UK site locations [12].

Table 2

List of variables considered in the study

Nomenclature	Variable	Unit
$T_{mean}$	Averaged air temperature	°C
$T_{soil}$	Soil temperature	°C
U	Wind speed	${mm}^{- 1}$
RH	Relative Humidity	%
Rs	Solar radiation	MJm²/day
Pr	Precipitation	mm
$ET$	Evapotranspiration	mm/day
VWC	Volumetric Water Content	${cm}^{3}$ ${cm}^{- 3}$ (%)

4. The proposed approach

The proposed approach encompasses four modules that are illustrated in Fig. 2 and explained in the following sub sections.

Fig. 2.

The proposed approach.

4.1. Data pre-processing module

Data pre-processing aims to convert raw data into a meaningful and clear format for machine learning. Data pre-processing is a paramount task to make accurate predictions when raw data is collected from particular sources. Because the raw dataset is missing some values that could significantly affect how well machine learning models work, we first interpolated those values. Interpolation consists of calculating the missing values for an observation using its preceding values. This interpolation technique’s sequential character corresponds to the temporal nature of time-series data. Furthermore, to compute daily averages of the feature values, this module also resamples the dataset. Moreover, we also applied normalization, which scales all data in the range of [0,1]. Secondly, the sliding window technique is applied to support time series data. According to Hota’s definition [20], sliding window is a short-term estimate of the time series data’s actual value. The window and segment sizes go bigger until we get the closest value with the least amount of error. In this study, sliding windows contain overlapping data. For instance, considering an interval size equal to 2, as depicted in the example of Fig. 3, to predict the evapotranspiration of the day $d 3$ ( $ET 3$ ), we use the ET of the two previous days, $ET 1$ and $ET 2$ . Moreover, besides the previous ET observations, the sliding window also contains the previous VWC observations. Indeed, after this step, each sample includes the different variables of the day d and the n previous ET and VWC, where n is the interval size of each window. The window size is determined based on experiments (see Section 5.1).

Fig. 3.

Example of sliding window of ET prediction with window size equal to 2.

4.2. MTR-SMET model building module

After sliding window pre-processing, the dataset can train the MTR-SMET model. The soil and climatic variables and the n previous values of ET and VWC are considered input variables (n is the window size). Notably, the multi-target model takes the form $y_{1}, y_{2} \sim x_{1} + x_{2} + x_{3} + x_{4} + x_{5} + x_{6}$ where $y_{1}$ , $y_{2}$ are ET and VWC. $x_{1}$ , $x_{2}$ , $x_{3}$ , $x_{4}$ , $x_{5}$ , $x_{6}$ represent $T_{mean}$ , $T_{soil}$ , U, $RH$ , $Rs$ , $\Pr$ , respectively. Besides, as depicted in Fig. 2, the n previous observations ${y_{1_{n}}, y_{2_{n}}, y_{1_{n - 1}}, y_{2_{n - 1}}, \dots, y_{1_{1}}, y_{2_{1}}}$ are also integrated into the input set of the MTR model.

Random forest of predictive clustering trees (RF-PCT) [22] is an ensemble method for multi-target learning that uses PCTs trees [22] as base regressors. To ensure the diversity among the base regressors, the bagging is used beside the feature set changing during learning. Notably, the most important feature is chosen from a random subset of the input features at each node in the decision trees. The best subset of features is selected among the overall features x by the Breiman function [9] $f (x) = ⌊ {log}_{2} (x) + 1 ⌋$ . This is done by using a function f of the total feature number of input features to identify the best subset of features that should be considered in the prediction of the two targets. Subsequently, the final prediction is obtained using the average of the predictions of the base regressors.

4.3. MTR-SMET irrigation module

The aim of this module is to determine daily irrigation quantity based on the evapotranspiration and soil moisture parameters. This study seeks to determine the daily amount of water, d, required for irrigation.

For this purpose, we use two irrigation methods: Evapotranspiration based method and soil moisture based approach. Below are brief description of the these two approaches.

4.3.1. Evapotranspiration based irrigation

According to [10], the water needs, and the actual evapotranspiration ( ${ET}_{c}$ ) are similar [10]. Indeed, the water need quantity ${IR}_{d}^{ET}$ for the day d is calculated using the Equation (1) [4]. $\begin{matrix} (1) & {IR}_{d}^{ET} = {ET}_{c} = K_{c} \times ET \end{matrix}$ Where $K_{c}$ is the average crop coefficient that depends on the crop type and the growth of the crop. For each plant growth represented by months, the adequate coefficient should be selected from the literature, such as FAO [5]. $ET$ represents the reference evapotranspiration, i.e., the evapotranspiration of an ideal plant stand with water available at will. $ET$ is predicted by the MTR-SMET model.

4.3.2. Soil moisture based irrigation

The aim of soil moistre-based irrigation is to obtain the irrigation quantity for the day d by considering the soil moisture. For doing so, we use in the first stage, the trained multi-target model to predict the root zone soil moisture ${VWC}_{d}$ on current day d based on the weather data and soil data of the day d, and the predicted root zone soil moisture ${{VWC}_{d - n}, {VWC}_{d - (n + 1)}, {VWC}_{d - 1}}$ and evapotranspirations ${{ET}_{d - n}, {ET}_{d - (n + 1)}, {ET}_{d - 1}}$ on the previous n days. Thereafter, we calculate the water need quantity ${IR}_{d}^{VWC}$ (cm) using the Equation (2) defined in the study of Gu et al. [18]. $\begin{matrix} (2) & {IR}_{d}^{VWC} = ({VWC}_{fc} - {VWC}_{d}) . D_{r} - P_{d + 4} \end{matrix}$ Where $D_{r}$ is the root depth on day d (cm), and $P_{d + 4}$ is the cumulative precipitation from day $(d + 1)$ to day $(d + 4)$ (cm).

4.4. xMTR-SMET based explanation module

To assist farmer for making a precise decision, the two water quantities of the day d, ${IR}_{d}^{ET}$ and ${IR}_{d}^{VWC}$ are compared, as depicted the Fig. 2. Thereafter, we rely on XAI to explain these two estimations since the decision of the water amount for irrigation is from a machine learning models that are considered as “back-box” and uninterpretable by humans. This module has two main objectives. The first one aims to explain to the farmer the MTR-SMET based prediction and subsequently the irrigation decision. The second objective consists in explaining the inconsistency of the two target prediction. These two objectives are reached by local and global explanations. Local explanation explains the output prediction of one observation. In other words, it describes how the features interact with each other to reach the predicted target value. This type of explanation is used also to realise the second objective that consists to explain the inconsistency between the ET-based irrigation and VWC-based irrigation for the day d. We believe that this will help the farmers to detect if there is a problem in the sensors by analysing the prediction results with respect to the features values of the day d. For local explanation, we rely on LIME tool. To generate a single explanation for one obsevation,the LIME-based local interpretation determine feature importance by comparing the prediction results between the artificially perturbed data and the selected observation.

As for the global explanation explains how the model makes decisions based on the input features and their impact to the target. Thus, global explanations aims to help the users to understand the distribution of the target results in relation to the set of features. In our study, the global explanation aims to plot the impact of meteorological data such as Wind speed and temperature as well the impact of previous $ET$ and VWC on the estimation of these laters. To generate the global explanation, Shapley values are combined in a matrix by running SHAP for every instance. This matrix has one row per data instance and one column per feature instance. Consequently, the entire model can be interpreted by analyzing the Shapley values in this matrix.

5. Experiments

Three series of experiments are carried out in the subsections that follow. The first evaluates the performance of the MTR-SMET, while the second assesses, based on experts, the MTR-SMET-based irrigation scheduling. The third experiment presents various global and local explanations based on the xMTR-SMET model.

5.1. MTR-SMET assessment

To better illustrate the performance of the MTR-SMET model, we compare the RF-PCT ensemble MTR method with the RC ensemble MTR method and PCTs MTR method. Moreover, we compare the MTR methods with single target methods (RF and XGB) that separately predict VWC and ET by building a model for each target in terms of performance.

The dataset was divided into training and test data to train and test the different models. Because we are dealing with time-series data, the split was performed sequentially to preserve the data’s temporal dynamics. Consequently, we considered Balruderry data (from the COSMOS dataset) ranging from 2014 to 2017 as a training set and data from 2018 and 2019 as a test set. To find the best parameters in the training phase, the performance of all regression methods in predicting $ET$ and $VWC$ was evaluated using 10-fold cross-validation. In this study, the 10-fold cross-validation was repeated 10 times and the overall performance measurements were computed by averaging over those 100 iterations.

To evaluate the different prediction models, we rely on performance metrics. The model performance evaluation is established by plotting observed versus predicted values [30]. The metrics used for this purpose are MSE, RMSE, MAE, and $R^{2}$ . To conduct this experiment, we first identify the best window size ( $ws$ ). We varied the sizes from 1 to 9. When the $ws$ is equal to 1, it means that the model does not consider previous predictions in the training. And, when the $ws$ is equal to 9, it means that the model considers the 8 previous days’ predictions to predict the VWC and ET values of the $10^{th}$ day. The performance results of the different regression methods with the different sizes of sliding windows are presented in the Tables 3, 4, 5, 6. As shown in the tables, the best $ws$ is equal to 3. In fact, the RF-PCT model when considering $ws = 3$ , achieved higher performance. In particular, for the $ET$ prediction $ws = 3$ enhances the average prediction performance by 0.63%, 4.93%, 5.5% and 22.41% for MSE, RMSE, MAE and $R^{2}$ , respectively. As for the VWC prediction, it enhances the performance by 0.02%, 1.01%, 0.2%, and 17.01%, for MSE, RMSE, MAE and $R^{2}$ , respectively. The other $ws > 1$ enhance also the performance of the different regression models. On the other hand, it is clear from the Tables 3, 4, 5, 6, the significant outperformance of the MTR method RF-PCT for all the evaluation metrics. Notably, it reaches 0.00015, 0.0387, 0.021, 96.76% for MSE, RMSE, MAE, $R^{2}$ , respectively. These results are largely better than those of the second MTR method, RC. This does not mean that the latter does not achieve good results. For instance, it reaches 0.00029 of MSE and 85.38% of $R^{2}$ when $ws = 3$ .

Table 3
The MSE average values with the standard deviation of the time window MTR prediction models

WS MTR

ST_RF ST_XGB PCT RC RF_PCT

ET VWC ET VWC ET VWC ET VWC ET VWC

1 0.360 $(\pm 0.087)$ 0.543 $(\pm 0.09)$ 0.055 $(\pm 0.91)$ 0.119 $(\pm 0.12)$ 0.095 $(\pm 0.078)$ 0.095 $(\pm 0.078)$ 0.052 $(\pm 0.047)$ 0.0176 $(\pm 0.009)$ 0.0078 $(\pm 0.001)$ 0.0002 $(\pm 10^{- 5})$

3 0.25 $(\pm 0.097)$ 0.128 $(\pm 0.173)$ 0.0435 $(\pm 0.022)$ 0.0098 $(\pm 0.021)$ 0.074 $(\pm 0.023)$ 0.073 $(\pm 0.023)$ 0.0273 $(\pm 0.011)$ 0.003 $(\pm 6 \times 10^{- 5})$ 0.00015 $(\pm 8 \times 10^{- 4})$ 0.0001 $(\pm 10^{- 5})$

5 0.25 $(\pm 0.035)$ 0.15 $(\pm 0.051)$ 0.044 $(\pm 0.025)$ 0.012 $(\pm 0.098)$ 0.075 $(\pm 0.02)$ 0.284 $(\pm 0.15)$ 0.0293 $(\pm 0.05)$ 0.003 $(\pm 10^{- 4})$ 0.0018 $(\pm 1.7 \times 10^{- 4})$ 0.0002 $(\pm 10^{- 5})$

7 0.260 $(\pm 0.176)$ 0.215 $(\pm 0.276)$ 0.045 $(\pm 0.11)$ 0.039 $(\pm 0.193)$ 0.035 $(\pm 0.028)$ 0.083 $(\pm 0.058)$ 0.027 $(\pm 0.01)$ 0.0008 $(\pm 0.0004)$ 0.0028 $(\pm 0.006)$ 0.00043 $(\pm 2 \times 10^{- 5})$

9 0.29 $(\pm 0.196)$ 0.255 $(\pm 0.179)$ 0.053 $(\pm 0.179)$ 0.057 $(\pm 0.097)$ 0.056 $(\pm 0.078)$ 0.088 $(\pm 0.068)$ 0.0432 $(\pm 0.03)$ 0.0012 $(\pm 0.0003)$ 0.0043 $(\pm 0.01)$ 0.00073 $(\pm 5 \times 10^{- 5})$

WS	MTR
1	0.360 $(\pm 0.087)$	0.543 $(\pm 0.09)$	0.055 $(\pm 0.91)$	0.119 $(\pm 0.12)$	0.095 $(\pm 0.078)$	0.095 $(\pm 0.078)$	0.052 $(\pm 0.047)$	0.0176 $(\pm 0.009)$	0.0078 $(\pm 0.001)$	0.0002 $(\pm 10^{- 5})$
3	0.25 $(\pm 0.097)$	0.128 $(\pm 0.173)$	0.0435 $(\pm 0.022)$	0.0098 $(\pm 0.021)$	0.074 $(\pm 0.023)$	0.073 $(\pm 0.023)$	0.0273 $(\pm 0.011)$	0.003 $(\pm 6 \times 10^{- 5})$	0.00015 $(\pm 8 \times 10^{- 4})$	0.0001 $(\pm 10^{- 5})$
5	0.25 $(\pm 0.035)$	0.15 $(\pm 0.051)$	0.044 $(\pm 0.025)$	0.012 $(\pm 0.098)$	0.075 $(\pm 0.02)$	0.284 $(\pm 0.15)$	0.0293 $(\pm 0.05)$	0.003 $(\pm 10^{- 4})$	0.0018 $(\pm 1.7 \times 10^{- 4})$	0.0002 $(\pm 10^{- 5})$
7	0.260 $(\pm 0.176)$	0.215 $(\pm 0.276)$	0.045 $(\pm 0.11)$	0.039 $(\pm 0.193)$	0.035 $(\pm 0.028)$	0.083 $(\pm 0.058)$	0.027 $(\pm 0.01)$	0.0008 $(\pm 0.0004)$	0.0028 $(\pm 0.006)$	0.00043 $(\pm 2 \times 10^{- 5})$
9	0.29 $(\pm 0.196)$	0.255 $(\pm 0.179)$	0.053 $(\pm 0.179)$	0.057 $(\pm 0.097)$	0.056 $(\pm 0.078)$	0.088 $(\pm 0.068)$	0.0432 $(\pm 0.03)$	0.0012 $(\pm 0.0003)$	0.0043 $(\pm 0.01)$	0.00073 $(\pm 5 \times 10^{- 5})$

Table 4

The RMSE average values with the standard deviation of the time window MTR prediction models

WS	MTR

	ST_RF		ST_XGB		PCT		RC		RF_PCT

	ET	VWC	ET	VWC	ET	VWC	ET	VWC	ET	VWC
1	0.6 $(\pm 0.167)$	0.736 $(\pm 0.184)$	0.234 $(\pm 0.18)$	0.345 $(\pm 0.238)$	0.974 $(\pm 0.128)$	0.308 $(\pm 0.157)$	0.228 $(\pm 0.128)$	0.133 $(\pm 0.019)$	0.088 $(\pm 0.017)$	0.0141 $(\pm 3 \times 10^{- 5})$
3	0.5 $(\pm 0.113)$	0.358 $(\pm 0.347)$	0.208 $(\pm 0.063)$	0.099 $(\pm 0.042)$	0.273 $(\pm 0.046)$	0.269 $(\pm 0.046)$	0.165 $(\pm 0.035)$	0.0172 $(\pm 1.2 \times 10^{- 4})$	0.0387 $(\pm 0.011)$	0.004 $(\pm 3.4 \times 10^{- 5})$
5	0.50 $(\pm 0.033)$	0.389 $(\pm 0.1)$	$0.211 \pm 0.071$	0.111 $(\pm 0.196)$	0.865 $(\pm 0.02)$	0.533 $(\pm 0.3)$	0.171 $(\pm 0.121)$	0.019 $(\pm 1.9 \times 10^{- 4})$	0.042 $(\pm 0.003)$	0.004 $(\pm 1.9 \times 10^{- 5})$
7	0.51 $(\pm 0.276)$	0.464 $(\pm 0.552)$	0.21 $(\pm 0.209)$	0.198 $(\pm 0.386)$	0.187 $(\pm 0.048)$	0.288 $(\pm 0.117)$	0.165 $(\pm 0.02)$	0.028 $(\pm 9.1 \times 10^{- 4})$	0.053 $(\pm 0.008)$	0.006 $(\pm 4 \times 10^{- 5})$
9	0.538 $(\pm 0.309)$	0.505 $(\pm 0.358)$	0.23 $(\pm 0.24)$	0.238 $(\pm 0.195)$	0.236 $(\pm 0.147)$	0.297 $(\pm 0.137)$	0.207 $(\pm 0.06)$	0.035 $(\pm 6.1 \times 10^{- 4})$	0.065 $(\pm 0.021)$	0.008 $(\pm 10^{- 4})$

Table 5

The MAE average values with the standard deviation of the time window MTR prediction models

WS	MTR

	ST_RF		ST_XGB		PCT		RC		RF_PCT

	ET	VWC	ET	VWC	ET	VWC	ET	VWC	ET	VWC
1	0.653 $(\pm 0.41)$	0.515 $(\pm 0.14)$	0.453 $(\pm 0.308)$	0.246 $(\pm 0.121)$	0.502 $(\pm 0.201)$	0.502 $(\pm 0.201)$	0.308 $(\pm 0.23)$	0.087 $(\pm 0.021)$	0.076 $(\pm 0.145)$	0.004 $(\pm 0.001)$
3	0.339 $(\pm 0.113)$	0.258 $(\pm 0.116)$	0.108 $(\pm 0.14)$	0.067 $(\pm 0.012)$	0.127 $(\pm 0.068)$	0.128 $(\pm 0.067)$	0.088 $(\pm 0.022)$	0.014 $(\pm 0.002)$	0.021 $(\pm 0.002)$	0.002 $(\pm 10^{- 4})$
5	0.44 $(\pm 0.111)$	0.298 $(\pm 0.224)$	0.168 $(\pm 0.26)$	0.087 $(\pm 0.035)$	0.195 $(\pm 0.234)$	0.195 $(\pm 0.234)$	0.111 $(\pm 0.101)$	0.018 $(\pm 0.007)$	0.02 $(\pm 0.046)$	0.002 $(\pm 3 \times \pm 10^{- 4})$
7	0.552 $(\pm 0.21)$	0.353 $(\pm 0.262)$	0.308 $(\pm 0.208)$	0.123 $(\pm 0.112)$	0.345 $(\pm 0.12)$	0.185 $(\pm 0.098)$	0.213 $(\pm 0.123)$	0.033 $(\pm 0.01)$	0.066 $(\pm 0.045)$	0.002 $(\pm 3.2 \times 10^{- 4})$
9	0.559 $(\pm 0.432)$	0.375 $(\pm 0.432)$	0.341 $(\pm 0.365)$	0.143 $(\pm 0.099)$	0.354 $(\pm 0.147)$	0.193 $(\pm 0.077)$	0.259 $(\pm 0.133)$	0.048 $(\pm 0.001)$	0.071 $(\pm 0.061)$	0.0032 $(\pm 9.1 \times 10^{- 4})$

Table 6

The $R^{2}$ average values with the standard deviation of the time window MTR prediction models

WS	MTR

	ST_RF		ST_XGB		PCT		RC		RF_PCT

	ET	VWC	ET	VWC	ET	VWC	ET	VWC	ET	VWC
1	63.25 $(\pm 10.5)$	71.82 $(\pm 5.5)$	69.22 $(\pm 4.4)$	71.33 $(\pm 4.4)$	67.41 $(\pm 5.201)$	70.87 $(\pm 2.59)$	74.63 $(\pm 7.23)$	72.81 $(\pm 2.23)$	76.35 $(\pm 4.145)$	79.75 $(\pm 1.145)$
3	79.55 $(\pm 6.13)$	73.78 $(\pm 4.13)$	88.34 $(\pm 8.01)$	75.64 $(\pm 3.01)$	92.37 $(\pm 11.8)$	74.87 $(\pm 2.8)$	94.48 $(\pm 9.41)$	85.38 $(\pm 2.41)$	98.76 $(\pm 1.87)$	96.76 $(\pm 1.09)$
5	$78.35 \pm 1.13$	73.12	$86.72 \pm 8.01$	$74.17 \pm 3.41$	$91.37 \pm 13.8$	$74.07 \pm 4.8$	$92.48 \pm 8.41$	$84.8 \pm 3.41$	$98.23 \pm 3.87$	$96.23 \pm 1.87$
7	$73.25 \pm 1.5$	$71.05 \pm 3.5$	$85.21 \pm 11.01$	$73.1 \pm 2.01$	$91.17 \pm 13.8$	$73.17 \pm 5.8$	$92.09 \pm 4.41$	$76.54 \pm 2.41$	$98.11 \pm 4.87$	$94.11 \pm 1.87$
9	74.25 $(\pm 2.21)$	73.14 $(\pm 7.21)$	82.21 $(\pm 5.01)$	74.01 $(\pm 6.004)$	90.56 $(\pm 10.8)$	71.83 $(\pm 5.8)$	91.09 $(\pm 6.41)$	81.09 $(\pm 1.41)$	96.11 $(\pm 5.87)$	96.2 $(\pm 0.87)$

Table 7

Prediction performance of the MTR models on the test dataset

Metric	ST_RF		ST_XGB		PCT		RC		RF_PCT

	ET	VWC	ET	VWC	ET	VWC	ET	VWC	ET	VWC
MSE	0.26	0.128	0.05	0.012	0.08	0.076	0.03	0.003	0.0017	0.002
RMSE	0.5	0.357	0.22	0.11	0.28	0.27	0.173	0.054	0.04	0.044
MAE	0.341	0.29	0.108	0.073	0.153	0.28	0.089	0.23	0.021	0.003
$R^{2}$	68.25	63.41	83.99	74.81	90.2	73.34	93.75	85.01	98.51	96.45

Moreover, we assess the ability of the MTR-SMET model, notably the RF-PCT model, to generate VWC and ET predictions for unseen observations. In particular, the MTR-SMET model and the other MTR models, trained with data ranging from 2014 to 2017, were also applied in predicting VWC and ET for samples from 2018 and 2019. Table 7 plots the prediction performance of the MTR models when tested on the test dataset. Table 7 shows that RF-PCT model generates accurate predictions for the test data. This highlights the robustness of the RF-PCT model for generating predictions. Furthermore, we observe that all MTR models achieve acceptable prediction accuracy for test data compared to train data. Hence, this implies the considerable impact of sliding window, that is applied for the test data, on the prediction performance.

5.2. MTR-SMET based irrigation scheduling: Expert based assessment

The objective of this series of experiments is to analyze the results of the irrigation module. For this purpose, we rely on an agronomist from the Precimed project [31], who is regarded as an expert. This agronomist assigned an irrigation quantity ( ${IR}_{Exp}$ ) for the tomato crop based on the soil, climate data and the real values of $ET$ and $VWC$ for the day in question by applying a soil water balance method presented in [1]. In particular, this method uses the daily crop water use and the remaining water in the soil with taking into account the rainfall as presented in the Equation (3). $\begin{matrix} (3) & {IR}_{Exp} = ({VWC}_{fc} - RAW) / 0.9 \end{matrix}$ Where RAW is the readily available water and it is calculated using the Equation (4). $\begin{matrix} (4) & RAW = p \times TAW \end{matrix}$ Where p represents a threshold for maximum crop production (the optimum yield threshold) [1]. $TAW$ is the Total available water for a crop and it is estimated as the difference between water content at field capacity and water content at wilting point and changes during the growing season as a function of root depth (Rd). $\begin{matrix} (5) & TAW = ({VWC}_{fc} - {VWC}_{wp}) / 100 \times Rd \end{matrix}$ The test of the MTR-SMET-based irrigation was conducted for two years, 2018 and 2019. Figure 4 presents the boxplot of the difference between the three types of irrigation ( ${IR}_{ET}$ , ${IR}_{vwc}$ and ${IR}_{Exp}$ ). In particular, D1 presents the difference between ${IR}_{ET}$ and ${IR}_{Exp}$ . D2 depicts the difference between ${IR}_{vwc}$ and ${IR}_{Exp}$ . While D3 presents the difference between ${IR}_{ET}$ and ${IR}_{vwc}$ . The D1 and D2 distributions indicate that the ${IR}_{ET}$ , ${IR}_{vwc}$ are, generally (in most cases), close to ${IR}_{Exp}$ . Hence, the proposed approach can efficiently schedule the water needed for a given crop. Similarly, the D3 indicates the close distribution of ${IR}_{ET}$ and ${IR}_{vwc}$ values since the median value in the D1 boxplot is relative to the lower quartile. As for the cases where the difference between the ${IR}_{ET}$ and ${IR}_{vwc}$ values is large, there are irrigation problems. For example, Table 8 presents an excerpt of the irrigation computing with the different parameters such as the predicted ET, the crop-specific coefficient $K_{c}$ . We should note that we took the tomato as a crop example. Indeed, the $K_{c}$ values were 0.75, 0.75, 0.76, 0.76, 0.76, 0.70, 0.63, 0.63, 0.72, 0.77, 0.75, 0.75 from January to December, respectively [38]. The Table 8 presents also the different irrigation quantities for a given day, ${IR}_{ET}$ , ${IR}_{VWC}$ , and ${IR}_{Exp}$ . For instance, for the day 2018-04-09, the computed ${IR}_{ET}$ based on the Equation (1) is equal to 1.1 mm, the computed ${IR}_{VWC}$ based on the Equation (2) is equal to 1.29 mm, and the value assigned by the expert is equal to 1.3. According to the expert judgment, the calculated values of that day are approximate and considered consistent and reasonable quantities.

Fig. 4.

Box plot of the difference between the three irrigation types ( ${IR}_{ET}$ , ${IR}_{VWC}$ and ${IR}_{Exp}$ ), where D1 = ${IR}_{ET} - {IR}_{Exp}$ , D2 $= {IR}_{VWC} - {IR}_{Exp}$ and D3 = ${IR}_{ET} - {IR}_{VWC}$ .

Table 8

Comparison between the irrigation methods in terms of water need quantity (mm) across the growing season (days)

On the other hand, to examine the capability of the MTR-SMET-based irrigation method in detecting sensor failure, we disrupted the observation of the day 2019-07-03 by changing the climatic data values. The results of this disruption are highlighted (red color) in Table 8 where the ${IR}_{ET}$ value is inconsistent with the ${IR}_{VWC}$ value and the expert irrigation value. Thus, we can conclude that using both ET-based and VWC-based irrigation methods can detect irrigation problems such as sensor failure. As for the second inconsistency highlighted in red in the table, it is caused by the MTR-SMET model itself. We plot this case in the table to show that we recognize the failure of AI-based models, even if this failure is minimal (see Tables 3–7). Indeed, as future work, we should enhance the model to distinguish between the two types of failure (sensor-based or AI-based) to avoid any false alerts.

Fig. 5.

SHAP values for the ET prediction.

5.3. xMTR-SMET assessment

5.3.1. Global explanation

This series of experiments aims to illustrate how the explanation module gives a global view of how the features affect the estimation of the two targets. In this regard, we used the SHAP summary plot (Figs 5 and 6) to identify the magnitude and direction of each attribute’s impact on a global scale. As presented in Figs 5 and 6, the feature names are shown on the y-axis in decreasing order of significance, and the SHAP values for each input predictor are listed on the x-axis. Higher values of the feature are represented by red points, while blue points represent lower ones.

Figure 5 plots the impacts of the distribution of input features on the estimation of the ET value based on the MTR-SMET model. As for Table 9, it presents SHAP Feature Importance (SFI) generated from the absolute average of Shapley values per feature across the data for the ET prediction. The results indicate that increased feature solar radiation (Rs) leads to higher SHAP values for the ET estimation (SFI = 0.584). Indeed, solar radiation has the most significant influence on ET prediction. Figure 5 and Table 9 also show the importance of other inputs, such as relative humidity (SFI = 0.212), and soil temperature (SFI = 0.074). Moreover, the previous ET, ET-1 and ET-2 have an important impact on the daily evapotranspiration prediction with SFI equal to 0.102 and 0.081, respectively. However, the last moisture soil predictions VWC-1, VWC-2, and VWC-3 have less influence on the ET prediction.

Fig. 6.

SHAP values for the VWC prediction.

Table 9

SHAP feature importance

Feature	SFI_ET	Feature	SFI_VWC
Solar Radiation	0.584	VWC-1	5.311
Relative Humidity	0.212	VWC-3	0.654
ET-1	0.102	Precipitation	0.419
ET-2	0.081	ET-1	0.318
Soil Temperature	0.074	VWC-2	0.174
Air Temperature	0.066	Solar Radiation	0.100
ET-3	0.034	Relative Humidity	0.077
WindSpeed	0.025	Soil Temperature	0.075
Precipitation	0.017	WindSpeed	0.071
VWC-1	0.010	Air Temperature	0.041
VWC-3	0.009	ET-2	0.040
VWC-2	0.008	ET-3	0.035

Let us now concentrate on the explanation of the global VWC prediction. Figure 5 and Table 9 show the impacts of the distribution of input features on the estimation of the VWC value. Unlike the ET prediction, the VWC prediction is influenced by the previous evapotranspiration. In particular, ET-1 greatly impacts the VWC prediction (SFI = 0.318). The most significant features that impact the VWC prediction are VWC-1 (SFI = 5.311) and VWC-3 (SFI = 0.654).

Fig. 7.

xMTR-SMET based application interface: input.

5.3.2. Local case explanation

This experiment aims to demonstrate the capability of xMTR-SMET to explain a given prediction with a local explanation of either ET or VWC. For this purpose, a realistic scenario is presented to show how xMTR-SMET could support the farmer in deciding on crop irrigation.

To get the irrigation values ( ${IR}_{ET}$ and ${IR}_{ET}$ ) for a given day (e.g., 09-04-2018), the farmer selects via a dedicated interface (see Fig. 7), the crop type, the average air temperature, the soil temperature, the wind speed, the relative humidity, the solar radiation, and the precipitation values. Based on these input variables, the xMTR-SMET approach predicts the VWC and ET values, computes the ${IR}_{ET}$ and ${IR}_{ET}$ quantities, and explains the ET prediction and the VWC prediction (see Fig. 8). As presented in Fig. 8, the ET-based irrigation equals 2.25 mm. To explain this value, the LIME explanation is divided into three parts. The first part (on the left) presents the predicted value (the predicted $ET$ is 2.21). The second part (middle) of the LIME explanation plots the contribution of the main features corresponding to the linear model weight to the prediction. For the ET prediction, when the solar radiation is greater than 93.5, it will have a positive impact (in orange). In contrast, as presented in the third part, the previous evapotranspiration ET-1 has a negative impact (in blue) on the $ET$ prediction since the ET-1 value is greater than 0.5 and less than or equal to 1.1 mm/day. Similarly, the previous VWC (VWC-2) has a negative impact on the predicted ET value since it is greater than 28.49.

On the other hand, the VWC-based irrigation is estimated to be 2.239 mm based on the predicted VWC value, which is equal to 28.42. As presented in the interface, this predicted value is explained by the negative impact of VWC-1 since its value is less than or equal to 28.66 ${cm}^{3} . {cm}^{3}$ and the positive impact of the windspeed, since its value is less than or equal to 1.85 ${mm}^{- 1}$ . The farmer could consider one of the two irrigation values for the irrigation decision since the difference between them is minimal.

Fig. 8.

xMTR-SMET-based application interface: output.

6. Conclusion

This study investigated the viability of a multi-target regression model for estimating evapotranspiration (ET) and soil moisture (VWC). Therefore, these two characteristics must be jointly and correlatively forecasted in order to optimally arrange daily water requirements. Several studies like [11,21,28] are relevant to the field of smart irrigation but suffers from three main limitations: (1) They can only predict the parameters (ET or VWC) that interfere with the irrigation process. (2) Their performance is based on how accurate the sensors are. (3) The complex decisions made by ML-based systems are hard to explain to farmers because they are considered “black box” predictions. This could make the irrigation system less clear and less reliable. To overcome these limitations, we propose Multi-Target soil moisture and evapotranspiration prediction (MTR-SMET) for estimating soil moisture and evapotranspiration. This is intended to offer an appropriate water demand quantity for the crop, as well as test the sensors’ functionality to warn farmers/users if an inconsistency is observed. In this context, our goal is to analyze and contrast multi-target regression models as a novel method of estimating ET and, and then choose the best regression to be used to determine the amount of water required for each using the two irrigation strategies of soil-based irrigation and ET-based irrigation. However, machine learning-based irrigation is always regarded as a “black box” that people cannot understand. Because of the inconsistency between the two irrigation strategies, farmers/users were unable to grasp the irrigation decision. Explainable AI is one of the most important requirements for understanding the rationale behind any particular choice in this regard. It dispels the view of machine learning as a “black box” and assists users in understanding the root reasons of the identified solution. We present an explainable MTR-SMET (xMTR-SMET) that explains ML-based irrigation to farmers/users utilizing several explainable AI to provide simple visual explanations for the provided predictions. This is the first attempt to explain and provide relevant insights into the result of a machine learning-based irrigation technique. The conducted experiments showed that the proposed MTR-SMET model achieves low error rates (i.e., MSE = 0.00015, RMSE = 0.0039, MAE = 0.002) and high $R^{2}$ score (i.e., 0.9676). As a future endeavor, we are considering improving the explanation approach (xMTR-SMET) so that it can assist stakeholders and alert them to potential errors in prediction as well as problems with data acquisition sensors. At the present time, the approach identifies problems but does not attribute them to specific causes. Moreover, we plan to test and enhance the MTR-SMET model by considering the Precimed dataset [31]. Following that, we could improve the proposed approach to effectively train and estimate from diverse and massive amounts of data.

Footnotes

Acknowledgements

The authors gratefully acknowledge the General Secretariat for Research and Technology of the Ministry of Development and Investments of Tunisia under the PRIMA Programme. PRIMA is an Art. 185 initiative supported and co-funded under Horizon 2020, the European Union’s Programme for Research and Innovation. (project application number: 155331/I4/19.09.18).

Conflict of interest

None to report.

References

M.T.

Abi Saab ,

Jomaa ,

Skaf ,

Fahed and

Todorovic , Assessment of a smartphone application for real-time irrigation scheduling in Mediterranean environments, Water 11(2) (2019), ISSN 2073-4441, https://www.mdpi.com/2073-4441/11/2/252. doi:10.3390/w11020252.

Adeyemi ,

Grove ,

Peets ,

Domun and

Norton , Dynamic neural network modelling of soil moisture content for predictive irrigation scheduling, Sensors 18(10) (2018), 3408. doi:10.3390/s18103408.

Aghelpour and

Norooz-Valashedi , Predicting daily reference evapotranspiration rates in a humid region, comparison of seven various data-based predictor models, Stochastic Environmental Research and Risk Assessment (2022), 1–23.

Allen ,

Pereira ,

Raes and

Smith , FAO irrigation and drainage paper no. 56, Food and Agriculture Organization of the United Nations 56 (1998), 26–40.

R.G.

Allen ,

L.S.

Pereira ,

Raes ,

Smith et al., Crop evapotranspiration-guidelines for computing crop water requirements-FAO irrigation and drainage paper 56, Fao, Rome 300(9) (1998), 05109.

Ben Abdallah ,

Grati and

Boukadi , A machine learning-based approach for smart agriculture via stacking-based ensemble learning and feature selection methods, in: 2022 18th International Conference on Intelligent Environments (IE), 2022, pp. 1–8. doi:10.1109/IE54923.2022.9826767.

Blockeel ,

De Raedt and

Ramon , Top-down induction of clustering trees, 2000, arXiv preprint arXiv:cs/0011032.

Borchani ,

Varando ,

Bielza and

Larranaga , A survey on multi-output regression, Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery 5(5) (2015), 216–233.

Breiman , Random forests, Machine learning 45(1) (2001), 5–32. doi:10.1023/A:1010933404324.

10.

Brouwer and

Heibloem , Irrigation water management: Irrigation water needs, Training manual 3 (1986), 1–5.

11.

Chatterjee ,

Dey and

Sen , Soil moisture quantity prediction using optimized neural supported model for sustainable agricultural applications, Sustainable Computing: Informatics and Systems 28 (2020), 100279, ISSN 2210-5379, https://www-sciencedirect-com-443.web.bisu.edu.cn/science/article/pii/S2210537918302464. doi:10.1016/j.suscom.2018.09.002.

12.

H.M.

Cooper ,

Bennett ,

Blake ,

Blyth ,

Boorman ,

Cooper ,

Evans ,

Fry ,

Jenkins ,

Morrison et al., COSMOS-UK: National soil moisture and hydrometeorology data for environmental science research, Earth System Science Data 13(4) (2021), 1737–1757. doi:10.5194/essd-13-1737-2021.

13.

Das and

Rad , Opportunities and challenges in explainable artificial intelligence (xai): A survey, 2020, arXiv preprint arXiv:2006.11371.

14.

J.G.

Evans ,

H.C.

Ward ,

J.R.

Blake ,

E.J.

Hewitt ,

Morrison ,

Fry ,

L.A.

Ball ,

L.C.

Doughty ,

J.W.

Libre ,

O.E.

Hitt ,

Rylett ,

R.J.

Ellis ,

A.C.

Warwick ,

Brooks ,

M.A.

Parkes ,

G.M.H.

Wright ,

A.C.

Singer ,

D.B.

Boorman and

Jenkins , Soil water content in southern England derived from a cosmic-ray soil moisture observing system – COSMOS-UK, Hydrological Processes 30(26) (2016), 4987–4999. doi:10.1002/hyp.10929.

15.

F. Food and A.O. of the United Nations, Crop Information – Tomato, 2020, (accessed on 05/29/2021).

16.

González Perea ,

Camacho Poyato ,

Montesinos and

J.A.

Rodríguez Díaz , Prediction of irrigation event occurrence at farm level using optimal decision trees, Computers and Electronics in Agriculture 157 (2019), 173–180, ISSN 0168-1699. doi:10.1016/j.compag.2018.12.043.

17.

Gu ,

Qi ,

Burghate ,

Yuan ,

Jiao and

Xu , Irrigation scheduling approaches and applications: A review, Journal of Irrigation and Drainage Engineering 146(6) (2020), 04020007. doi:10.1061/(ASCE)IR.1943-4774.0001464.

18.

Gu ,

Zhu ,

Jiao ,

Xu and

Qi , Neural network soil moisture model for irrigation scheduling, Computers and Electronics in Agriculture 180 (2021), 105801, ISSN 0168-1699, https://www-sciencedirect-com-443.web.bisu.edu.cn/science/article/pii/S0168169920313016. doi:10.1016/j.compag.2020.105801.

19.

Han ,

Wu ,

Zhai ,

Pan ,

Huang ,

Wu and

Zeng , Coupling a bat algorithm with xgboost to estimate reference evapotranspiration in the arid and semiarid regions of China, Advances in Meteorology 2019 (2019).

20.

Hota ,

Handa and

Shrivas , Time series data prediction using sliding window based RBF neural network, International Journal of Computational Intelligence Research 13(5) (2017), 1145–1156.

21.

Jahanbani and

A.H.

El-Shafie , Application of artificial neural network in estimating monthly time series reference evapotranspiration with minimum and maximum temperatures, Paddy and Water Environment 9(2) (2011), 207–220. doi:10.1007/s10333-010-0219-1.

22.

Kocev ,

Vens ,

Struyf and

Džeroski , Ensembles of multi-objective decision trees, in: Machine Learning: ECML 2007,

J.N.

Kok ,

Koronacki ,

R.L.D.

Mantaras ,

Matwin ,

Mladenič and

Skowron , eds, Springer, Berlin, Heidelberg, 2007, pp. 624–631. doi:10.1007/978-3-540-74958-5_61.

23.

P.J.

Kramer and

J.S.

Boyer , Water Relations of Plants and Soils, Academic Press, 1995.

24.

S.M.

Lundberg ,

G.G.

Erion and

S.-I.

Lee , Consistent individualized feature attribution for tree ensembles, 2018, arXiv preprint arXiv:1802.03888.

25.

S.M.

Lundberg and

S.-I.

Lee , A unified approach to interpreting model predictions, Advances in neural information processing systems 30 (2017).

26.

Madjarov ,

Kocev ,

Gjorgjevikj and

Džeroski , An extensive experimental comparison of methods for multi-label learning, Pattern recognition 45(9) (2012), 3084–3104. doi:10.1016/j.patcog.2012.03.004.

27.

Moradi and

Samwald , Post-hoc explanation of black-box classifiers using confident itemsets, Expert Systems with Applications 165 (2021), 113941, ISSN 0957-4174, https://www-sciencedirect-com-443.web.bisu.edu.cn/science/article/pii/S0957417420307302. doi:10.1016/j.eswa.2020.113941.

28.

Mosavi and

Edalatifar , A hybrid neuro-fuzzy algorithm for prediction of reference evapotranspiration, in: International Conference on Global Research and Education, Springer, 2018, pp. 235–243.

29.

Navarro-Hellín ,

Martínez-del-Rincon ,

Domingo-Miguel ,

Soto-Valles and

Torres-Sánchez , A decision support system for managing irrigation in agriculture, Computers and Electronics in Agriculture 124 (2016), 121–131, ISSN 0168-1699. doi:10.1016/j.compag.2016.04.003.

30.

Piñeiro ,

Perelman ,

J.P.

Guerschman and

J.M.

Paruelo , How to evaluate models: Observed vs. predicted or predicted vs. observed?, Ecological Modelling 216(3) (2008), 316–322, ISSN 0304-3800. doi:10.1016/j.ecolmodel.2008.05.006.

31.

Precimed, https://precimed-prima.org/fr/a-propos-de-precimed/, 2022 (accessed on 09/15/2022).

32.

Read ,

Pfahringer ,

Holmes and

Frank , Classifier chains for multi-label classification, in: Joint European Conference on Machine Learning and Knowledge Discovery in Databases, Springer, 2009, pp. 254–269. doi:10.1007/978-3-642-04174-7_17.

33.

M.T.

Ribeiro ,

Singh and

Guestrin , “Why should I trust you?” Explaining the predictions of any classifier, in: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2016, pp. 1135–1144. doi:10.1145/2939672.2939778.

34.

Sami ,

S.Q.

Khan ,

Khurram ,

M.U.

Farooq ,

Anjum ,

Aziz ,

Qureshi and

Sadak , A deep learning-based sensor modeling for smart irrigation system, Agronomy 12(1) (2022), ISSN 2073-4395, https://www.mdpi.com/2073-4395/12/1/212. doi:10.3390/agronomy12010212.

35.

Sayari ,

Mahdavi-Meymand and

Zounemat-Kermani , Irrigation water infiltration modeling using machine learning, Computers and Electronics in Agriculture 180 (2021), 105921, ISSN 0168-1699. doi:10.1016/j.compag.2020.105921.

36.

B.B.

Sinha and

Dhanalakshmi , Recent advancements and challenges of Internet of Things in smart agriculture: A survey, Future Generation Computer Systems 126 (2022), 169–184. doi:10.1016/j.future.2021.08.006.

37.

Spyromitros-Xioufis ,

Tsoumakas ,

Groves and

Vlahavas , Multi-label classification methods for multi-target regression, 2012, pp. 1159–1168, arXiv preprint arXiv:1211.6581.

38.

Steduto ,

T.C.

Hsiao ,

Fereres and

Raes , FAO Irrigation and drainage paper 66, Crop yield response to water, Food and Agriculture Organization of the United Nations (2012).

39.

Togneri ,

Felipe dos Santos ,

Camponogara ,

Nagano ,

Custódio ,

Prati ,

Fernandes and

Kamienski , Soil moisture forecast for smart irrigation: The primetime for machine learning, Expert Systems with Applications 207 (2022), 117653, ISSN 0957-4174, https://www-sciencedirect-com-443.web.bisu.edu.cn/science/article/pii/S0957417422009563. doi:10.1016/j.eswa.2022.117653.

40.

Touil ,

Richa ,

Fizir ,

J.E.

Argente García and

A.F.

Skarmeta Gómez , A review on smart irrigation management strategies and their effect on water savings and crop yield, Irrigation and Drainage (2022).

41.

Wang ,

Zhang ,

Yu ,

Jia ,

Liu ,

Sun ,

Zheng and

Zhu , Grassland soil moisture fluctuation and its relationship with evapotranspiration, Ecological Indicators 131 (2021), ISSN 1470-160X, https://www-sciencedirect-com-443.web.bisu.edu.cn/science/article/pii/S1470160X2100861X. doi:10.1016/j.ecolind.2021.108196.

42.

M.A.

Yassin ,

A.A.

Alazba and

M.A.

Mattar , Artificial neural networks versus gene expression programming for estimating reference evapotranspiration in arid climate, Agricultural Water Management 163 (2016), 110–124, ISSN 0378-3774. doi:10.1016/j.agwat.2015.09.009.

43.

Zheng ,

Li ,

Chu and

Hu , A survey on multi-label data stream classification, IEEE Access 8 (2019), 1249–1275. doi:10.1109/ACCESS.2019.2962059.