Application of fuzzy-genetic and regularization random forest (FG-RRF): Estimation of crop evapotranspiration (ETc) for maize and wheat crops

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Application of fuzzy-genetic and regularization random forest (FG-RRF): Estimation of crop evapotranspiration (ETc) for maize and wheat crops Mandeep Kaur Saggi*, Sushma Jain Department of Computer Science, Thapar Institute of Engineering & Technology, India

ARTICLE INFO

ABSTRACT

Keywords: Reference evapotranspiration Crop ETc Fuzzy-Genetic Algorithm Regularized random forest

Smart farming has played a significant role in decision support system to maximize the yield with minimum consumption of water in the field of agriculture. The main objective of this paper is to design and develop an innovative multilevel model ensembling for accurate estimation of crop coefficient (Kc) and reference evapotranspiration (ETc) using Fuzzy-Genetic (FG) and Regularization Random Forest(RRF) models. This study present the water requirement of three crops namely (maize, wheat1 and wheat2) in which ETc is a function of the product of the crop coefficient Kc and reference evapotranspiration (ETo). The proposed model is used to analyze the data collected by IMD, Pune and PAU, Ludhiana (case study) for decision making in a crop water model. The proposed FG-RRF(ETc) crop prediction model efficiently estimated Kc and ETc and make an efficient decision.

1. Introduction In the arid and semi-arid climates, accurate estimation of evapotranspiration (ETo) can provide a scientific basis for developing irrigation scheduling. For saving irrigation water and efficiently use water (ETo) is required. Evapotranspiration is the combination of two separate processes whereby water is lost on the one hand from the soil surface by evaporation and on the other hand from the crop by transpiration (Jensen and Allen, 2016). Since Allen et al. (1998), established the first version of FAO-56 with the Penman-Monteith equation (FAO-PM), FAO-PM became a standard for calculating reference evapotranspiration (Allen et al., 1998). FAO-PM has been widely used due to its satisfactory results under various climate conditions around the world. But, it requires a large amount of meteorological data (Hobbins, 2016), which originates from standard metrological observation stations. To overcome the existing limits of the FAO-PM model, various attempts aiming to estimate ETo with limited observed data have been conducted. A large number of studies have focused on estimating ETo using limited ground data such as the Hargreaves and Samani equation, Priestley-Taylor equation, and Thornthwaite equation were used for estimating (ETo) (Djaman et al., 2015; Vicente-Serrano et al., 2017). The demand of water for industries and agriculture sector in India is continuously growing to meet the demands of 1.2 billion people. Wheat and maize are the most commonly cultivated crops and have high water consumption in the region of Punjab, India.

⁎

Punjab, known as the bread basket of India, has 3.51 million ha land under wheat cultivation with production and productivity of 17 million tonnes and 4.85 tonnes ha1, respectively. The state alone contributes 40% of wheat to the central pool i.e. critical for the food security of India (Go, 2014). Since the central zone of Punjab is facing problem of declining water table, increased energy cost for pumping, and scanty rainfall, so there is a need to manage the available surface and groundwater resources optimally to sustain agriculture. Over estimation of crop water requirement leads to waste water, water logging, nutrient leaching in the soil and polluting the groundwater resources. The problems in irrigation sector in India include low irrigation efficiency (30–35%), uncontrolled water delivery, tail-end water deprivation, seepage loss, siltation, waterlogging, and soil salinity. To avoid such negative impact, proper policies and measures are needed for the quantification of crop growth as well as water In this context, state-of-the-science agricultural models have been widely accepted tools for developing water management information for increased water productivity in agriculture (McNider et al., 2015; Saseendran et al., 2015). Several computer simulation techniques and decision support systems have been developed to estimate ETo, ETc and Crop water requirement (CWR). Examples include the FAO CROPWAT model, the Global Crop Water Model (GCWM) (Siebert and Döll, 2008) and Water Requirements Satisfaction Index (GeoWRSI) developed by the Food and Agriculture Organization of the United Nations (Verdin and Klaver,

Corresponding author. E-mail address: [email protected] (M.K. Saggi).

https://doi.org/10.1016/j.agwat.2019.105907 Received 30 May 2019; Received in revised form 4 November 2019; Accepted 5 November 2019 0378-3774/ © 2019 Elsevier B.V. All rights reserved.

Please cite this article as: Mandeep Kaur Saggi and Sushma Jain, Agricultural Water Management, https://doi.org/10.1016/j.agwat.2019.105907

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2002) and crop-specific model packages (CERES, CropSyst and InfoCrop) several other models (Jones et al., 2003). Following are the widely used software in agricultural systems i.e. EPIC (Environmental Policy-Integrated Climate; Williams et al., 1989), APSIM (Agricultural Production Systems Simulator; McCown et al., 1996), and DSSAT (Decision Support System for Agrotechnology Transfer; Jones et al., 2003). Crop growth models have been developed to increase the understanding of the dynamic behavior of crops, and to make predictions about crop growth and yield under various agronomic conditions (Bouman et al., 1996). The (Kc) value is sensitive and depends on several aspects such as type of crop, weather variable, canopy cover density, growth stage, soil moisture and agriculture operations (Allen et al., 1988). The concept of crop coefficient (Kc) is introduced by (Jensen, 1968) and later many researchers have further improved (Jensen, 1968; Doorenbos, 1975; Burman et al., 1980). However, Kc approach has the potential to precisely calculate the actual crop evapotranspiration (ETc). According to the FAO methodology by (Allen et al., 1998), the four growing stages of a crop are the initial stage, crop development stage, mid-season stage and end-season stage Allen et al. (1998). The crop coefficient method can be expressed as follows (Allen et al., 1998):

water during its growing season (Kingra et al., 2004). Tang et al. (2018) presented the support vector machine (SVM) and artificial neural network, in modeling actual ET in a rainfed maize field under nonmulching (CK) and partial plastic film mulching (MFR) (Tang et al., 2018). (Mehta and Pandey, 2015) demonstrated the reference evapotranspiration (ETo), correct value of crop coefficient (Kc) and the crop water requirement (ETc) of wheat and maize of Gujarat using long period weather data of different stations of Gujarat (Mehta and Pandey, 2015). In addition to the improvements in ETc equations based on reducing the dependency of climatic data, artificial intelligence approaches were also introduced to develop ETc models in a new pattern. Several studies in Punjab have investigated the irrigation water requirements/pan evaporation/soil water deficit (SWD) based on ET (Timsina et al., 2008; Prihar et al., 1976, 1978) H2o model for crop water ETo and reported survey on smart agriculture using analytics (Saggi and Jain, 2019, 2018). Recently, machine learning models are found to show excellent reliability in ET estimation and modeling. There are variety of machine learning models based on prediction for reference crop evapotranspiration. However, how to accurately separate and estimate the contribution of weather and crop changes on ET variation remains uncertain. The main purpose of this research is to determine the crop coefficients (Kc) and crop evapotranspiration (ETc) for wheat and maize grown in the ludhiana district of Punjab, India using ensembling method, such as the Fuzzy-Genetic and regularization random forest models. There is a great need to modernize agricultural practices for better water productivity and resource conservation. Any changes in meteorological variables due to climate change will affect evapotranspiration, crop water requirement, and eventually affect water allocation for agriculture and food production (Zhang et al., 2011). In this paper, the proposed model is designed on the basis of two factors. Firstly, agriculture analyst can predict the (Kc) crop coefficient without having prior knowledge of stages (initial, development, middle and late) using weather dataset for maize and wheat crops. Secondly, after estimating (Kc) coefficient value, it can also be applied to predict the (ETc) value for a particular crop. The field experiment and crop data for this study has been collected from the package of practices for crops and vegetables of Punjab Agriculture University, Ludhiana (Anonymous, 2007a). Moreover, the model has been calibrated for three selected crops of different varieties including maize(PMH-2) sown on 6th Feb, wheat1 (PBW-621) sown on 12th Dec and wheat2 (PBW-502) sown on 25th Oct categorized as timely crops cultivation. The objectives of the present study are: (i) To develop an application that prepares weather input files for a crop growth model of wheat and maize. (ii) To predict the (Kc) and ETc of crops based on machine learning technology using case study of Punjab Agriculture University (PAU) Ludhiana, India. In this sense, our research goal is to firstly train our model with Kc value to predict the crop coefficient Kc for crops. It will help us to observe how much the predicted (Kc) value is different from the actual value. Another factor is designed to predict the (ETc) value with weather and crop coefficient (Kc) value. The fuzzy approach ensures that the rules determining the (Kc) and (ETc) are always comprehensible, accessible, and adjustable to the specific agriculture application in order to achieve the target of saving water. The remainder of this paper is organized as follows. Section 2, presents the material and method of the proposed FG-RRF(ETc) model with analytical discussions. Section 3 addresses the experimental results and discussion. Conclusion and future directions are presented in Section 4.

(1)

ETc = K c × ETo −1

where ETc represents the crop water requirement (mm d ), Kc the crop coefficient, ETo the reference crop water requirement (mm d−1). Two main strategies can be used to improve the use of water in the agriculture sector: (i) upgrading the irrigation planning and management. (ii) decision support system based on artificial and machine learning technology. Knowing the daily ETc requirements of crops can be used to help producers decide when and how much water to apply to increase crop yields leading to farm profits while reducing costs, and negative environmental impacts. In recent years, numerous studies have been conducted to examine the potential impact of climate change on reference evapotranspiration (ETc). For efficient crop evapotranspiration ETc modeling using VIP (Vegetation Interface Processes) for wheat and maize (Mo et al., 2013), durum wheat in Tunisia (Lhomme et al., 2009), APSIM-Maize model (Liu et al., 2018), SEBAL model for wheat (Rawat et al., 2017), yield, WUE, IWUE and HUE for wheat crop (Salama et al., 2015), weighing lysimeters for Kc and ETc (Anapalli et al., 2016) have been used. Wheat is a major cereal crop of India after rice and it provides more protein than any other cereal crops. Wheat is grown on 29.64 m ha area with a total production of 92.46 m t and average productivity of 3.12 t ha−1 Prasad (2011). In Punjab, wheat is grown in rotation with rice, maize and cotton, constituting rice-wheat, maize-wheat and cottonwheat cropping system. Ludhiana is one of the major wheat producing district and contributes 12% of total wheat produced by Punjab (Gill et al., 2018). Weather factors such as temperature, rainfall and solar radiation are important for wheat production. Importance of change in temperature in wheat growing areas of India has been highlighted by Sandhu et al. (2016). Siad et al. (2019) presented the review study on the coupling of crop growth models and hyrdological models (Siad et al., 2019). Hussain et al. (2019) investigated the continuos maize and maize in rotation with soyabean crop to determine the crop water use in southwest Michigan USA (Hussain et al., 2019). Kisi et al. (2005) calculated the (ETo) using Penman-Monetith method and analyze the calculated (ETo) using ANN and RBF model (Kisi and Yildirim, 2005). In addition, Kingra et al. (2004) computed crop water requirement for wheat and transplanted rice at Ludhiana, reported that the wheat crop used about 315 mm water whereas rice crop used about 780 mm

2

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Fig. 1. Map of study areas.

2. Material and Methods

The crops are chosen to perform the analysis during (Feb 2012 to April 2012) for maize and two wheat growing seasons (Dec 2012-April 2013 and Oct 2013-March 2014) at the research farms of Punjab Agricultural University (PAU), Ludhiana, India (30 (°C) 54 N, 75 (°C) 48 E, elevation 247 m above sea level). The weather data has been obtained from the meteorological observatory, PAU, located 200 m from the experimental site. For model training, the daily climatic data is collected from School of Climate Change and Agro-meteorology, Punjab Agriculture University, Ludhiana. For model testing, weather data collected (1970-2016) from the India Meteorological Department (IMD), Pune (India). Table 1 presents the data of the year when wheat and maize were grown under six weather attributes namely maximum air temperature (Tmax), minimum air temperature (Tmin), relative humidity (RH), wind speed (u2), solar-radiation (Rs), and sunshine hours (Is). The FAO-56 Penman-Monteith (FAO-PM56) (Allen et al., 1998) has been broadly used to analyze ETo from meteorological factors and it is suggested as the standard technique by the Food and Agriculture Organization of the United Nations (FAO) Allen et al. (1998). In this study, the ETo is estimated by the PM method through software CROPWAT 8.0, which is developed by the Land and Water Development Division of Food and Agriculture Organization (FAO) of the United Nations for crop growth model (Mu noz and Grieser, 2006).

2.1. Data collection and experimental site The study was conducted for Ludhiana District which is one of the centrally located District of Punjab (India) with 3706 sq km geographical area. The topography of the study area is a typical representation of an alluvial plain. The climate of the area is sub-tropical steppe, semi-arid with hot dry summers from April to June, hot and humid monsoon period from July to September, cold winters from November to January and mild climate during February to March. Fig. 1 shows the map of the study area and the location of the climatology stations Table 1 shows the statistical parameters of meteorological variables at Ludhiana site. During winter, the average minimum temperature range between 2 and 18 (°C) and the average maximum temperature goes up to 16–47 (°C) in summer. The mean relative humidity is lowest during summer and ranges between 30 and 60%. However, it is highest during monsoon and generally rises up to 90% in July and August. The average annual rainfall varies from 500 to 650 mm, which is received during the monsoon season from July to September and about 70 to 80 mm rainfall is received during winter months (Khadatare et al., 2006). Table 1 Statistical parameters of available meteorological variables and ETo of Ludhiana station. Year

Months

Tmax

Tmin

Rhmax

Rhmin

u2

Is

Rs

ETo

2012

Feb March April Dec Jan Feb March April Oct Nov Dec Jan Feb March

20.98 27.93 33.92 19.43 17.04 20.54 27.63 31.22 28.80 27.16 20.44 16.14 22.75 24.20

8.16 12.94 18.58 7.44 5.12 9.62 13.17 15.66 13.30 10.89 8.27 7.10 10.28 12.11

70.71 59.39 54.57 91.35 94.48 97.11 94.26 54.00 75.29 82.23 85.29 94.48 88.57 82.59

42.58 31.71 30.40 58.81 60.61 67.54 50.45 27.80 44.14 44.37 59.94 72.90 57.14 55.68

4.21 4.71 4.70 3.85 3.23 3.79 3.46 3.82 1.86 1.67 3.10 2.77 4.25 3.41

7.43 7.17 8.64 5.17 5.19 6.38 9.27 10.87 8.61 8.83 6.03 4.60 7.75 8.10

15.16 17.32 24.94 9.70 10.36 13.60 19.89 23.80 15.91 14.63 11.05 9.87 15.66 18.10

1.923 2.714 4.735 2.081 1.834 2.340 4.398 6.728 2.284 1.890 1.204 1.123 2.118 2.765

2013

2014

ET0 =

0.408· ·(Rn

900

G ) + · T + 273 · u2 ·(es + (1 + 0.34u2 )

ea) (2)

where ET0 is the reference crop evapotranspiration (mm/day^-1); Δ= slope of saturation vapor pressure function (kPa °C−1); Rn= net radiation (MJ m−2day−1); G = soil heat flux density (MJ m−2day−1); γ = psychometric constant (kPa °C−1); T = mean air temperature (°C); u2 = average 24-h wind speed at 2 m height (ms^-1); es = saturation vapour pressure(kPa); ea = actual vapour pressure(kPa) and (es − ea) = vapour pressure deficit (kPa). 2.2. Wheat and maize crops simulation The study is conducted for prediction of maize and wheat crops coefficient (Kc) and (ETc) using machine learning (Patel et al., 2017). (Kc) is defined as the ratio of actual crop evapotranspiration (ETc) to reference evapotranspiration (ETo). Crop daily (ETc) has been made using a crop growth model that relies on four categories of input data including weather, crop, soil and management. The Kc values of wheat1 crop were 0.4, 1.15 & 0.4 while for wheat2 were 0.5, 1.36, 1.42 and 0.42 for the initial, mid and last stage of

Note: where, TMax (°C) is the maximum temperature; TMin (°C) is the minimum temperature; Rhmax (%) is the maximum relative humidity; Rhmin (%) is the minimum relative humidity; u2 (km/h) is the wind speed; Is (h) is the sunshine hours; Rs (MJ m−2 day−2) is the solar radiation; ETo (mm) is the reference evapotranspiration. 3

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Fig. 2. Monthly mean variations of daily dataset showing max and min temperature, max and min relative humidity, wind speed, sunshine hour, solar radiation and evapotranspiration during 2012–2014.

4

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Table 2 Crop coefficient (Kc) values of different crops at different stages of Ludhiana for the training dataset. Period

06/02/2012-30/04/2012 01/12/2012-05/04/2013 25/10/2013-22/03/2014

Crop

Maize Wheat Wheat

Variety

PMH-2 PBW621 PBW502

Initial

Development

Mid

Late

TD

Kc

TGD

Kc

TGD

Kc

TGD

Kc

TGD

0.7 0.4 0.5

35 29 24

0.85 1.15 1.36

18 55 46

1.15 1.15 1.42

17 14 35

1.05 0.4 0.42

15 32 42

85 130 147

Abbreviations represent the following- Crop coefficient: Kc; Total Growing days: TGD; Total days: TD; Station: Ludhiana-II; Longitude: 30.9010(°N); Latitude: 75.8573(°E); Elevation: 262 m; Table 3 Crop coefficient (Kc) values of different crops at different stages of Ludhiana for testing. Period

06/02/2014-30/04/2014 01/12/2014-05/04/2015 25/10/2015-22/03/2016

Crop

Maize Wheat Wheat

Variety

PMH-2 PBW621 PBW502

Initial

Development

Mid

Late

TD

Kc

TGD

Kc

TGD

Kc

TGD

Kc

TGD

0.7 0.4 0.5

35 29 24

0.85 1.15 1.36

18 55 46

1.15 1.15 1.42

17 14 35

1.05 0.4 0.42

15 32 42

85 130 147

Abbreviations represent the following- Crop coefficient: Kc; Total Growing days: TGD; Total days: TD; Station: Ludhiana-II; Longitude: 30.9010 (°N); Latitude: 75.8573(°E); Elevation: 262 m;

growth respectively. The length of time (days) for initial, development, mid and late seasons for wheat1 were 29, 55, 14 & 32 days while for wheat2 24, 46, 35, 42 days. Maize is globally a top ranking cereal in productivity, human food, animal feed and as a source of a large number of industrial products (Meena et al., 2014). It is the third most important crop of Kharif season after paddy and cotton in Punjab. The area under maize in Punjab has declined from 1.65 lakh ha in 2000-01 to 1.27 lakh ha in 2015–16 (Anonymous, 2007b). The Kc values of maize crop were 0.7, 0.85, 1.15 & 1.05 for the initial, mid and end stage of growth respectively. The length of time (days) for initial, development, mid and late seasons for maize were 35, 18, 17 and 15 days used in different stage. Detail of selected crops and period of data for the study are shown in Tables 2 and 3 using training and testing datasets respectively. Fig. 3. Flowchart of fuzzy-genetic system.

2.3. Methods

Finally, the fuzzy system with the best performance is obtained. For the development of model, we have set maximum number of rules as 5, maximum variables per rule set as 4 and a number of generations considered are 100 to 150, and the population as 200. The elitist parameter was set to be 20% out of every generation. The flowchart of Fuzzy-Genetic system is presented in Fig. 3.

The Fuzzy-Genetic (FG) and regularized random forest (RRF) are the models which estimate the crop coefficient Kc and reference crop evapotranspiration ETc for Ludhiana station using training and testing datasets. 2.3.1. Crop modeling fuzzy-genetic simulation A genetic algorithm is an evolutionary algorithm to construct a fuzzy system that adequate to fit the given training data. It can be used as a prediction model composed of fuzzy logic rules that provide a good linguistic representation. The package ”fugeR” (Bujard, 2012) implements genetic algorithms to construct an FRBS from numerical data for classification Bujard and Rcpp (2012). An idea of applying genetic algorithms in the field of fuzzy modeling appeared in the early nineties of the last century. The package fugeR is designed for training fuzzy systems based on evolutionary algorithms. It is based on fuzzy cooperative coevolution where two co-evolving species are defined: the database and the rulebase. In this package, there are two main functions which are fugeR.run() for construction of the FRBS model and fugeR.predict() for prediction. The genetic algorithm generates a random population of the fuzzy system. At each generation, all the fuzzy systems are tested and their predictions are then compared with the labels and a ”performance” is given at each system. The top best system elitism are taken without modification for the next generation. The population is used to generate the population for the next generation using crossover and mutation.

2.3.2. Regularized random forest Random forest (RF) is a well-established supervised machine learning algorithm for classification and regression models. There are several techniques to construct the ensemble, for instance, bagging, and boosting etc. Our experiments investigate the performance of the regularized random forest (RRF) tree as the analyst ensemble model. RRF is a recent augmentation of random forest (RF), apply a regularization framework to random forests that incorporates into the tree growing algorithm (Deng, 2013). Regularization usually involves the additional penalty to a loss function in order to prevent overfitting. In this paper, we implemented RRF using the ’caret’ and ’RRF’ packages. The RRF model has been known by its two primary reasons, firstly RRFs are well-known to provide high accuracies that are competitive with state-of-the-art across a wide range of classification or regression problems. Secondly, RRFs are relatively efficient to train, which is important to our study, since we must train one RRF for each possible subset of features (up to some maximum size). The regularization framework is applied to the random forest and boosted trees, and can be 5

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Fig. 4. Division of dataset for reference crop ETc model.

Fig. 5. Proposed reference crop ETc model. 6

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Table 4 Performance comparison of selected models for Patiala. Maize Models Results MSE RMSE r2 MAE Acc NSE

ETc 0.024 0.153 0.99 0.113 98 0.993

Wheat1 Fuzzy-Gentic Kc 0.003 0.055 0.96 0.040 100 0.91

RRF ETc 0.071 0.267 0.99 0.158 97 0.98

ETc 0.073 0.271 0.98 0.149 93 0.95

Wheat2

Fuzzy-Gentic Kc 0.064 0.253 0.71 0.151 93.1 0.77

easily applied to other tree models.

The Fuzzy-Genetic and regularized random forest (FG-RRF) proposed model is implemented using Rstudio version 3.5.2 to simulate the reference crop coefficient Kc and ETc The proposed model consists of five different stages, namely, data collection stage, data pre-processing, modeling, multilevel modeling, and estimated output stage presented in Fig. 5. Fig. 4 shows the division of weather and crop dataset (training (50%) and testing (50%)). It consists of three samples of crop dataset: MaizeCP1, WheatCP2 and WheatCP3. These samples are used to predict the two subsets of each sample namely Kc and ETc. The historical weather dataset is collected from IMD and case study of crop coefficient Kc values of three crops such as Maize, Wheat1, Wheat2 by PAU, ludhiana. In the Data preprocessing stage, the reference evapotranspiration ETo and solar radiation Rs parameters are estimated using CROPWAT 8.0 software. The ETc is calculated on the basis of estimated ETo and Kc values using the equation (2). In third stage, Fuzzy-Genetic model is applied to simulate the Kc and ETc values using training dataset. Based on the fuzzy-genetic model prediction results, both Kc and ETc prediction probabilities are combined in newly dataset with previous weather dataset. This ensemble dataset is evaluated on the basis of performance metrics to check accuracy of results. In the fourth stage, the ensembling dataset is used to train the RRF model for predicting the ETc values of each sample of the crop. After getting the best accuracy from training model, the testing dataset is applied to validate the accuracy of model. In this section, the proposed FG-RRF algorithm has demonstrated the process of ensemble modeling:

• • • • • • • • • • • •

• Weather dataset (T , T , Rh , Rh , u , I , Rh , ET ) and Crop dataset (Maize ), (Wheat ) and (Wheat ) K • and ET values. • Crop coefficient K the dataset are (K TR ), (K TR ) and (K TR ) max

c

min

max

min

2

CP2

s

s

o

CP3

c

c

ETc 1.145 1.070 0.79 0.725 75 0.97

Fuzzy-Gentic Kc 0.015 0.123 0.97 0.065 100 0.92

RRF ETc 0.267 0.516 0.92 0.355 85 0.84

(ETc3TR3) for (MaizeCP1TR1), (WheatCP2TR2) and (WheatCP3TR3). c the dataset are (Kc1TS1), (Kc2TS2) and (Kc3TS3) for (MaizeCP1), (WheatCP2) and (WheatCP3) and Reference Crop Evapotranspiration ETc dataset are (ETc1TS1), (ETc2TS2) and (ETc3TS3) for (MaizeCP1), (WheatCP2) and (WheatCP3). Fuzzy-GeneticM1, Fuzzy-GeneticM2 and Fuzzy-GeneticM3. RRFM1, RRFM2 and RRFM3. For Training EnsembleETc1(TR1), EnsembleETc2(TR2), EnsembleETc3(TR3) and For Testing EnsembleETc1(TS1), EnsembleETc2(TS2), EnsembleETc3(TS3). ⟶ Input Dataset: Weather dataset is collected from Indian Meteorological Department (IMD) and crop Kc case study is obtained from Punjab Agriculture University (PAU), Ludhiana, India. ⟶ Data Preprocessing: Estimating ETo, Kc and ETc: For estimation of reference evapotranspiration ETo, we have used CROPWAT 8.0 software for weather dataset from (2012 to 2016). Further, for estimation of crop evapotranspiration ETc is obtained by the given equation (2). Training and Testing Dataset: The dataset is divided into two sets i.e. Training and Testing. Further, training dataset is categorized into three samples of weather and crop dataset namely (MaizeCP1), (WheatCP2) and (WheatCP3). For each sample, target values are categorized into two classified subsets as Kc and ETc. ⟶ Crop ETc Model Development: Model Kc: Fuzzy-GeneticM1, Fuzzy-GeneticM2 and Fuzzy-GeneticM3 models are trained by (Kc1TR1), (Kc2TR2) and (Kc3TR3). Similarly, Fuzzy-GeneticM1, Fuzzy-GeneticM2 and Fuzzy-GeneticM3 models are tested by (Kc1TS1), (Kc2TS2) and (Kc3TS3). Model ETc: Fuzzy-GeneticM1, Fuzzy-GeneticM2 and Fuzzy-GeneticM3 models are trained by (ETc1TR1), (ETc2TR2) and (ETc3TR3). Similarly, Fuzzy-GeneticM1, Fuzzy-GeneticM2 and Fuzzy-GeneticM3 models are tested by (ETc1TS1), (ETc2TS2) and (ETc3TS3). ⟶ Multilevel Model Ensembling: Predictions: (Fuzzy-GeneticM1,M2,M3) models will give prediction probabilities on training dataset of (KcPred1,Pred2,Pred3)and (ETcPred1,Pred2,Pred3) values. Further, the generated Ensemble dataset is combined by predicted (KcPred1,Pred2,Pred3) and (ETcPred1,Pred2,Pred3) values of (MaizeCP1TR1), (WheatCP2TR2) and (WheatCP3TR3) datasets. Ensemble Datasets: The EnsembleETc1(TR1), EnsembleETc2(TR2)

• Crop coefficient K

2.4. Model development

CP1

RRF ETc 0.064 0.254 0.98 0.148 97.5 0.95

c1

1

c2

2

c3

3

for (MaizeCP1), (WheatCP2) and (WheatCP3) and Reference Crop Evapotranspiration ETc dataset are (ETc1TR1), (ETc2TR2) and

•

Table 5 Performance comparison of selected models for Patiala. Maize Models Results MSE RMSE r2 MAE Acc NSE

Fuzzy-Gentic ETc Kc 0.0209 0.0134 0.1447 0.1160 0.990 0.990 0.1048 0.0512 99.0 100.0 0.99 0.59

Wheat1 RRF ETc 0.069 0.263 0.990 0.187 98.0 0.97

ETc 0.124 0.352 0.940 0.218 94.0 0.89

Wheat2

Fuzzy-Gentic Kc 0.104 0.323 0.830 0.250 94.0 0.75

7

RRF ETc 0.156 0.396 0.890 0.264 93.0 0.97

Fuzzy-Gentic ETc Kc 0.0125 0.0257 0.1121 0.1603 0.94 0.88 0.0538 0.0519 99.0 96.0 0.97 0.88

RRF ETc 0.075 0.273 0.830 0.118 94.0 0.68

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•

and EnsembleETc3(TR3) datasets are used to train the RRFM1, RRFM2 and RRFM3 models for predicting the Final ETc1, ETc2 and ETc3 value of each sample of crop dataset. For validation purpose, the testing datasets are used to evaluate this model by EnsembleETc1(TS1), EnsembleETc2(TS2) and EnsembleETc3(TS3). ⟶ Estimated Output: The comparison of the proposed model is shown in Fig. 6. The proposed fuzzy-genetic and RRF model makes effective decisions using the multilevel ensembling for the each crop sample.

during growing seasons of (2012-2014) of crops maize, wheat1 and wheat2 for the training dataset. It also describes the changing trend of max and min temperature, relative humidity, wind speed, sunshine hours, radiation, and ETo. To present more detailed climatic condition of the study area, seasonal ETo the trend is also shown in Fig. 2 and Table 1. It is observed that in the weather dataset of maize crop during Feb (2012) to April (2014), the value of ETo (0.9-7.08) mm day−1 value is considered for the training dataset. Similarly, during Feb (2014) to April (2014), ETo value is (1.2-5.33) mm day−1 for testing dataset. For ludhiana station, the ETo value (272.3) and (250) mm day−1 is considered for training and testing dataset respectively. The weather dataset during Dec (2012) to April (2013), for wheat1 crop, the ETo (0.77–7.9) mm day−1, value is considered for the training dataset. Similarly, during Dec (2014) to April (2015) for testing dataset consist the ETo value (0.4-7.9) mm day−1. Ludhiana station for ETo value (356.8) and (308.9) mm day−1 of training and testing dataset respectively. However, it is also observed that weather dataset of wheat2 crop during Oct (2015) to March(2016), the ETo value (0.9-3.01) mm day−1 is considered for training dataset. Similarly, during Oct (2015) to March (2016), ETo (0.73-3.26) mm day−1, value is considered for testing dataset. Ludhiana station for ETo value (243.4) and (229.3) mm day−1 of training and testing dataset respectively.

Once all the above stages are successfully completed, the output prediction of each sample is obtained. Then, the obtained results are evaluated by the different performance metrics such as ACC, MSE, RMSE, MAE, NSE, r2 for each sample. Performance analysis of the proposed model is depicted in Tables 4 and 5 . 2.4.1. Evaluation parameters/criteria To evaluate the performance of models, the following statistical indicators have been selected such as mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE), Nash–Sutcliffe efficiency coefficient (NSE), coefficient of determination (r2), and accuracy (ACC). The following parameters are defined as follows: ET ic,PM

ˆ

= observed/actual values, ETi c , M = simulated or predicted values and M = total number of data points. In our experiment, we have taken (threshold error) Ae = 0.5. 1. Mean square error

MSE =

1 N

N

(ETic ,PM i=1

ˆ

ETi c , M ) 2

2. Root mean square error:

1 N

RMSE =

N

3. Mean absolute error

MAE =

1 N

ˆ

(ETic,PM

ETi c, M )2

i=1

N

|ETic,PM i=1

ˆ

ETi c, M |

3.2. Trends in the simulated Maize crop reference evapotranspiration The results of the daily Kc and ETc (2012 and 2014) are simulated for training and testing datasets, as presented in Fig. 6. Crop coefficient values Kc are taken from PAU ludhiana and published data (Patel et al., 2017). It is observed that the Kc value of maize crop in year (Feb 2012–April 2012) is varying from (0.7, 0.83, 1.15, 1.05) and (0.7, 0.83, 1.15, 1.05) in year (Feb 2014–April 2014) for training and testing dataset respectively. Similarly, parameter metrics results have also reported that the Fuzzy-Genetic model provided a slightly better accuracy results in training dataset than testing results for Kc value. However, Fig. 11 shows the Fuzzy-genetic model results (MSE = 0.0003 and 0.0134, RMSE = 0.055 and 0.1160, ACC= 100% and 100%) for splitting of training and testing datasets in ratio (50% and 50%). During the initial stage, the mean water requirement ETc varies in 1.27 to 2.15 mm day−1 for maize using Fuzzy-Genetic model. However, there is a slight variation observed with RRF model i.e. 1.22 to 2.05 mm day−1. During the developmental stage, ETc increases and as the ratio between 2.2 to 2.73 mm day−1, whereas across the RRF model it varies between 1.99 to 2.85 mm day−1. During the mid season, stage mean water requirement also increases and varies between 2.81 to 5.27 mm day−1 whereas across the RRF model it varies between 2.29 to 5.27 mm day−1. During the late-season stage ETc increases progressively up to end of crop season using Fuzzy-Genetic (5.27 to 7.05) mm day−1 and (5.11 to 6.79) mm day−1 for RRF model. It is observed that Fuzzy-Genetic and RRF model presented the best performance during testing dataset for predicted ETc in terms of MSE (0.0240 and 0.0711) mm day−1 and MSE of (0.0209 and 0.069) mm day−1 using training and testing respectively. The other evaluation of statistical results show ETc with RMSE of (0.1530 and 0.2670) mm day−1, MAE of (0.1130 and 0.1580) mm day−1, ACC of (98% and 97%) mm day−1 using Fuzzy-Genetic and RRF model for the training dataset. The other evaluation statistics results show that ETc with RMSE of (0.1447 and 0.2630) mm day−1, MAE of (0.1048 and 0.1870) mm day−1, ACC of (99% and 98%) mm day−1 suggesting a good agreement between Fuzzy-Genetic and RRF model for the testing dataset.

(3)

(4)

(5)

4. Coefficient of determination (6)

r 2 = r *r 5. Accuracy

ACC = (

ETic =

M i=1

ETic

M

× 100)

1 if |ETic,PM 0

ETic, M | error otherwise

(7)

3. Experimental results and discussion In this section, we have described the experimental results of FGRRF(ETc) model for each sample of crops. Statistical measurements have been used to estimate daily performance of Kc and ETc model.

3.3. Trends in the simulated Winter wheat1 crop reference evapotranspiration

3.1. Trends in the climate meteorological variables

It is observed that the Kc value of wheat1 crop in a year (Dec

Table 1 presents seasonal variations of meteorological variables 8

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Fig. 6. Estimated Kc and ETc values for actual and predicted of maize crop.

increases and it varies between 0.9 to 3.35 mm day−1, whereas across the RRF model it varies between 0.65 to 3.19 mm day−1. During the mid season stage, the mean water requirement also increases and varies between 1.3 to 3.44 mm day−1, whereas across the RRF model it varies between 1.74 to 3.70 mm day−1. During the late-season stage, ETc increases progressively up to end of crop season using Fuzzy-Genetic (1.11 to 3.55) mm day−1 and (1.5 to 1.83) mm day−1 for RRF model. Similar parameter metrics results have also been reported that Fuzzy-Genetic and RRF model provided slightly better accuracy results in training dataset than testing results. However, Fig. 11 shows the Fuzzy-genetic and RRF models with (MSE= 0.073 and 0.0640, RMSE=

2012–April 2013) and (Dec 2014-April 2015) is varying from 0.4 (stage I), 1.15 (stage II), 1.15 (stage III), and 0.4 (stage IV) for training and testing datasets respectively. Comparisons of measured and observed Kc value under FuzzyGenetic model, during training periods, have presented best performance than testing dataset using statistical metrics with (MSE= 0.064 and 0.104, RMSE= 0.253 and 0.323, MAE= 0.151 and 0.250). During the initial stage, mean water requirement ETc for wheat1 using Fuzzy-Genetic model is (0.9 to 2.64) mm day−1, however, the stage slight variation is observed with RRF, where it varies between (0.8 and 1.51) mm day−1. During the developmental stage, ETc 9

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Fig. 7. Estimated Kc and ETc values for actual and predicted of wheat1 crop.

0.271 and 0.254, ACC= 93% and 97%, MAE= 0.149 and 0.148) during training dataset. The other evaluation statistics results show that ETc with RMSE of (0.352 to 0.396) mm day−1, MSE of (0.124 to 0.156) mm day−1, MAE of (0.218 to 0.264) mm day−1, ACC of (94% and 96%) mm day−1 using Fuzzy-Genetic and RRF model during testing dataset. Comparison of observed and predicted Kc and ETc values for Wheat1 crop using the proposed model for training and testing are presented in Fig. 7.

3.4. Trends in the simulated Winter wheat2 crop reference evapotranspiration It is observed that the Kc value of wheat2 crop in the year (Oct 2013March 2014) and (Oct 2015-March 2016) is varying from 0.5 (stage I), 1.36 (stage II), 1.42 (stage III), and 0.42 (stage IV) for training and testing datasets respectively. Similar parameter metrics results have also been reported that

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Fig. 8. Estimated Kc and ETc values for actual and predicted of wheat2 crop.

2.18 mm day−1. During the late-season stage ETc increases progressively up to end of crop season using Fuzzy-Genetic (0.55 to 1.37) mm day−1 and (0.6 to 1.23) mm day−1 for RRF model. The other evaluation statistics results show that ETc with RMSE of (1.070 to 0.516) mm day−1, MSE of (1.145 to 0.2670) mm day−1, MAE of (0.7250 to 0.3550) mm day−1, ACC of (75% and 85%) mm day−1 using Fuzzy-Genetic and RRF model for the training dataset. The other evaluation statistics results show that ETc with RMSE of (0.150 to 0.273) mm day−1, MSE of (0.022 to 0.075) mm day−1, MAE of (0.119 to 0.118) mm day−1, ACC of (99% and 94%) mm day−1 using Fuzzy-Genetic and RRF model for testing dataset. Fig. 8 presented the comparison of the predicted and observed Kc and ETc values for Wheat2 crop using proposed model for training and testing periods.

Fuzzy-Genetic model provided slightly better accuracy results in training dataset than testing results. However, Fig. 11 shows the FuzzyGenetic model results (MSE= 0.0150 and 0.0720, RMSE= 0.1230 and 0.2680, ACC= 100% and 97%, MAE= 0.065 and 0.1580) for (50% and 50%) splitting of training and testing datasets. During the initial stage, mean water requirement ETc for wheat2 using Fuzzy-Genetic model is (0.5 to 1.12) mm day−1, however the stage slight variation is observed with RRF, where it varies between (0.6 to 1.12) mm day−1. During the developmental stage, ETc increases and it varies between 1.36 to 2.24 mm day−1, whereas across the RRF model it varies between 0.6 to 2.11 mm day−1. During the mid season stage, mean water requirement also increases and varies between 1.28 to 2.34 mm day−1 whereas across RRF model it varies between 0.8 to 11

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Fig. 9. Taylor diagram representation of predicted and actual ETc for maize, wheat1 and wheat2.

Fig. 10. Taylor diagram representation of predicted and actual Kc for maize, wheat1 and wheat2.

Fig. 11. The comparison results of forecasted maize, wheat1 and wheat2 for training and testing datasets.

Fig. 12. Forecasted maize, wheat1 and wheat2 actual and proposed model ETc values in range of low, medium, high and very high.

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3.5. Comparison of different ETc models

Acknowledgments

Fig. 6 shows the comparison of observed ETc and predicted ETc for Fuzzy-Genetic and RRF models using training and testing datasets. The observed Kc (Blue) and predicted Kc (orange and red) color are also presented in training and testing datasets for maize crop. The comparison of predicted and observed ETc values using FuzzyGenetic and RRF models of training and testing periods are shown in Figure 7. Also obtained observed Kc (Blue) and predicted Kc (green and red) color values are presented in training and testing datasets for wheat1 crop. The scatter plots of the observed and predicted ETc using FuzzyGenetic and RRF models of training and testing periods presented in Fig. 8. The observed Kc (Blue) and predicted Kc (green and orange) color values are presented over the training and testing period of wheat2 crop. Figs. 9 and 10 indicate the statistical summary of how well patterns match each other in terms of their correlation, their root mean square difference and the ratio of their variances using the Taylor diagram. The colors indicate training and testing dataset results of maize, wheat1 and wheat2 crops observed and predicted values of ETc and Kc. Fig. 11 shows the comparison results of Kc and ETc using FuzzyGenetic and RRF model by a statistical performance with MSE, RMSE, r2, MAE and ACC. Fig. 12 shows by the range of ETc at different stages. The proposed model ETc was found to be in a low range (between 0 and 2 mm day−1) indicated by blue colour, medium range (between 2 and 4 mm day−1) indicated by red colour, high range (between 4 and 6 mm day−1) indicated by green colour and very high range (greater than 6 mm day−1) indicated by purple colour for training and testing. Moreover, it indicates that the crop evapotranspiration ETc is divided in to four categories such as (low, medium, high and very-high) for further analysis over training and testing periods.

Mandeep Kaur Saggi was supported by CSIR, funded by Ministry of Minority Affairs, Government of India. The authors wish to express their gratitude to the India Meteorology Department of Pune, (IMD) for access to their weather station data and Dr. Rakesh Sharda, Senior Extension Specialist, Department of Soil and Water Engineering in Punjab Agriculture University, Ludhiana (PAU) for his helpful suggestions. References Allen, R.G., Pereira, L.S., Raes, D., Smith, M., et al., 1998. Crop evapotranspiration-guidelines for computing crop water requirements-fao irrigation and drainage paper 56, FAO. Rome 300 (9), D05109. Anapalli, S.S., Ahuja, L.R., Gowda, P.H., Ma, L., Marek, G., Evett, S.R., Howell, T.A., 2016. Simulation of crop evapotranspiration and crop coefficients with data in weighing lysimeters. Agric. Water Manag. 177, 274–283. Anonymous, 2007a. Package of practices for rabi crops of punjab. Rabi, Punjab Agriculture University, Ludhiana 1–28. Anonymous, 2007b. 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4. Conclusion Accurate estimation and management of crop evapotranspiration (ETc) are critical for optimizing crop productivity in irrigated agriculture. Here, cropping system models are potential decision support tools for predicting ETc in agriculture across different climate parameters. Time series forecasting of evapotranspiration is very important in order to help the decision makers to build up proper systems to sustain and manage water resources. Because time series considered that the history repeats itself, hence by analyzing the past values, better choices, or forecasts, can be carried out for the future. This study has investigated the performance of two models as fuzzyGenetic and regularized random forest estimating value for Kc and ETc of ludhiana station. The ETc ranged from 1.22 to 7.05 mm day−1 for maize crop, 0.65 to 3.70 mm day−1 for wheat1 crop and 1.22 to 7.05 mm day−1 for wheat2 crop. In this respect, our analysis depicts that the models have high performance for modeling daily Kc and ETc (e.g. MSE= 0.0134-0.156, RMSE= 0.1160-0.396, r2= 0.830-0.99, ACC= 94-99) in testing set. The total water requirement for maize crop during whole growing period observed as 263 and predicted as 255 mm while wheat1 recorded actual is 245 and predicted 255.1 mm, wheat2 recorded actual is 191 and predicted 190 mm for the testing scenario. Overall results of model simulation performance of Kc and ETc methods using the proposed model showed that maize crop performed better than the other crops (wheat1 and wheat2) in training and testing scenario respectively. Findings of this study can be applied for other stations with similar Kc and ETc for considered crops selecting and optimum use of water. The obtained Kc values can help farmers to determine the water requirement of these crops. Further studies should be conducted by calibrating the ETc using this models to improve its performance for more stations. 13

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M.K. Saggi and S. Jain Punjab northern India using deep learning. Comput. Electron. Agric. 156, 387–398. Salama, M., Yousef, K.M., Mostafa, A., 2015. Simple equation for estimating actual evapotranspiration using heat units for wheat in arid regions. J. Radiation Res. Appl. Sci. 8 (3), 418–427. Sandhu, S., Tripathi, P., Patel, S., Prasad, R., Solanki, N., Kumar, R., Singh, C., Dubey, A., Rao, V., et al., 2016. Effect of intra-seasonal temperature on wheat at different locations of India: A study using ceres-wheat model. J. Agrometeorol. 18 (2), 222. Siad, S.M., Iacobellis, V., Zdruli, P., Gioia, A., Stavi, I., Hoogenboom, G., 2019. A review of coupled hydrologic and crop growth models. Agric. Water Manag. 224, 105746. Siebert, S., Döll, P., 2008. The global crop water model (gcwm): Documentation and first results for irrigated crops, Tech. rep., Frankfurt Hydrology Paper 07. University of Frankfurt (Main), Germany. Tang, D., Feng, Y., Gong, D., Hao, W., Cui, N., 2018. Evaluation of artificial intelligence models

for actual crop evapotranspiration modeling in mulched and non-mulched maize croplands. Comput. Electron. Agric. 152, 375–384. Timsina, J., Godwin, D., Humphreys, E., Kukal, S., Smith, D., et al., 2008. Evaluation of options for increasing yield and water productivity of wheat in punjab, india using the dssat-csmceres-wheat model. Agric. Water Manag. 95 (9), 1099–1110. Vicente-Serrano, S.M., Tomas-Burguera, M., Beguería, S., Reig, F., Latorre, B., Pe na-Gallardo, M., Luna, M.Y., Morata, A., González-Hidalgo, J.C., 2017. A high resolution dataset of drought indices for Spain. Data 2 (3), 22. Williams, J., Jones, C., Kiniry, J., Spanel, D.A., 1989. The epic crop growth model. Trans. ASAE 32 (2), 497–0511. Zhang, X., Chen, S., Sun, H., Shao, L., Wang, Y., 2011. Changes in evapotranspiration over irrigated winter wheat and maize in north china plain over three decades. Agric. Water Manag. 98 (6), 1097–1104.

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