Estimation of transpiration coefficient and aboveground biomass in maize using time-series UAV multispectral imagery

Guomin Sho ,Wnting Hn,* ,Huihui Zhng ,Yi Wng ,Liyun Zhng ,Yxio Niu ,Yu Zhng,Pi Co

a College of Mechanical and Electronic Engineering,Northwest A&F University,Yangling 712100,Shaanxi,China

b Key Laboratory of Agricultural Internet of Things,Ministry of Agriculture,Yangling 712100,Shaanxi,China

c Institute of Water-Saving Agriculture in Arid Areas of China,Northwest A&F University,Yangling 712100,Shaanxi,China

d Water Management and Systems Research Unit,USDA-ARS,2150 Centre Avenue,Bldg.D.,Fort Collins,CO 80526,USA

e College of Information,Xi’an University of Finance and Economics,Xi’an 710100,Shaanxi,China

f Institute of Soil and Water Conservation,Northwest A&F University,Yangling 712100,Shaanxi,China

g University of Chinese Academy of Sciences,Beijing 100049,China

Keywords:Crop transpiration Normalized difference red-edge index Unmanned aerial vehicles Random forest regression Biomass

ABSTRACT Estimating spatial variation in crop transpiration coefficients (CTc) and aboveground biomass (AGB)rapidly and accurately by remote sensing can facilitate precision irrigation management in semiarid regions.This study developed and assessed a novel machine learning (ML) method for estimating CTc and AGB using time-series unmanned aerial vehicle (UAV)-based multispectral vegetation indices (VIs)of maize under several irrigation treatments at the field scale.Four ML regression methods:multiple linear regression (MLR),support vector regression (SVR),random forest regression (RFR),and adaptive boosting regression (ABR),were used to address the complex relationship between CTc and VIs.AGB was then estimated using exponential,logistic,sigmoid,and linear equations because of their clear mathematical formulations based on the optimal CTc estimation model.The UAV VIs-derived CTc using the RFR estimation model yielded the highest accuracy (R2=0.91,RMSE=0.0526,and nRMSE=9.07%).The normalized difference red-edge index,transformed chlorophyll absorption in reflectance index,and simple ratio contributed significantly to the RFR-based CTc model.The accuracy of AGB estimation using nonlinear methods was higher than that using the linear method.The exponential method yielded the highest accuracy(R2=0.76,RMSE=282.8 g m-2,and nRMSE=39.24%) in both the 2018 and 2019 growing seasons.The study confirms that AGB estimation models based on cumulative CTc performed well under several irrigation treatments using high-resolution time-series UAV multispectral VIs and can support irrigation management with high spatial precision at a field scale.

1.Introduction

Timely,nondestructive,and accurate estimation of crop growth status is desirable for crop field management before harvesting[1].Aboveground biomass (AGB) is closely associated with crop yield and can be used as an indicator of crop growth status[2].Mapping within-field spatial variation in biomass can provide support for specific fertilization,irrigation,pesticide,and seed breeding applications on a field or farm scale [3,4].Previous studies have tested various AGB estimation methods such as ground-based sampling[5] and remote sensing-based methods [6].Manual ground-based sampling is time-consuming and labor-intensive[7].Remote sensing for monitoring crop growth parameters offers the advantages of high efficiency and non-destructive data acquisition [8].

In recent years,the development of sensor technologies has extended the application of unmanned aerial vehicles (UAV) to data acquisition with high spatial and temporal resolution relative to that of airborne and satellite platforms [9,10].UAV platforms have been used for high-throughput plant phenotyping [11,12].Canopy spectral information derived from UAV-based multispectral or hyperspectral imagery has been used to characterize crop physiological traits such as leaf area index [13],canopy cover[14],biomass [2],crop evapotranspiration [15],geometric properties [16],and grain yield [17-19].UAV-based multispectral vegetation indices (VIs) are commonly used for maize biomass estimation [20],but model accuracy is usually limited by saturation of VIs due to the full canopy coverage and soil background effects [21,22].UAV-based hyperspectral VIs provide a large amount of spectral information on crops[2,23]and better explanations for variation in modeling AGB than multispectral VIs [24];however,the cost of a hyperspectral camera is high at present.

Under deficit irrigation conditions,water stress is the main factor affecting crop growth,AGB,and yield when nutrients are sufficient.Spectral vegetation indices cannot accurately reflect crop response to water shortages [25].Crop transpiration can intrinsically reflect water stress [26] and provide information about crop water use[27].To better explain the variability of AGB under water stress conditions at a field scale,crop transpiration should be considered a key measurement parameter.FAO Irrigation and Drainage Paper No.56 (FAO56) [28] showed that crop transpiration is the product of crop transpiration coefficient (CTc) and reference crop evapotranspiration (ET0),and ET0can be calculated using weather data [29].Thus,CTcis the main factor related to AGB for a given crop in a given climate.Although CTccan be calculated using the FAO56 method from weather data and crop physiological parameters,characterizing the spatial distribution of CTcwithout aerial-based imagery is impossible.

CTcis the product of the basal crop coefficient(Kcb) with water stress coefficient [28].Campos et al.[30] reported that the linear correlation between Kcband the soil-adjusted vegetation index(SAVI) was high for irrigated and rain-fed maize.Ballester et al.[31]also found that VIs have the potential to estimate water stress status,and the relationship between VIs and water stress is nonlinear and complex.We hypothesized that CTccould be estimated using spectral VIs with complex regression models.A single VI,such as the normalized difference vegetation index (NDVI),uses limited spectral information and may also be affected by soil background and light conditions [32].Accordingly,we proposed to use a combination of multiple VIs as the input variables of the model.In the literature,ML regression models,such as random forest regression,extreme gradient boost,adaptive boosting regression,and support vector regression,have been used to predict crop evapotranspiration coefficient [33],crop transpiration [34],crop evapotranspiration[35],and crop yield [36]for various crop types based on multiple VIs and meteorological data.These models provide easy solutions for nonlinear functions and do not require knowledge of internal factors compared to conventional models[37].We accordingly proposed to estimate CTcusing UAV-based VIs with ML methods under diverse irrigation conditions.

The FAO66 manual [38] describes the conversion of the cumulative value of crop transpiration (CTc× ET0) into AGB over the growing cycle using a factor affected by the severity of water stress and temperature (cold) stress.Some studies [39-42] have suggested that the relationship between AGB and cumulative CTcis linear during the growing season,and others [43-48] have found that the slope of the fitted curve between AGB and cumulative CTcchanges during the growing season.The above results raise the issue of the influence of the slope as variable and constant values on the accuracy of the AGB estimation model by cumulative CTcunder different irrigation treatments.To our knowledge,the accuracy of AGB estimation using cumulative CTcwith nonlinear methods for maize under deficit irrigation conditions is still not established,especially in the semiarid region of Northwest China.Thus,it is reasonable to estimate the AGB using seasonal cumulative CTcwith nonlinear methods.A few recent studies have investigated the potential of cumulative CTcderived from time-series UAV-based VIs to estimate maize AGB.

The objectives of this study were (1) to develop an optimized CTcestimation model with time-series UAV-based multispectral VIs using ML methods for maize under multiple irrigation treatments;(2)to determine the best combination of VIs for the optimal CTcestimation model;(3) to assess the performance of the AGB estimation models based on the cumulative values of CTcderived from UAV-based VIs using nonlinear regression methods;and (4)to estimate a high-resolution(centimeter-level pixel)spatial distribution of AGB at field scale.

2.Materials and methods

2.1.Study site and experimental setup

Field experiments were conducted in 2018 and 2019 at the Zhaojun Town Agricultural Experiment Site (40°26′0.29′′N,109°36′25.99′′E),Ordos,Inner Mongolia,China.The elevation is 1010 m above sea level.Ordos has a temperate continental climate with mean annual temperature 7.5-9.1°C,mean annual precipitation ranging from 206 to 383 mm,and annual cumulative hours of sunshine ranging from 2797 to 3516 h.The soil type is loamy sand.

Planting dates of summer maize (Junkai 918) were May 11,2018 and May 7,2019.Maize growth was divided into vegetative(V),reproductive (R),and maturation (M) stages,as shown in Table S1.The study site was a circular area with a radius of 60 m.The area was divided into five fan-shaped regions of approximately 2260 m2each.Three plots (6 × 6 m) (black rectangles in Fig.1) were established to record maize growth status in each region.Field data were collected from three subplots (1 × 1 m)chosen randomly from each plot.Five irrigation treatments (TRs)were designed following local irrigation practices each year,for a total of 10 TRs:TR1-TR5 in 2018 and TR6-TR10 in 2019,as shown in Table S2.The local full irrigation amount near the study site was approximately 400 mm,based on the maize water requirements.For the 2018 growing season,two high-irrigation (≥360 mm,TR1 and TR2) and three deficit-irrigation treatments (<360 mm,TR3-TR5) were applied,accounting for approximately 94%,90%,87%,83%,and 88%of local irrigation.For the 2019 growing season,five deficit irrigation treatments (TR6-TR10) were applied,accounting for 62%,54%,53%,51%,and 48% of the full irrigation amount.For each treatment,irrigation and precipitation depth during the reproductive stage (R1-R3) was highest to ensure normal growth of the crop,followed by the vegetative (VE-VT) and maturation (R4-R6) growth stages.A central pivot sprinkler system(Valmont Industries Inc.,Omaha,NE,USA)was used for irrigation,and the rotation speed of the sprinkler was adjusted to obtain desired irrigation amounts.Field management of maize followed local practical standards.

Fig.1.The experimental site in Zhaojun town,Dalate Banner,Ordos,Inner Mongolia,China.TR1 to TR5 represent five irrigation treatments in 2018,and TR6 to TR10 represent five irrigation treatments in 2019.TDR represents the time-domain reflectometry probe.

Fig.2.Comparison of measured and estimated AGB based on UAV-based CTc using exponential (Exp) and linear (Lin) methods in 2018 and 2019.

2.2.UAV multispectral image acquisition and vegetation index selection

A UAV remote sensing system with a RedEdge camera (Mica-Sense Inc.,Seattle,WA,USA) was used to capture maize canopy images during multiple growth stages on sunny and cloudless days(Table S3).The camera captures five bands (blue,green,red,NIR,and red-edge),and the center wavelengths of the bands were 475,560,668,840,and 717 nm,respectively.A gray board with fixed reflectances (58.446%,57.958%,57.339%,56.682%,and 57.128%) was used to calibrate the original multispectral images for generating reflectance images.Canopy multispectral images were captured during 11:00-13:00 Beijing time at an altitude of 70 m with an 85%overlap between images along and across tracks,and ground resolution was 5 cm per pixel.Geographic registration of the ortho-reflectance image of the experimental site was performed based on six ground control points (GCPs) measured with a GNSS GPS Z-survey i50 instrument (CHCNAV CO.,Shanghai,China).The orthophoto was rectified to the Gauss-Kruger,China Geodetic Coordinate System 2000 (CGCS2000),108E,coordinate system.Detailed information about multispectral image acquisition is presented in Shao et al.[33].

Canopy spectral VIs were calculated by combinations of multispectral bands using the Band Math tool in ENVI 5.3 software(Harris Corporation,Jersey,NJ,USA).Ten VIs (Eqs.1-10)were selected from previous studies [25,33,49].

where NDVI is the normalized difference vegetation index;SAVI is the soil-adjusted vegetation index;EVI is the enhanced vegetation index;TCARI is the transformed chlorophyll absorption in reflectance index;GNDVI is the green normalized vegetation index;VARI is the visual atmospheric resistance index;SR is the simple ratio;NDRE is the normalized difference red-edge;NDREI is the normalized difference red-edge index;MCARI is the modified chlorophyll absorption in reflectance index;RB,RG,RR,RNIR,and RRErepresent the reflectance of blue,green,red,near-infrared,and rededge bands,respectively;and L is a soil calibration factor equal to 0.5 in this study.

2.3.Measurements of maize AGB and leaf area index (LAI)

Maize physiological parameters (LAI,plant height,and AGB)measurements were made concurrently during the UAV acquisition days.Three LAI readings were taken for each subplot using a LAI-2200C (LI-COR Biosciences,Lincoln,NE,USA) canopy analyzer at sunset,avoiding direct sunlight.The mean of three LAI readings was used to represent the LAI of the subplot.Ten plants were randomly selected for height measurement with a measuring tape in each plot(black rectangles,Fig.1).AGB(g m-2)was measured with three repetitions for each plot,and four representative plants were selected for each repetition in the vicinity of each plot to decrease the effects of destructive practices on each fixed plot.All plant samples were heated to 105 °C,maintained at 105 °C for 30 min,and then oven-dried at 80°C to constant weight in the laboratory.Fig.S1 shows box plots of the measured AGB in ten TRs.

Weather parameters (air temperature,relative humidity,wind speed,net solar radiation,and precipitation)(Table S4)were measured at an agricultural meteorological station approximately 200 m from the study site.The crop cover under the weather station was well-watered alfalfa.Soil water content was measured by a conventional gravimetric method with three repetitions in each plot and also monitored with a time-domain reflectometer sensor,TDR-315L(Acclima Inc.,Merdian,ID,USA) in each TR,as shown in Fig.1.More information about the soil water content is provided by Shao et al.[33].

2.4.CTc calculation and estimation

2.4.1.CTccalculation

CTc(Eq.(11))was calculated by the FAO56 method and detailed information can also be found in Shao et al.[33] as follows:

where Tris crop transpiration in mm per day;ET0is the reference crop evapotranspiration calculated by the Penman-Monteith equation in mm per day;Ksis the crop water stress coefficient with a range of 0 to 1;Kcb,a(Eq.(13)) represents basal crop coefficient(Kcb,Eq.(12)) corrected by canopy cover (CC,Eq.(14));Kc,minis the minimum value of bare soil crop coefficient with a range of 0.15 to 0.20;Kcb,tabis the FAO56-recommended value for Kcb;in this study,Kcb,tabvalues were respectively 0.15,1.15,and 0.15 at the three (rapid,middle,and late) growth stages;u2is the mean value of daily wind speed at 2 m height in m s-1;RHminis the mean value of daily minimum relative humidity in%;h is the mean plant height in m;k is the canopy attenuation coefficient,and the value of k was 0.7 following Ding et al.[50];LAI is leaf area index.

2.4.2.CTcestimation by VIs using ML methods

The CTcwas estimated based on the combination of multiple UAV-based VIs (NDVI,SAVI,EVI,TCARI,GNDVI,VARI,SR,NDRE,NDREI,and MCARI)using ML methods.The four ML methods were multiple linear regression (MLR),support vector regression (SVR),random forest regression (RFR),and adaptive boosting regression(ABR).The original dataset was divided into training (n=475)and validation (n=119) datasets.MLR,SVR,RFR,and ABR were implemented using the scikit-learn module (https://scikit-learn.org) in Python.The MLR parameters were set to default values.In SVR,the kernel function was the radial basis function (RBF),and penalty parameter(cost)and kernel parameter(gamma)were optimized with values ranging from 0.1 to 1.5 at 0.1 intervals.In RFR,tree number (n_estimators) and maximum depth of trees(max_depth) were optimized with values ranging from 50 to 500 at 50 intervals and from 5 to 15 at 1 interval.In ABR,the maximum number of estimators (max_estimators) and learning rate (learning_rate) were optimized with values ranging from 50 to 500 at 50 intervals and ranging from 0.01 to 1 at 0.01 intervals.The above parameters were determined using tenfold cross-validation [51],and other parameters in SVR,RFR,and ABR methods were default values.

2.5.AGB estimation

Four models were used to establish the relationship between measured AGB (g m-2) and VI-based cumulative CTc,including logistic (Log),sigmoid (Sig),exponential (Exp),and linear (Lin)models.

The Log equation (Eqs.(15-16)) [52] is as follows:

where Blog,iis the Log-based AGB(g m-2)on i days after planting(DAP),Bmis the potential final AGB without water stress (g m-2),and was 2634 g m-2(measured) in the study;B0is the initial AGB(g m-2);δ is the potential AGB growth index;is the cumulative CTc,ifrom planting day to i DAP,and CTc,iwas calculated by linear interpolation [53];CTc,irepresents VI-based CTc(in Section 2.4.2) on i DAP.

The Sig equation (Eq.(17)) is as follows:

where Bsig,iis the Sig-based AGB (g m-2) on i DAP;Tcis thevalue corresponding to the half-maximum response of the biomass;η is a constant.

The Exp (Eq.(18)) and Lin (Eq.(19)) equations are as follows:

where Bexp,iand Blin,iare respectively the Exp-and Lin-based AGB (g m-2) on i DAP;c,d,and e are coefficients calibrated with local data.

2.6.Framework for maize AGB estimation using UAV-based VIs

Cumulative CTcand AGB estimation models were established based on UAV-based multispectral VIs using the four regression methods,as shown in Fig.S2.CTcwas calculated using the FAO56 method based on local field data(meteorological,soil,crop,and field management data).The FAO56-based CTcwas then estimated using UAV VIs and ML methods (MLR,SVR,RFR,and ABR),and spatial distribution of CTcmaps was exported in TIF format.The CTcmaps were then registered using the Image-to-Image Tool in ENVI,and daily CTcmaps were developed using a linear interpolation method.Cumulative CTcwas calculated from daily CTcfrom the planting day to the day of AGB measurement.Next,AGB was estimated using Lin,Log,Sig,and Exp regression methods based on the cumulative CTccalculated by UAV-based VIs under the various irrigation treatments during the growing season.Finally,the high-resolution spatial distribution of AGB was generated using the VI-based cumulative CTc.

2.7.Model training,validation,and evaluation

Cross-validation[54]is a resampling method that uses separate subsets of dataset to test and train ML models on different iterations.It is used mainly on a limited data sample and combines average measures of fitness in prediction to derive a more accurate evaluation of model prediction [55].For the AGB estimation models using 2018 and 2019 data,cross-validation was used to validate these models.Parameter K in the cross-validation method was set as 5 using the ‘‘KFold” function in Python’s ‘‘sklearn.model_select ion”module.Eighty percent of the samples were selected for modeling,and the remaining 20% were used as the validation dataset.This process was repeated five times.

The model validation metrics were root mean squared error(RMSE),coefficient of determination (R2),and normalized RMSE(nRMSE).The mean values of R2,RMSE,and nRMSE were used for accuracy assessment.Smaller RMSE values indicate a better model performance.A lower nRMSE value indicates low residual variance between the predicted and measured values.The R2measures the closeness of the predicted and measured values to a 1:1 line.A higher R2value indicates a closer agreement of measure with predicted values.The Pearson correlation coefficient (r) was used to quantify the degree of linear association between the variables.The values of r range from -1 to 1.An absolute value of r equal to 0 or 1 indicates that there is respectively no or a perfect linear association between two variables.

The recursive feature elimination (RFE) method [56] was used to select informative VIs for the ML-based AGB model by recursively eliminating a VI with low contribution from all VIs until all VIs were eliminated,following these steps:

(1) Individual VI was removed with replacement,and the accuracy (R2and RMSE) of the CTcmodels was calculated based on the remaining VIs using the RFR method.

(2) CTcmodels were ranked by the accuracy obtained in step 1 and the CTcmodel with the highest accuracy was identified.

(3) The VI(removed in step 1)not included in the most accurate CTcmodel (obtained in step 2) was dropped.

(4) Steps 1,2,and 3 were repeated until all VIs were eliminated.

3.Results

3.1.CTc estimation by ML methods

Ten VIs were used to estimate maize CTcbased on both 2018 and 2019 data at the field scale.The values of Pearson correlation coefficient (r) between the UAV-based VIs and CTcranged from 0.19 to 0.65 with a P value lower than 0.01 representing a statistical difference (Fig.S3).The linear correlation between NDREI and CTcwas highest (r=0.65) among the 10 VIs,and the linear correlation between TCARI and CTcwas lowest (r=0.19).TCARI also showed relatively low linear correlations with the other nine VIs with r ranging from 0.19(NDRE)to 0.77(MCARI).The linear correlation between some pairs of VIs,such as SAVI and NDVI,GNDVI and NDVI,and NDRE and NDVI,was relatively high(r>0.90).These values indicated high multicollinearity between VIs.

The performance of MLR,SVR,RFR,and ABR models for predicting daily maize CTcbased on UAV-based multispectral VIs are summarized in Table 1.The accuracies of RFR,SVR,and ABR models were higher than those of the MLR model.This finding indicates that the performance of ML methods(RFR,SVR,and ABR)was adequate for estimating CTcderived from UAV-based VIs under diverse irrigation treatments in both years.The accuracy of the RFR model for estimating CTcwas highest,followed by ABR and SVR models in 2018 and 2019.Comparison of the RFR-and FAO56-based CTc(Fig.S4a) indicates the high performance of the CTcestimation model derived from UAV VIs.SR,SAVI,GNDVI,and NDREI showed high relative importance to the RFR-based CTcmodel,and the relative importance of SR was the highest among the 10 VIs(Fig.S4b).

3.2.AGB estimation from RFR-based CTc

Scatterplots of AGB and cumulative CTcestimated by the RFR method using Exp,Log,Sig,and Lin regression models are shown in Fig.S5.Most of the scatter points between AGB and cumulative CTcduring the vegetative growth stage were below the linear fitted curve for 2018(Fig.S5a).The plot shows that the slope of the linear regression of AGB on cumulative CTcwas overestimated during the vegetative growth stage in the year.The scatter points deviated from the fitted curves during the maturation growth stage in 2019 (Fig.S5b) and both years (Fig.S5c).

As seen in Table 2,the estimation accuracy of CTc-based AGB models using nonlinear regression methods (Exp,Log,and Sig)was close in 2018,and higher than that using the Lin model in the year.This finding indicates that the nonlinear methods were more suitable for estimating AGB than the Lin method in 2018.Similarly,the estimation accuracy of AGB models using the nonlinear method also was close in 2019 but was slightly higher than that using the Lin model in the year (RMSE of 226.3-229.9 g m-2vs.242.7 g m-2).The estimation accuracy(nRMSE)of the AGB models using the nonlinear and linear methods in 2018 was higher than that in 2019.Comparison (Fig.2) between the measured and estimated AGB based on the UAV-based cumulative CTcusing the Exp and Lin methods in 2018 and 2019 indicates the adequate performance of AGB model using the Exp method.

4.Discussion

4.1.Main factors for the RFR-based CTc estimation model

CTcwas estimated using UAV-based VIs using ML methods to generate its spatial distribution.The linear correlation between VIs and CTcvaried(r=0.19-0.65)with variation in irrigation treatments(Fig.S3).The linear correlation between CTcand VI was low.Kang et al.[57] reported a strong nonlinear correlation between CTcand LAI for winter wheat and maize.The above results indicate that it is necessary to estimate CTcusing nonlinear models.The worst CTcwas estimated using the MLR method because of the strong multicollinearity caused by the high linear correlation between the input variables.The accuracy of CTcestimation by the SVR,ABR,and RFR methods was higher than that using the MLR method.This finding indicates that it is essential to combinemultiple VIs using ML methods to estimate the CTc,as demonstrated by the high accuracy of the RFR method(Table 1).The high performance of the RFR-based CTcmodel established in this study under various irrigation treatments is due to the advantages of RFR for modeling complex nonlinear correlations [36].In addition,the RFR-based CTcmodel using UAV VIs was used to generate highresolution (centimeter-level pixel) spatial distributions of CTcvalues(Fig.S6)to detect spatial variability of CTc,which is critical for precision irrigation management at a field scale.

Table 1 Maize transpiration coefficient(CTc)estimation models based on UAV VIs using multiple linear regression(MLR),support vector regression(SVR),random forest regression(RFR),and adaptive boosting regression (ABR) regression methods with optimal parameters.

Fig.3.Residuals of the regression of estimated on measured AGB using the exponential (Exp) and linear (Lin) methods during the growing season in 2018 and 2019.The residuals were calculated as estimated minus measured values.V,R,and M represent vegetative,reproductive,and maturation growth stages,respectively.

It is critical to select explanatory VIs for the RFR-based CTcmodel to avoid overfitting and to simplify the model.This study used the RFE method (Section 2.7) to select optimal VIs for the RFR-based AGB model.The accuracy results of the CTcestimation models based on the optimal VIs combinations are listed in Table 3.The RMSE and nRMSE values of the RFR-10 model were slightly lower than those of the RFR-7 model.This finding indicates that a CTcestimation model with more variables often does not yield the best accuracy.One explanation could be overfitting.Sakamoto[36] reported similar results for the RFR.It is often assumed [58]that RFR is insensitive to overfitting,so that the careful selection of input variables is necessary.The similar accuracies of RFR-7,RFR-6,RFR-5,and RFR-4 can be attributed to the redundancy of input variables.The RFR-3 model included SR,TCARI,and NDREI(Table 3) and the three VIs contributed significantly to the RFRbased CTcmodel.SR was not included in the RFR-2 model as it was in the RFR-3 model,and TCARI was not included in the RFR-1 model although it was in the RFR-2 model.Thus,NDREI and TCARI contributed more to the CTcmodel than SR,and the contribution of NDREI to the CTcmodel was higher than that of TCARI.This result contrasts with the finding of highest relative importance for SR in the RFR-based CTcmodel compared to the other nine VIs,as shown in Fig.S4b.The explanation may be that the relative importance of variables in the RFR was calculated using the mean decrease impurity [59],rather than the RMSE and R2used in the study.Thus,it’s important to test the performance of the RFR method based on different combinations of input variables using various evaluation metrics (R2and RMSE).

Fig.4.Comparison of measured and estimated final AGB based on Exp regression in 2018 and 2019.

Table 2 Statisticis of measured and estimated AGB derived by RFR-based CTc using exponential(Exp),logistic(Log),sigmoid(Sig),and linear(Lin)regression methods in 2018 and 2019.

Table 3 Accuracy of CTc estimation using random forest regression (RFR) based on optimal combinations of VIs selected by recursive feature elimination.

When water stress occurs,leaf area and chlorophyll concentration often decrease to reduce light absorption owing to adaptive mechanisms at the leaf level [60,61].TCARI was used to estimate crop chlorophyll content[62]and NDREI was used to detect green leaf area during senescence[63].The results of the previous studies indicate that TCARI and NDREI are important to the CTcmodel.They also show that the red-edge,red,and green bands are important parameters for CTcestimation.In future,multiple combinations of three bands (red-edge,red,and green) can be investigated further using multiple mathematical formulas.SR had relatively high importance for the CTcmodel (e.g.,the RFR-3 model).SR is sensitive to the status of crop growth under high crop coverage conditions[64].Major et al.[65]showed that SR is sensitive to background changes caused by soil color or surface soil moisture content.This study used only the ratio (SR) of the NIR and red bands as input variables.Next,other types of ratio VIs using two wavelengths among multispectral bands can be tested to identify the two optimal bands for RFR-based CTcprediction model.

4.2.Accuracy of AGB estimation by RFR-based cumulative CTc

RFR method showed the highest accuracy in estimating CTcbased on VIs among the four ML methods used in the study,and the linear and nonlinear methods were used to predict AGB by the cumulative RFR-based CTc.Under diverse irrigation conditions,the accuracy of AGB estimation using nonlinear methods was similar and higher than that using the linear method in both years(see Table 2).The Lin method overestimated AGB during the vegetative growth stage in 2018(Fig.3).Zhan et al.[46]also reported that the slope between AGB and cumulative CTcfor maize was low during the early growth stage in comparison with the other growth stages.These results show that the slope of AGB vs cumulative CTcwas not constant in 2018.Fig.3 shows the high residuals of the regression of estimated on measured AGB during the maturation growth stages in 2018 and 2019.This observation may be due to the variation in AGB affected by water stress and other factors that were not accounted for in the study during this growth stage.

Li et al.[66],Zhang et al.[67],and Wang et al.[68] reported maize AGB estimation models directly using UAV-based highresolution stereo imagery(RMSE=270 g m-2),hyperspectral imagery (RMSE=395 g m-2),and fusion of hyperspectral and LiDAR data(RMSE=321 g m-2),respectively.Fig.4 shows that the results of comparison between the measured and estimated final AGB using the Exp method were adequate in 2018 (RMSE=332.9 g m-2)and 2019(RMSE=342.8 g m-2),which is important for the estimation of final yield[42].Overall,the accuracy of the AGB estimation model using nonlinear methods was acceptable in both years.The above results also suggest that the cumulative value of CTcderived by UAV VIs is recommended for predicting AGB under various irrigation treatments(83%-94%and 48%-62%of full irrigation)during the growing season.Although the accuracies of AGB models using nonlinear methods were similar in this study,the Exp method is recommended to estimate AGB because fewer parameters need to be calibrated and the mathematical formula is relatively simple.The AGB model using VIs-based CTccan also generate a high-resolution spatial distribution of AGB (Fig.S7),which is important for precision field irrigation management and decision-making.

4.3.Limitations and future research

The spatial resolution of UAV multispectral images used in this study was 5 cm per pixel.In future,investigating the effect of spatial resolution of UAV-based multispectral images on the CTcestimation model will be helpful for further practical applications.The ML methods (SVR,RFR,and ABR) used in this study depend on many parameters.Some were corrected in this study and some remained as default values.The accuracy of the ML-based CTcestimation model may be improved by correcting more parameters in ML methods.For the maize AGB estimation model generated in this study,data from two years were used to train and validate the model,and the effect of irrigation amount was considered for the model.If more factors can be considered in the future,such as climate,fertilization treatment,date of planting,and crop variety,an AGB model derived from UAV data will be more reliable for application in diverse ecological regions.

5.Conclusions

The RFR-based CTcmodel established in this study showed high applicability under multiple irrigation treatments,and UAV-based NDREI,TCARI,and SR contributed more to the RFR-based CTcestimation model than did the other seven VIs.The accuracy of AGB estimation using Exp,Log,and Sig methods was higher than that using Lin method.Compared with Log and Sig methods,the Exp method was the most suitable for estimating AGB from cumulative CTcunder diverse irrigation treatments during the entire growing season because of its high accuracy,simple mathematical formula,and fewer parameters requiring correction.The accuracy of AGB model using the linear (Lin) regression method was close to those of the nonlinear (Exp,Log,and Sig) methods under severe deficit irrigation conditions.The AGB model using RFR-based CTcshould be further investigated across various climates,fertilizer application amounts,and crop species.

CRediT authorship contribution statement

Guomin Shao:Conceptualization,Methodology,Software,Formal analysis,Investigation,Visualization,Writing -original draft,Writing -review &editing.Wenting Han:Conceptualization,Funding acquisition,Writing -review &editing.Huihui Zhang:Conceptualization,Writing -original draft,Writing -review &editing.Yi Wang:Investigation,Writing-review&editing.Liyuan Zhang:Investigation,Writing -review &editing.Yaxiao Niu:Investigation.Yu Zhang:Investigation.Pei Cao:Writing -review&editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This research was funded by the National Natural Science Foundation of China(51979233)and the Natural Science Basic Research Plan in Shaanxi Province of China (2022JQ-363).We would like to thank Liyuan Zhang,Yaxiao Niu,Yi Wang,Jiandong Tang,and Guang Li for ground truth data and UAV imagery collection.

Appendix A.Supplementary data

Supplementary data for this article can be found online at https://doi.org/10.1016/j.cj.2022.08.001.