\documentclass[10pt]{article}

\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
\usepackage{hyphenat}





\PassOptionsToPackage{hyphens}{url}
\usepackage[colorlinks = true,
            linkcolor = blue,
            urlcolor  = blue,
            citecolor = blue,
            anchorcolor = blue]{hyperref}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{%
  \errmessage{\noexpand\@combinedblfloats could not be patched}%
}%
\makeatother


\usepackage{natbib}




\renewenvironment{abstract}
  {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize}
  {\bigskip}

\titlespacing{\section}{0pt}{*3}{*1}
\titlespacing{\subsection}{0pt}{*2}{*0.5}
\titlespacing{\subsubsection}{0pt}{*1.5}{0pt}


\usepackage{authblk}


\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%

\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}

\usepackage[utf8]{inputenc}
\usepackage[T2A]{fontenc}
\usepackage[ngerman,greek,polish,english]{babel}



\usepackage{float}








\begin{document}

\title{Estimating leaf and canopy nitrogen contents in major field
crops across the growing season from hyperspectral images using
nonparametric regression}



\author[1]{Dong wang}%
\author[1]{Paul C. Struik}%
\author[1]{Lei Liang}%
\author[1]{Xinyou Yin}%
\affil[1]{Affiliation not available}%


\vspace{-1em}



  
  \date{June 17, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup








\sloppy


Dong Wang\textsuperscript{a,b}, Paul C. Struik\textsuperscript{a}, Lei
Liang\textsuperscript{b,*} \& Xinyou Yin\textsuperscript{a,*}

\textsuperscript{a} Centre for Crop Systems Analysis, Department of
Plant Sciences, Wageningen University \& Research, P.O. Box 430, 6700 AK
Wageningen, The Netherlands

\textsuperscript{b} Shanghai Lankuaikei Technology Development Co. Ltd.,
No. 888 Huanhu West 2nd Road, Pudong New District, Shanghai, China

\textsuperscript{*}Corresponding Authors

E-mail address: xinyou.yin@wur.nl, lei.liang@lankuaikei.cn

\textbf{Abstract}

Estimating leaf nitrogen (N) status is crucial for site- and
time-specific crop N management, and can be accomplished more routinely
than ever before with the advent of hyperspectral imaging techniques. We
conducted field experiments with different nitrogen supply for rice,
wheat and maize, in China, in which three types of hyperspectral
features were extracted, including canopy reflectance (Ref), vegetation
indices (VIs), and texture information (Tex). These features as well as
crop development stage (DS) were applied to estimate crop N parameters,
using five nonparametric regression algorithms: Partial Least Squares
Regression (PLSR), Support Vector Regression (SVR), Random Forest
Regression, Deep Neural Network, and Convolution Neural Network. The
performance of PLSR and SVR models was more robust than that of the
others and could be improved by incorporating the combined feature set
RefVIsTex, although there was no further improvement when also
incorporating DS. The prediction of the mass-based leaf N trait, leaf N
concentration (LNC), was better than that of the area-based trait,
specific leaf N (SLN). The models also predicted specific leaf area
(SLA) better than its reciprocal, specific leaf weight. Values of SLN
were better predicted via an indirect method (predicted via SLA; denoted
as SLN\textsubscript{sla}) than via the direct method
(SLN\textsubscript{dir}). However, when upscaled to canopy, the
predicted canopy N content (\emph{N} \textsubscript{canopy}) using
SLN\textsubscript{dir} agreed better with measured\emph{N}
\textsubscript{canopy} than that using SLN\textsubscript{sla}, and even
better than the direct prediction\emph{N} \textsubscript{canopy,dir} in
rice and maize. These results were discussed in view of coupling the
predicted leaf and canopy N traits with dynamic crop growth models that
can be used for optimizing field N management in sustainable
agricultural production.

\textbf{Keywords}

Major crop, nonparametric regression algorithm, hyperspectral image,
leaf nitrogen trait, crop nitrogen management

\textbf{1. Introduction}

The security and sustainability of modern agricultural production are at
risk. While crop production has increased 50\% since 2000, global
agricultural land area decreased by 2\% and the overall fertilizer use
was 40\% higher in 2018 than in 2000, while 52\% of the increase was
nitrogen (N) (FAO, 2020). Fertilization with N is needed as it strongly
influences crop growth, production and quality (Beeckman et al., 2018;
Lemaire et al., 2008) while soils often cannot supply enough N to meet
the demands of modern varieties to achieve high yields. Crop N uptake,
the N absorption by the roots, depends on soil N availability and crop N
demand. Crop demand changes during the vegetative and reproductive
phases, while N movement and reallocating within the crop occur as well
(Ohyama, 2010). Based on the understanding of these and other
physiological processes, numerous dynamic crop models have been
developed (e.g., Kropff et al., 1994; Yin and Struik, 2017), which can
simulate responses of crop growth to N fertilization. In general, N
fertilization can increase crop yield. However, in view of the cost of N
fertilizers and the diminishing return of productivity (yield gain per
unit N-fertilizer diminishes with increasing application of N), the
amount of fertilizers applied to crops may be excessive (Schr\selectlanguage{ngerman}öder et
al., 2000; Skiba, 2014). Moreover, severe environmental issues have
arisen because of N losses, through volatilization (Davidson, 2009),
leaching (Padilla et al., 2018) and runoff (Zeng et al., 2021). Thus, it
is necessary to guide farmers to perform a sustainable site- and
time-specific N-fertilizer management (Weiss et al., 2020). To this end,
monitoring crop N status in time and linking this with crop models to
more accurately predict crop growth (Jin et al., 2018) may allow the
development of effective strategies for smart crop N management.

Monitoring crop N status via destructive sampling and biophysical
chemical analyses of crop N is costly and time consuming. Instead,
remote sensing has been developed as a powerful tool to monitor crop N
status. Although multispectral satellite images tend to be temporally
frequent, hyperspectral satellite images suit better for crop
phenotyping because of the higher spectral resolution (Marshall and
Thenkabail, 2015). However, hyperspectral satellite images cannot be
acquired in time: delivery always takes weeks, while crop N status
rapidly changes especially during the vegetative phase, like from
tillering to panicle-initiation for rice, during which fertilizers are
applied mostly. Consequently, hyperspectral sensors equipped on an
Unmanned Aerial Vehicle (UAV) serve with a high versatility for meeting
the requirements on spectral, spatial, and temporal resolution (Homolová
et al., 2013). Of the studies on predicting N from hyperspectral images
in an agricultural context, more than two thirds are about rice, wheat
and maize (Berger et al., 2020), mirroring the large agricultural areas
around the globe cropped with these crops (Khoury et al., 2014).

For site-specific field N management, the monitoring of the aboveground
leaf-N content in a canopy (\emph{N} \textsubscript{canopy}) is crucial
as it determines canopy photosynthetic capacity and thus crop
productivity (Peng et al., 1995). In crop models, canopy photosynthesis
is calculated as the integration of photosynthetic rates of individual
leaves in a canopy, while leaf photosynthesis is often related to leaf N
status (Boote et al., 1998; Kropff et al., 1994; Yin \& van Laar 2005).
To parameterize this relationship, data for leaf photosynthesis as
measured by gas exchange are used, which are expressed on a leaf-area
basis (Evans, 1983). It follows that leaf-N parameters used to model
leaf photosynthesis are also expressed on a leaf area basis. Indeed,
specific leaf N content (SLN, g N m\selectlanguage{english}\textsuperscript{-2}) has been widely
used as a typical leaf-N parameter in crop models to calculate leaf
photosynthesis rate (Evans, 1983; Kropff et al., 1994; Wang et al.,
2022; Yin et al., 2009). Thus, predicting crop N status (e.g., based on
SLN) from UAV-based hyperspectral imaging and linking this prediction
with crop modelling can guide farmers for better crop N management.

Investigating SLN is also supported by the expectation that the light
reflected or transmitted by a leaf is considered to interact within the
whole leaf thickness in spectral domains of absorption, and thus, the
reflectance and transmittance are supposed to be more directly sensitive
to the variation in the area-based content of absorbing constituents,
like SLN, but rather less to the mass-based concentration, leaf N
concentration (LNC, g g\selectlanguage{english}\textsuperscript{-1}) (Baret and Fourty, 1997).
However, it is surprising that the estimation of SLN is still rare
(Berger et al., 2020) whereas there are many studies regarding the
prediction of LNC from remote sensing images (e.g., Moharana and Dutta
(2016); Raj et al. (2021)). Very few studies have compared predictions
of SLN and LNC. For instance, Ecarnot et al. (2013) showed that the
prediction of LNC in wheat leaf samples collected from a broad range of
genotypes (wild and cultivated forms) had better accuracy than that of
SLN. However, Li et al. (2018) found that SLN in rice and wheat had
better correlation than LNC with the determined features in the
shortwave infrared region (1000 to 2500 nm). Given that these few
studies already showed inconsistencies, predictions of SLN and LNC
should be further evaluated and compared, especially across various crop
species.

On the other hand, SLN can be calculated from LNC, using the leaf
thickness parameter specific leaf weight (SLW, g m\selectlanguage{english}\textsuperscript{-2})
(Baret and Fourty, 1997), or its reciprocal, specific leaf area (SLA,
m\textsuperscript{2} g\selectlanguage{english}\textsuperscript{-1}). This implies that, while
SLN can be directly predicted, it can also be indirectly estimated based
on the prediction of LNC and SLW or SLA. Note that SLA is a parameter
that can inherently cause differences in photosynthetic N use efficiency
across species (Poorter and Evans, 1998); therefore, predicting SLA may
generate additional information. While it has been reported that SLN in
wheat was better predicted by the indirect approach than by the direct
method (Ecarnot et al., 2013), a comparison of performance of indirect
and direct approaches in predicting SLN is yet to be made for more
species. Similarly, the performance of indirectly predicted\emph{N}
\textsubscript{canopy} by upscaling SLN and LNC, compared with that of
the directly predicted \emph{N} \textsubscript{canopy}, should be
investigated as well. Kattenborn et al. (2019) indicated that the
area-based indicators of leaf pigment are supposed to be more suitable
for upscaling from leaf to canopy level, since upscaling area-based leaf
N only requires an estimate of the canopy state variable leaf area index
(LAI), as is done in crop models (Kropff et al., 1994; Yin and Struik,
2017). Nevertheless, the prediction of area- and mass-based leaf N for
upscaling from leaf to canopy level need to be further quantified.

Methodologies relating to N prediction from remote sensing have been
developed since the pioneering work by Thomas and Oerther (1972).
Generally, predicting methods can be classified into four categories:
parametric regression methods like methods based on vegetation indices
(VIs), nonparametric regression methods including linear and nonlinear
regression algorithms, physical methods like inversion of radiative
transfer models, and hybrid regression methods by combining physically
based methods with nonparametric regression methods (Verrelst et al.,
2019). Nonparametric regression methods, which explore the direct link
between target traits and the given spectral data, are receiving more
attention than the other three methods in the recent decade (Berger et
al., 2020). Although regression algorithms like Artificial Neural
Networks (ANN) have been employed in recent studies (Liu et al., 2016;
Yao et al., 2015), deep learning (DL)-based regression methods, such as
Deep Neural Network (DNN) and Convolution Neural Network (CNN), are
still under-utilized for crop N prediction based on canopy-level
hyperspectral reflectance (Fu et al., 2020). Given that DNN has shown
more potential than other regression methods in combining different
types of features, like canopy spectral, VIs and texture information,
for predicting soybean yield (Maimaitijiang et al., 2020), predicting
leaf and canopy N by DL-based regression algorithms should be explored.

Spectral and textural features are fundamental pattern elements in
imagery interpretation. The full spectrum has been widely used in
chemometrics (Atzberger et al., 2010), while the spectrum within visible
(VIS, 400 to 700 nm) and near infrared (NIR, 800 to 1300 nm) regions are
frequently reported for crop N estimation (Homolova et al., 2013). For
instance, as a chlorophyll molecule contains four N atoms, there is an
association between N supply and reflectance of the visible (400 to 700
nm) spectrum and also the so-called red-edge, located between VIS and
NIR and defined as the position of the sharp change in leaf reflectance
between 680 to 750 nm (e.g. Horler et al., 1983; Berger et al., 2020).
Serbin et al. (2012) suggested that visible and NIR spectra data could
be promising raw data to establish the robust calibration that allows to
infer some leaf parameters such as LNC and its temporal variation.
Spectral information has also been widely used in numerous VIs. While
spectral features describe the variations in various bands of an
electromagnetic spectrum, textural features contain the information
about the spatial characteristics of canopy architecture within a band
(Colombo, 2003; Haralick et al., 1973). Fusing canopy texture
information together with spectral features is gaining momentum in
phenotyping crop traits such as LAI (Liu et al., 2021), biomass (Zheng
et al., 2018b), and yield (Maimaitijiang et al., 2020). Zheng et al.
(2018a) showed that LNC in rice was better predicted after incorporating
texture information into VIs by using stepwise multiple linear
regression. Thus, texture features should also be taken into
consideration in predicting SLN and \emph{N} \textsubscript{canopy}.
Especially, taking advantage of high spatial resolution of the
UAV-acquired hyperspectral images (the ground pixel size is usually less
than a meter), texture information is supposed to be one type of the
important features in site-specific field N management.

In this study, the prediction of area- and mass-based leaf N traits from
hyperspectral images will be conducted by combining canopy spectral, VIs
and texture information by nonparametric regression algorithms for three
major crops (rice, wheat, maize). Our objectives are: 1) to explore the
utilization of the combinations of different feature types and
nonparametric regression algorithms in the prediction of leaf N traits
at leaf level, SLN and LNC, and at canopy level,\emph{N}
\textsubscript{canopy}, in different crop species; 2) to compare the
performance in estimating \emph{N} \textsubscript{canopy} between
directly predicted \emph{N} \textsubscript{canopy} and its values
upscaled from SLN and LNC; and 3) to identify the most robust
nonparametric regression algorithms and the most effective pathways
(direct vs. indirect) that can be applied in obtaining crop N
information of major crops. Achieving these objectives would help
monitor crop N status that can be linked with crop models for more
accurately predicting crop growth and guide N-fertilizer management in
the context of sustainable precision agriculture.

\textbf{2. Materials \& Methods}

\emph{2.1 Experimental design}

Field experiments with different N rates from deficient to excessive
were conducted in China: rice experiment was in Chongming, Shanghai,
while maize and winter wheat experiments were in Luohe and Zhoukou,
respectively, Henan province (Fig. 1). Treatments for each experiment
were arranged as a randomized block design. There were four replications
(four blocks) in the rice experiment, and within each block, six N
rates, varying from 0 to 320 kg N ha\textsuperscript{-1}, were applied
to rice (cv. Nanjing 46), planted on 4 June 2020 with a row spacing of
20 cm and a within-row plant spacing of 2-3 cm. The plot size was 6 x 30
m. Experiments of maize (cv. Zhengdan 958) and winter wheat (cv. Bainong
4199) were designed with eight blocks, and in each block seven N rates,
varying from 0 to 400 kg N ha\textsuperscript{-1}, were applied. Each
plot of maize was 10 x 20 m and each plot of wheat was 9 x 18 m (Fig.
1). Maize was sown on 9 June 2020 with 60 cm row spacing and 25 cm plant
spacing in the row. Winter wheat was planted after harvesting maize on
24 October 2020 with a row spacing of 21 cm and a within-row plant
spacing of 1-2 cm. Urea N fertilizer (N, 46\%) was split-applied
according to the rate and the time schedule described in Table S1. Based
on the local practice, for each experiment, sufficient phosphate (112.5,
120 and 75 kg P\textsubscript{2}O\textsubscript{5}ha\textsuperscript{-1}
for rice, maize and winter wheat, respectively) and potash (112.5, 120
and 105 kg K\textsubscript{2}O ha\textsuperscript{-1} for rice, maize
and winter wheat) fertilizers were applied to prevent phosphorus and
potassium deficiencies. Irrigation, and pest, disease and weed control
were the same for all treatments within a crop species and followed
local standard practices. Figure 2 presents a flow chart detailing the
overall procedure used in this study. The acronyms of the targeted leaf
traits at the leaf and canopy level are summarized in Table 1.

\emph{2.2 Data acquisition}

\emph{2.2.1 Canopy leaf trait measurements}

Crops were destructively sampled from all experimental plots on six
dates (Table 2). At each sampling date, aboveground plants were cut
within an area of 2.25, 2.4, and 1.0 m\textsuperscript{2} in each plot
for rice, wheat and maize, respectively. The total fresh samples were
weighted immediately and ca. 20\% of the biomass was used as subsamples
to be dissected into component plant parts, including green leaves,
stems, and grains. Yellow leaves were not included. LAI was measured on
the fresh green leaves using a LI-3100C Area Meter (Li-Cor, Lincoln, NE,
USA). Then, green leaves were weighed after being oven-dried at
70\textsuperscript{o}C to constant weight. All green leaf samples were
mixed and ground, and then stored for chemical testing. LNC, expressed
on the basis of leaf dry weight, was determined by the Micro-Keldjahl
method. \emph{N} \textsubscript{canopy} was calculated as the product of
LNC and leaf weight per unit ground area. SLW was calculated as the
ratio of leaf weight to LAI and SLA was calculated as 1/SLW. SLN was
calculated as the product of LNC and SLW. Data records of wheat at
maturity were excluded in this study, as there were no green leaves
remaining at that time.

\emph{2.2.2 Canopy reflectance measurements}

Canopy reflectance data were obtained before each field destructive
sampling by a Cubert S185 hyperspectral snapshot camera (Cubert GmbH,
Ulm, Baden-Wu\selectlanguage{english}rttemberg, Germany). The hyperspectral camera was equipped
with a DJI Ronin-MX three-axis gimbal stabilizer and installed on a DJI
M600 PRO hexacopter with global positioning system (GPS) and inertial
navigation system modules (DJI, Shenzhen, China). The gimbal stabilizer
ensured that the view angle of the camera was constant and acquired the
nadir images. The hyperspectral camera captures 125 spectral bands in
the range of 450-950 nm with a sampling interval of 4 nm. The light is
split into two beams after passing through the camera lens. 80\% of the
entire light entering the hyperspectral camera creates a 50\selectlanguage{ngerman}×50 pixels
hyperspectral cube with a 12-bit dynamic range and the remaining 20\%
enters the panchromatic camera to create a panchromatic image with a
resolution of 1000×1000 pixels (e.g., Aasen et al., 2015; Lu et al.,
2020). After pan-sharpening the hyperspectral cube to the resolution of
panchromatic image by the Cube-Pilot software (Cubert GmbH, Ulm,
Baden-Wu\selectlanguage{english}rttemberg, Germany), hyperspectral images with a size of
1000\selectlanguage{ngerman}×1000 pixels can be generated.

The flight campaigns were performed between 10 a.m. and 2 p.m. in
consistent weather conditions (cloudless or heavy cloud) to minimize
changes in illumination. The hyperspectral camera was calibrated by a
white and black board before flying. The flight height was 60 m,
resulting in a spatial resolution of ca. 2 cm, and the flying speed was
fixed at 6 m s\textsuperscript{-1}. The hyperspectral images were
created automatically at a sampling time interval of 1 ms and the
forward and side overlaps were set to 80\% and 60\%, respectively, under
the control of a connected microcomputer. The hyperspectral images were
orthographically stitched by the Agisoft PhotoScan software (Agisoft
LLC, St. Petersburg, Russia) based on GPS coordinates or image textures.
Finally, the region of interest was drawn from the sampling area on the
obtained hyperspectral ortho-images. The mean spectrum of the
destructive sampling area was used as the corresponding reflectance of
each sample. The bands beyond 902 nm and below 470 nm were dropped in
the later data analysis, due to the low spectral quality (Lu et al.,
2020).

\emph{2.3} \emph{Features collections for leaf traits prediction}

\emph{2.3.1 Canopy spectral features and vegetation indices}

The raw bands from hyperspectral images were used as canopy spectral
features. Additionally, a set of VIs was selected for predicting leaf
traits. In our study, 37 narrowband hyperspectral VIs were collected, in
which 6 were directly related to N, 16 were related to chlorophyll, and
15 were related to canopy traits like biomass, coverage or LAI (Table
S2). One more red-edge position was added in the list of VIs (Table S2),
which was regressed by the inverted Gaussian method (Miller et al.,
1990). The wavelengths with the sampling interval of 4 nm in our study
were linearly interpolated to 1 nm to match the needs of calculation of
hyperspectral VIs.

\emph{2.3.2 Canopy texture information extraction}

Texture information from each hyperspectral band was extracted by the
commonly used grey level co-occurrence matrix algorithm (GLCM) (Haralick
et al., 1973). Eight GLCM-based texture features, including mean,
variance, homogeneity, contrast, dissimilarity, entropy, second moment
and correlation, were computed using the ENVI 5.2 software (Exelis
Visual Information Solutions, Boulder, Colorado, USA). To avoid
complexity of computation, only four bands, 470, 550, 638, and 850 nm
(for blue, green, red, and NIR bands, respectively), were selected here
for canopy texture information extraction.

\emph{2.3.3 Crop development stage}

As leaf traits were measured at various dates during crop growth and
these traits varied in time, we considered to include crop development
stage as a co-predictor in nonparametric regression algorithms.
Development stage was simulated by the crop growth simulation model
GECROS (Yin and Struik, 2017), in which the development stage at
seedling emergence, flowering and maturity were denoted as dimensionless
values 0.0, 1.0 and 2.0, respectively, and the effect of temperature
fluctuations on rate of crop development was taken into account.

\emph{2.4 Nonparametric regression algorithms}

Commonly used linear nonparametric regression algorithms like Partial
Least Squares Regression (PLSR), two machine learning algorithms
including Support Vector Regression (SVR) and Random Forest Regression
(RFR), and two DL-based algorithms DNN and CNN were implemented in the
canopy leaf traits predictions (Fig. 2). The prepared feature
information, including canopy reflectance (Ref), hyperspectral VIs,
texture information (Tex), and development stage (DS), was selectively
assembled and then compressed into a one-dimensional vector as the
feature set (Table 3). Random assignment of instances was used for
splitting the training and testing data for each model, in which 75\%
data at each growing stage was randomly selected and pooled in the
training dataset and the remaining 25\% was used for independent
testing. Thus, the full-growth-stage models were built on the training
set and validated on the testing set. All data analysis and model
training were conducted in the Python environment. Regression models
were implemented relying on the package of scikit-learn (0.24.1)
(Pedregosa et al., 2011) and TensorFlow (2.5) (Abadi et al., 2015) in
Python. Table S3 gives the specific properties and numerical settings of
the hyperparameters for each regression algorithms. \emph{k} -fold cross
validated \emph{RMSE} was minimized to tune the pivotal hyperparameters
in machine learning models.

\emph{2.4.1 Partial Least Squares Regression (PLSR)}

PLSR is characterized by the ability to perform regression modeling even
when the independent variables have severe multiple correlations. PLSR
also allows regression modeling even when there are fewer sample points
than given variables, thereby allowing all original independent
variables being included in the final model (Geladi and Kowalski, 1986).
The only hyperparameter in PLSR optimized in this study was the number
of potential components (``n\_components'', Table S3).

\emph{2.4.2 Support Vector Regression (SVR)}

SVR has unique advantages in the case of small samples as well as
nonlinear and high-dimensional inputs (Drucker et al., 1997). It
improves the predictability by mapping low-dimensional samples into
high-dimensional space and thus the non-linear inputs can be linearly
separated by using a kernel function. SVR is efficient in finding sample
information to achieve the best compromise between model complexity and
learning ability.

\emph{2.4.3 Random Forest Regression (RFR)}

RFR is a robust ensemble learning technique able to handle large numbers
of input variables. RFR combines a large set of decision trees (Breiman,
2001). Together with the number of trees, tree traits and the number of
input features can be optimized to get the best model (Table S3).

\emph{2.4.4 Artificial Neural Networks (ANNs)}

Normally, an ANN is composed of an input layer, several hidden layers
and an output layer and each layer contains a number of neurons. In this
study, the fully connected feedforward DNN is based on simply increasing
the depth (number of layers) of ANNs (Längkvist et al., 2014) (Fig.
S1a). Fully connected 1-D CNN with several layers of convolution and
pooling was designed as well (Fig. S1b). The stacking multiple layers
are able to extract higher-order feature information (Längkvist et al.,
2014). The optimum composition of hidden layers was determined by the
minimum value of \emph{RMSE} in validation dataset, while the number of
neurons in each layer was asserted beforehand. Herein, the selected
activation function for hidden layers was the Rectified Linear Unit with
the form of f(z) = max(0, z) (LeCun et al., 2015). The weights of model
neurons were initialized by the initialization method of He et al.
(2015) and then updated by applying the gradient descent algorithm of
the Adam optimizer. A reduced learning rate on plateau and early
stopping were implemented as well to prevent overfitting.

\emph{2.5 Model performance evaluation}

The performances of all models were evaluated by the results in the
testing sets (unless specified), with the coefficient of determination
(\emph{R} \textsuperscript{2}) and the root mean square error
(\emph{RMSE} ) with the following equation:

\begin{equation}
R^{2}=1-\frac{\sum_{i\ =\ 1}^{n}{(y_{i}-{\hat{y}}_{i})}^{2}}{\sum_{i\ =\ 1}^{n}{(y_{i}-\overset{\overline{}}{y})}^{2}}\nonumber \\
 \end{equation}\begin{equation}
RMSE=\sqrt{\frac{1}{n}\sum_{i\ =\ 1}^{n}{(y_{\text{\ i}}-{\hat{y}}_{i})}^{2}}\nonumber \\
 \end{equation}

where \({\hat{y}}_{i}\) is a predicted value, \emph{y}
\textsubscript{i}is a measured value, \(\overset{\overline{}}{y}\) is the average
value of measured values across the whole growing season, and \emph{n}
is the number of measurements.

Additionally, the normalized \emph{RMSE} (\emph{NRMSE} ) was applied
here as the metric of model performance evaluation in the needs of the
comparison among crop species or among leaf traits, calculated by:

\begin{equation}
NRMSE=\ \frac{\text{RMSE}}{\overset{\overline{}}{y}\ }\nonumber \\
 \end{equation}

\textbf{3. Results}

\emph{3.1 Canopy spectral reflectance and canopy and leaf N traits}

Differences in canopy reflectance were observed across growth stages in
the three crop species and the change tended to be similar in rice and
wheat (Fig. 3a-c). Values of SLN in rice and wheat became lower with the
progress of the growth stage, but SLN in maize even increased at
maturity (Fig. 3d), which might be caused by the rapid decline in LAI
associated with senescence of the upper leaves while the cob leaves
remained green (Fig. S2). Values of LNC decreased from the tillering
stage of rice and wheat or the early stem-elongating stage of maize
onwards (Fig. 3e). Measured \emph{N} \textsubscript{canopy} in both rice
and wheat reached the peak at the stem-elongating stage and then
decreased until maturity, while the highest values of\emph{N}
\textsubscript{canopy} in maize occurred at flowering (Fig. 3f). Unlike
in rice and wheat, there was no significant difference in measured SLN,
LNC and \emph{N} \textsubscript{canopy} between treatments in maize
(results not shown), presumably because the residual N supply from soil
was very high.

\emph{3.2 Correlograms of collected features with respect to leaf and
canopy N traits}

Among the three crops, the correlation coefficients (\emph{r} )
of\emph{N} \textsubscript{canopy} with canopy reflectance changed in a
similar trend and slightly decreased when wavelength was between 680 nm
and 710 nm, which belongs to the red-edge region (Fig. S3). SLN and LNC
in rice showed weaker correlations than \emph{N}
\textsubscript{canopy}with canopy reflectance in the NIR region and the
\emph{r} ranged from 0.15 to 0.27 and -0.06 to 0.11, respectively (Fig.
S3a). Within the collected VIs, the highest values of \emph{r} for SLN,
LNC and\emph{N} \textsubscript{canopy}, with VIs were up to 0.77, 0.86
and 0.82 in rice, and 0.72, 0.93 and 0.95 in wheat (Fig. S4a-f). In
maize, LNC displayed a weak correlation with collected VIs and the
\emph{r} ranged from -0.37 to 0.40 (Fig. S4g-i).

Regarding correlations with the texture information, leaf N traits were
more correlated with the features extracted from blue, green and red
bands than those from NIR in rice (Fig. S5a-d), while the higher
correlations tended to be achieved from the bands of red and NIR in
wheat and maize (Fig. S5e-l). The LNC in maize was highly correlated
with the texture information from the NIR band and the highest value
of\emph{r} was up to 0.81 (Fig. S5l).

\emph{3.3 Performance of nonparametric regression algorithms}

For SLN and LNC, PLSR and SVR models tended to improve their performance
in rice and wheat when incorporating more features and the predicted LNC
agreed with its measurements better than the predicted SLN among three
crop species (Figs 4a-f, S7). For SLN in rice and wheat from PLSR and
SVR, \emph{NRMSE} decreased after incorporating VIs and Tex into the
feature set of Ref, whereas \emph{NRMSE} in maize tended to increase
(Fig. 4a-c). For LNC, the performance of PLSR and SVR hardly changed in
wheat while incorporating different feature types, but improved slightly
in maize (Fig. 4e-f). For the predicted SLN and LNC, RFR tended to
perform better than DNN among three crop species, albeit worse than PLSR
and SVR (Fig. 4a-f). Although there was a chance that CNN performed
better than other regression algorithms (Fig. 4a), its performance
lacked the consistency and tended to become worse when incorporating
more feature types into the model (Fig. 4b-f).

For the predictions of \emph{N} \textsubscript{canopy}, PLSR and SVR
always performed better than others and their performance tended to be
consistently improved in the testing dataset when incorporating
different types of features among three crop species (Fig. 4g-i). In
detail, \emph{NRMSE} of predicted \emph{N} \textsubscript{canopy} in
rice from PLSR decreased from 0.352 to 0.303 after incorporating VIs
into the feature set of Ref and hardly changed thereafter, while that of
SVR further decreased to 0.291 after incorporating the feature of Tex
(Fig. 4g). Also in wheat and maize, no increment of model performance
was obtained while further incorporating the DS (Fig. 4h-i). Due to the
increased complexity of their algorithms, RFR, DNN and CNN models were
more likely to be overfitted in the training set (Fig. S6g-i) and their
performance for \emph{N} \textsubscript{canopy} of the testing set in
different crops tended to be highly variable while incorporating
different types of features (Fig. 4g-i). For instance, after
incorporating VIs into the feature set of Ref, \emph{NRMSE} of
predicted\emph{N} \textsubscript{canopy} in rice from DNN decreased from
0.345 to 0.305 and then increased to 0.388 after further incorporating
the DS (Fig. 4g).

\emph{3.4 Performance in modelling canopy and leaf N by direct and
indirect predictions}

The best performing regression algorithm for predicting SLW and SLA
changed among crop species, and in general, the predicted SLA agreed
with its measurements better than SLW (Fig. 5, S8). The incorporation of
feature sets also improved the predictions of SLW and SLA by PLSR and
SVR in three crops (Fig. 5). Among different regression algorithms, PLSR
and SVR performed better than others in rice (Fig. 5a, d), while DNN and
CNN performed better in wheat (Fig. 5b, e). In maize, the predictions of
SLW from RFR agreed with the measurements better, while PLSR and SVR
performed better in the predictions of SLA (Fig. 5c, f).

As SLA was better predicted than SLW, the indirect predictions of SLN
from SLA, SLN\textsubscript{sla}, are only presented here (Table 4).
Compared with the directly predicted SLN (SLN\textsubscript{dir}),
SLN\textsubscript{sla} tended to agree better with the measurements, in
which \emph{NRMSE} decreased from 0.241, 0.254, and 0.189 to 0.240,
0.244 and 0.183, while \emph{R} \textsuperscript{2} increased from
0.699, 0.557 and 0.540 to 0.725, 0.583 and 0.611, for rice, wheat and
maize, respectively. Both direct and indirect predictions from PLSR were
better than those from SVR. Regarding the utilized feature sets, in rice
and wheat, both predicted SLN agreed better with measurements while
using the feature set of RefVIsTex. However, in maize, better
performance was achieved when using the feature set of Ref only.

To upscale the predicted SLN to \emph{N} \textsubscript{canopy}, LAI was
predicted well using the feature set of Ref or RefVIsTex while applying
the regression algorithms of PLSR and SVR (Figs S9-S10). The indirect
predictions of \emph{N} \textsubscript{canopy,SLNdir} and\emph{N}
\textsubscript{canopy,SLNsla} were estimated from SLN\textsubscript{dir}
and SLN\textsubscript{sla}, respectively. Using more features from Ref
to RefVIsTex universally improved directly or indirectly predicted
\emph{N} \textsubscript{canopy}, except for the slight decrease in the
indirect predictions from SVR in wheat and maize (Fig. 6). Therefore,
for further analysis, we only show the predictions from applying the
feature set of RefVIsTex. Within the comparison between direct and
indirect predictions,\emph{N} \textsubscript{canopy,dir} in wheat agreed
with the measurements better than others, while in rice and
maize\emph{N} \textsubscript{canopy} tended to be better predicted via
the indirect method (\emph{N} \textsubscript{canopy,SLNdir}). For
instance, compared with \emph{N} \textsubscript{canopy,dir} from PLSR,
\emph{NRMSE}of \emph{N} \textsubscript{canopy,SLNdir} in rice decreased
from 0.307 to 0.286 (Fig. 6a). Between the two indirect predictions, the
predicted\emph{N} \textsubscript{canopy,SLNdir} generally had a lower
NRMSE in the three crop species than the predicted\emph{N}
\textsubscript{canopy,SLNsla} (Fig. 6).

\emph{3.5 Predicted N} \textsubscript{canopy} \emph{along stages of the
whole season}

The predicted \emph{N} \textsubscript{canopy} values in rice, wheat and
maize were mapped in the whole experimental area and illustrated for
different growing stages (Figs 7, S11-S12). Taking rice as an example,
in line with the field measurements (Fig. 3f), the highest\emph{N}
\textsubscript{canopy} occurred at stem elongation and remarkable
differences were shown between experimental plots (Fig. 7b). Such
differences among treatments gradually narrowed after stem elongation
(Fig. 7b-f). A similar trend was observed in mapped\emph{N}
\textsubscript{canopy} of wheat (Fig. S11), in agreement with its field
measurements (Fig. 3f). In maize, the differences in\emph{N}
\textsubscript{canopy} among growing stages were predicted well (Fig.
S12). The hardly observed differences of predicted\emph{N}
\textsubscript{canopy} between experimental plots also agreed with the
fact that there was no significant difference in measured\emph{N}
\textsubscript{canopy} between treatments (Figs 3f, S12). Moreover, the
differences in crop growth status within an experimental plot was also
noticeable (Figs 7, S11-S12).

\textbf{4. Discussion}

Leaf and canopy N contents across growing stages for three major field
crops were predicted from UAV based hyperspectral image features, by
adopting different nonparametric regression algorithms and predicting
pathways (direct vs. indirect). The mapped\emph{N}
\textsubscript{canopy} across successive growth stages demonstrates the
potential utilization of the prediction models.

\emph{4.1 Comparison of direct and indirect predictions}

As SLA and SLW are reciprocals of each other, the difference between
them has been hardly noticed. But there are still some debates about
predicting them from remote sensing images. For instance, SLW could be
predicted well and the reported \emph{R} \textsuperscript{2} values were
ca. 0.90 (Ecarnot et al., 2013; Silva-Perez et al., 2018). However, Ali
et al. (2017) indicated that SLA tended to be more correlated with leaf
reflectance than SLW, whereas Hussain et al. (2020) showed that the
predictions of SLW matched its measurements better than the predictions
of SLA did. With crop growth, our data range of SLW tended to become
wider than that of SLA in three crop species (results not shown) whereas
the differences of canopy reflectance between treatments tended to be
diminished (Fig. 3a-c), which might contribute to the better predicted
SLA than that of SLW (Figs 5, S8).

Both SLN and LNC are common leaf level indicators to monitor leaf N. As
the components in whole leaf thickness accounts for the light reflection
or absorption, SLN is supposed to be better predicted than LNC (Baret
and Fourty, 1997). However, our results showed that the predicted LNC
agreed with its measurements better than the predicted SLN did (Figs
4a-f, S7), in line with the previous results of Ecarnot et al. (2013)
and Li et al. (2018) using measured raw reflectance spectra. Under N
shortage, leaf weight increases because of accumulation of starch and
cell wall material (McDonald et al., 1986; Terry et al., 1983) and thus
SLA or SLW varies significantly (Jones and Hesketh, 1980). As leaf
expansion is limited, the change of leaf N status is reflected less in
SLN than in LNC. Moreover, as SLN is normally determined from LNC and
SLA, meaning that it requires more measurement steps to determine SLN
than to determine LNC, data for SLN must contain more measurement noise
than for LNC. Due to the better predicted LNC and SLA, the indirectly
predicted SLN\textsubscript{sla} tended to match measurements than
directly predicted SLN\textsubscript{dir} (Table 4). However, when
upscaling to canopy level, the indirectly predicted\emph{N}
\textsubscript{canopy} from SLN\textsubscript{sla} became worse than
that from SLN\textsubscript{dir} (Fig. 6). As SLN\textsubscript{sla} was
estimated from predicted LNC and SLA, this result supported the
assertion by Kattenborn et al. (2019) that area-based leaf traits, like
SLN, are more suitable for upscaling from leaf to canopy level than
mass-based leaf traits, like LNC, as less regression error was
introduced. The indirect predictions of\emph{N}
\textsubscript{canopy,SLN} in rice and maize tended to agree with
measurements than the directly predicted\emph{N}
\textsubscript{canopy,dir} (Fig. 6). Even though the indirect methods
achieved better prediction in our results (Table 4, Fig. 6), as more
regression processes were introduced, the results might be more
uncertain (Malenovsk\selectlanguage{ngerman}ý et al., 2019). Thus, the uncertainty of the
regression processes should be further investigated.

\emph{4.2 Contribution of feature types in canopy and leaf nitrogen
prediction}

Fusing different types of features contributes to plant N traits
prediction. Besides the raw bands, VIs have also been considered as
supplementary information serving as canopy spectral features
(Maimaitijiang et al., 2020). There were tight correlations between VIs
and leaf N traits (Fig. S4). However, with Ref features used as the
baseline, adding VIs to the model did not always yield better prediction
(Fig. 4), which might be caused by the introduced noisy information from
VIs and/or the correlations between Ref and VIs features. Due to the
different changing rate in crop biomass accumulation or N uptake between
before and after heading, the predictability using hyperspectral VIs
could be significantly influenced (Li et al., 2010; Yu et al., 2013). On
the other hand, as VIs are normally derived from several bands (Table
S2), the information provided from VIs might be limited compared with
that from Ref in the full spectrum (Wang et al., 2021). From the
extracted canopy texture features, the additional information associated
with spatial canopy architecture and structure characteristics is
potentially provided (Colombo, 2003). The fusion of canopy texture
information benefits the predictions not only of the canopy traits like
LAI and biomass (Liu et al., 2021; Zheng et al., 2018b), but also of
crop N status like leaf chlorophyll and plant aboveground N content
(Qiao et al., 2020; Zheng et al., 2018a). Similar to these previous
studies, our results also showed that fusing canopy texture information
contributed to the prediction of leaf N traits, especially for the
regression models based on PLSR and SVR (Table 4, Figs 4, 6).

Although both measured canopy reflectance and leaf N traits changed
across growth stages (Fig. 3), the performance of the regressing models
in predicting leaf N traits hardly improved after directly incorporating
DS into the models (Fig. 4). The feature of DS might be utilized in a
more proper way. For instance, Li et al. (2022) found that the
coefficient values (slope and intercept) of ordinary least squares
regression of aboveground biomass in wheat with VIs had a strong
relationship with phenological stages. With the calibrated slopes and
intercepts at different stages, aboveground biomass can be well
estimated over the entire growing season (Li et al., 2022). Moreover,
the appropriate digital indicator of crop growth stages is of importance
as well. The simulated DS in this study is only one way of quantifying
development stages, which is calculated from hourly temperatures, using
a bell-shaped temperature response function capturing base, optimum and
ceiling temperatures (Yin and van Laar, 2005). It is similar to growth
stages with the Zadoks scale, using a numeric system between 0 and 100
representing stages from sowing to harvest (Zadoks et al., 1974). Li et
al. (2022) showed that compared with the thermal-based digital indicator
of growth stages, growth stages with the Zadoks scale performed better
in the prediction of aboveground biomass of wheat.

\emph{4.3 Characteristics of regression algorithms in canopy and leaf
nitrogen prediction}

The performance of five popular nonparametric regression algorithms were
evaluated for N traits in three major field crops in this study. Among
these methods, PLSR used the least number of hyperparameters and SVR
next to it, compared with RFR, DNN and CNN that have many
hyperparameters (Table S3) and thus, in principle, should have the more
flexibility in the prediction of leaf N traits. However, our results
showed that PLSR and SVR tended to be more stable and PLSR was likely to
achieve the best model performance in the prediction of\emph{N}
\textsubscript{canopy}, as well as SLN and LNC (Figs 4, S7), in line
with the results in the prediction of LNC in wheat (Yao et al., 2015).
This might be caused by the limited size of our dataset, as PLSR is
known to be more effective than others, when the number of samples is
smaller than the number of variables (Geladi and Kowalski, 1986). With
nearly 1000 samples, DNN based yield prediction models systematically
performed better than PLSR and SVR based models while increasing feature
types (Maimaitijiang et al., 2020). Moreover, with more than 7000
samples from different years and locations, CNN provided higher accuracy
in LNC prediction in grass (Pullanagari et al., 2021). Thus, as the
numerous combinations of hyperparameters in RFR and of hidden layers and
neuro numbers in DNN and CNN have already been trialed in this study
(Table S3, Fig. S1), increasing the number of samples might be the
essential for improving the predictability of DNN and CNN.

5. \textbf{Conclusions}

We evaluated the prediction of area- and mass-based leaf N traits using
different regression algorithms and feature sets extracted from
hyperspectral images for three major crops, rice, wheat and maize. Our
results showed that for the prediction of N traits at leaf level, SLN
and LNC, and at canopy level \emph{N} \textsubscript{canopy} using the
limited size of the dataset, regression algorithms of PLSR and SVR
tended to perform better than others, and the incorporation of different
types of features, like canopy spectral, VIs and texture information,
helped improve model performance. The regression algorithm of PLSR
performed slightly better than SVR in the prediction of\emph{N}
\textsubscript{canopy}. Predicting\emph{N} \textsubscript{canopy} in an
indirect way by upscaling SLN contributed to the further improvement of
prediction of\emph{N} \textsubscript{canopy}, compared with the directly
predicted\emph{N} \textsubscript{canopy}, although the regression
process might be more uncertain. These results provide useful
information for the next-step work that will couple the real-time
accurately retrieved leaf N traits into dynamic crop models so as to
predict the real-time growth status more accurately, given that canopy
photosynthesis is directly linked with crop N status and primarily
determines crop growth rates. This would better enable crop models as a
decision-making tool to guide farmers for in situ field N management
targeting the maximal yield or resource use efficiency.

\textbf{Appendix A. Supplementary data}

Supplementary tables and figures related to this article can be found in
the supplementary material.

\textbf{References}

Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro. Craig,
Corrado, G. S., Davis, A., Dean, J., Devin, M., Ghemawat, S.,
Goodfellow, I., Harp, A., Irving, G., Isard, M., Jozefowicz, R., Jia,
Y., Kaiser, L., Kudlur, M., Levenberg, J., Mané, D., Schuster, M.,
Monga, R., Moore, S., Murray, D., Olah, C., Shlens, J., Steiner, B.,
Sutskever, I., Talwar, K., Tucker, P., Vanhoucke, V., Vasudevan, V.,
Viégas, F., Vinyals, O., Warden, P., Wattenberg, M., Wicke, M., Yu, Y.,
\& Zheng, X. (2015). TensorFlow: A System for Large-Scale Machine
Learning. Software available from tensflow.org.

Ali, A. M., Darvishzadeh, R., Skidmore, A. K., \& van Duren, I. (2017).
Specific leaf area estimation from leaf and canopy reflectance through
optimization and validation of vegetation indices. \emph{Agricultural
and Forest Meteorology, 236} , 162-174.
doi:10.1016/j.agrformet.2017.01.015

Aasen, H., Burkart, A., Bolten, A., \& Bareth, G. (2015). Generating 3D
hyperspectral information with lightweight UAV snapshot cameras for
vegetation monitoring: From camera calibration to quality
assurance.\emph{ISPRS Journal of Photogrammetry and Remote Sensing, 108}
, 245-259. doi:10.1016/j.isprsjprs.2015.08.002

Atzberger, C., Guérif, M., Baret, F., \& Werner, W. (2010). Comparative
analysis of three chemometric techniques for the spectroradiometric
assessment of canopy chlorophyll content in winter wheat.\emph{Computers
and Electronics in Agriculture, 73} , 165-173.
doi:10.1016/j.compag.2010.05.006

Baret, F., \& Fourty, T. (1997). Radiometric estimates of nitrogen
status of leaves and canopies \emph{Diagnosis of nitrogen status in
crops} (pp. 201-227): Springer.

Beeckman, F., Motte, H., \& Beeckman, T. (2018). Nitrification in
agricultural soils: impact, actors and mitigation. \emph{Current Opinion
in Biotechnology, 50} , 166-173.

Berger, K., Verrelst, J., Féret, J.-B., Wang, Z., Wocher, M.,
Strathmann, M., Danner, M., Mauser, W., \& Hank, T. (2020). Crop
nitrogen monitoring: Recent progress and principal developments in the
context of imaging spectroscopy missions. \emph{Remote Sensing of
Environment, 242} , 111758. doi:10.1016/j.rse.2020.111758

Boote, K. J., Jones, J. W., Hoogenboom, G., \& Pickering, N. B. (1998).
The CROPGRO model for grain legumes \emph{Understanding options for
agricultural production} (pp. 99-128): Springer.

Breiman, L. (2001). Random forests. \emph{Machine learning, 45} , 5-32.

Colombo, R. (2003). Retrieval of leaf area index in different vegetation
types using high resolution satellite data. \emph{Remote Sensing of
Environment, 86} , 120-131. doi:10.1016/s0034-4257(03)00094-4

Davidson, E. A. (2009). The contribution of manure and fertilizer
nitrogen to atmospheric nitrous oxide since 1860. \emph{Nature
Geoscience, 2} , 659-662.

Drucker, H., Burges, C. J., Kaufman, L., Smola, A., \& Vapnik, V.
(1997). Support vector regression machines. In M. Mozer, J. Jordan, \&
T. Petscbe (Eds.), \emph{Neural information processing systems 9} (pp.
155-161). Cambridge, MA: MIT Press.

Ecarnot, M., Compan, F., \& Roumet, P. (2013). Assessing leaf nitrogen
content and leaf mass per unit area of wheat in the field throughout
plant cycle with a portable spectrometer. \emph{Field Crops Research,
140} , 44-50. doi:10.1016/j.fcr.2012.10.013

Evans, J. R. (1983). Nitrogen and photosynthesis in the flag leaf of
wheat (Triticum aestivum L.). \emph{Plant Physiology, 72} , 297-302.

FAO. (2020). \emph{World Food and Agriculture - Statistical Yearbook
2020} . Rome.

Fu, Y., Yang, G., Li, Z., Li, H., Li, Z., Xu, X., Song, X., Zhang, Y.,
Duan, D., Zhao, C., \& Chen, L. (2020). Progress of hyperspectral data
processing and modelling for cereal crop nitrogen
monitoring.\emph{Computers and Electronics in Agriculture, 172} ,
105321. doi:10.1016/j.compag.2020.105321

Geladi, P., \& Kowalski, B. R. (1986). Partial least-squares regression:
a tutorial. \emph{Analytica Chimica Acta, 185} , 1-17.

Haralick, R. M., Shanmugam, K., \& Dinstein, I. H. (1973). Textural
features for image classification. \emph{IEEE Transactions on systems,
man, and cybernetics} , 610-621.

He, K., Zhang, X., Ren, S., \& Sun, J. (2015). \emph{Delving deep into
rectifiers: Surpassing human-level performance on imagenet
classification} .

Homolová, L., Malenovský, Z., Clevers, J. G. P. W., García-Santos, G.,
\& Schaepman, M. E. (2013). Review of optical-based remote sensing for
plant trait mapping. \emph{Ecological Complexity, 15} , 1-16.
doi:10.1016/j.ecocom.2013.06.003

Horler, D. N. H., Dockray, M., \& Barber, J. (1983). The red edge of
plant leaf reflectance. \emph{International Journal of Remote Sensing,
4} , 273-288.

Hussain, S., Gao, K., Din, M., Gao, Y., Shi, Z., \& Wang, S. (2020).
Assessment of UAV-Onboard Multispectral Sensor for Non-Destructive
Site-Specific Rapeseed Crop Phenotype Variable at Different Phenological
Stages and Resolutions. \emph{Remote Sensing, 12} (3).
doi:10.3390/rs12030397

Jin, X., Kumar, L., Li, Z., Feng, H., Xu, X., Yang, G., \& Wang, J.
(2018). A review of data assimilation of remote sensing and crop
models.\emph{European Journal of Agronomy, 92} , 141-152.
doi:10.1016/j.eja.2017.11.002

Jones, J. W., \& Hesketh, J. D. (1980). Predicting leaf expansion. In J.
D. Hesketh \& J. W. Jones (Eds.), \emph{Predicting Photosynthesis for
Ecosystem Models. Volume II} (pp. 85-122). Boca Raton, FL: CRC Press.

Kattenborn, T., Schiefer, F., Zarco-Tejada, P., \& Schmidtlein, S.
(2019). Advantages of retrieving pigment content {[}\selectlanguage{greek}μ\selectlanguage{english}g/cm2{]} versus
concentration {[}\%{]} from canopy reflectance. \emph{Remote Sensing of
Environment, 230} . doi:10.1016/j.rse.2019.05.014

Khoury, C. K., Bjorkman, A. D., Dempewolf, H., Ramirez-Villegas, J.,
Guarino, L., Jarvis, A., Rieseberg, L. H., \& Struik, P. C. (2014).
Increasing homogeneity in global food supplies and the implications for
food security. \emph{Proc Natl Acad Sci U S A, 111} , 4001-4006.
doi:10.1073/pnas.1313490111

Kropff, M. J., Van Laar, H. H., \& Matthews, R. B. (1994). \emph{ORYZA1:
An ecophysiological model for irrigated rice production} . Wageningen:
DLO-Research Institute for Agrobiology and Soil Fertility.

L\selectlanguage{ngerman}ängkvist, M., Karlsson, L., \& Loutfi, A. (2014). A review of
unsupervised feature learning and deep learning for time-series
modeling. \emph{Pattern Recognition Letters, 42} , 11-24.
doi:10.1016/j.patrec.2014.01.008

LeCun, Y., Bengio, Y., \& Hinton, G. (2015). Deep learning.\emph{Nature,
521} , 436-444. doi:10.1038/nature14539

Lemaire, G., Jeuffroy, M.-H., \& Gastal, F. (2008). Diagnosis tool for
plant and crop N status in vegetative stage: Theory and practices for
crop N management. \emph{European Journal of Agronomy, 28} , 614-624.
doi:10.1016/j.eja.2008.01.005

Li, D., Wang, X., Zheng, H., Zhou, K., Yao, X., Tian, Y., Zhu, Y., Cao,
W., \& Cheng, T. (2018). Estimation of area- and mass-based leaf
nitrogen contents of wheat and rice crops from water-removed spectra
using continuous wavelet analysis. \emph{Plant Methods, 14} , 76.
doi:10.1186/s13007-018-0344-1

Li, F., Miao, Y., Hennig, S. D., Gnyp, M. L., Chen, X., Jia, L., \&
Bareth, G. (2010). Evaluating hyperspectral vegetation indices for
estimating nitrogen concentration of winter wheat at different growth
stages. \emph{Precision Agriculture, 11} , 335-357.
doi:10.1007/s11119-010-9165-6

Li, Z., Zhao, Y., Taylor, J., Gaulton, R., Jin, X., Song, X., Li, Z.,
Meng, Y., Chen, P., Feng, H., Wang, C., Guo, W., Xu, X., Chen, L., \&
Yang, G. (2022). Comparison and transferability of thermal, temporal and
phenological-based in-season predictions of above-ground biomass in
wheat crops from proximal crop reflectance data. \emph{Remote Sensing of
Environment, 273} , 112967. doi:10.1016/j.rse.2022.112967

Liu, H., Zhu, H., \& Wang, P. (2016). Quantitative modelling for leaf
nitrogen content of winter wheat using UAV-based hyperspectral
data.\emph{International Journal of Remote Sensing, 38} , 2117-2134.
doi:10.1080/01431161.2016.1253899

Liu, S., Jin, X., Nie, C., Wang, S., Yu, X., Cheng, M., Shao, M., Wang,
Z., Tuohuti, N., Bai, Y., \& Liu, Y. (2021). Estimating leaf area index
using unmanned aerial vehicle data: shallow vs. deep machine learning
algorithms. \emph{Plant Physiology, 187} , 1551-1576.
doi:10.1093/plphys/kiab322

Lu, J., Li, W., Yu, M., Zhang, X., Ma, Y., Su, X., Yao, X., Cheng, T.,
Zhu, Y., Cao, W., \& Tian, Y. (2020). Estimation of rice plant potassium
accumulation based on non-negative matrix factorization using
hyperspectral reflectance. \emph{Precision Agriculture, 22} , 51-74.
doi:10.1007/s11119-020-09729-z

Maimaitijiang, M., Sagan, V., Sidike, P., Hartling, S., Esposito, F., \&
Fritschi, F. B. (2020). Soybean yield prediction from UAV using
multimodal data fusion and deep learning. \emph{Remote Sensing of
Environment, 237} , 111599. doi:10.1016/j.rse.2019.111599

Malenovský, Z., Homolová, L., Luke\selectlanguage{polish}š, \selectlanguage{english}P., Buddenbaum, H., Verrelst, J.,
Alonso, L., Schaepman, M. E., Lauret, N., \& Gastellu-Etchegorry, J.-P.
(2019). Variability and Uncertainty Challenges in Scaling Imaging
Spectroscopy Retrievals and Validations from Leaves Up to Vegetation
Canopies. \emph{Surveys in Geophysics, 40} , 631-656.
doi:10.1007/s10712-019-09534-y

Marshall, M., \& Thenkabail, P. (2015). Advantage of hyperspectral EO-1
Hyperion over multispectral IKONOS, GeoEye-1, WorldView-2, Landsat ETM+,
and MODIS vegetation indices in crop biomass estimation. \emph{ISPRS
Journal of Photogrammetry and Remote Sensing, 108} , 205-218.
doi:10.1016/j.isprsjprs.2015.08.001

McDonald, A. J. S., Lohammar, T., \& Ericsson, A. (1986). Growth
response to step-decrease in nutrient availability in small birch
(Betula pendula Roth). \emph{Plant, Cell \& Environment, 9} , 427-432.

Miller, J. R., Hare, E. W., \& Wu, J. (1990). Quantitative
characterization of the vegetation red edge reflectance 1. An
inverted-Gaussian reflectance model. \emph{International Journal of
Remote Sensing, 11} , 1755-1773. doi:10.1080/01431169008955128

Moharana, S., \& Dutta, S. (2016). Spatial variability of chlorophyll
and nitrogen content of rice from hyperspectral imagery. \emph{ISPRS
Journal of Photogrammetry and Remote Sensing, 122} , 17-29.
doi:10.1016/j.isprsjprs.2016.09.002

Mulla, D. J. (2013). Twenty five years of remote sensing in precision
agriculture: Key advances and remaining knowledge gaps. \emph{Biosystems
Engineering, 114} , 358-371. doi:10.1016/j.biosystemseng.2012.08.009

Ohyama, T. (2010). Nitrogen as a major essential element of plants. In
T. Ohyama \& K. Sueyoshi (Eds.), \emph{Nitrogen Assimilation in
Plants}(pp. 1--18): Research Signpost.

Padilla, F. M., Gallardo, M., \& Manzano-Agugliaro, F. (2018). Global
trends in nitrate leaching research in the 1960--2017
period.\emph{Science of the Total Environment, 643} , 400-413.

Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B.,
Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V.,
Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., \&
Duchesnay, E. (2011). Scikit-learn: Machine learning in
Python.\emph{Journal of machine Learning research} , 2825-2830.

Peng, S., Cassman, K. G., \& Kropff, M. J. (1995). Relationship between
leaf photosynthesis and nitrogen content of field-grown rice in
tropics.\emph{Crop science, 35} , 1627-1630.

Poorter, H., \& Evans, J. R. (1998). Photosynthetic nitrogen-use
efficiency of species that differ inherently in specific leaf
area.\emph{Oecologia, 116} , 26-37.

Pullanagari, R. R., Dehghan-Shoar, M., Yule, I. J., \& Bhatia, N.
(2021). Field spectroscopy of canopy nitrogen concentration in temperate
grasslands using a convolutional neural network. \emph{Remote Sensing of
Environment, 257} , 112353. doi:10.1016/j.rse.2021.112353

Qiao, L., Gao, D., Zhang, J., Li, M., Sun, H., \& Ma, J. (2020). Dynamic
Influence Elimination and Chlorophyll Content Diagnosis of Maize Using
UAV Spectral Imagery. \emph{Remote Sensing, 12} (16).
doi:10.3390/rs12162650

Raj, R., Walker, J. P., Pingale, R., Banoth, B. N., \& Jagarlapudi, A.
(2021). Leaf nitrogen content estimation using top-of-canopy airborne
hyperspectral data. \emph{International Journal of Applied Earth
Observation and Geoinformation, 104} , 102584.
doi:10.1016/j.jag.2021.102584

Schr\selectlanguage{ngerman}öder, J. J., Neeteson, J. J., Oenema, O., \& Struik, P. C. (2000).
Does the crop or the soil indicate how to save nitrogen in maize
production?: Reviewing the state of the art. \emph{Field Crops Research,
66} , 151-164.

Serbin, S. P., Dillaway, D. N., Kruger, E. L., \& Townsend, P. A.
(2012). Leaf optical properties reflect variation in photosynthetic
metabolism and its sensitivity to temperature. \emph{Journal of
Experimental Botany, 63} , 489-502. doi:10.1093/jxb/err294

Silva-Perez, V., Molero, G., Serbin, S. P., Condon, A. G., Reynolds, M.
P., Furbank, R. T., \& Evans, J. R. (2018). Hyperspectral reflectance as
a tool to measure biochemical and physiological traits in wheat. \emph{J
Exp Bot, 69} (3), 483-496. doi:10.1093/jxb/erx421

Skiba, U. M. (2014). Nitrous oxide, climate change and
agriculture.\emph{CAB Reviews: Perspectives in Agriculture, Veterinary
Science, Nutrition and Natural Resources, 9} .
doi:10.1079/pavsnnr20149010

Terry, N., Waldron, L. J., \& Taylor, S. E. (1983). Environmental
influences on leaf expansion. In J. E. Dale \& F. L. Milthorpe
(Eds.),\emph{The growth and functioning of leaves} (pp. 179-205).
Cambridge: Cambridge University Press.

Thomas, J. R., \& Oerther, G. F. (1972). Estimating nitrogen content of
sweet pepper leaves by reflectance measurements. \emph{Agronomy Journal,
64} , 11-13.

Verrelst, J., Malenovský, Z., Van der Tol, C., Camps-Valls, G.,
Gastellu-Etchegorry, J.-P., Lewis, P., North, P., \& Moreno, J. (2019).
Quantifying Vegetation Biophysical Variables from Imaging Spectroscopy
Data: A Review on Retrieval Methods. \emph{Surveys in Geophysics, 40} ,
589-629. doi:10.1007/s10712-018-9478-y

Wang, D., Rianti, W., Gálvez, F., van der Putten, P. E. L., Struik, P.
C., \& Yin, X. (2022). Estimating photosynthetic parameter values of
rice, wheat, maize and sorghum to enable smart crop
cultivation.\emph{Crop and Environment, 1} (2), 119-132.
doi:10.1016/j.crope.2022.05.004

Wang, L., Chen, S., Li, D., Wang, C., Jiang, H., Zheng, Q., \& Peng, Z.
(2021). Estimation of Paddy Rice Nitrogen Content and Accumulation Both
at Leaf and Plant Levels from UAV Hyperspectral Imagery. \emph{Remote
Sensing, 13} , 2956. doi:10.3390/rs13152956

Weiss, M., Jacob, F., \& Duveiller, G. (2020). Remote sensing for
agricultural applications: A meta-review. \emph{Remote Sensing of
Environment, 236} , 111402.

Yao, X., Huang, Y., Shang, G., Zhou, C., Cheng, T., Tian, Y., Cao, W.,
\& Zhu, Y. (2015). Evaluation of Six Algorithms to Monitor Wheat Leaf
Nitrogen Concentration. \emph{Remote Sensing, 7} , 14939-14966.
doi:10.3390/rs71114939

Yin, X., \& Struik, P. C. (2017). Can increased leaf photosynthesis be
converted into higher crop mass production? A simulation study for rice
using the crop model GECROS. \emph{Journal of Experimental Botany, 68} ,
2345-2360. doi:10.1093/jxb/erx085

Yin, X., Struik, P. C., Romero, P., Harbinson, J., Evers, J. B., PE, V.
D. P., \& Vos, J. (2009). Using combined measurements of gas exchange
and chlorophyll fluorescence to estimate parameters of a biochemical C3
photosynthesis model: a critical appraisal and a new integrated approach
applied to leaves in a wheat (Triticum aestivum) canopy. \emph{Plant,
Cell and Environment, 32} , 448-464.
doi:10.1111/j.1365-3040.2009.01934.x

Yin, X., \& van Laar, H. H. (2005). \emph{Crop systems dynamics: an
ecophysiological simulation model for genotype-by-environment
interactions} . Wageningen, the Netherlands: Wageningen Academic
Publishers.

Yu, K., Li, F., Gnyp, M. L., Miao, Y., Bareth, G., \& Chen, X. (2013).
Remotely detecting canopy nitrogen concentration and uptake of paddy
rice in the Northeast China Plain. \emph{ISPRS Journal of Photogrammetry
and Remote Sensing, 78} , 102-115. doi:10.1016/j.isprsjprs.2013.01.008

Zadoks, J. C., Chang, T. T., \& Konzak, C. F. (1974). A decimal code for
the growth stages of cereals. \emph{Weed research, 14} , 415-421.

Zeng, F., Zuo, Z., Mo, J., Chen, C., Yang, X., Wang, J., Wang, Y., Zhao,
Z., Chen, T., Li, Y., Zhang, Z., Hu, Z., \& Xu, H. (2021). Runoff Losses
in Nitrogen and Phosphorus From Paddy and Maize Cropping Systems: A
Field Study in Dongjiang Basin, South China. \emph{Frontiers in Plant
Science, 12} , 675121. doi:10.3389/fpls.2021.675121

Zheng, H., Cheng, T., Li, D., Yao, X., Tian, Y., Cao, W., \& Zhu, Y.
(2018a). Combining Unmanned Aerial Vehicle (UAV)-Based Multispectral
Imagery and Ground-Based Hyperspectral Data for Plant Nitrogen
Concentration Estimation in Rice. \emph{Frontiers in Plant Science, 9} ,
936. doi:10.3389/fpls.2018.00936

Zheng, H., Cheng, T., Zhou, M., Li, D., Yao, X., Tian, Y., Cao, W., \&
Zhu, Y. (2018b). Improved estimation of rice aboveground biomass
combining textural and spectral analysis of UAV imagery. \emph{Precision
Agriculture, 20} , 611-629. doi:10.1007/s11119-018-9600-7

Table 1. List of acronyms of leaf traits at the leaf and canopy level
with their definitions or calculations, and units.\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
Acronym & Definition or calculation & Unit\tabularnewline
\midrule
\endhead
LAI & Leaf area index & m\textsuperscript{2} leaf (m\textsuperscript{2}
ground)\textsuperscript{-1}\tabularnewline
LNC & Leaf nitrogen concentration & g N (g dry
matter)\textsuperscript{-1}\tabularnewline
SLA & Specific leaf area & m\textsuperscript{2} leaf (g dry
matter)\textsuperscript{-1}\tabularnewline
SLN & Specific leaf nitrogen content & g N (m\textsuperscript{2}
leaf)\textsuperscript{-1}\tabularnewline
SLN\textsubscript{dir} & SLN directly predicted from hyperspectral
images & g N (m\textsuperscript{2}
leaf)\textsuperscript{-1}\tabularnewline
SLN\textsubscript{sla} & SLN indirectly predicted as the predicted LNC
divided by the predicted SLA & g N (m\textsuperscript{2}
leaf)\textsuperscript{-1}\tabularnewline
SLW & Specific leaf weight (= 1/SLA) & g dry matter
(m\textsuperscript{2} leaf)\textsuperscript{-1}\tabularnewline
\emph{N}\textsubscript{canopy} & Leaf nitrogen content at the canopy
level & g N (m\textsuperscript{2}
ground)\textsuperscript{-1}\tabularnewline
\emph{N}\textsubscript{canopy,dir} & \emph{N}\textsubscript{canopy}
directly predicted from hyperspectral images & g N (m\textsuperscript{2}
ground)\textsuperscript{-1}\tabularnewline
\emph{N}\textsubscript{canopy,SLNdir} & \emph{N}\textsubscript{canopy}
indirectly predicted as the SLN\textsubscript{dir} divided by the
predicted LAI & g N (m\textsuperscript{2}
ground)\textsuperscript{-1}\tabularnewline
\emph{N}\textsubscript{canopy,SLNsla} & \emph{N}\textsubscript{canopy}
indirectly predicted as the SLN\textsubscript{sla} divided by the
predicted LAI & g N (m\textsuperscript{2}
ground)\textsuperscript{-1}\tabularnewline
\bottomrule
\end{longtable}

Table 2. Sampling dates and the number of destructive field samples at
corresponding growth stages of rice, maize and wheat.\selectlanguage{english}
\begin{longtable}[]{@{}lllllll@{}}
\toprule
Growth stage & Rice & No. of samples & Maize & No. of samples & Winter
wheat & No. of samples\tabularnewline
\midrule
\endhead
Tillering stage/ Early stem-elongating stage & 22 July & 24 & 7 July &
19 & 22 March & 56\tabularnewline
Stem-elongating stage & 15 August & 24 & 20 July & 19 & 8 April &
56\tabularnewline
Flowering stage & 8 September & 24 & 4 August & 19 & 27 April &
56\tabularnewline
Grain-filling stage & 21 September & 24 & 25 August & 19 & 10 May &
56\tabularnewline
Grain-filling stage & 10 October & 24 & 7 September & 19 & 25 May &
56\tabularnewline
Maturity & 30 October & 24 & 23 September & 18 & 4 June &
-\tabularnewline
Total no. of samples & & 144 & & 113 & & 280\tabularnewline
\bottomrule
\end{longtable}

Table 3. Description of the combinations of feature sets from
hyperspectral images and crop model simulations.\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
\begin{minipage}[b]{0.32\columnwidth}\raggedright\strut
Acronym\strut
\end{minipage} & \begin{minipage}[b]{0.32\columnwidth}\raggedright\strut
Feature type\strut
\end{minipage} & \begin{minipage}[b]{0.32\columnwidth}\raggedright\strut
Feature number\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
Ref\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
Canopy reflectance\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
109\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
RefVIs\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
Canopy reflectance + Vegetation indices\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
146\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
RefVIsTex\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
Canopy reflectance + Vegetation indices + Texture information\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
178\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
All\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
Canopy reflectance + Vegetation indices + Texture information +
Development stage\strut
\end{minipage} & \begin{minipage}[t]{0.32\columnwidth}\raggedright\strut
179\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

Table 4: The prediction performance in the testing dataset of directly
and indirectly predicted specific leaf nitrogen (SLN) in rice, wheat and
maize using feature sets of Ref and RefVIsTex (see Table 3 for their
definition) and applying the regression algorithms of Partial Least
Squares Regression (PLSR) and Support Vector Regression
(SVR)\textsuperscript{a}.\selectlanguage{english}
\begin{longtable}[]{@{}lllllllll@{}}
\toprule
Method & Feature set & & Rice & & Wheat & & Maize &\tabularnewline
\midrule
\endhead
& & & SLN\textsubscript{dir} & SLN\textsubscript{sla} &
SLN\textsubscript{dir} & SLN\textsubscript{sla} & SLN\textsubscript{dir}
& SLN\textsubscript{sla}\tabularnewline
PLSR & Ref & \emph{R}\textsuperscript{2} & \textbf{0.666} & 0.659 &
0.462 & \textbf{0.564} & 0.540 & \textbf{0.611}\tabularnewline
& & \emph{NRMSE} & \textbf{0.254} & 0.266 & 0.281 & \textbf{0.251} &
0.189 & \textbf{0.183}\tabularnewline
& RefVIsTex & \emph{R}\textsuperscript{2} & 0.699 & \textbf{0.725} &
0.557 & \textbf{0.583} & \textbf{0.471} & 0.440\tabularnewline
& & \emph{NRMSE} & 0.241 & \textbf{0.240} & 0.254 & \textbf{0.244} &
\textbf{0.200} & 0.207\tabularnewline
SVR & Ref & \emph{R}\textsuperscript{2} & 0.546 & \textbf{0.626} & 0.522
& \textbf{0.533} & 0.432 & \textbf{0.582}\tabularnewline
& & \emph{NRMSE} & 0.301 & \textbf{0.276} & 0.258 & \textbf{0.256} &
0.215 & \textbf{0.183}\tabularnewline
& RefVIsTex & \emph{R}\textsuperscript{2} & \textbf{0.677} & 0.661 &
\textbf{0.582} & 0.563 & 0.369 & \textbf{0.481}\tabularnewline
& & \emph{NRMSE} & \textbf{0.250} & 0.262 & \textbf{0.243} & 0.246 &
0.224 & \textbf{0.197}\tabularnewline
\bottomrule
\end{longtable}

\textsuperscript{a} For each set of analysis, there is a directly
predicted SLN (SLN\textsubscript{dir}) and an indirectly predicted SLN
(SLN\textsubscript{sla}), the SLN calculated as the predicted leaf
nitrogen concentration divided by the predicted specific leaf area (see
also Table 1). The regression algorithms for the prediction of SLA were
specified as SVR, Convolution Neural Network, and PLSR for rice, wheat
and maize, respectively, as these algorithms yielded the best
performance for the three crops. For the better predicted SLN in the
direct vs indirect predictions' comparison, its corresponding\emph{R}
\textsuperscript{2} and NRMSE values are given in bold.

\textbf{Hosted file}

\verb`image1.emf`  available at \url{https://authorea.com/users/701034/articles/689314-estimating-leaf-and-canopy-nitrogen-contents-in-major-field-crops-across-the-growing-season-from-hyperspectral-images-using-nonparametric-regression}

Fig. 1. Study sites of the field experiments of maize (a), wheat (b) and
rice (c). The true color images (Red: 638 nm, Green: 550 nm, Blue: 470
nm) at the stem-elongating stage are illustrated here. N0, N40, N80,
N160, N240, N320 and N400 denote different nitrogen (N) application
rates (see Table S1 for details).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

Fig. 2. The workflow diagram of data acquisition, feature collection,
and data analysis in this study. Nonparametric regression algorithms
are: PLSR = Partial Least Squares Regression, SVR = Support Vector
Regression, RFR = Random Forest Regression, DNN = Deep Neural Network,
CNN = Convolution Neural Network. Crop traits are: SLW = specific leaf
weight, SLA = specific leaf area, SLN = specific leaf nitrogen, LNC =
leaf nitrogen concentration, LAI = leaf area index,\emph{N}
\textsubscript{canopy} = canopy nitrogen content.\emph{N}
\textsubscript{canopy,dir} and SLN\textsubscript{dir} represent the
direct predictions of \emph{N} \textsubscript{canopy} and SLN,
respectively. Within the indirect predictions, SLN\textsubscript{sla}was
calculated as the predicted LNC divided by the predicted SLA,\emph{N}
\textsubscript{canopy,SLNdir} was derived from predicted LAI and
SLN\textsubscript{dir}, and \emph{N} \textsubscript{canopy,SLNsla} was
derived from predicted LAI and SLN\textsubscript{sla} (indirectly
predicted SLN via SLA).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

Fig. 3. Range of the collected canopy reflectance of rice (a), wheat (b)
and maize (c), and the data distribution of destructively sampled
specific leaf nitrogen (SLN) (d), leaf nitrogen concentration (LNC) (e),
and canopy nitrogen content (\emph{N} \textsubscript{canopy}) (f) at
different stages during the whole growing season.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

Fig. 4. The prediction performance, \emph{R} \textsuperscript{2} (full
lines) and \emph{NRMSE} (dotted lines), in the testing dataset of
different regression models in directly predicted specific leaf nitrogen
(SLN) (a-c), leaf nitrogen concentration (LNC) (d-f) and canopy nitrogen
content (\emph{N} \textsubscript{canopy}) (g-i) in rice, wheat and maize
with various sets of input feature types. Nonparametric regression
algorithms: PLSR = Partial Least Squares Regression, SVR = Support
Vector Regression, RFR = Random Forest Regression, DNN = Deep Neural
Network, CNN = Convolution Neural Network. Acronyms in the x-axis for
four sets of feature types are defined in Table 3.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

Fig. 5. The prediction performance, \emph{R} \textsuperscript{2} (full
lines) and \emph{NRMSE} (dotted lines), in the testing dataset of
different regression models in directly predicted specific leaf weight
(SLW) (a-c) and specific leaf area (SLA) (d-f) in rice, wheat and maize
with various sets of input feature types. Nonparametric regression
algorithms: PLSR = Partial Least Squares Regression, SVR = Support
Vector Regression, RFR = Random Forest Regression, DNN = Deep Neural
Network, CNN = Convolution Neural Network. Acronyms in the x-axis for
four sets of feature types are defined in Table 3.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

Fig. 6. The prediction performance in the testing dataset of directly
and indirectly predicted canopy nitrogen content (\emph{N}
\textsubscript{canopy}) in rice (a, b), wheat (c, d) and maize (e, f)
using feature sets of Ref and RefVIsTex (see Table 3 for their
definition) and regression algorithms of Partial Least Squares
Regression (PLSR) and Support Vector Regression (SVR). The directly
predicted \emph{N} \textsubscript{canopy} was labeled as\emph{N}
\textsubscript{canopy,dir}. The indirectly predicted\emph{N}
\textsubscript{canopy,SLNdir} and\emph{N} \textsubscript{canopy,SLNsla}
were upscaled from directly predicted specific leaf nitrogen (SLN)
SLN\textsubscript{dir} and from indirectly predicted
SLN\textsubscript{sla}, respectively (also see Table 1).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image7/image7}

\end{center}
\end{figure}

Fig. 7. The predicted canopy nitrogen content (\emph{N}
\textsubscript{canopy}) from its indirect predictions\emph{N}
\textsubscript{canopy,SLNdir} (see Table 1 for its definition) at the
experimental area of rice across the whole growing season using feature
set of RefVIsTex (see Table 3 for its definition) and regression
algorithm of Partial Least Squares Regression. Predicted\emph{N}
\textsubscript{canopy,SLNdir} at the stage of tillering (a),
stem-elongating (b), flowering (c), ca. 15 days after flowering (d), ca.
30 days after flowering (e), and maturity (f) are shown.

\selectlanguage{english}
\FloatBarrier
\end{document}

