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Computers and Electronics in Agriculture 218 (2024) 108699
Available online 13 February 2024
0168-1699/© 2024 Elsevier B.V. All rights reserved.
Improving potato above ground biomass estimation combining
hyperspectral data and harmonic decomposition techniques
Yang Liu
a
,
b
,
c
,
1
, Haikuan Feng
a
,
d
,
1
,
*
, Yiguang Fan
a
, Jibo Yue
e
, Riqiang Chen
a
, Yanpeng Ma
a
,
Mingbo Bian
a
, Guijun Yang
a
a
Key Laboratory of Quantitative Remote Sensing in Agriculture of Ministry of Agriculture and Rural Affairs, Information Technology Research Center, Beijing Academy of
Agriculture and Forestry Sciences, Beijing 100097, China
b
Key Lab of Smart Agriculture System, Ministry of Education, China Agricultural University, Beijing 100083, China
c
Key Laboratory of Agricultural Information Acquisition Technology, Ministry of Agriculture and Rural Affairs, China Agricultural University, Beijing 100083, China
d
College of Agriculture, Nanjing Agricultural University, Nanjing, Jiangsu 210095, China
e
College of Information and Management Science, Henan Agricultural University, Zhengzhou 450002, China
ARTICLE INFO
Keywords:
AGB
ASD
UHD185
Harmonic components
PLSR
ABSTRACT
Accurately estimating potato above-ground biomass (AGB), which is closely associated with the growth and yield
of crops, carries signicant importance for guiding eld management practices. Hyperspectral techniques have
emerged as a powerful and efcient tool for quickly and non-invasively acquiring information about AGB due to
its capability to provide rich spectral data closely related to crop physiology and biochemistry. However, using
spectral features obtained from hyperspectral data, such as spectral reectance and vegetation indices (VIs),
often leads to inaccurate estimations of crop AGB at multiple growth stages due to spectral saturation effects and
dynamic changes in spectral responses. To enhance the robustness of AGB estimation models, this study proposed
a harmonic decomposition (HD) method derived from Fourier series to extract energy features. The ground
(referred to as ASD) and unmanned aerial vehicle hyperspectral (referred to as UHD185) remote sensing data
from three growth stages of potatoes in 2018 (validation set) and 2019 (calibration set) were utilized in the
study. Firstly, a comparison was made between the spectral reectance of the potato canopy measured by the
ASD and UHD185 sensors. Subsequently, the correlation between spectral reectance, VIs, and harmonic com-
ponents obtained from ASD and UHD185 sensors was analyzed in relation to AGB at both the individual and
whole growth stage. Then, sensitive bands selected through CARS (competitive adaptive reweighted sampling),
the entire spectral reectance, VIs, and harmonic components, were utilized to construct AGB estimation models
by partial least squares regression (PLSR). Finally, the optimal model performance was validated across different
years, growth stages, and treatment conditions. The results showed there were differences in spectral reectance
acquired by ASD and UHD185 sensors across various wavelengths, but overall, there was a high level of con-
sistency between the two. The correlation of spectral reectance and VIs with potato AGB at individual growth
stage was notably higher than that observed for entire growth stages. The accuracy of AGB estimation using VIs
obtained from ASD (the R
2
, RMSE and NRMSE of validation sets were 0.52, 592 kg/hm
2
and 26.91 %, respec-
tively) and UHD185 (the R
2
, RMSE and NRMSE of validation sets were 0.46, 612 kg/hm
2
and 27.82 %,
respectively) sensors were low. Utilizing sensitive bands and full spectral reectance separately improved the
precision of models, although the enhancement was somewhat limited. The HD-PLSR models from ASD (the R
2
,
Abbreviations: AGB, Above-ground biomass; VIs, Vegetation indices; HD, Harmonic decomposition; CARS, Competitive adaptive reweighted sampling; PLSR,
Partial least squares regression; UAV, Unmanned aerial vehicle; R
2
, Coefcient of determination; RMSE, Root mean square error; NRMSE, Normalized root mean
square error; OSAVI, Optimized soil adjusted vegetation index; NDVI, Normalized difference vegetation index; NDRE, Normalized difference red edge index; GNDVI,
Green normalized difference vegetation index; MSR, Modied simple ratio; EVI, Enhanced vegetation index; RDVI, Renormalized difference vegetation index; FD,
First-order derivative; CWT, Continuous wavelet transform; SG, Savitzky-Golay; P, Planting densities; N, Nitrogen levels; S1, May 23, 2018; S2, June 5, 2018; S3,
June 15, 2018; P1, May 28, 2019; P2, June 10, 2019; P3, June 20, 2019; ASD, ASD FieldSpec spectrometer; UHD185, UHD 185-Firey imaging spectrometer; A0/2,
Harmonic constants; Ax, Bx and Cx, Amplitudes; φx, Phases.
* Corresponding author at: Key Laboratory of Quantitative Remote Sensing in Agriculture of Ministry of Agriculture and Rural Affairs, Information Technology
Research Center, Beijing Academy of Agriculture and Forestry Sciences, Beijing 100097, China.
E-mail address: fenghk@nercita.org.cn (H. Feng).
1
These authors contributed equally to this work.
Contents lists available at ScienceDirect
Computers and Electronics in Agriculture
journal homepage: www.elsevier.com/locate/compag
https://doi.org/10.1016/j.compag.2024.108699
Received 6 December 2023; Received in revised form 22 January 2024; Accepted 30 January 2024
Computers and Electronics in Agriculture 218 (2024) 108699
2
RMSE and NRMSE of validation sets were 0.69, 477 kg/hm
2
and 21.69 %, respectively) and UHD185 (the R
2
,
RMSE and NRMSE of validation sets were 0.66, 481 kg/hm
2
and 21.86 %, respectively) achieved the best AGB
estimation results. Using the HD-PLSR model to estimate AGB for two years, the R
2
values were 0.79 and 0.76 for
ASD and UHD185, with RMSE values of 381 kg/hm
2
and 386 kg/hm
2
and NRMSE values of 22.35 % and 22.70
%, respectively. The capability of the HD-PLSR model was conrmed at various growth stages and treatments.
This work offers valuable remote sensing technical support for implementing potato growth monitoring and yield
assessment in the eld.
1. Introduction
Monitoring potato’s growth status is critical to ensuring national
food security (Liu et al., 2022a; Liu et al., 2022b, Feng et al., 2023).
Above ground biomass (AGB) is an especially important crop trait
characterizing the crop growth, which is related to the photosynthetic
potential and nitrogen content of crops (Fan et al., 2022; Li et al., 2021).
In contrast to traditional ground-based measurements suffering from
inefciency and destructive disadvantages, visible and near-infrared
spectral analysis techniques based on unmanned aerial vehicle (UAV)
provide the possibility to accurately estimate AGB with the benets of
nondestructive and speed (Yue et al., 2021a; Yue et al., 2021b; Li et al.,
2022). However, AGB estimation based on spectroscopy usually faces
the challenge of low robustness due to spectral features losing sensitivity
at high AGB or coverage, and is not applicable to the entire growth stage
of the crop (Yue et al., 2019). Thus, aiming to enhance the accuracy and
applicability of potato AGB estimation, this research provides a method
for mining hyperspectral features to mitigate the inuence of spectral
saturation and achieve interannual transferability of AGB estimation
models.
Hyperspectral techniques play an extensive role in the spectral
analysis of crops since it provides continuous spectral signals of the
study target (Li et al., 2020; Liu et al., 2022c). Usually, there exists
notable differences in wavelength locations of hyperspectral features for
estimating AGB among different crops, which are located at sites of light
absorption or reection (Fan et al., 2023; Liu et al.,2020; Yue et al.,
2023). Shu et al. (2021) found that maize AGB could be estimated using
the spectral reectance of 718 and 770 nm with an accuracy of 58 %.
Wang et al. (2017) found that the sensitive wavelength positions asso-
ciated with winter wheat AGB were located at 470, 570, 895, 1170,
1285, and 1355 nm, and used these spectral features to estimate AGB
with an accuracy of 76 %. Zheng et al. (2019) observed that spectral
reectance of 550, 720, and 800 nm was correlated with rice AGB, and
combinations formed based on spectral features obtained the estimation
accuracy values of 45 %-63 %. The sensitivity of canopy spectral
reectance to AGB changes in crops may highly vary since it is a
superimposed signal consisting of physicochemical parameters and
background noise. As a result, the robustness of some estimation models
constructed using the spectral reectance of sensitive wavelengths may
be decreased since the wavelength positions are not xed across crops
and the reectance uctuates across growth cycles.
On the opposite side of the spectral analysis, vegetation indices (VIs)
are proposed to suppress soil and environmental interference and
enhance the reection signal of vegetation (Liu et al., 2022d; Wang
et al., 2022; Duan et al., 2021). VIs are usually calculated as a ratio or
normalized by combining bands’ reectance, including OSAVI, NDVI,
NDRE, GNDVI and so on (Narine et al., 2019; Luo et al., 2021; Xu et al.,
2022). Yue et al. (2019) used OSAVI to estimate wheat AGB and ob-
tained R
2
of 0.38–0.64 and 0.16 at jointing, agging, owering stages
and three stages. Xu et al. (2022) used enhanced vegetation index (EVI)
to estimate rice AGB with R
2
of 0.15–0.25 and 0.01 at three single-
growth stages and total growth duration. Yang et al. (2021) used
renormalized difference vegetation index (RDVI) to estimate potato AGB
with R
2
of 0.13–0.48 and 0.39 at two single-growth stages and whole
growth stages. OSAVI, EVI, and RDVI consist of red and near-infrared
bands whose reectance loses sensitivity to AGB during the later
growth stages of the crop, leading to spectral saturation and affecting the
AGB estimation. Thus, features adapted to crop growth variations need
to be mined from the rich hyperspectral information to enhance the
robustness of AGB estimation models.
To accurately estimate crop’s AGB, various spectral pre-processing
methods including rst-order derivative (FD) (Liu et al., 2021a; Xing
et al., 2017), band depth analysis (Marabel and Alvarez-Taboada, 2014;
Fu et al., 2014), and continuous wavelet transform (CWT) (Liu et al.,
2021b), are applied to extract potential features for modeling optimi-
zation. Gnyp et al. (2014) used FD features to estimate rice AGB with R
2
of 0.32–0.59 and 0.55 at four single-growth stages and all growth stages,
and the raw spectra obtained R
2
of 0.22–0.36 and 0.51. Yue et al.
(2021b) used the CWT technique to decompose hyperspectral reec-
tance and found the continuous wavelet coefcients remained strongly
correlated with wheat AGB in single and whole growth stages.
Numerous studies have conrmed that hyperspectral features obtained
based on the processed spectral reectance can improve the robustness
of AGB estimation models. Although FD and CWT parameters show the
ability to estimate AGB at crop’s various growth stages, changes in
spectral energy are not intuitively observed in the time domain, which
can complicate spectral analysis applications.
Given the above description, there is still a need for new methods to
acquire hyperspectral features for AGB estimation. Harmonic decom-
position techniques (HD) derived from the Fourier transform can
convert spectral information from the time to the frequency domain to
highlight a spectrum’s energy distribution or suppress interference from
other components (Luo et al., 2022; Duan et al., 2019). The ideal har-
monic components obtained from HD can serve as feature variables for
remote sensing tasks. Jiang et al. (2021) demonstrated that the iron
content in various soil types can be more accurately estimated using the
optimal components of HD as opposed to the raw spectral data. Simi-
larly, harmonic decomposition techniques have also been applied to
crop yield estimation (Dado et al., 2020), acreage extraction (Xu et al.,
2021; Shew and Ghosh, 2019), and crop classication (Pott et al., 2022;
Jakubauskas et al., 2002). Therefore, we hypothesize that the frequency-
domain information acquired through HD could be advantageous in
estimating AGB because of the inconsistent energy distributions of
various AGB spectral curves.
This research aims to propose a method for mining high-spectral
features through HD to enhance the potato AGB estimation model’s
robustness. First, the canopy spectral reectance of potatoes was ac-
quired from ground- and UAV-based hyperspectral remote sensing and
smoothed using a Savitzky-Golay (SG) lter. Secondly, the differences in
hyperspectral reectance obtained from two platforms were compared,
and VIs and harmonic components were extracted. Then, sensitive
spectral bands were extracted from two hyperspectral data using CARS.
Finally, the performance of full spectrum, VIs, sensitive spectral bands,
and harmonic components for potato AGB estimation was compared in
2018 and 2019. The main objectives of this study were (i) comparison of
potato canopy spectral reectance obtained from ground-based and
UAV-based hyperspectral data; (ii) comparison of the AGB estimation
performance using full spectrum, VIs, CARS-selected spectral features
from ground-based and UAV-based hyperspectral reectance; (iii)
whether the potato AGB estimation model constructed using harmonic
components obtained through HD exhibit robustness across growth
stages and between different years.
Y. Liu et al.
Computers and Electronics in Agriculture 218 (2024) 108699
3
2. Experiments and methods
The data utilized for this study was derived from 2018 to 2019. The
specic experimental scheme is shown in Fig. 1. The main contents of
this study included ground-based and UAV-based hyperspectral imagery
and AGB acquisition and preprocessing, sensitivity analysis of spectral
and harmonic features to AGB, and construction and evaluation of AGB
estimation models. The process of implementation was detailed in the
subsequent sections.
2.1. Experimental design
This work took place at the Xiaotangshan Experiment Base (Beijing,
China). The region was at and had a temperate monsoon climate that
was semi-humid. The annual mean sunshine, precipitation, and tem-
perature were 2700 h, 550 mm and 12 ℃, respectively. The trial area
had uvo-aquic soil, which was mainly rich in nutrients such as nitro-
gen, phosphorus, and potassium. The experimental location and the
specic plan are shown in Fig. 2.
Potatoes were planted in 2018 and 2019 with the same treatments.
The potato varieties were treated with different planting densities (P)
and nitrogen levels (N) for each year. Each treatment was repeated three
times for different varieties. The overall number of experimental plots
per year was forty-two. The experimental eld occupied 0.17 ha. The
size of each plot was 32.5 m
2
. The eld management mainly included
watering, weeding and disease prevention. To rectify UAV images, we
evenly distributed nine ground control points (G1-G9) across the test
plots and determined their three-dimensional spatial position informa-
tion using differential GPS. The annual experimental plan is shown in
Table 1.
2.2. AGB and ground hyperspectral measurements
The AGB and hyperspectral data were acquired at three growth
stages (tuber formation, tuber growth and starch accumulation) each
year. The detailed sampling dates were listed below: May 23 (S1), June 5
(S2) and June 15 (S3), 2018; and May 28 (P1), June 10 (P2) and June 20
(P3), 2019.
Three potatoes were randomly harvested from every plot, their roots
were removed, and the remaining ones were transported back to the
indoor. The stems and leaves of these plants were separated. The stems
were cut into multiple sections, while the leaves were packed together in
paper bags for drying. The treated samples were then placed in an oven
for 30 min at 105 ◦C for killing, followed by a temperature adjustment to
80 ◦C for continuous drying until the samples’ mass remained constant.
Finally, we calculated the AGB of each plot based on the weight of
samples and planting density.
Once the AGB measurements were completed, ground-based
Fig. 1. The technical process of this study.
Y. Liu et al.
Computers and Electronics in Agriculture 218 (2024) 108699
4
hyperspectral data acquisition was performed. The hyperspectral
reectance of the potato canopy at ground level was measured using an
ASD FieldSpec spectrometer (referred to as ASD) between 11:30 a.m.
and 12:00p.m. under sunny, windless, and cloudless weather. The de-
vice spanned a spectral range from 350 to 2500 nm, with spectral res-
olutions of 1.4 nm and 2 nm for the ranges 350 to 1050 nm and 1050 to
3500 nm, respectively. Typically, the acquired spectral data were con-
verted to 1 nm spectral resolution for subsequent processing. Prior to
each spectral data acquisition, the BaSO4 whiteboard was employed to
calibrate the spectral reectance of potato canopies (Chen et al., 2011;
Abdel-Rahman et al., 2014). The canopy’s spectral reectance was
determined ten times at 1.4 m above the ground at a location chosen to
represent the potato growth level across the plot. The study utilized the
average spectral reectance data as the ground spectrum. To evaluate
the potential of UAV-based and ground-based hyperspectral data, we
obtained the spectral reectance within the 454–950 nm range using an
averaging method on the ground spectrum.
2.3. UAV hyperspectral measurements
The UAV hyperspectral images were collected using the M600 Pro
UAV equipped with the UHD 185-Firey imaging spectrometer (referred
to as UHD185). The sensor had dimensions of 195×67×60 mm, a weight
of 470 g, a spectral sampling interval of 4 nm, and provided 125 bands
spanning from 454 to 950 nm. The ight paths and takeoff positions of
the UAV remained consistent throughout the various annual growth
stages, with the heading and sideways overlap of 85 % and 93 %. Every
ight was conducted at a 20-meter altitude under clear, windless, and
cloudless weather conditions. A total of 28 G of raw hyperspectral data
were collected over two years. The image’s spatial resolution was 1.3
cm. To obtain the spectral reectance of the potato canopy, a BaSO
4
plate was employed to perform radiation calibration on the ground prior
to each hyperspectral image acquisition.
The process of stitching UAV hyperspectral images primarily
involved two main steps: panchromatic image stitching and hyper-
spectral image fusion. The panchromatic image stitching mainly
involved the following steps: (i) optimizing the alignment of acquired
photos using the location data of obtained G1-G9 to ensure spatial
consistency of panchromatic images captured at each growth stage; (ii)
generating point clouds, meshes, and textures using structure-from-
motion algorithms and completing image mosaicking; and (iii) obtain-
ing digital orthoimages of the experimental area from the PhotoScan
software. The generation of hyperspectral images of the potato canopy
required the use of CubePilot software to integrate the panchromatic
and hyperspectral images. The ENVI software was used to extract the
mean spectral reectance of the potato canopy, utilizing vector data
associated with each plot.
2.4. Hyperspectral data preprocessing
The spectral data was smoothed by using a SG lter to enhance the
signal response. The extent of smoothing with the SG lter was deter-
mined by both the window size and the polynomial order chosen (Luo
et al., 2019; Guo et al., 2021). The SG could remove the high-frequency
information from the original signal by convolution operation (Haghbin
et al., 2023). The spectral reectance of potato canopy obtained in this
study by using an SG lter with a quadratic polynomial and a window
Fig. 2. The Geographical region (a) and the experimental design (b).
Table 1
The planting scheme for potatoes in 2018–2019.
Year Treatments
2018 Cultivar: Zhongshu 3, Zhongshu 5 and Zhongshu 195 with twenty-one, nine,
and twelve plots, respectively
Planting density: P1-P3 represent 63 000, 72 000 and 81 000 tubers/hm
2
Nitrogen: N0-N3 represent 0, 75, 150, and 225 kg/hm
2
pure N
2019 Cultivar: Zhongshu 3 and Zhongshu 5 with twenty-one plots, respectively
Planting density: P1-P3 represent 60 000, 72 000 and 84 000 tubers/hm
2
Nitrogen: N0-N3 represent 0, 112, 225, and 337 kg/hm
2
pure N
Y. Liu et al.
Computers and Electronics in Agriculture 218 (2024) 108699
5
size of twenty-one is shown in Fig. 3. The SG-smoothed spectra was used
for subsequent analysis.
2.5. The selection of VIs
According to previous studies, some VIs related to AGB were
selected, as shown in Table 2. These parameters were compared with the
components obtained after harmonic decomposition in terms of their
performance for estimating AGB.
2.6. Harmonic decomposition
Harmonic analysis, also called spectral analysis or Fourier analysis,
breaks down time-varying periodic patterns into a set of sinusoidal
functions. Distinct amplitude and phase values characterize each of
these functions (Jakubauskas et al., 2001; Jiang et al., 2021). Namely,
harmonic analysis asserts that any time series f(t), in relation to time t,
can be represented as a combination of multiple cosine or sine waves.
The reectance curve of each AGB sample, consisting of N bands, can be
considered a continuous function of N cycles. HD aims to decompose
each spectral curve into multiple sine or cosine waves, consisting of
energy features, such as harmonic constants (A0/2), amplitudes (Ax, Bx
and Cx) and phases (φx). Hyperspectral data were decomposed into
multiple harmonic energy features through HD for AGB estimation. A
spectrum group is expressed as R(k) =[r1, r2, …, rN], and the reec-
tance of each band is denoted as rk (k =1,2, …, N). The expression for x-
times HD is as follows.
R(k) = A0
2+
∞
x=1
[Axcos(2
π
xk/N) + Bxsin(2
π
xk/N)]
=A0
2+
∞
x=1
Cxsin2
π
xk
N+φx(1)
A0
2=1
N
N
k=1
rk (2)
Ax =2
N
N
k=1
rkcos(2
π
xk/N)(3)
Bx =2
N
N
k=1
rksin(2
π
xk/N)(4)
Cx =
Ax2+Bx2
(5)
φx =arctan(Ax/Bx)(6)
Where x (x =1, 2, 3, …) is the number of HD. A0/2 is the remainder of
HD and Cxsin(2
π
xk/N+φx)is the HD component of x times. Ax, Bx, Cx
and φx are the amplitude of cosine and sine, harmonic component
amplitude and phase of x times HD, respectively. A0/2, Cx and φx
represent the average energy, the energy changes and the position
associated with the energy change for each band, respectively.
The lower order harmonics capture the primary energy features of
the spectrum, whereas the higher order harmonics often intermingle
with noise information. Amplitudes and phases derived from HD encode
details about the spectral energy distribution and the precise location of
radiation peaks, providing insights into the spectrum’s specic features.
Hence, HD not only reduces or removes background noise but also ac-
centuates the spectral attributes of targets with low-order harmonic
components, achieving data compression as a result.
2.7. Modeling methods
To assess the estimation performance of harmonic components and
spectral reectance, CARS is chosen to select characteristic bands. CARS
is a feature selection method that combines Monte Carlo sampling with
partial least squares regression (PLSR) (Shu et al., 2021; Zhang et al.,
2020). It selects N subsets of bands from N iterations, utilizing an
Fig. 3. Spectral reectance of raw, and SG for ASD and UHD185 in 2018 and 2019. (a), (c), (e), and (g) represent raw and SG-treated potato canopy spectral
reectance obtained in 2018 and 2019 based on the ASD. (b), (d), (f), and (h) represent raw and SG-treated potato canopy spectral reectance obtained in 2018 and
2019 based on the UHD185.
Table 2
The VIs selected for this study.
VIs Expression Reference
MSR (R800/R670-1)/(R800/R670 +1)
1/2
Steele et al. (2008)
OSAVI 1.16(R800-R670)/(R800 +R670 +0.16) Wu et al. (2008)
GNDVI (R750-R550)/(R750 +R550) Rao et al. (2007)
EVI 2.5×(R800–R670)/(1 +R800 +6 ×R670-7.5 ×
R500)
Gurung et al.
(2009)
NDRE (R790-R720)/(R790 +R720) Tilling et al. (2007)
NDVI (R800-R680)/(R800 +R680) Rao et al. (2007)
Y. Liu et al.
Computers and Electronics in Agriculture 218 (2024) 108699
6
exponential decay function and an adaptive reweighting sampling
method to identify features based on regression coefcients. Subse-
quently, the sensitive bands are determined from the PLSR model with
the lowest error. In this study, Monte Carlo sampling was performed 100
times, and the signicance of bands in each model was assessed through
a 10-fold cross-validation.
Given the strengths offered by PLSR, which synergizes the benets of
both principal component analysis and regression analysis, this research
has chosen it as the method to build an AGB estimation model. PLSR is
one of the most popular data analysis techniques for handling inter-
correlated regressors. PLSR can extract relevant information from high-
dimensional datasets while mitigating the problem of multicollinearity
between independent variables, which contributes to the stability and
reliability of the models (Liu et al., 2023a; Liu et al., 2023b). Given the
relatively small size of the dataset, a ten-fold cross-validation method is
employed to assess the model’s accuracy.
To show the interannual reliability of the model constructed in this
study, the calibration set for the AGB estimation model is derived from
2019, and the validation set, which is used to evaluate the model’s
performance across different contexts, is based on 2018. The sample size
for the calibration and validation sets was 126, respectively. The per-
formance of the AGB estimation models was evaluated with the coef-
cient of determination (R
2
), root mean square error (RMSE), and
normalized root mean square error (NRMSE). The model’s accuracy was
evaluated using R
2
and RMSE, and the model’s stability was evaluated
using NRMSE. The larger the R
2
, and the smaller the RMSE and NRMSE,
indicated that the model’s performance was better. The formula is as
follows:
R2=1−n
i=1(xi−xi)2
n
i=1(xi−x)2(7)
RMSE =
n
i=1(xi−xi)2
n
(8)
NRMSE =RMSE
x(9)
Where xi and xi were the measured and the estimated AGB, respectively;
x was the average of the measured samples; and n was the total number
of measured samples.
3. Results and analysis
3.1. Statistical analysis of potato AGB
The AGB statistics for 2018 and 2019 are presented in Table 3. The
AGB ranges for the calibration and validation sets are 329–2898 kg/hm
2
and 702–4177 kg/hm
2
, respectively. Despite the smaller AGB range in
2019 compared to 2018, the higher coefcient of variation is advanta-
geous for improving the model’s generalization.
3.2. Comparative analysis of canopy spectra of ASD and UHD185
The comparison of potato canopy spectra obtained from ground-
based and UAV-based for 2018 and 2019 is illustrated in Fig. 4(a and
b). Despite the differences in remote sensing platforms and sensor types,
the spectral reectance obtained from both ground-based and UAV-
based sources exhibited similar variations within certain wavelength
ranges. Before 680 nm, during different growth stages over the two
years, the canopy spectra of UHD185 was higher than that of ASD. Green
peaks and red valleys were observed around at 550 nm and 670 nm. In
the wavelength range of 754–950 nm, there were substantial differences
in their spectral curves, with UHD185 showing pronounced uctuations,
while the ASD curve exhibited relatively minor uctuations.
To further assess the consistency of spectral reectance between
UHD185 and ASD during different growth stages over the two years,
their reectance was tted, as shown in Fig. 4(c and d). The results
indicated that both UHD185 and ASD achieved R
2
values exceeding 0.96
in the tting process over the different growth stages within the two
years, suggesting that despite differences in the spectral curves, the
obtained spectral reectance exhibited a high level of consistency. This
phenomenon underscored the importance of studying their performance
for AGB estimation.
3.3. The correlation analysis of the full spectrum and AGB
The Pearson correlation coefcients of spectral reectance with AGB
for different bands obtained based on ASD [Fig. 5(a)] and UHD185
[Fig. 5(b)] are shown in Fig. 5. In general, the correlation between the
spectral reectance based on ASD and UHD185 acquisitions and the
total stage AGB was weaker than that of the individual growth stages,
which might be the result of spectral saturation effects. For different
growth stages, ASD and UHD185
′
s sensitive spectral areas to AGB were
primarily found in the green peak, red valley, red edge, and near-
infrared regions. For ASD and UHD185, the correlation of spectral
reectance obtained at various growth stage with AGB varied. However,
the correlation was stronger near 550 nm, 650 nm, and after 750 nm.
The AGB estimation model built using reectance at a xed wavelength
might not be very robust because the correlation between the spectral
reectance and the AGB at the same wavelength was oating.
3.4. Determination of the sensitive bands for ASD and UHD185
The sensitive bands for ASD [Fig. 6(a)] and UHD185 [Fig. 6(b)]
obtained based on the calibration set are shown in Fig. 6, and the
detailed locations are shown in Table 4. The sensitive wavelengths
selected by CARS for ASD and UHD185 were 26 and 35, respectively,
and were mainly located in the green peak, red valley, red edge, and
near-infrared regions. The performance of harmonic component AGB
estimation was compared using the reectance of these distinctive
bands.
3.5. The correlation analysis of sensitive bands and VIs and AGB
The VIs (MSR, OSAVI, GNDVI, EVI, NDRE, NDVI) and the selected
feature bands were arranged in order. The correlation coefcients be-
tween these features of ASD and UHD185 and AGB at single and whole
growth stages are shown in Fig. 7. As shown in Fig. 7(a and d), the
correlation of the VIs and sensitive bands obtained from ASD and
UHD185 with the overall stages’ potato AGB decreased compared to the
individual growth stage. This phenomenon indicated that spectral fea-
tures applicable to a single growth stage might not be appropriate to the
entire growth stage. For example, GNDVI and R754 from ASD [Fig. 7(b
and c)] and UHD185 [Fig. 7(e and f)] did not change notably with
increasing AGB, which might be inuenced by the spectral saturation
effect that reduced the correlation with AGB throughout the growth
stages. This nding indicated that the AGB estimate models built using
conventional spectral features might not be very robust.
Table 3
The descriptive statistics of potato AGB (kg/hm
2
).
Years Data set Range Mean Standard
deviation
Coefcient of
variation (%)
2018 Validation
set
702–4177 2201 741 33.64
2019 Calibration
set
329–2898 1236 462 37.36
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Computers and Electronics in Agriculture 218 (2024) 108699
7
Fig. 4. Potato canopy spectra obtained by ASD and UHD185. (a) and (b) represent the spectral reectance curves based on ASD and UHD185 acquired at each
growth stage in 2018 and 2019. (c) and (d) represent the tted curves based on spectral reectance obtained from ASD and UHD185 at each growth stage in 2018
and 2019.
Fig. 5. Correlation coefcients between full spectrum and AGB for ASD and UHD185. (a) and (b) represent the correlation coefcient between spectral reectance
obtained based on ASD and UHD185 and both individual and entire growth stage AGB.
Y. Liu et al.
Computers and Electronics in Agriculture 218 (2024) 108699
8
3.6. The correlation analysis between the features obtained through HD
and AGB
To illustrate the process of harmonic decomposition, the spectrum of
an arbitrary experimental plot was used as an example to compute the
harmonic components. The harmonic amplitudes obtained by six times
harmonic decompositions (x =1, 2, … 6) are shown in Fig. 8. The
ndings demonstrated that the amplitudes of the rst four de-
compositions differed greatly, and afterwards these differences
decreased. Thus, seventeen harmonic components were obtained by HD
with four times.
These harmonic features are arranged in order (A0/2, Ax1, Ax2, …).
The correlation coefcients of harmonic features from ASD and UHD185
with AGB are shown in Fig. 9. As shown in Fig. 9(a and d), harmonic
Fig. 6. Distribution of sensitive bands obtained through CARS based on calibration sets. (a) and (b) represent the sensitive bands obtained based on ASD
and UHD185.
Table 4
The selected sensitive bands for ASD and UHD185.
Data
types
Number Bands
ASD 26 526, 546–550, 566, 586, 602, 650, 670, 682, 694–698,
706–710, 754–758, 770, 786–790, 862, 878–890, 902–914,
922
UHD185 35 522, 530, 542, 550–554, 566, 574, 582, 590, 602, 610–614,
630–634, 646, 658, 666, 674, 682–694, 702, 722, 730–734,
742–746, 754, 786–794, 846–854
Fig. 7. Correlation coefcients between AGB (kg/hm
2
) and spectral features obtained based on ASD and UHD185. (a) and (d) represent the correlation coefcients of
spectral features from ASD and UHD185 with potato single and whole stage AGB. (b) and (e) represent the correlation of GNDVI from ASD and UHD185 with potato
AGB. (c) and (f) represent the correlation of R754 from ASD and UHD185 with potato AGB.
Y. Liu et al.
Computers and Electronics in Agriculture 218 (2024) 108699
9
features were signicantly correlated with potato AGB in single and
throughout the growth stages. For example, Ax1 and Cx1 from ASD
[Fig. 9(b and c)] and UHD185 [Fig. 9(e and f)] not only maintained a
high correlation with AGB during a single growth stage, but also with
AGB throughout the entire growth stages. This suggested that harmonic
features obtained by HD might reduce spectral saturation.
3.7. AGB estimation model construction
The accuracy of estimating AGB based on (i) full spectrum, (ii) VIs,
(iii) sensitive bands (obtained through CARS), and (iv) harmonic com-
ponents (obtained through HD) from ASD and UHD185 is shown in
Table 5. Generally, the estimation of AGB based on features extracted
from ASD tended to outperform that from UHD185. The AGB estimation
using VIs obtained from ASD (Validation: R
2
=0.52, RMSE =592 kg/
hm
2
, NRMSE =26.91 %) and UHD185 (Validation: R
2
=0.46, RMSE =
612 kg/hm
2
, NRMSE =27.82 %) was yielding poor results. While uti-
lizing full spectrum data from ASD (Validation: R
2
=0.53, RMSE =564
kg/hm
2
, NRMSE =25.62 %) and UHD185 (Validation: R
2
=0.49, RMSE
=577 kg/hm
2
, NRMSE =26.23 %) improved the AGB estimation, it also
added complexity to the model due to a large number of features
introduced. The utilization of CARS-selected sensitive bands for AGB
estimation had reduced the model’s complexity and led to an
enhancement in model accuracy. For ASD, the R
2
values for the cali-
bration and validation sets are 0.54 and 0.60, with RMSE values of 302
and 536 kg/hm
2
, and NRMSE values of 24.47 % and 24.37 %, respec-
tively. For UHD185, the R
2
values for the calibration and validation sets
are 0.55 and 0.58, with RMSE values of 303 and 574 kg/hm
2
, and
Fig. 8. Diagram showing the various harmonic decomposition times.
Fig. 9. Correlation coefcients between AGB (kg/hm
2
) and harmonic components obtained based on ASD and UHD185. (a) and (d) represent the correlation co-
efcients of harmonic components from ASD and UHD185 with potato single and whole stage AGB. (b) and (e) represent the correlation of Ax1 from ASD and
UHD185 with potato AGB. (c) and (f) represent the correlation of Cx1 from ASD and UHD185 with potato AGB.
Y. Liu et al.
Computers and Electronics in Agriculture 218 (2024) 108699
10
NRMSE values of 24.54 % and 26.09 %, respectively. Harmonic com-
ponents from ASD (Validation: R
2
=0.69, RMSE =477 kg/hm
2
, NRMSE
=21.69 %) and UHD185 (Validation: R
2
=0.66, RMSE =481 kg/hm
2
,
NRMSE =21.86 %) usually yielded the highest AGB estimation accu-
racy. Therefore, we hypothesized that HD might be suitable for esti-
mating AGB at various growth stages and years.
The AGB estimation for two years (2018, 2019) based on (i) the full
spectrum, (ii) VIs, (iii) sensitive spectral bands, and (iv) harmonic
components is shown in Fig. 10. The VIs extracted from ASD (R
2
=0.66,
RMSE =467 kg/hm
2
, NRMSE =27.44 %) and UHD185 (R
2
=0.66,
RMSE =479 kg/hm
2
, NRMSE =28.10 %) exhibited poor performance in
the dataset spanning two years. The sensitive spectral bands selected
from ASD (R
2
=0.71, RMSE =435 kg/hm
2
, NRMSE =25.57 %) and
UHD185 (R
2
=0.68, RMSE =464 kg/hm
2
, NRMSE =27.22 %) using
CARS yielded better results compared to the full spectrum data (ASD: R
2
=0.69, RMSE =449 kg/hm
2
, NRMSE =26.34 %; UHD185: R
2
=0.68,
RMSE =473 kg/hm
2
, NRMSE =27.77 %). Harmonic components
showed good estimation performance in the two-year dataset (ASD: R
2
=0.79, RMSE =381 kg/hm
2
, NRMSE =22.35 %; UHD185: R
2
=0.76,
RMSE =386 kg/hm
2
, NRMSE =22.70 %). In summary, using features
extracted from ASD for AGB estimation across different timeframes
generally outperformed the results obtained from UHD185. The HD-
PLSR model was used for subsequent analyses because it performed
well in the two-year dataset.
3.8. Assessment of model applicability
To compare the applicability of the AGB estimation model at indi-
vidual stages, the HD-PLSR model was applied for each growth stage in
2018 and 2019, respectively, as shown in Fig. 11. The results showed the
HD-PLSR model obtained R
2
in the range of 0.54–0.76 and 0.61–0.76,
RMSE in the range of 455–504 kg/hm
2
and 231–280 kg/hm
2
, NRMSE in
the range of 19.02–24.52 % and 19.17–21.95 % for ASD in 2018 and
2019. The HD-PLSR model was equally applicable to UHD185. This
model obtained R
2
in the range of 0.48–0.73 and 0.48–0.76, RMSE in the
range of 413–512 kg/hm
2
and 244–285 kg/hm
2
, NRMSE in the range of
17.27–24.94 % and 20.28–23.68 % for ASD in 2018 and 2019. The HD-
PLSR model exhibited relatively high accuracy and low errors, which
showed that harmonic components were more sensitive to AGB.
To further assess the applicability of the HD-PLSR model, it was
applied to different treatments (planting density, nitrogen levels, and
varieties), as shown in Fig. 12. The outcomes revealed that the model
achieved acceptable estimation accuracy for ASD and UHD185 under
different treatments. In 2018 and 2019, for ASD, the R
2
values spanned
from 0.62 to 0.74 and 0.50 to 0.75 across various treatments, with
corresponding RMSE values of 453–501 kg/hm
2
and 220–293 kg/hm
2
,
and NRMSE values of 19.87–23.63 % and 18.76–22.46 %. For UHD185,
the HD-PLSR model achieved satisfactory precision under different
treatments in both 2018 and 2019. The R
2
values fell within the ranges
of 0.55 to 0.63 and 0.41 to 0.71, with RMSE values spanning from 471 to
Table 5
The performance comparison of estimating AGB using different features.
Types Features Calibration sets (2019) Validation sets (2018)
R
2
RMSE (kg/hm
2
) NRMSE (%) R
2
RMSE (kg/hm
2
) NRMSE (%)
ASD full spectra 0.55 312 25.28 0.53 564 25.62
VIs 0.53 323 26.13 0.52 592 26.91
sensitive bands 0.54 302 24.47 0.60 536 24.37
HD 0.68 259 20.96 0.69 477 21.69
UHD185 full spectra 0.51 327 26.48 0.49 577 26.23
VIs 0.48 332 26.93 0.46 612 27.82
sensitive bands 0.55 303 24.54 0.58 574 26.09
HD 0.60 269 21.78 0.66 481 21.86
Fig. 10. Potato AGB estimation results in two-year data (2018, 2019) by PLSR models developed from ASD and UHD185. (a) and (e) represent full spectra, (b) and (f)
represent VIs, (c) and (g) represent sensitive bands, (d) and (h) represent harmonic components.
Y. Liu et al.
Computers and Electronics in Agriculture 218 (2024) 108699
11
492 kg/hm
2
and 264 to 274 kg/hm
2
, while NRMSE values ranged be-
tween 21.17 and 22.45 % and 19.06–25.56 %. This phenomenon indi-
cated that employing harmonic decomposition techniques to extract
energy features from hyperspectral data had effectively addressed the
challenge arising from spectral response variations throughout the
entire growth stages.
Spatial distribution map of estimated potato AGB at eld scale ob-
tained from the optimal model, which is useful for exploring the po-
tential application in the eld. The spatial distribution of potato eld
AGB in 2019 is shown in Figs. 13 and 14. The estimated AGB obtained
from the optimal model based on ASD and UHD185 closely aligned with
the actual AGB. In most cases, the actual AGB values at different growth
stages were higher in nitrogen-treated plots compared to density-treated
plots. Looking at the spatial patterns, the AGB estimates obtained with
the optimal model using ASD were generally considered to be more
dependable compared to those derived from UHD185. Furthermore, the
errors in AGB estimation for each growth stage are illustrated in Fig. 13
and Fig. 14. During various growth stages, the errors in AGB estimation
were primarily concentrated within the nitrogen-treated plots. In gen-
eral, the estimation errors were relatively larger in high-nitrogen areas.
This could be attributed to the excessive growth of potatoes leading to
increased AGB, which might not be adequately represented by the
spectral information obtained from the canopy. In summary, excessive
nitrogen fertilization could potentially impact the AGB estimation
Fig. 11. Comparison of AGB estimation performance by HD-PLSR models at the individual stages during 2018 and 2019 years.
Fig. 12. Comparison of AGB estimation performance by HD-PLSR models at the different densities, nitrogen and varieties during 2018 and 2019 years.
Y. Liu et al.
Computers and Electronics in Agriculture 218 (2024) 108699
12
model’s accuracy, resulting in less precise AGB predictions and, conse-
quently, impacting effective eld management practices.
4. Discussion
Hyperspectral remote sensing technology had emerged as a crucial
tool for AGB monitoring due to its rich spectral information, which was
well-suited for feature extraction and analysis (Liu et al., 2022c).
However, spectral features extracted from hyperspectral data changed
as the growth stages progressed, leading to poor robustness of the con-
structed AGB estimation model (Luo et al., 2022). Therefore, this study
proposed a method that utilized harmonic decomposition to extract
energy features from hyperspectral reectance data, mitigating the
impact of growth dynamics and enhancing the AGB estimation model’s
robustness.
4.1. Analysis of typical features related to AGB during the growth stages
The potato canopy spectral reectance obtained from ASD and
UHD185 showed differences, but distinctive reection peaks and ab-
sorption troughs were observed around 550 nm and 650 nm [Fig. 4(a
and b)], primarily due to the presence of leaf pigments. Before 680 nm,
the reectance captured by UHD185 was higher than that of ASD,
whereas it decreased afterward. This could be attributed to the limited
impact of soil background on canopy spectra in the visible light range,
contrasting with its greater inuence in the near-infrared area (Liu et al.,
2022d; Fu et al., 2014). The spectral reectance obtained from ASD and
UHD185 showed excellent ts across various growth stages during the
two years, with R
2
values exceeding 0.9 [Fig. 4(c and d)], suggesting a
remarkable level of spectral consistency.
Spectral reectance from ASD and UHD185 at identical wavelengths
exhibited differing correlations with potato AGB at various growth
stages (Fig. 5). This phenomenon suggested that AGB estimation models
constructed using xed-wavelength spectral features might lack
robustness (Li et al., 2020). The correlation between spectral reectance
and AGB was higher at individual growth stages than over the entire
growth period. Similar ndings were conrmed by Xu et al. (2022) and
Yue et al. (2019), which could be due to the presence of spectral satu-
ration effects. Spectral positions of ASD and UHD185 primarily exhibi-
ted sensitivity to AGB within the green peak, red valley, red edge and
near-infrared regions. These spectral positions had frequently been
utilized in previous research for estimating AGB (Liu et al., 2021a; Yue
et al., 2021b; Zhang et al., 2021). The sensitive spectral bands selected
through CARS were primarily located within the aforementioned spec-
tral region (Fig. 6 and Table 4). The VIs utilized in this study mostly
encompassed the red, red-edge, and near-infrared spectral bands, pri-
marily because these bands were sensitive to changes in AGB. The sen-
sitive bands and VIs from both ASD and UHD185 exhibited notably
higher correlations with potato AGB during individual growth stages
compared to considering the entire growth period [Fig. 7(a), Fig. 7(d)].
From the outcome presented in Fig. 7(b – e), it could be observed that
GNDVI and R754 tended to stabilize as AGB increased, which reduced
their sensitivity to AGB. This has been conrmed in previous studies (Liu
et al., 2022a; Luo et al., 2019; Zhang et al., 2020). The uctuation in the
correlation between traditional spectral features and AGB across various
growth stages and wavelengths resulted in limited transferability of AGB
estimation models constructed based on these features between different
years.
The harmonic components derived from Fourier series-based har-
monic decomposition maintained strong correlations with potato AGB
Fig. 13. ASD-based eld distribution graphic showing AGB truth, estimated, and error values at various growth stages in 2019.
Y. Liu et al.
Computers and Electronics in Agriculture 218 (2024) 108699
13
during both individual and the entire growth stages [Fig. 9(a), Fig. 9(d)].
The results presented in Fig. 9(b)-9(c) and 9(d)-9(e) indicated that Ax1
and Cx1 rose in tandem with increasing AGB, suggesting that the energy
features extracted through the method applied in this study could
effectively mitigate spectral saturation. AGB estimation models con-
structed based on harmonic components might be more robust. Jiang
et al. (2012) conrmed this when estimating soil iron content. Although
prior studies had employed multiple techniques to improve the link
between spectral features and AGB throughout the growth stage, such as
continuous wavelet transform (Yue et al., 2021b) and band-depth
analysis (Fu et al., 2014), they had struggled to accurately represent
the variability in spectral signals within the temporal domain. The
harmonic decomposition technique converted temporal information
into the frequency domain, providing the potential to extract features
that were sensitive to AGB by offering an intuitive view of light energy
distribution (Luo et al., 2022). Therefore, we believed that the harmonic
decomposition technique proposed in this study might offer advantages
in addressing the transferability and applicability of AGB estimation
models.
4.2. Application of the proposed harmonic decomposition method
The VIs derived from ASD and UHD185 data for AGB estimation over
two years exhibited relatively low accuracy, with R
2
values of 0.66 in
both cases, RMSE values of 467 kg/hm
2
and 479 kg/hm
2
, and NRMSE
values of 27.44 % and 28.10 % [Fig. 10(b and f)]. This could be
attributed to the spectral dynamics response and spectral saturation
associated with xed-wavelengths (Fan et al., 2022). Although the
sensitive bands (ASD: R
2
increased by 7 %, RMSE and NRMSE all
decreased by 7 %; UHD185: R
2
increased by 3 %, RMSE and NRMSE all
decreased by 3 %) and full-spectrum (ASD: R
2
increased by 5 %, RMSE
and NRMSE all decreased by 4 %; UHD185: R
2
increased by 3 %, RMSE
and NRMSE all decreased by 1 %) features from ASD and UHD185 ob-
tained via CARS had enhanced the precision of AGB estimation over two
years, their potential for improvement was constrained. Zhang et al.
(2020) estimated sugar beet AGB using the full spectrum and sensitive
bands, attaining R
2
values ranging from 0.75 to 0.78 and from 0.78 to
0.80 across three growth stages. Taking into account the limitations of
estimating AGB using hyperspectral reectance, the use of harmonic
components could yield accurate AGB estimates (ASD: R
2
increased by
20 %, RMSE and NRMSE all decreased by 18 %; UHD185: R
2
increased
by 15 %, RMSE and NRMSE all decreased by 19 %) within two years.
This could be attributed to the consistency between the acquired har-
monic components and the variations in AGB [Fig. 9]. In addition,
through constant decomposition of the potato canopy spectral reec-
tance curve by HD, some noise signals might be eliminated when spec-
tral data was converted from the time domain to the frequency domain
(Jiang et al., 2021), thus capturing more accurately the frequency
components associated with crop growth, which was at the core of
improving the accuracy of AGB estimation.
The optimal model derived from this research was successfully
applied across various growth stages and under various treatments over
a span of two years [Figs. 11 and 12]. This result showed that mining the
latent information in the spectra through the harmonic decomposition
method was benecial for enhancing AGB estimation model’s stability.
Taking the year 2019 as an example, the optimal model derived from
ASD and UHD185 data provided the spatial distribution map of esti-
mation values and estimation errors at the eld scale, which could serve
Fig. 14. UHD185-based eld distribution graphic showing AGB truth, estimated, and error values at various growth stages in 2019.
Y. Liu et al.
Computers and Electronics in Agriculture 218 (2024) 108699
14
as guidance for practical eld management [Figs. 13 and 14]. We found
that the errors in estimating AGB for ASD and UHD185 were predomi-
nantly concentrated within the plots subjected to nitrogen treatments.
This could be attributed to the more obvious spatial variability in AGB
under nitrogen treatments than other treatments, likely since potato
growth relies on nitrogen accumulation (Shu et al., 2021; Xun et al.,
2021). Through the validation of the proposed HD-PLSR model, it
became evident that harmonic components had the potential to serve as
valuable features for characterizing variations in crop AGB.
4.3. The prospect of future research
The method proposed in this study was based on hyperspectral data
from two platforms. However, some limitations were typically faced in
acquiring and utilizing these data. While these two hyperspectral data-
sets covered different wavelength ranges, both contained hundreds of
bands, posing a signicant challenge for data mining due to the vast
amount of information. Using the full spectrum without considering
redundancy between wavelengths to estimate crop AGB, or actively
selecting specic wavelengths to construct VIs to estimate crop AGB, the
model’s accuracy was usually less than optimal. Although some
advanced feature selection methods, such as CARS, were used to
improve the accuracy of AGB estimation models signicantly by
obtaining sensitive variables associated with AGB, the non-xed posi-
tion of features might have limited their applicability in other regions.
Decomposing crop canopy spectral curves through HD to obtain har-
monic features proved effective in AGB estimation, facilitating
straightforward generalization and application due to being less sus-
ceptible to external interference.
In reality, the widespread adoption of hyperspectral technology was
more susceptible to the impact of data collection costs and applicability
range. The hyperspectral data used in this study, obtained from ASD and
UHD185, had sensors with excessively high prices, particularly in the
case of hyperspectral technology equipped with UAVs. For ASD, data
collection for larger eld plots was impractical due to prolonged
acquisition times and the need for substantial manpower. Despite the
convenience of data acquisition using drone-based hyperspectral tech-
nology, it was constrained by battery capacity, introducing increased
risk during aerial operations. When utilizing UAV-based hyperspectral
technology to acquire crop canopy spectral reectance, the data pro-
cessing time was longer and more complex compared to ASD. This un-
doubtedly increased the technology’s usability threshold. With
technological advancements, there is a possibility of compressing the
application costs of hyperspectral technology, making data collection
and processing simpler. This could potentially facilitate the widespread
adoption of the method proposed in this study.
While the model proposed in this study was validated using a two-
year dataset from potato crops, further in-depth research is needed to
assess its applicability to other crop types. Exploring whether variable
screening of harmonic components enhanced model accuracy by miti-
gating information redundancy and eliminating redundant features is a
topic that warrants investigation. The optimal model utilized in this
study was not applied for potato yield estimation, which represented an
imperfection in this work. In theory, there was a positive correlation
between potato AGB and yield, which might also be applicable to yield
estimation. Future research will take this into consideration. The model
proposed in this study demonstrates interannual transferability. How-
ever, its applicability in different regions remains to be conrmed. When
merging data from two years and subsequently partitioning the dataset,
it is worth discussing whether the AGB model constructed in this manner
remains applicable under all conditions.
5. Conclusions
This work introduced an HD-PLSR method for extracting energy
features from hyperspectral data to elevate the accuracy and
applicability of AGB estimation for potato crops at both individual and
multiple growth stages in 2018 and 2019. The primary conclusions were
as follows: (1) the spectral reectance obtained from ASD and UHD185
sensors exhibited high consistency across the entire wavelength range,
and the R
2
values obtained from tting data in the two years exceeded
0.9. (2) The correlation between spectral reectance and VIs from ASD
and UHD185 sensors with AGB across the entire growth stages was
notably lower than that observed for individual growth stages. (3) The
accuracy of AGB estimation using VIs in the two years was low.
For ASD and UHD185, the model’s R
2
values were 0.66, with RMSE
values of 467 and 479 kg/hm
2
, and NRMSE values of 27.44 % and 28.10
%, respectively. (4) Using the reectance of full spectral or sensitive
bands enhanced the precision of AGB estimation, though the enhance-
ment in accuracy was limited. (5) The HD-PLSR models from ASD and
UHD185 achieved the best results. For ASD, R
2
increased by 20 %, RMSE
and NRMSE all decreased by 18 %; For UHD185, R
2
increased by 15 %,
RMSE and NRMSE all decreased by 19 %. The model’s performance was
validated across various growth stages and treatments over two years.
This study demonstrated that the proposed method could enhance AGB
estimation model’s robustness and accuracy, offering valuable scientic
insights for potato growth management and yield assessment.
CRediT authorship contribution statement
Yang Liu: Writing – original draft. Haikuan Feng: Writing – review
& editing, Writing – original draft, Funding acquisition. Yiguang Fan:
Data curation. Jibo Yue: Writing – review & editing, Supervision.
Riqiang Chen: Investigation, Data curation. Yanpeng Ma: Investiga-
tion. Mingbo Bian: Investigation. Guijun Yang: Supervision.
Declaration of competing interest
The authors declare that they have no known competing nancial
interests or personal relationships that could have appeared to inuence
the work reported in this paper.
Data availability
The authors do not have permission to share data.
Acknowledgements
This study was supported by the Key scientic and technological
projects of Heilongjiang province (2021ZXJ05A05), the National Nat-
ural Science Foundation of China (41601346).
References
Abdel-Rahman, E.M., Mutanga, O., Odindi, J., Adam, E., Odindo, A., Ismail, R., 2014.
A comparison of partial least squares (PLS) and sparse PLS regressions for predicting
yield of Swiss chard grown under different irrigation water sources using
hyperspectral data. Comput. Electron. Agric. 106, 11. https://doi.org/10.1016/j.
compag.2014.05.001.
Chen, S., Li, D., Wang, Y.F., Peng, Z.P., Chen, W.Q., 2011. Spectral characterization and
prediction of nutrient content in winter leaves of litchi during ower bud
differentiation in southern China. Precis. Agr. 12, 682–698. https://doi.org/
10.1007/s11119-010-9213-2.
Dado, W.T., Deines, J.M., Patel, R., Liang, S.Z., Lobell, D.B., 2020. High-resolution
soybean yield mapping across the US Midwest using subeld harvester data. Remote
Sens. 12, 3471. https://doi.org/10.3390/rs12213471.
Duan, B., Liu, Y.T., Gong, Y., Peng, Y., Wu, X.T., Zhu, R.S., Fang, S.H., 2019. Remote
estimation of rice LAI based on Fourier spectrum texture from UAV image. Plant
Methods. 15, 124. https://doi.org/10.1186/s13007-019-0507-8.
Duan, B., Fang, S.H., Gong, Y., Peng, Y., Wu, X.T., Zhu, R.S., 2021. Remote estimation of
grain yield based on UAV data in different rice cultivars under contrasting climatic
zone. Field Crop Res. 267, 108148 https://doi.org/10.1016/j.fcr.2021.108148.
Fan, Y.G., Feng, H.K., Jin, X.L., Yue, J.B., Liu, Y., Li, Z.H., Feng, Z.H., Song, X.Y., Yang, G.
J., 2022. Estimation of the nitrogen content of potato plants based on morphological
parameters and visible light vegetation indices. Front. Plant Sci. 13, 1012070.
https://doi.org/10.3389/fpls.2022.1012070.
Y. Liu et al.
Computers and Electronics in Agriculture 218 (2024) 108699
15
Fan, Y.G., Feng, H.K., Jin, X.L., Yue, J.B., Liu, Y., Li, Z.H., Feng, Z.H., Song, X.Y., Yang, G.
J., 2023. Comparison of different dimensional spectral indices for estimating
nitrogen content of potato plants over multiple growth periods. Remote Sens. 15,
602–622. https://doi.org/10.3390/rs15030602.
Feng, H.K., Yue, J.B., Fan, Y.G., Yang, G.J., Zhao, C.J., 2023. Estimation of potato above-
ground biomass based on VGC-AGB model and hyperspectral remote sensing.
Spectrosc. Spect. Anal. 43, 2876–2884. https://doi.org/10.3964/j.issn.1000-0593
(2023)09-2876-09.
Fu, Y., Yang, G., Wang, J., Song, X., Feng, H., 2014. Winter wheat biomass estimation
based on spectral indices, band depth analysis and partial least squares regression
using hyperspectral measurements. Comput. Electron. Agric. 100, 51–59. https://
doi.org/10.1016/j.compag.2013.10.010.
Gnyp, M.L., Miao, Y.X., Yuan, F., Ustin, S.L., Yu, K., Yao, Y.K., Huang, S.Y., Bareth, G.,
2014. Hyperspectral canopy sensing of paddy rice aboveground biomass at different
growth stages. Field Crop. Res. 155, 42–55. https://doi.org/10.1016/j.
fcr.2013.09.023.
Guo, J.B., Zhang, J., Xiong, S.P., Zhang, Z.Y., Wei, Q., Zhang, W., Feng, W., Ma, X.M.,
2021. Hyperspectral assessment of leaf nitrogen accumulation for winter wheat
using different regression modeling. Precis. Agr. 22, 1634–1658. https://doi.org/
10.1007/s11119-021-09804-z.
Gurung, R.B., Breidt, F.J., Dutin, A., Ogle, S.M., 2009. Predicting enhanced vegetation
index (EVI) curves for ecosystem modeling applications. Remote Sens Environ. 113,
2186–2193. https://doi.org/10.1016/j.rse.2009.05.015.
Haghbin, N., Bakhshipour, A., Zareiforoush, H., Mousanejad, S., 2023. Non-destructive
pre-symptomatic detection of gray mold infection in kiwifruit using hyperspectral
data and chemometrics. Remote Sens. 19, 53–75. https://doi.org/10.1186/s13007-
023-01032-y.
Jakubauskas, M.E., Legates, D.R., Kastens, J.H., 2001. Harmonic analysis of time-series
AVHRR NDVI data. Photogramm. Eng. Rem. Sens. 67, 461–470.
Jakubauskas, M.E., Legates, D.R., Kastens, J.H., 2002. Crop identication using harmonic
analysis of time-series AVHRR NDVI data. Comptut. Electron. Agr. 37, 127–139.
https://doi.org/10.1016/S0168-1699(02)00116-3.
Jiang, X.Q., Luo, S.J., Fang, S.H., Cai, B.W., Xiong, Q., Wang, Y., Huang, X., Liu, X.J.,
2021. Remotely sensed estimation of total iron content in soil with harmonic
analysis and BP neural network. Plant Methods. 17, 116. https://doi.org/10.1186/
s13007-021-00812-8.
Li, B., Xu, X.M., Zhang, L., Han, J.W., Bian, C.S., Li, G.C., Liu, J.G., Jin, L.P., 2020. Above-
ground biomass estimation and yield prediction in potato by using UAV-based RGB
and hyperspectral imaging. ISPRS J. Photogram. 162, 161–172. https://doi.org/
10.1016/j.isprsjprs.2020.02.013.
Li, Z.H., Zhao, Y., Taylor, J., Gaulton, R., Jin, X.L., Song, X.Y., 2022. Comparison and
transferability of thermal, temporal and phenological-based in-season predictions of
above-ground biomass in wheat crops from proximal crop reectance data. Remote
Sens. Environ. 273, 112967 https://doi.org/10.1016/j.rse.2022.112967.
Li, C.H., Zhou, L.Z., Xu, W.B., 2021. Estimating aboveground biomass using sentinel-2
MSI data and ensemble algorithms for grassland in the Shengjin lake wetland. China.
Remote Sens. 13, 1595–1616. https://doi.org/10.3390/rs13081595.
Liu, Y., Zhang, H., Feng, H.K., Sun, Q., Huang, J., Wang, J., Yang, G.J., 2021a. Estimation
of potato above ground biomass based on hyperspectral images of UAV. Spectrosc.
Spect. Anal. 41, 2657–2664. https://doi.org/10.3964/j.issn.1000-0593(2021)09-
2657-08.
Liu, Y., Sun, Q., Feng, H.K., Yang, F.Q., 2021b. Estimation of above-ground biomass of
potato based on wavelet analysis. Spectrosc. Spect. Anal. 41, 1205–1212. https://
doi.org/10.3964/j.issn.1000-0593(2021)04-1205-08.
Liu, Y., Feng, H.K., Yue, J.B., Li, Z.H., Yang, G.J., Song, X.Y., Yang, X.D., Zhao, Y., 2022a.
Remote-sensing estimation of potato above-ground biomass based on spectral and
spatial features extracted from high-denition digital camera images. Comptut.
Electron. Agr. 198, 107089 https://doi.org/10.1016/j.compag.2022.107089.
Liu, Y., Feng, H.K., Yue, J.B., Jin, X.L., Li, Z.H., Yang, G.J., 2022b. Estimation of potato
above-ground biomass based on unmanned aerial vehicle red-green-blue images
with different texture features and crop height. Front. Plant. Sci. 13, 938216 https://
doi.org/10.3389/fpls.2022.938216.
Liu, Y., Feng, H.K., Yue, J.B., Li, Z.H., Jin, X.L., Fan, Y.G., Feng, Z.H., Yang, G.J., 2022c.
Estimation of aboveground biomass of potatoes based on characteristic variables
extracted from UAV hyperspectral imagery. Remote Sens. 14, 5121–5149. https://
doi.org/10.3390/rs14205121.
Liu, Y., Feng, H.K., Yue, J.B., Fan, Y.G., Jin, X.L., Song, X.Y., Yang, H., Yang, G.J., 2022d.
Estimation of potato above-ground biomass based on vegetation indices and green-
edge parameters obtained from UAVs. Remote Sens. 14, 5323–5341. https://doi.
org/10.3390/rs14215323.
Liu, Y., An, L., Wang, N., Tang, W.J., Liu, M.J., Liu, G.H., Sun, H., Li, M.Z., Ma, Y.T.,
2023a. Leaf area index estimation under wheat powdery mildew stress by
integrating UAV-based spectral, textural and structural features. Comptut. Electron.
Agr. 213, 108169 https://doi.org/10.1016/j.compag.2023.108169.
Liu, Y., Feng, H.K., Yue, J.B., Fan, Y.G., Bian, M.B., Ma, Y.P., Jin, X.L., Song, X.Y.,
Yang, G.J., 2023b. Estimating potato above-ground biomass by using integrated
unmanned aerial system-based optical, structural, and textural canopy
measurements. Comptut. Electron. Agr. 213, 108229 https://doi.org/10.1016/j.
compag.2023.108229.
Liu, N., Zhao, R.M., Qiao, L., Zhang, Y., Li, M.Z., Sun, H., Xing, Z., Wang, X.B., 2020.
Growth stages classication of potato crop based on analysis of spectral response and
variables optimization. Sensors. 20, 3995–4015. https://doi.org/10.3390/
s20143995.
Luo, S.J., He, Y.B., Wang, Z., Duan, D., Zhang, J.K., Zhang, Y.T., Zhu, Y.Q., Yu, J.K.,
Zhang, S.L., Xu, F., 2019. Comparison of the retrieving precision of potato leaf area
index derived from several vegetation indices and spectral parameters of the
continuum removal method. Eur. J. Remote Sens. 52, 155–168. https://doi.org/
10.1080/22797254.2019.1572460.
Luo, S.J., Jiang, X.Q., He, Y.B., Li, J.P., Jiao, W.H., Zhang, S.L., Xu, F., Han, Z.C., Sun, J.,
Yang, J.P., 2022. Multi-dimensional variables and feature parameter selection for
aboveground biomass estimation of potato based on UAV multispectral imagery.
Front. Plant. Sci. 13, 948249 https://doi.org/10.3389/fpls.2022.948249.
Luo, M., Wang, Y.F., Xie, Y.H., Zhou, L., Qiao, J., Qiu, S.Y., Sun, Y.J., 2021. Combination
of feature selection and CatBoost for prediction: the rst application to the
estimation of aboveground biomass. Forests. 12, 216–238. https://doi.org/10.3390/
f12020216.
Marabel, M., Alvarez-Taboada, F., 2014. Spectroscopic determination of aboveground
biomass in grasslands using spectral transformations, support vector machine and
partial least squares regression. Sensors. 13, 10027–10051. https://doi.org/
10.3390/s130810027.
Narine, L., Popescu, S.C., Malambo, L., 2019. Synergy of ICESat-2 and Landsat for
mapping forest aboveground biomass with deep learning. Remote Sens. 11,
1503–1555. https://doi.org/10.3390/rs11121503.
Pott, L.P., Amado, T.C., Schwalbert, R.A., Corassa, G.M., Ciampitti, I.A., 2022. Crop type
classication in Southern Brazil: Integrating remote sensing, crop modeling and
machine learning. Comptut. Electron. Agr. 201, 107320 https://doi.org/10.1016/j.
compag.2022.107320.
Rao, N.R., Kapoor, M., Sharma, N., Venkateswarlu, K., 2007. Yield prediction and
waterlogging assessment for tea plantation land using satellite image-based
techniques. Int. J. Remote Sens. 28, 1561–1576. https://doi.org/10.1080/
01431160600904980.
Shew, A.M., Ghosh, A., 2019. Identifying dry-season rice-planting patterns in Bangladesh
using the Landsat archive. Remote Sens. 11, 1235. https://doi.org/10.3390/
rs11101235.
Shu, M.Y., Zuo, J.Y., Yin, P.F., Wang, M., Xie, Z.W., Tang, J.H., Wang, R.L., Li, B.G.,
Yang, X.H., 2021. The application of UAV-based hyperspectral imaging to estimate
crop traits in maize inbred lines. Plant Phenomics. 21 (9890745), 10.34133/2021/
9890745.
Steele, M.R., Gitelson, A., Rundquist, D.C., 2008. A comparison of two techniques for
nondestructive measurement of chlorophyll content in grapevine leaves. Agron. J.
100, 779–782. https://doi.org/10.2134/agronj2007.0254N.
Tilling, A.K., Ferwerda, J.G., Jones, S.D., Fitzgerald, G.J., Rodriguez, D., Belford, R.,
2007. Remote sensing of nitrogen and water stress in wheat. Field Crop Res. 104,
77–85. https://doi.org/10.1016/j.fcr.2007.03.023.
Wang, C., Feng, M., Yang, W., Ding, G., Xiao, L., Li, G., Liu, T., 2017. Extraction of
Sensitive bands for monitoring the winter wheat (Triticum aestivum) growth status
and yields based on the spectral reectance. Plos One. 12, 167679 https://doi.org/
10.1371/journal.pone.0167679.
Wang, Z.L., Ma, Y.M., Chen, P., Yang, Y.G., Fu, H., Yang, F., 2022. Estimation of rice
aboveground biomass by combining canopy spectral reectance and unmanned
aerial vehicle-based red green blue imagery data. Front. Plant Sci. 13, 903643
https://doi.org/10.3389/fpls.2022.903643.
Wu, C.Y., Niu, Z., Tang, Q., Huang, W.J., 2008. Estimating chlorophyll content from
hyperspectral vegetation indices: Modeling and validation. Agr. Forest. Meteorol.
148, 1230–1241. https://doi.org/10.1016/j.agrformet.2008.03.005.
Xing, H.M., Xu, X.G., Li, Z.H., Chen, Y.J., Feng, H.K., Yang, G.J., Chen, Z.X., 2017. Global
sensitivity analysis of the AquaCrop model for winter wheat under different water
treatments based on the extended Fourier amplitude sensitivity test. J. Integr. Agr.
16, 2444–2458. https://doi.org/10.1016/S2095-3119(16)61626-X.
Xu, L., Zhou, L.F., Meng, R., Zhao, F., Lv, Z.G., Xu, B.Y., Yu, X., Peng, S.B., 2022. An
improved approach to estimate ratoon rice aboveground biomass by integrating
UAV-based spectral, textural and structural features. Precis. Agric. 23, 1276–1301.
https://doi.org/10.1007/s11119-022-09884-5.
Xun, L., Zhang, J.H., Cao, D., Wang, J.W., Zhang, S., Yao, F.M., 2021. Mapping cotton
cultivated area combining remote sensing with a fused representation-based
classication algorithm. Comput. Electron. Agric. 181, 105940 https://doi.org/
10.1016/j.compag.2020.105940.
Yang, H.B., Li, F., Wang, W., Yu, K., 2021. Estimating above-ground biomass of potato
using random forest and optimized hyperspectral indices. Remote Sens. 13,
2339–2362. https://doi.org/10.3390/rs13122339.
Yue, J., Yang, G., Tian, Q., Feng, H., Xu, K., Zhou, C., 2019. Estimate of winter-wheat
above-ground biomass based on UAV ultrahigh-ground-resolution image textures
and vegetation indices. Isprs J. Photogramm. Remote Sens. 150, 226–244. https://
doi.org/10.1016/j.isprsjprs.2019.02.022.
Yue, J., Guo, W., Yang, G., Zhou, C., Feng, H., Qiao, H., 2021a. Method for accurate
multi-growth-stage estimation of fractional vegetation cover using unmanned aerial
vehicle remote sensing. Plant Methods. 17, 51. https://doi.org/10.1186/s13007-
021-00752-3.
Yue, J., Yang, H., Yang, G., Fu, Y., Wang, H., Zhou, C., 2023. Estimating vertically
growing crop above-ground biomass based on UAV remote sensing. Comput.
Electron. Agric. 205, 107627 https://doi.org/10.1016/j.compag.2023.107627.
Yue, J.B., Zhou, C.Q., Guo, W., Feng, H.K., Xu, K.J., 2021b. Estimation of winter-wheat
above-ground biomass using the wavelet analysis of unmanned aerial vehicle-based
digital images and hyperspectral crop canopy images. Int. J. Remote Sens. 42,
1602–1622. https://doi.org/10.1080/01431161.2020.1826057.
Zhang, J., Tian, H.Q., Wang, D., Li, H.J., Mouazen, A.M., 2020. A novel approach for
estimation of above-ground biomass of sugar beet based on wavelength selection and
Y. Liu et al.
Computers and Electronics in Agriculture 218 (2024) 108699
16
optimized support vector machine. Remote Sens. 12, 620. https://doi.org/10.3390/
rs12040620.
Zhang, Y., Xia, C.Z., Zhang, X.Y., Cheng, X.H., Feng, G.Z., Wang, Y., Gao, Q., 2021.
Estimating the maize biomass by crop height and narrowband vegetation indices
derived from UAV-based hyperspectral images. Ecolo. Indic. 129, 107985 https://
doi.org/10.1016/j.ecolind.2021.107985.
Zheng, H., Cheng, T., Zhou, M., Li, D., Yao, X., Tian, Y.C., Cao, W.X., Zhu, Y., 2019.
Improved estimation of rice aboveground biomass combining textural and spectral
analysis of UAV imagery. Precis. Agric. 20, 611–629. https://doi.org/10.1007/
s11119-018-9600-7.
Y. Liu et al.
