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Feasibility of applying hyperspectral imaging as a
rapid method for estimating potassium content
across different plant species datasets
Piotr Baranowski ( p.baranowski@ipan.lublin.pl )
Institute of Agrophysics PAS: Instytut Agrozyki im Bohdana Dobrzanskiego Polskiej Akademii Nauk
https://orcid.org/0000-0003-0979-177X
Anna Siedliska
Jaromir Krzyszczak
Artur Banach
Marcin Siłuch
Piotr Bartmiński
Agnieszka Wolińska
Przemysław Tkaczyk
Research Article
Keywords: potassium, hyperspectral imaging, precision farming, machine learning, regression models
Posted Date: November 9th, 2022
DOI: https://doi.org/10.21203/rs.3.rs-2190182/v1
License: This work is licensed under a Creative Commons Attribution 4.0 International License.
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1
Feasibility of applying hyperspectral imaging as a rapid method for estimating potassium content across 1
different plant species datasets 2
Anna Siedliska1, Piotr Baranowski1*, Jaromir Krzyszczak1, Artur Banach2, Marcin Siłuch3, Piotr Bartmiński3, 3
Agnieszka Wolińska2, Przemysław Tkaczyk4 4
1Institute of Agrophysics, Polish Academy of Sciences, ul. Doświadczalna 4, 20-290 Lublin, Poland 5
2The John Paul II Catholic University of Lublin, Department of Biology and Biotechnology of Microorganisms, 6
ul. Konstantynów. 1 I, 20-708 Lublin, Poland 7
3Institute of Earth and Environmental Sciences, Maria Curie-Skłodowska University in Lublin, al. Kraśnicka 2d, 8
20-718 Lublin, Poland 9
4 Department of Agricultural and Environmental Chemistry, University of Life Sciences in Lublin, Akademicka 10
15, 20-950 Lublin, Poland. 11
*corresponding author: Piotr Baranowski, p.baranowski@ipan.lublin.pl 12
Abstract 13
Purpose The accurate and frequent estimation of the leaf plant potassium concentration enabled by hyperspectral 14
imaging techniques has allowed growers to optimize fertilizer applications and reduce the negative impact on the 15
environment. In this study, we examined the feasibility of using leaf spectral data to accurately estimate the 16
potassium content in sugar beet and celery plants. 17
Methods Leaf images in the visible and near infrared region (VNIR: 400–1000 nm) and short-wavelength infrared 18
region (SWIR: 1000-2500 nm) were captured by a hyperspectral camera. The potassium content was measured by 19
ordinary destructive laboratory methods. The correlation-based feature selection (CFS) algorithm was 20
implemented to select important wavelengths that carried the most useful information for predicting the potassium 21
content in plant leaves. Four multivariate regression methods were tested to find a model with strong predictive 22
performance. 23
Results The experimental results showed that the Random Forest (RF) model using 12 bands (425, 443, 479, 599, 24
631, 662, 798, 863, 897, 921, 1978 and 2053 nm) had the highest accuracy for predicting potassium content in 25
sugar beet, celery and both plant datasets (Rp2 = 0.85, Rp2 = 0.79, and Rp2 = 0.81, respectively). 26
Conclusion The results confirm the universality of the described method. Although further validation studies 27
involving other plant species are needed, it appears that the spectral reflectance technique could be a promising 28
2
tool for the rapid, noninvasive and cost-effective estimation of K content in plant leaves, contributing to a 29
significant step forward in precision fertilization management. 30
Keywords: potassium; hyperspectral imaging; precision farming; machine learning; regression models 31
Introduction 32
Potassium (K) is a macronutrient that is crucial for plant growth and development. It plays an important role in 33
many physiological and biochemical processes, such as photosynthesis, osmoregulation, the transportation of 34
metabolites, the synthesis of enzymes, proteins, starches, and cellulose, and plant stress alleviation (Ahmad and 35
Maathuis 2014; Chen et al. 2021a; Lu et al. 2021). Potassium deficiency causes restrained development of the 36
rooting system, slow growth, low resistance to stress and diseases, delayed maturity, and reduced yields (Hafsi et 37
al. 2014; Hasanuzzaman et al. 2018). Although soil has rich K reserves, only 1-2% is available to plants (Zhang 38
and Kong 2014). Therefore, the appropriate supplementation of potassium to plants during their crucial stages of 39
growth is necessary to promote plant growth and increase crop yield. Excess doses and ineffective utilization of K 40
fertilizers may lead to pollution of the environment and underground water. Therefore, knowledge of spatial and 41
temporal variability is necessary to improve crop yield production while reducing operation costs and 42
environmental pollution. The current methods available for the diagnosis of crop K deficiency are mainly based 43
on visual observation followed by chemical diagnosis (de Bang et al. 2021), which is destructive, tedious and 44
neither economically viable on a large scale nor environmentally acceptable. Precision farming, which combines 45
sensors, robots, GPS, mapping tools and data analytics software to improve crop quality and farm profitability 46
while reducing the negative impact on the environment, needs rapid, accurate and timely determination of crop K 47
status for large fields. Hyperspectral imaging (HSI) offers rapid and nondestructive monitoring of plant growth 48
conditions (Asaari et al. 2019), soil parameters (Shen et al. 2020; Lin et al. 2020) and agricultural product quality 49
(Siedliska et al. 2018), so it can be successfully used for precise agriculture. 50
Studies have shown that the HSI technique can not only be successfully used to estimate nutrient element 51
contents, especially nitrogen, in plants (Li et al. 2021; Pancorbo et al. 2021; Song et al. 2021; Guo et al. 2021; 52
Wan et al. 2022) but also effectively overcome the limitations of traditional monitoring methods. Compared with 53
the prediction of N content, there are a limited number of reports that have attempted to estimate the potassium 54
content in plants. 55
Highly accurate results were obtained for monitoring K levels in rice (Lu et al. 2019, 2021), wheat 56
(Pimstein et al. 2011; Mahajan et al. 2014; Weksler et al. 2021), apple tree leaves (Guo et al. 2017; Chen et al. 57
3
2021b), olive (Gómez-Casero et al. 2007) and tea plants (Wang et al. 2020). Peng et al. (2020) used wavelengths 58
from 300 to 1000 nm to quantify the K contents of tree, shrub and grass species. Hyperspectral data within the 59
spectral range of 908–1735 nm were used to estimate the K content in tea leaves (Wang et al. 2020). These studies 60
have focused on the use of signals from the VNIR to estimate K nutritional status and have not taken advantage of 61
numerous spectral features related to leaf biochemistry, which can be observed in the SWIR spectrum. A 62
determination coefficient of 0.89 has been reached for the prediction of K concentrations in barley leaves based 63
on hyperspectral data in the range of 1,000 to 2,500 nm (Grieco et al. 2022). The same algorithm was used to 64
quantify the K content in maize and soybean leaves with an accuracy of 83% (Pandey et al. 2017) 65
Although many studies have attempted to estimate K content with reflectance spectra, no studies have 66
explored the quantitative models of K nutrition in vegetable crops and their transferability across different plant 67
species. The objectives of this paper were (1) to analyze the relationship between leaf spectral reflectance and K 68
content in plants and (2) to develop a model based on hyperspectral data for estimating plant K nutritional status 69
across different plant species. 70
Materials and methods 71
Plant materials 72
Here, 108 celery plants (Apium graveolens L., cv. Neon) and 108 sugar beet plants (Beta vulgaris L., cv. 73
Tapir) were used for the experiment. The celery (produced by SEMO) and sugar beet (produced by 74
SESVanderHave) seeds were purchased commercially. The celery and sugar beet seeds were sown in plastic pots 75
containing peat moss. After 7 weeks, seedlings of similar sizes were transplanted to 20 cm-diameter pots (one 76
seedling per pot) containing sand as the growth media. The plants were grown in the greenhouse under natural 77
sunlight supplemented with LED light using a day/night photoperiod of 12/12 h, with temperatures ranging from 78
20 °C to 22 °C during March – June and September and from 24 °C to 26 °C during July – August. Since the 79
ultimate goal of regression analysis was to predict the amount of K in plant leaves across different plant species, 80
we wanted to record a wide range of measured K content values. Therefore, in this experiment, the plants from 81
each species were divided equally into four groups with 27 plants each and were subjected to four different K 82
rates, where K was applied to the pots to stimulate different nutrient levels in plant leaves to test the hyperspectral 83
imaging system. Plants were irrigated with a treatment solution containing various quantities of potassium sulfate 84
(K2SO4) to obtain four different fertilization doses, K33, K67, K100, and K133. The K concentration of the control 85
4
treatment solution (K100) was 164.8 mg L-1 (Inthichack et al., 2012). Other treatments included 1/3, 2/3, and 4/3 86
of this value. To provide a source of nitrogen and phosphorus, the treatment solution contained 33.3 mg/l of N and 87
13.3 mg/l of P applied as NH4NO3 and Ca(H2PO4)2, respectively. The concentrations of the micronutrients B, Fe, 88
Zn and Mo were 0.28, 2.4, 1.0, 0.35 and 0.05 mg/l, respectively. They were applied as a commercial fertilizer, 89
Micro Plus (produced by Intermag, Olkusz, Poland). Each plant was irrigated with treatment solution every two 90
days for 60 days. Data collection was performed three times (21, 31 and 51 days after transplanting) at differing 91
stages of plant development. The developmental stages of sugar beet correspond to leaf development (BBCH 14) 92
and rosette growth (BBCH 28 and 35). For celery, we recorded data at BBCH stages 14, 42 and 45. In these stages, 93
potassium supplementation is expected to have the greatest effect on plant growth and yield (Prośba-Białczyk., 94
2017). At each stage, the leaf gas exchange of nine samples from each experiment was measured. After that, the 95
plants were scanned using hyperspectral imaging and transferred to the laboratory for chemical analysis. 96
Chemical analysis of macronutrient content 97
The potassium content of plant leaves was measured using a standard chemical procedure. Fresh leaves 98
were cut and oven-dried (105 °C for 0.5 h followed by 80 °C) until a constant weight was attained. Dried leaves 99
(ca. 0.3 g) were digested in triplicate in a mixture of 65% HNO3 and 30% H2O2 (6:2) using ultra-pure reagents. 100
Digestion was conducted using a microwave Ethos One mineralizer (Milestone Srl., Italy). The obtained solutions 101
were diluted to 100 ml and analyzed for K using a Hitachi Z-8200 spectrophotometer (Hitachi, Japan). The results 102
were expressed as mg/g dry weight. The total leaf phosphorous content was determined colorimetrically 103
(AutoAnalyser AA3, BranLuebbe) according to the manufacturer’s instructions: Method No. G-189-97 Rev.3. 104
Before analysis, the samples were digested in 8 ml of concentrated sulfuric acid (VI) using an Ethos One 105
(Milestone) mineralizer. The total leaf nitrogen content was determined by a LECO TruSpec analyzer using a dry 106
combustion method at a temperature of 950 °C. 107
Leaf gas exchange 108
Leaf gas exchange, such as the photosynthetic rate and transpiration rate, was measured using an LCi-SD 109
Portable Photosynthesis System (ADC Bio Scientific Ltd., UK). The measurements were carried out between 110
10:00 and 12:00 on the first fully expanded leaves from nine plants for each treatment. 111
Hyperspectral imaging system 112
5
To extract spectral information from each leaf, two cameras were used to capture both VNIR and SWIR 113
images. The cameras were mounted 40 cm above a belt conveyor (Reall, Lublin, Poland) with the belt speed 114
regulated for each camera separately (to conduct line scanning of the plant leaves). The illumination system Brilum 115
(Piaseczno, Poland) model LAVADO416 has 4 lighting modules, each of which contain four 20-W halogen lamps 116
(Philips, Netherlands) fixed in two opposite frames positioned at an angle of 45° toward the conveyor belt surface. 117
The VNIR images covering 269 spectral bands in the range of 400 nm to 1000 nm were obtained with a spectral 118
sampling interval of 2.8 nm using a VNIR camera with an ImSpector V10E imaging spectrograph. The SWIR 119
camera with an N25E 2/3” imaging spectrometer (Specim, Oulu, Finland) captured a total of 224 images from 120
each plant leaf, with each value corresponding to a specific wavelength inside the 1000–2500 nm range. 121
Spectral data preprocessing 122
The spectral data obtained from hyperspectral instruments usually contain a considerable amount of 123
background information and noise in addition to the sample information. Spectral preprocessing enhances the 124
absorbance features of spectra by reducing abnormalities in spectral measurements, such as noise, uncertainties, 125
variabilities, interactions, and unrecognized features (Mishra et al. 2020). Data at both ends of the spectrum 126
obtained from VNIR (<400 nm and >970 nm) and SWIR (<1100 nm and >2400 nm) were excluded due to 127
increased noise most likely caused by ambient light or a low signal-to-noise ratio (Duranovich et al. 2020). First, 128
raw spectra obtained from plant leaves were transformed using baseline correction, in which the lowest value was 129
subtracted from all the remaining values in the spectrum. Second, the second derivative Savitzky–Golay filter 130
(second-order polynomial fitting and nine-data-points window size) was applied. The data processing methods 131
were implemented using Unscramble X10.3 software (CAMO Software, Inc., Oslo, 133 Norway). 132
Optimal wavelength selection 133
Selection of the wavelengths carrying the most information is necessary for reducing multicollinearity and 134
redundancy between adjacent wavelengths, as well as for the improvement of the predictive performance of 135
models. If the redundant wavelengths are eliminated and the optimal variables are selected, the modeling process 136
can be simplified and the model performance improved while also facilitating online industrial applications or 137
simple cost-effective multispectral systems. In the current study, the CFS algorithm with the greedy stepwise 138
selection method was applied to the second derivative transformation of the original spectra. The usefulness of the 139
CFS method for selecting the optimal feature subset was confirmed in previous studies (Siedliska et al. 2017; Guo 140
et al. 2020). 141
6
Modeling framework 142
In this study, three different datasets (two datasets for each plant species and one for both plant species 143
together) were used for the determination of the K content in plant leaves. These datasets contained varying types 144
of input information: measured leaf K content and leaf reflectance at 400–2400 nm. To evaluate the model 145
performance, leaf samples in each dataset were randomly divided into calibration and prediction datasets at a ratio 146
of 75:25 using a standard procedure within an open-source computer program called the Waikato Environment for 147
Knowledge Analysis (WEKA). This subsampling proportioning for calibration of the prediction sets was 148
recommended and commonly used for plant samples (Li et al. 2020; Siedliska et al. 2021) To evaluate the 149
effectiveness of machine learning approaches, four regression algorithms were selected for comparison and further 150
understanding of the relationship between dependent and independent variables: the k-nearest neighbors algorithm 151
(kNN), support vector regression (SVR), random forest (RF) and linear regression (LR). The chosen algorithms 152
represent various approaches to machine learning, covering the classes of functions, decision trees and lazy 153
regressors (used only to prepare their inputs until classification time). These algorithms were successfully used in 154
previous studies for regression problems associated with hyperspectral data analysis (Siedliska et al. 2018; Garg 155
et al. 2019; Wu et al. 2020; Gargade and Khandekar 2021). The features of all the algorithms used, their 156
differences, and their advantages and disadvantages are presented in Table. 1. All the algorithm tuning steps were 157
performed on the calibration data, and evaluations of model performance were performed on the prediction dataset. 158
The accuracy and performance of each model were evaluated using the coefficient of determination (R2), root 159
mean square error of calibration (RMSEC) and prediction (RMSEP), and mean square error of calibration (MSEC) 160
and prediction (MSEP). 161
162
Table 1 The description and main parameters of the model used for prediction of potassium content in sugar beet 163
and celery plants 164
7
Name of
classifier’s
library
Description of algorithm
Acronym
Chosen
parameters
of classifier
kNN
K-nearest neighbours classifier (also known as “Instance
based” learning) is a simple classification and regression
algorithm based on similarity (distance) calculation between
the instances. It implements rote learning which is based on a
local average calculation (Altman, 1992).
Advantages: Simplicity and intuitiveness of use. Highly
flexible decision boundary adjusting the value of K. No
training time for classification. When adding new data to the
dataset, the prediction is adjusted without having to retrain a
new model. It’s very easy to tune hyperparameter K.
Disadvantages: Problems with large datasets (prediction
complexity, long processing time). The algorithm assumes
equal importance to all features. Sensitive to outliers. A single
mislabeled example can change the class boundaries.
kNN
Num of
neighbours: 3
Batch Size: 100;
Debug: false;
Distance
Function:
Euclidean
distance;
Linear
Regression
A class for using linear regression for prediction (Adichien,
1967).
Advantages: Performs exceptionally well for linearly
separable data. Easy to implement, interpret and efficient to
train. Possible extrapolation beyond a specific data set.
Resistant to overfitting problems.
Disadvantages: Sensitive to outliers. Quite prone to
underfitting. In many cases the assumption of the linearity
between dependent and independent variables is too big
simplification (multicollinearity must be removed before
applying the algorithm).
LR
Attribute selection
method: M5
method;
Batch size:100;
Debug: false;
Num of Decimal
Places:4
Support
Vector
Regression
A supervised learning algorithm that is used to predict
discrete values. It uses the same principle as the Support
Vector Machines (SVM). The algorithm tries to find the best
fit line which is the hyperplane that has the maximum number
of points (Smola and Schölkopf , 2004).
Advantages: Excellent generalization capability. Usually,
high prediction accuracy. Robust to outliers. Easy to be
implemented. Decision model can be easily updated.
Disadvantages: Not always effective with large datasets.
Does not perform very well when the data set has more noise.
Underperforms, if the number of features for each data point
exceeds the number of training data samples.
SVR
Debug: false;
Kernel function
Type:
Polynominal
Kernel;
C: 1;
gamma: 0.1;
Epsilon: 0.01;
Normalize: true;
Random
Forests
Classifier for constructing a forest of random trees (Breiman,
2001).
Advantages: Suitable for complicated tasks because of
handlling variables very fast. Very effective when working
with big data with numerous variables. Contains algorithms
for filling in missing values in datasets.
Disadvantages: The computations may go far more complex
compared to other algorithms (time and resources
consuming).
RF
Debug: false;
MaxDepth: 0;
Num of Features :
0;
Num of Trees: 10;
Seed : 1
8
Results 165
Leaf nutrient concentrations and changes in photosynthesis parameters at different potassium fertilization 166
doses 167
The average K concentrations, transpiration rates, photosynthetic rates (bars) and standard deviations 168
(whiskers) across three stages of plant growth and for various doses of soil K supply for sugar beet and celery are 169
presented in Fig. 1 and Fig. 2. It was observed that independent of the studied species, the highest concentrations 170
of K in the plant leaves occurred in the first stage of plant development for all K supply doses (Fig. 1a and 2a). 171
The K concentrations in the first development stage for all levels of K supply were up to 2 times higher than those 172
for the two other stages of plant development. This result confirms that at the plant development stage, K 173
accumulates mainly in the leaves, while at the leaf development stage, when root development prevails, the 174
accumulation of K in the leaves diminishes as a result of the higher K needs for root growth. Figs. 1 (b-c) and 2 175
(b-c) also show that both transpiration rates and photosynthetic rates reach the highest values for the recommended 176
K supply dose (K100) and the second stage of plant development. A shortage (K33) or excess (K133) of K caused 177
a considerable decrease in transpiration and photosynthetic rates for both studied species at each developmental 178
stage. These results indicated that an inappropriate K supply could limit photosynthesis through stomatal 179
restrictions, which is consistent with previous studies (Cakmak 2005; Xu et al. 2020). 180
The K, P and N contents in the plant leaves under various doses of K supplied to the soil, combined with 181
data from the entire experiment (3 stages of plant development), are shown in Fig. 3 and Fig. 4 in the form of 182
boxplots. These plots display the distribution of the data based on a five-number summary, including minimum 183
and maximum values (ends of the whiskers), the first and third quartiles (2 horizontal lines closing boxes), the 184
median (the bold lines inside the boxes) and the outliers (individual points in the plots). As expected, the medians 185
of the leaf potassium content increased gradually with increasing doses of potassium for both studied species, with 186
the K133 level in sugar beet being the only exception (Fig. 3a and Fig. 4a). The lowest variations in leaf K content, 187
expressed as the lowest range between the minimum and maximum values, were observed for K33, both in celery 188
and sugar beet, and the highest variation was observed for K133. The range of K contents between the first and 189
third quartiles is the lowest in both studied species for K33, which confirms that at this level of K concentration in 190
the soil, the accumulation in the plant was limited and did not change across plant growth stages. This suggests 191
that during plant growth, the content of K in the leaves changes considerably depending on the availability of this 192
macroelement in the soil. 193
9
194
Fig. 1 Bar charts of leaf potassium content (a), transpiration rate (b) and photosynthetic rate (c) in response to 195
different potassium fertilization doses on sugar beet. Values followed by different letters in the same lines are 196
significantly different according to Duncan's multiple range test (p < 0.05) 197
198
0
10
20
30
40
50
K33 K67 K100 K133
Potassium content (mg/g)
Sugar Beet
I stage II stage III stage
c
a
b
a
b
b
b
b
b
a
a
b
a)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
K33 K67 K100 K133
Transpiration rate (mmol m-2 s-1)
I stage II stage III stage
a
a
a
a
a
b
b
a
a
b
a
a
a
b)
0
1
2
3
4
5
6
7
8
K33 K67 K100 K133
Photosyntetic rate (µmol m-2 s-1)
I stage II stage III stage
b
b
a
a
a
a
ab
a
a
a
a
c)
a
10
199
Fig. 2 Bar charts of leaf potassium content (a), transpiration rate (b) and photosynthetic rate (c) in response to 200
different potassium fertilization doses on celery. Values followed by different letters in the same lines are 201
significantly different according to Duncan's multiple range test (p < 0.05) 202
203
204
a)
b
0
10
20
30
40
50
K33 K67 K100 K133
Potassium content (mg/g)
Celery
I stage II stage III stage
a
b
a
b
b
a
a
b
b
b
b
b)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
K33 K67 K100 K133
Transpiration rate (mmol m-2s-
1)
I stage II stage III stage
a
a
b
b
a
a
b
a
a
a
a
a
a
0
1
2
3
4
5
6
7
8
K33 K67 K100 K133
Photosyntetic rate (µmol m-2 s-
1)
I stage II stage III stage
a
a
a
a
a
a
a
a
b
c
a
a
c)
11
K fertilization rates had no significant effect on the P content in sugar beet foliage (Fig. 3b). This result 205
is in agreement with a study by Abdel-Motagally et al. (2009). On the other hand, the P concentration in K33, K67 206
and K100 for celery plants slightly increased with an increase in K supply (Fig. 4b). However, a further increase 207
in the K dose (K133) caused a decrease in the P concentration in celery leaves. The data presented in Fig. 3c and 208
Fig. 4c revealed that the leaf nitrogen content in both plant species was not significantly affected by the K 209
application dose. 210
211
Fig. 3 Boxplots of leaf potassium (A), phosphorus (B) and nitrogen (C) contents in response to different potassium 212
fertilization doses on sugar beet. Boxes represent interquartile range, whiskers represent minimum and maximum 213
values, dots represent outliers, and bold lines represent median values 214
12
215
Fig. 4 Boxplots of leaf potassium (A), phosphorus (B) and nitrogen (C) contents in response to different potassium 216
fertilization doses on celery. Boxes represent interquartile range, whiskers represent minimum and maximum 217
values, dots represent outliers, and bold lines represent median values 218
Spectral features of leaves 219
Example raw reflectance spectra and spectra transformed with the second derivative of chosen leaves 220
from different experiments (various K supply doses) are presented in Fig. 5. The leaf spectra showed similar 221
patterns across all sugar beet and celery treatments. However, the K100 spectra differed significantly from those 222
for the other treatments, especially in the NIR and SWIR ranges. In the second derivative spectra, this difference 223
was also visible, especially for the peaks at 700, 1400, 1850, 1920, 2300 and 2350 nm. Because the main objective 224
of the study was to estimate the K content in the plant leaves using the hyperspectral characteristics, the spectra 225
transformed with the second derivative were used as inputs into the chosen machine learning algorithms. 226
13
227
Fig. 5 Mean reflectance spectra (a, b) and their second derivatives (c, d) for sugar beet and celery leaves treated 228
with four different potassium fertilization doses 229
K prediction models based on spectral characteristics 230
After the evaluation of the reflectance spectra of the plant leaves under different treatments, it was 231
expected that in the band selection process for artificial intelligence processing, the spectral wavelengths from 232
NIR/SWIR ranges would be dominant, which was partially confirmed for the spectra of the two studied species. 233
However, after performing the automatic CFS algorithm for wavelength selection, among the twelve characteristic 234
wavelengths selected for supervised regression analysis, there were six VNIR bands. All the bands selected for the 235
prediction of K content were as follows: 425, 443, 479, 599, 631, 662, 798, 863, 897, 921, 1978 and 2053 nm. 236
The subsampling of the data for the calibration and prediction datasets yielded similar statistical properties 237
and a wide variation in the K content in these datasets, which was especially important from the point of view of 238
proper model creation and testing. The statistical properties of the calibration and prediction datasets are 239
summarized in Table 2. The distributions of outcome and predictor variables on the calibration and prediction sets 240
were similar. The effect of leaf potassium content (mg/g) in sugar beet on the calibration dataset had a median of 241
21.06 and a range of 5.52 to 43.45, and on the prediction dataset, its median was 23.61 with a range of 7.08-41.91. 242
For celery leaves, the effect of the potassium leaf content on the calibration dataset had a median of 16.81 and a 243
14
range of 5.24-50.69, and on the prediction dataset, its median was 19.37 with a range of 5.76 to 50.88 mg/g. This 244
suggests that the K contents in the calibration and prediction datasets were within very similar ranges, indicating 245
that the sample divisions were reasonable and that the prediction set could have been employed to assess the 246
performance of the developed models. 247
Table 2 Summary statistics of measured K content (mg/g) in sugar beet and celery leaves in training and test data 248
sets 249
Plant
Sample set
N
Range
Mean
Median
SD
Sugar beet
Training
81
5.52 - 43.45
22.25
21.06
9.39
Test
27
7.08 - 41.91
25.65
23.61
10.62
Celery
Training
81
5.23 - 50.69
19.06
16.81
10.43
Test
27
5.76 - 50.88
23.05
19.37
13.13
N, number of samples; SD, standard deviation
The results of the supervised regression modeling of the K content in sugar beet, celery and both species 250
datasets, performed with the use of four selected algorithms from the calibration and prediction datasets, are 251
presented in Table 3. This table contains the main statistical parameters of the created models, including MSE, 252
RMSE and R2 values. The results from this table show that all studied models yield good performance with R2
253
values for the calibration dataset ranging from 0.83 to 0.98 and those for the prediction set ranging from 0.68 to 254
0.85 (considering all the algorithms used). The best-fitted model was selected based on the highest values of R2 255
and the smallest values of RMSE. From all the selected model classes, the RF models based on 12 selected 256
wavelengths showed the best effectiveness. The RF model for the sugar beet K content gave higher prediction 257
accuracy (Rp2 equal to 0.85, MSEP 4.93 and RMSEP 5.77) than that for celery (Rp2 equal to 0.79, MSEP 6.57 and 258
RMSEP 8.27). Comparably high prediction performance of the RF model for K content (Rp2 equal to 0.81, MSEP 259
5.09 and RMSEP 6.33) was obtained based on the dataset incorporating both celery and sugar beet spectral 260
characteristics. This result indicates the possibility for universal use of the created K content models, i.e., 261
independent of the species and stage of plant growth. This result is especially encouraging as it was not found in 262
previous studies. Of course, the authors are conscious that further studies incorporating more vegetable species 263
differing in spectral features of their leaves and growth physiology are urgently needed to confirm the versatility 264
of the created models. 265
15
Table 3 Performances of the models for predicting potassium content (mg/g) in the leaves of sugar beet, celery 266
and both plants together 267
Model
Calibration set
Prediction set
MSEC
RMSEC
Rc2
MSEP
RMSEP
Rp2
Sugar beet
kNN
3.13
4.12
0.90
5.77
7.30
0.73
SVR
3.58
5.10
0.85
5.96
7.70
0.74
RF
1.80
2.30
0.98
4.93
5.77
0.85
LR
3.86
4.99
0.85
5.76
7.45
0.72
Celery
kNN
3.35
4.42
0.91
6.93
8.28
0.78
SVR
3.87
5.93
0.83
7.66
10.45
0.68
RF
1.68
2.13
0.98
6.57
8.26
0.79
LR
4.23
5.51
0.85
0.71
9.74
0.71
Sugar beet and Celery
kNN
3.52
4.79
0.89
5.48
6.61
0.81
SVR
4.44
6.12
0.83
5.28
6.99
0.78
RF
1.84
2.34
0.98
5.09
6.33
0.81
LR
4.61
6.03
0.83
5.62
7.10
0.77
268
The scatter plots of the regression analysis for predicted and measured values of K content in sugar beet, 269
celery and the combined dataset for these two plant species are shown in Fig. 6, including the results of the RF 270
models created based on the spectral data of 12 effective wavelengths. The plots contain the data points belonging 271
to the calibration and prediction sets, marked as circles and triangles, respectively, and statistical parameters of 272
model performance. In general, all three created models show a good fit to the 1:1 line (dashed line in the plot), 273
indicating that the predicted values of the models were close to the value measured by the chemical method. All 274
three RF models were prone to slightly overestimating low values and underestimating the highest values of K 275
content in plant leaves. 276
16
277
Fig. 6 The measured and predicted potassium contents in sugar beet (a), celery (b) and both plant datasets (c) 278
obtained by the RF model based on spectral data from 12 selected wavelengths 279
Discussion 280
The presented results broaden the existing knowledge about the possibility of using hyperspectral 281
reflectance data for evaluating the K content in the plants. The previous attempts to discover the relation between 282
the reflectance spectra and the K content in the leaves was mainly focused on cereals (Pimstein et al. 2011; Mahajan 283
et al. 2014; Pandey et al. 2017; Lu et al. 2021; Weksler et al. 2021; Grieco et al. 2022) and trees ( Gómez-Casero 284
et al. 2007; Guo et al. 2017; Chen et al. 2021b), while the root vegetables which are very sensitive for K deficiency 285
(Prośba-Białczyk et al. 2017) were not considered. Our study is also an one of the few attempts to include in the 286
supervised regression models the reflectance data including the VNIR/SWIR ranges. Among the wavelengths 287
selected by the automatic CFS procedure, two were within the far SWIR range (1978 and 2053 nm) what is in 288
agreement with the studies of Xu et al. (2020) and Rani et al. (2021), who emphasized the importance of these 289
wavelengths in K content estimation. The absorption bands in this region are related to changes in starch 290
(wavelengths near 1978 nm) and protein contents (2055 nm), which are highly influenced by K fertilization. 291
17
Although the automatic selection of the wavelengths for regression models was used in our study, the majority of 292
VNIR wavelengths were close to these used by Peng et al. (2020) and Liu et al. (2020). In general the CFS 293
algorithm is applied to remove irrelevant and redundant information from the spectra, based on the individual 294
predictive ability of each feature and the degree of correlation between all the features (Hall 1998), however it was 295
indicated in the previous studies that the bands selected using this algorithm strongly correlate with some physical 296
features of the studied biological materials (Baranowski et al. 2013, Siedliska et al. 2017). K deficiency was 297
suggested to produce an intensification of the reddish color as a consequence of increased anthocyanin content in 298
the distal part of the plant (Rustioni et al. 2018), which explains the band selection results in the range between 299
520 and 650 nm. Wavelengths of approximately 443 nm and 471 nm are associated with carotenoid content, and 300
those of approximately 662 nm are associated with chlorophyll b (Zhang et al. 2020), which has some correlation 301
with plant potassium fertilization, as demonstrated in previous work (Xu et al. 2020). 302
To date, the possibility of applying the HSI technique for the determination of K status in plants has been 303
poorly documented. Our results showed better performance of the machine learning regression model than that 304
found in previous studies. For instance, Zhang et al. (2013) employed the hyperspectral image analysis technique 305
and PLSR model to map the distribution of K in oilseed rape leaves and achieved the best prediction with a 306
coefficient of determination of Rp2 = 0.746. The potassium concentration of tea plant leaves has also been predicted 307
with Rp2 = 0.84 based on eight wavelengths selected from the spectral range of 908.15–1735.68 nm by using a 308
successive projections algorithm (Wang et al. 2020). However, in this study, the effects of different fertilization 309
conditions and growing seasons on the K concentration were not considered. The prediction of K content in the 310
orange leaves was conducted by Osco et al. (2020) with an Rp2 = 0.76 for one cultivar at a specific growth stage 311
(vegetative stage). Another study of K content determination in rice leaves focused on the creation of three-band 312
indices (Lu et al., 2019). In their study, prediction models with R2 = 0.74 were obtained with selected bands that 313
were similar to the ones used in our models. The red edge bands, from 660 to 800 nm, showed improved accuracies 314
and stabilities for estimating K content. From all models studied in our research the best performance (Rp2 0.85, 315
0.79, and 0.81 for sugar beet, celery and dataset incorporating both plants, respectively) was obtained for RF 316
model. It may be because this model combines ensemble learning methods with the decision tree framework and 317
averages the results to output a new result. This algorithm led to strong predictions in previous studies concerning 318
problems due to complicated relationships between attributes (Breiman, 2001; Shuryak, 2022). Its practical use 319
for K content estimation in plants is especially promising because of its ability to process datasets with many 320
18
attributes related in a complicated way and capture linear and nonlinear dependencies and interactions. Moreover, 321
this model can handle numerical as well as categorical variables, which is especially useful for analyzing data on 322
macronutrient content in plant leaves across different plant species. The wide range of variability in the potassium 323
content as a predictor in the elaborated models was a consequence of the experiment containing multiple treatment 324
combinations (leaves of two species treated with four potassium fertilization doses measured at three development 325
stages). Due to the broad range of K content values in the leaves of the studied plants, the main disadvantage of 326
RF modeling, i.e., the inability of this approach to extrapolate data outside the calibration set, was minimized , 327
which contributed to the best prediction accuracy of RF models. The efficiency of the three other regression 328
algorithms used for K content estimation was slightly lower (in the prediction sets, Rp2 changed from 0.68 to 0.81, 329
RMSEP from 6.61 to 10.45 and MSEP from 5.28 to 7.66). From among these models, the kNN regressor gave the 330
best prediction results for all the treatments during modeling and was not much worse than the RF algorithm. This 331
good performance of the kNN algorithm was confirmed in previous studies (Osco et al. 2020) of biophysical 332
materials, which emphasized the advantage of modeling based on local average calculations, which enables the 333
description of nonlinear processes dominating the functioning of live organs. It was found in a previous study 334
(Ragel et al. 2019) that the K+ transition in the living organs of plants shows a steep curvilinear relationship 335
between the concentration of K+ in tissues and plant growth. Therefore, models based on linear correlations 336
between variables, such as PLSR, which was used frequently in previous studies (Zhang et al., 2013), gave much 337
worse correlations between the K content and spectral features of the leaves. Similar results were found for the LR 338
model used in our study (its prediction accuracy was the worst among all the studied algorithms). 339
The high accuracy of our models can be partially explained by the broad spectral range (400-2500 nm) 340
used for the analysis, while previous studies mostly used the VNIR spectral range (Zhang et al. 2013; Li et al. 341
2018; Peng et al. 2020). Furthermore, our study is the first to use HSI for the prediction of the K content across 342
two different plant species combined into one model. 343
Conclusions 344
The proposed approach uses reflectance spectral data in the visible and near-infrared regions of leaf 345
surfaces to predict the K content in two vegetable plant species. It was found that leaf spectral reflectance, 346
especially in visible and near-infrared regions, was very sensitive to plant K fertilization status. The advantage of 347
the performed analyses and the created regression models is that a broad range of K concentrations and 3 stages 348
of plant development were considered. An important outcome of this study involves the identification of the 349
19
universal wavelengths for reflectance spectra (only partially coinciding with previously reported spectra), which 350
contributes to the prediction of the K content in different plant species that is responsible for changes in 351
anthocyanin, carotenoid and chlorophyll b contents as well as starch and protein concentrations. The current study 352
showed the great potential of using hyperspectral imaging to predict K content with high accuracy across different 353
plant species. The modeling approach based on testing several different regression procedures enabled the 354
identification of an RF algorithm that combines ensemble learning methods with the decision tree framework as 355
the best suited model for the task of K concentration analysis in plants. This model resulted in prediction accuracies 356
reaching 85%, which seems very promising given that no earlier attempts to evaluate the K content in celery and 357
sugar beet have been reported in the literature. The measurement and analytical methods used here are a good 358
starting point for developing a multispectral imaging system that measures K content in real time. In the future, 359
we plan to adapt the methods and results of this study to create a system that will be able to evaluate K status in a 360
broad range of plant species. Such a multispectral set of sensors embedded in UAVs operating under field 361
conditions is highly needed for precision farming and would reduce labor/time consumption and costly chemical 362
K analyses. 363
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Statements and Declarations 513
Funding: This paper was partially financed by funds from the Polish National Centre for Research and 514
Development in the frame of the project “MSINiN”, contract number: BIOSTRATEG3/343547/8/NCBR/2017. 515
The funding source had no role in the design of this study, data collection analyses or interpretation, the decision 516
to publish results or the preparation of the manuscript. 517
Competing interests: All the authors declare they have no financial interests. 518
Data availability: The datasets generated during and/or analysed during the current study are available from the 519
corresponding author on reasonable request. 520
25
521
