# Machine Learning for Estimating Leaf Dust Retention Based on Hyperspectral Measurements

Authors: Wenlong Jing; Xia Zhou; Chen Zhang; Chongyang Wang; Hao Jiang
Journal: Journal of Sensors
 (2018)

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## Abstract

Hyperspectral sensors provide detailed information for dust retention content (DRC) estimation. However, rich hyperspectral data are not fully utilized by traditional image analysis techniques. We integrated several recently developed machine learning algorithms to estimate DRC on plant leaves using the spectra measured by the ASD FieldSpec 3. The experiments were carried out on three common green plants of southern China. The important hyperspectral variables were first identified by applying the random forest (RF) algorithm. Three estimation models were then developed using the support vector machine (SVM), classification and regression tree (CART), and RF algorithms. The results showed that the increase in dust retention contents on plant leaves enhanced their reflectance in the visible wavelength but weakened their reflectance in the infrared wavelength. Wavelengths in the ranges of 450–500 nm, 550–600 nm, 750–1000 nm, and 1100–1300 nm were identified as important variables using the RF algorithm and were used to estimate the DRC. The comparison of the three machine learning techniques for DRC estimation confirmed that the SVM and RF models performed well because their estimations were similar to the measured DRC. Specifically, the averageR2 for SVM and RF model are 0.85 and 0.88. The technical approach of this study proved to be a successful illustration of using hyperspectral measurements to estimate the DRC on plant leaves. The findings of this study can be applied to monitor the DRC on leaves of other plants and can also be integrated with other types of spectral data to measure the DRC at a regional scale.


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## Body

## 1. Introduction

Haze has been an increasing air pollution issue with the rapid industrialization and urbanization of China [1, 2]. Urban green plants play a significant role in improving the urban atmospheric environment by retaining dust [3–5]. Measurement of the dust retention capacity of green plants is helpful for monitoring and controlling urban air pollution [6, 7]. It is also valuable for evaluation of the influence of green plants upon the urban atmospheric environment, further directing the arrangement and management of urban green plants [8, 9].The mass difference method is the most basic measuring approach of dust retention content (DRC) of plants [10, 11]. However, this method is complicated and time-consuming. In addition, the monitoring of DRC at the regional scale is impossible using the mass difference method. Remotely sensed hyperspectral technology has provided an efficient way for monitoring effects of environmental pollution on plants by measuring plant spectral characteristics [12–15]. Previous studies have investigated the influence of dust upon the spectral curve and characteristics of plants [16, 17]. According to Horler et al. [18], dust retention on leaves leads to a change in the red edge position, but experiments conducted by Xiao [19] showed that dust retention has no impact on the red edge position. The red edge position, according to Wang et al. [20], is not sensitive to the influence of detained dust on leaves, but the red edge slope and the area of the spectra of dust-covered leaves are smaller than those of dust-less leaves. In summary, the spectral characteristics of clean leaves differ from those of dust-covered leaves, which makes it possible to estimate the DRC of plant leaves based on remotely sensed spectral information [12, 19, 21, 22].Spectral information provided by hyperspectral measurement devices or sensors commonly includes hundreds of bands. Selecting the appropriate bands for a DRC estimation model is significant. The normalized difference vegetation index (NDVI), three-edge (blue, red, and yellow) positions, and slopes for use in constructing a DRC estimation model have been assessed through experimentation by some scholars [21, 23–25]. These variables, however, are mostly selected empirically; considerable useful information was excluded. Univariate/multiple linear regression and the partial least squares regression algorithm have been investigated to simulate the relationship between the DRC and spectral characteristics [16]. However, few studies have been conducted using machine learning. Machine learning, as a powerful modeling tool, has successfully improved the estimation and classification accuracy of environmental variables (air pollution, vegetation health condition, soil moisture, land surface temperature, etc.) and land cover types from remotely sensed images [26–32]. In addition, machine learning algorithms are excellent in solving nonlinear problems of variables with very high dimensions. Therefore, this study attempted to investigate the possibilities of constructing an estimation model for DRC using machine learning algorithms.The objectives of this study were to (1) investigate the effects of the DRC on the spectral characteristics of leaf surfaces, (2) extract important bands from hyper spectra to reduce the very high dimensions of the variables and further evaluate the effectiveness of the selected bands, and (3) construct a DRC estimation model using machine learning algorithms. In this study, we conducted the experiments on three commonly planted green plants in southern China, and the spectra were measured using an ASD FieldSpec 3 device. Three machine learning regression algorithms were used for DRC estimation model construction for comparison purposes.


## 2. Materials and Methods

### 2.1. Experimental Plants and Sampling Collection

For the research purpose, three plants were chosen as study objects, includingFicus microcarpa L. f. cv Golden leaves (GL), Loropetalum chinense (R. Br) Oliv. var. rubrum Yieh (LC), and Cordyline fruticosa (L.) A. Cheval (CF). These plants are the most common and typical green plants in southern China; investigation on these plants is beneficial to promoting the simulation of DRC to regional scale in the experiment area. Moreover, as is shown in Table 1, the leaves of three plants have different characteristics on color, size, shape, and surface texture. This is also helpful in detecting the usefulness and possibilities of simulating the DRC by using a machine learning algorithm on different plant leaves. To reduce the influence of extreme rainfall and wind, the plants were planted under an open greenhouse in Guangzhou (Figure 1). Figure 2 shows the three plants and their leaves.Table 1
Physical characteristics of the leaf surface.
Plants
Characteristics of the leaf surface
Microscopic feature
Dust retention feature
Color
Size
Shape
Texture
GL
Golden yellow or glossy dark green
3–8 cm
Ellipse
Leathery, fleshy and entire leaf, two sides smooth and glabrous
Many depressions in leaf caused by unequal-sized graininess wax, that lots of particle can adhere to them
Massive stratification
LC
Dull-red or green
2–5 cm
Oval or oblate ellipsoid, round root but deflect, asymmetric
Leathery and entire leaf, stellate leaf trichome in two sides
Rough leaf surface with villus
Mosaic particle
CF
Green or purplish red
25–50 cm
Ellipse to elliptical lanceolate
Smooth leaf surface
Cell profile distinct and aligned
Sporadic mosaic particleFigure 1
In situ experiment.Figure 2
The three plants and their leaves.Ten experiments were carried out from October 2017 to January 2018. Before the experiments, the plants were sufficiently washed to ensure a dust-free state on the leaves. Later, the leaves of the three plants were collected at an interval of 5–7 days on cloudless days. Leaves of similar health and age conditions were collected at the top, middle, and bottom of the canopy, respectively, and then sealed in sampling bags for the measurement of dust retention. Considering the different sizes of the leaves, the number of leaves collected for each plant was different. Among these, there were 30 pieces for GL, 50 pieces for LC, and 5 pieces for CF. Three replicate measurements were taken each time.


### 2.2. Measurement of Leaf Reflectance Spectra and Dust Content

#### 2.2.1. Measurement of Leaf Reflectance Spectra

Spectral measurements were recorded for each plant before and after dust retention to obtain the precise measurement of dust-related spectral changes. In the study, an ASD FieldSpec 3 spectrograph was used to measure the spectral reflectance of the leaves. The equipment was based on the basic theory of electromagnetic waves. The optical probe collected the electromagnetic waves reflected from the ground objects, which were later transformed into digital signals. The spectral range of this spectrograph was 350–2500 nm and with a sampling interval of 1 nm. The measuring speed was fixed at 0.1 s. The length of the optical probe was 1 m. The front field angle was 25°. The reflectance, radiation, and irradiance of the ground objects were simultaneously collected.At the same time of leaf collection, the spectral reflectance was measured from 10 : 00 to 14 : 30. The front sides of five leaves were both measured and repeated five times. After measurement, the leaves were sealed in corresponding bags and used to measure the DRC with the collected leaves. The probe should be perpendicular to the leaf, and the height should change according to the leaf size to guarantee spectrometer probe falls within the scope of the leaf. Specifically, the height from the probe to the leaf surface is calculated based on the equation as follows:(1)H≤WL/2tanθ/2,where H is the height, WL is the width of the leaf, and θ is the front field angle. Considering that the leaf size for one plant could also be different, we take the minimum width of each plant type as WL when calculating the height. For GL and LC, we take 2 cm as WL, then H is less equal to 4.5 cm; for CF, we take 20 cm as WL, then H is less equal to 45 cm. In practice, we used H of 4 cm for GL and LC, and 10 cm for CF.


#### 2.2.2. Measurement of Dust Content

In this study, the plant’s dust retention ability is represented by the dust content per unit leaf area, which is measured by the ratio of the leaf dust content and unit leaf area within a certain time [6]. The leaf dust content is measured by the weight difference method, and the unit leaf area is measured using a leaf area meter.The first procedure of the weight difference method is washing the leaves and then drying them. The weights of the two conditions should be measured, and the difference is considered to be the dust content. To avoid other effects on the experiment, the control variate method was used in this research. That means except for the liquid in the beaker, the soak time, dried water, drying temperature, drying time, and cooling time were the same. The detailed method is as follows:(1)
The collected leaves were sealed in a dried and weighted beaker (W1) corresponding to the bags, then soaked in pure water for 5–6 hours. At the same time, the sampling bag was washed using pure water and then poured into a beaker.(2)
The beaker was stirred with a clean glass rod to make the dust dissolve into the water. Then, the leaves were sufficiently washed twice using a tweezer and pure water. After washing, the tweezer and glass rod were washed, and the flushing water was poured into the soak beaker.(3)
The beaker was placed in the drying apparatus, and the temperature was set to 85°C and the drying time set to 25 hours. After drying, the beaker was placed in a drying vessel for 5 hours to cool down.(4)
The leaves were weighted (W2) using a ten-thousandth electronic analytical balance. The difference weight (ΔW=W2−W1) is the dust retention of the collected sample. The leaf area on the dried clean leaves of each bag was measured using the leaf area meter device. The ratio of dust retention ΔW/leaf area S is the unit leaf dust retention value.


### 2.3. Spectral Data Process

Before the spectral characteristic analysis, the noise and nonsensitive wave band needed to be removed from the collected spectral data, and the spectral transformation should be completed for the following research. First, to ensure the accuracy of the spectral measured data, we examined the five-times repeated spectral data of each point and removed the evident deviated curves. Then, the mean value was calculated. Second, to ensure the comparability of the measured data from different times and conditions and eliminate errors caused by the experimental environment, we divided it by the white board reflectance because the spectral reflectance should follow the principle of proximity. Then, we removed the bands that were assimilated by water vapor because water vapor assimilation has a great effect on the spectral curve, and this wavelength band range is meaningless in botany spectral research. To simplify the following data process, the wave bands were removed directly during this research. The result is shown in Figure3.Figure 3
Comparison before and after water vapor assimilation wave deletion.The first derivative spectra can reduce sublinear and quadratic background noise; it can also reduce the impact of the hyperspectral remote-sensing measurement because of the scattering and absorption of atmosphere to light [33]. It is also able to reduce the impact of multiplicative factors that are produced by changing lighting conditions [22]. Therefore, the first derivative spectra computed from the original measured reflection spectra were implemented to establish the estimation model of the DRC. The equation of the first derivative (dR) is expressed as follows:
(2)dRλi=Rλi+1−Rλi−1λi+1−λi−1.λ
i
+
1, λi, and λi−1 are the adjacent wavelengths; dR (λi) is the first derivative of wavelength λi; R (λi+1), R (λi), and R (λi−1) are the original reflectance of the wavelengths λi+1, λi, and λi−1, respectively.


### 2.4. Identifying Feature Importance and Estimating the DRC

In this section, we present our key innovation: integrating machine learning algorithms to identify the important spectral features (bands). We estimated the DRC based on these selected features and compared the effectiveness of the various machine learning algorithms. Our design is depicted in Figure4.Figure 4
Flowchart of the DRC estimation model.


#### 2.4.1. Identifying Feature Importance

The first derivative spectra were computed from the original measured reflection spectra. Over a thousand independent variables are provided in the original sample datasets. A feature selection needed to be conducted on the very high-dimensional datasets to exclude the redundant bands, further reducing the dimension of the sample sets. In this study, we implemented random forest (RF) to measure the feature importance (FI) of each band [34–36]. The FI values were then sorted from highest to lowest, and the cumulative value of 0.9 was used to derive the important variables.RF is an outstanding ensemble learning algorithm. The basic concept of the algorithm is to construct numerous tree-based predictors to obtain better performance [37, 38]. A number of subsets are extracted randomly from the total sample with replacement. The remaining samples are out-of-bag data (OOB). Then, a classification and regression tree (CART) was generated at each subset. The prediction was obtained by averaging all the outputs from the prediction of each subset. The feature importance of the bands can be described as follows:
(1)
The OOB of each subset were used to test the estimation of the corresponding tree, and the average errors of the OOB of all trees were calculated.(2)
The order of values of thekth variable was permuted while the other variables remain unchanged.(3)
The OOB error of the permuted set was calculated.(4)
The difference in the OOB error before and after the permutation was calculated for each variable, and the differences of all the variables were then normalized to a range of from 0 to 1.0, which were the FI values of the variables.


#### 2.4.2. Model for DRC Estimation

The DRC estimation model was established based on the selected variables. Three commonly used machine learning algorithms were used to construct the models between DRC and first derivative spectra. SVM, as a supervised learning algorithm, has performed well in many remote-sensing applications [39–42]. CART, as a tree-based algorithm, is easily implemented and has been widely used in a variety of fields [43–45]. The aforementioned RF algorithm, which has been used for variable selection, was also implemented to model the DRC. These three machine learning algorithms were selected for comparison of their effectiveness in establishing the DRC estimation model because of their extensive use, good performance, and easy implementation. For validation purposes, the total sample set was randomly divided into two subsets, with the 70% part used to train the model and the 30% part set aside for testing.


## 2.1. Experimental Plants and Sampling Collection

For the research purpose, three plants were chosen as study objects, includingFicus microcarpa L. f. cv Golden leaves (GL), Loropetalum chinense (R. Br) Oliv. var. rubrum Yieh (LC), and Cordyline fruticosa (L.) A. Cheval (CF). These plants are the most common and typical green plants in southern China; investigation on these plants is beneficial to promoting the simulation of DRC to regional scale in the experiment area. Moreover, as is shown in Table 1, the leaves of three plants have different characteristics on color, size, shape, and surface texture. This is also helpful in detecting the usefulness and possibilities of simulating the DRC by using a machine learning algorithm on different plant leaves. To reduce the influence of extreme rainfall and wind, the plants were planted under an open greenhouse in Guangzhou (Figure 1). Figure 2 shows the three plants and their leaves.Table 1
Physical characteristics of the leaf surface.
Plants
Characteristics of the leaf surface
Microscopic feature
Dust retention feature
Color
Size
Shape
Texture
GL
Golden yellow or glossy dark green
3–8 cm
Ellipse
Leathery, fleshy and entire leaf, two sides smooth and glabrous
Many depressions in leaf caused by unequal-sized graininess wax, that lots of particle can adhere to them
Massive stratification
LC
Dull-red or green
2–5 cm
Oval or oblate ellipsoid, round root but deflect, asymmetric
Leathery and entire leaf, stellate leaf trichome in two sides
Rough leaf surface with villus
Mosaic particle
CF
Green or purplish red
25–50 cm
Ellipse to elliptical lanceolate
Smooth leaf surface
Cell profile distinct and aligned
Sporadic mosaic particleFigure 1
In situ experiment.Figure 2
The three plants and their leaves.Ten experiments were carried out from October 2017 to January 2018. Before the experiments, the plants were sufficiently washed to ensure a dust-free state on the leaves. Later, the leaves of the three plants were collected at an interval of 5–7 days on cloudless days. Leaves of similar health and age conditions were collected at the top, middle, and bottom of the canopy, respectively, and then sealed in sampling bags for the measurement of dust retention. Considering the different sizes of the leaves, the number of leaves collected for each plant was different. Among these, there were 30 pieces for GL, 50 pieces for LC, and 5 pieces for CF. Three replicate measurements were taken each time.


## 2.2. Measurement of Leaf Reflectance Spectra and Dust Content

### 2.2.1. Measurement of Leaf Reflectance Spectra

Spectral measurements were recorded for each plant before and after dust retention to obtain the precise measurement of dust-related spectral changes. In the study, an ASD FieldSpec 3 spectrograph was used to measure the spectral reflectance of the leaves. The equipment was based on the basic theory of electromagnetic waves. The optical probe collected the electromagnetic waves reflected from the ground objects, which were later transformed into digital signals. The spectral range of this spectrograph was 350–2500 nm and with a sampling interval of 1 nm. The measuring speed was fixed at 0.1 s. The length of the optical probe was 1 m. The front field angle was 25°. The reflectance, radiation, and irradiance of the ground objects were simultaneously collected.At the same time of leaf collection, the spectral reflectance was measured from 10 : 00 to 14 : 30. The front sides of five leaves were both measured and repeated five times. After measurement, the leaves were sealed in corresponding bags and used to measure the DRC with the collected leaves. The probe should be perpendicular to the leaf, and the height should change according to the leaf size to guarantee spectrometer probe falls within the scope of the leaf. Specifically, the height from the probe to the leaf surface is calculated based on the equation as follows:(1)H≤WL/2tanθ/2,where H is the height, WL is the width of the leaf, and θ is the front field angle. Considering that the leaf size for one plant could also be different, we take the minimum width of each plant type as WL when calculating the height. For GL and LC, we take 2 cm as WL, then H is less equal to 4.5 cm; for CF, we take 20 cm as WL, then H is less equal to 45 cm. In practice, we used H of 4 cm for GL and LC, and 10 cm for CF.


### 2.2.2. Measurement of Dust Content

In this study, the plant’s dust retention ability is represented by the dust content per unit leaf area, which is measured by the ratio of the leaf dust content and unit leaf area within a certain time [6]. The leaf dust content is measured by the weight difference method, and the unit leaf area is measured using a leaf area meter.The first procedure of the weight difference method is washing the leaves and then drying them. The weights of the two conditions should be measured, and the difference is considered to be the dust content. To avoid other effects on the experiment, the control variate method was used in this research. That means except for the liquid in the beaker, the soak time, dried water, drying temperature, drying time, and cooling time were the same. The detailed method is as follows:(1)
The collected leaves were sealed in a dried and weighted beaker (W1) corresponding to the bags, then soaked in pure water for 5–6 hours. At the same time, the sampling bag was washed using pure water and then poured into a beaker.(2)
The beaker was stirred with a clean glass rod to make the dust dissolve into the water. Then, the leaves were sufficiently washed twice using a tweezer and pure water. After washing, the tweezer and glass rod were washed, and the flushing water was poured into the soak beaker.(3)
The beaker was placed in the drying apparatus, and the temperature was set to 85°C and the drying time set to 25 hours. After drying, the beaker was placed in a drying vessel for 5 hours to cool down.(4)
The leaves were weighted (W2) using a ten-thousandth electronic analytical balance. The difference weight (ΔW=W2−W1) is the dust retention of the collected sample. The leaf area on the dried clean leaves of each bag was measured using the leaf area meter device. The ratio of dust retention ΔW/leaf area S is the unit leaf dust retention value.


## 2.2.1. Measurement of Leaf Reflectance Spectra

Spectral measurements were recorded for each plant before and after dust retention to obtain the precise measurement of dust-related spectral changes. In the study, an ASD FieldSpec 3 spectrograph was used to measure the spectral reflectance of the leaves. The equipment was based on the basic theory of electromagnetic waves. The optical probe collected the electromagnetic waves reflected from the ground objects, which were later transformed into digital signals. The spectral range of this spectrograph was 350–2500 nm and with a sampling interval of 1 nm. The measuring speed was fixed at 0.1 s. The length of the optical probe was 1 m. The front field angle was 25°. The reflectance, radiation, and irradiance of the ground objects were simultaneously collected.At the same time of leaf collection, the spectral reflectance was measured from 10 : 00 to 14 : 30. The front sides of five leaves were both measured and repeated five times. After measurement, the leaves were sealed in corresponding bags and used to measure the DRC with the collected leaves. The probe should be perpendicular to the leaf, and the height should change according to the leaf size to guarantee spectrometer probe falls within the scope of the leaf. Specifically, the height from the probe to the leaf surface is calculated based on the equation as follows:(1)H≤WL/2tanθ/2,where H is the height, WL is the width of the leaf, and θ is the front field angle. Considering that the leaf size for one plant could also be different, we take the minimum width of each plant type as WL when calculating the height. For GL and LC, we take 2 cm as WL, then H is less equal to 4.5 cm; for CF, we take 20 cm as WL, then H is less equal to 45 cm. In practice, we used H of 4 cm for GL and LC, and 10 cm for CF.


## 2.2.2. Measurement of Dust Content

In this study, the plant’s dust retention ability is represented by the dust content per unit leaf area, which is measured by the ratio of the leaf dust content and unit leaf area within a certain time [6]. The leaf dust content is measured by the weight difference method, and the unit leaf area is measured using a leaf area meter.The first procedure of the weight difference method is washing the leaves and then drying them. The weights of the two conditions should be measured, and the difference is considered to be the dust content. To avoid other effects on the experiment, the control variate method was used in this research. That means except for the liquid in the beaker, the soak time, dried water, drying temperature, drying time, and cooling time were the same. The detailed method is as follows:(1)
The collected leaves were sealed in a dried and weighted beaker (W1) corresponding to the bags, then soaked in pure water for 5–6 hours. At the same time, the sampling bag was washed using pure water and then poured into a beaker.(2)
The beaker was stirred with a clean glass rod to make the dust dissolve into the water. Then, the leaves were sufficiently washed twice using a tweezer and pure water. After washing, the tweezer and glass rod were washed, and the flushing water was poured into the soak beaker.(3)
The beaker was placed in the drying apparatus, and the temperature was set to 85°C and the drying time set to 25 hours. After drying, the beaker was placed in a drying vessel for 5 hours to cool down.(4)
The leaves were weighted (W2) using a ten-thousandth electronic analytical balance. The difference weight (ΔW=W2−W1) is the dust retention of the collected sample. The leaf area on the dried clean leaves of each bag was measured using the leaf area meter device. The ratio of dust retention ΔW/leaf area S is the unit leaf dust retention value.


## 2.3. Spectral Data Process

Before the spectral characteristic analysis, the noise and nonsensitive wave band needed to be removed from the collected spectral data, and the spectral transformation should be completed for the following research. First, to ensure the accuracy of the spectral measured data, we examined the five-times repeated spectral data of each point and removed the evident deviated curves. Then, the mean value was calculated. Second, to ensure the comparability of the measured data from different times and conditions and eliminate errors caused by the experimental environment, we divided it by the white board reflectance because the spectral reflectance should follow the principle of proximity. Then, we removed the bands that were assimilated by water vapor because water vapor assimilation has a great effect on the spectral curve, and this wavelength band range is meaningless in botany spectral research. To simplify the following data process, the wave bands were removed directly during this research. The result is shown in Figure3.Figure 3
Comparison before and after water vapor assimilation wave deletion.The first derivative spectra can reduce sublinear and quadratic background noise; it can also reduce the impact of the hyperspectral remote-sensing measurement because of the scattering and absorption of atmosphere to light [33]. It is also able to reduce the impact of multiplicative factors that are produced by changing lighting conditions [22]. Therefore, the first derivative spectra computed from the original measured reflection spectra were implemented to establish the estimation model of the DRC. The equation of the first derivative (dR) is expressed as follows:
(2)dRλi=Rλi+1−Rλi−1λi+1−λi−1.λ
i
+
1, λi, and λi−1 are the adjacent wavelengths; dR (λi) is the first derivative of wavelength λi; R (λi+1), R (λi), and R (λi−1) are the original reflectance of the wavelengths λi+1, λi, and λi−1, respectively.


## 2.4. Identifying Feature Importance and Estimating the DRC

In this section, we present our key innovation: integrating machine learning algorithms to identify the important spectral features (bands). We estimated the DRC based on these selected features and compared the effectiveness of the various machine learning algorithms. Our design is depicted in Figure4.Figure 4
Flowchart of the DRC estimation model.


### 2.4.1. Identifying Feature Importance

The first derivative spectra were computed from the original measured reflection spectra. Over a thousand independent variables are provided in the original sample datasets. A feature selection needed to be conducted on the very high-dimensional datasets to exclude the redundant bands, further reducing the dimension of the sample sets. In this study, we implemented random forest (RF) to measure the feature importance (FI) of each band [34–36]. The FI values were then sorted from highest to lowest, and the cumulative value of 0.9 was used to derive the important variables.RF is an outstanding ensemble learning algorithm. The basic concept of the algorithm is to construct numerous tree-based predictors to obtain better performance [37, 38]. A number of subsets are extracted randomly from the total sample with replacement. The remaining samples are out-of-bag data (OOB). Then, a classification and regression tree (CART) was generated at each subset. The prediction was obtained by averaging all the outputs from the prediction of each subset. The feature importance of the bands can be described as follows:
(1)
The OOB of each subset were used to test the estimation of the corresponding tree, and the average errors of the OOB of all trees were calculated.(2)
The order of values of thekth variable was permuted while the other variables remain unchanged.(3)
The OOB error of the permuted set was calculated.(4)
The difference in the OOB error before and after the permutation was calculated for each variable, and the differences of all the variables were then normalized to a range of from 0 to 1.0, which were the FI values of the variables.


### 2.4.2. Model for DRC Estimation

The DRC estimation model was established based on the selected variables. Three commonly used machine learning algorithms were used to construct the models between DRC and first derivative spectra. SVM, as a supervised learning algorithm, has performed well in many remote-sensing applications [39–42]. CART, as a tree-based algorithm, is easily implemented and has been widely used in a variety of fields [43–45]. The aforementioned RF algorithm, which has been used for variable selection, was also implemented to model the DRC. These three machine learning algorithms were selected for comparison of their effectiveness in establishing the DRC estimation model because of their extensive use, good performance, and easy implementation. For validation purposes, the total sample set was randomly divided into two subsets, with the 70% part used to train the model and the 30% part set aside for testing.


## 2.4.1. Identifying Feature Importance

The first derivative spectra were computed from the original measured reflection spectra. Over a thousand independent variables are provided in the original sample datasets. A feature selection needed to be conducted on the very high-dimensional datasets to exclude the redundant bands, further reducing the dimension of the sample sets. In this study, we implemented random forest (RF) to measure the feature importance (FI) of each band [34–36]. The FI values were then sorted from highest to lowest, and the cumulative value of 0.9 was used to derive the important variables.RF is an outstanding ensemble learning algorithm. The basic concept of the algorithm is to construct numerous tree-based predictors to obtain better performance [37, 38]. A number of subsets are extracted randomly from the total sample with replacement. The remaining samples are out-of-bag data (OOB). Then, a classification and regression tree (CART) was generated at each subset. The prediction was obtained by averaging all the outputs from the prediction of each subset. The feature importance of the bands can be described as follows:
(1)
The OOB of each subset were used to test the estimation of the corresponding tree, and the average errors of the OOB of all trees were calculated.(2)
The order of values of thekth variable was permuted while the other variables remain unchanged.(3)
The OOB error of the permuted set was calculated.(4)
The difference in the OOB error before and after the permutation was calculated for each variable, and the differences of all the variables were then normalized to a range of from 0 to 1.0, which were the FI values of the variables.


## 2.4.2. Model for DRC Estimation

The DRC estimation model was established based on the selected variables. Three commonly used machine learning algorithms were used to construct the models between DRC and first derivative spectra. SVM, as a supervised learning algorithm, has performed well in many remote-sensing applications [39–42]. CART, as a tree-based algorithm, is easily implemented and has been widely used in a variety of fields [43–45]. The aforementioned RF algorithm, which has been used for variable selection, was also implemented to model the DRC. These three machine learning algorithms were selected for comparison of their effectiveness in establishing the DRC estimation model because of their extensive use, good performance, and easy implementation. For validation purposes, the total sample set was randomly divided into two subsets, with the 70% part used to train the model and the 30% part set aside for testing.


## 3. Results and Discussion

### 3.1. Spectral Characteristics

Figure5 shows the temporal changes in the unit DRC of the three green plants. It was found that the unit DRC increases with time but tends to remain stable or decrease because of a saturation effect after a long time. In addition, it was also found that the dust retention capability of CF is the most significant among the three green plants, with a mean unit DRC of 2.23 g/m3, followed by that of LC (2.21 g/m3). The dust retention capability of GL was the lowest at 2.12 g/m3. The DRC of plant leaves, as a result, increased temporally and reached saturation after a certain time, without rainfall and wind disturbance.Figure 5
Temporal changes in unit DRC of the three green plants.In general, the reflectance of the three green plants with or without dust on the leaves showed a universal characteristic, which is similar to the reflectance of many other plants. Due to the pigment absorption of the plants, the reflectance of the three green plants in the visible wavelength is low (less than 20%) and they usually have a reflection peak (at approximately 550 nm for GL and LC and approximately 600 nm for CF). The reflectance in the infrared band is high (greater than 60%) as contributed by the structure of the plants’ leaves.For the same plant, the reflectance of the leaves with dust and those that are clean was significantly different, particularly in the visible-infrared wavelength (Figure6). Compared to the reflectance of clean leaves, that of the dust-covered leaves in the visible wavelength markedly increased by more than 70%. It is well known that the reflectance of plant leaves in the visible wavelength is dependent on the absorption and reflection of the leaves’ pigments. The dust retention on the leaves not only influences the pigment absorption but also increases the leaves’ reflection, which causes high reflectance in the visible wavelength.Figure 6
Feature importance of different bands calculated using RF for each plant: (a) GL, (b) LC, and (c) CF.
(a)
(b)
(c)However, the reflectance of dust-covered leaves in the infrared wavelength is significantly lower than that of the clean leaves. The main reason is that dust on the leaves can decrease multiple reflections in the leaves’ structure, particularly of CF (Figure7). The characteristic of the reflectance in the shortwave infrared wavelength of the three green plants with or without dust on the leaves is random, because the reflectance in the shortwave infrared wavelength of the leaves was mainly affected by leaf water. Dust retention had little impact on leaf water (Figure 7).Figure 7
Reflectance of dust-covered and clean leaves.Based on the aforementioned analysis, it was found that significant correlations between the reflectance in the visible-infrared wavelength of the plant leaves and dust retention exist. Thus, it is possible to establish a model for estimating the DRC on plant leaves by using spectral information.


### 3.2. Dust Retention Estimation Model

#### 3.2.1. Band Selection Results

As in the aforementioned analysis, the reflectance in the shortwave infrared wavelength of the leaves was mainly affected by leaf water and only slightly influenced by dust retention. Therefore, we only included spectra between the wavelengths of 351 and 1350 nm. There is a total of 1000 bands from the 351 nm to 1350 nm wavelength with an interval of 1 nm. As a result, 1000 independent variables were provided in the sample datasets.The RF regression algorithm was run for the total samples for each plant, respectively. FI values of bands in a range of 351–1350 nm were then derived from the algorithm outputs. Figure6 presents the distribution of FI estimated using RF at different bands. It can be seen that FI values for the three plants show a different distribution pattern. Overall, the FI for the three plants all reach peak values between a wavelength of 750 nm and 800 nm, which are the near infrared bands that are sensitive to vegetation health [46]. However, for GL and CF, the high FI values are mainly concentrated between 750 nm and 800 nm, whereas the FI values of LC range from 550 to 600 nm and overwhelm those of the near infrared bands. In addition, FI values also occur at 460 nm and 630 nm for GL and CF, respectively.The FI values were then sorted from highest to lowest; we then accumulated the FI values from highest to lowest. The accumulating was stopped when the accumulated FI value reached 0.9. Then the bands that have been accumulated were considered as important variables and selected to establish the DRC model. Figure8 shows the selected bands for each plant based on the threshold of 0.9 for the cumulative FI value. The number of selected bands for GL, LC, and CF is 94, 167, and 73, respectively, much less than the total number of samples. Because the distribution of FI values for three plants is different, the number of selected bands is different. For GL and CF, the selected bands are mainly in the ranges of 350–500 nm, 750–900 nm, and 1100–1350 nm. For LC, except for the same ranges of GL and CF, many bands were also selected from 550 to 600 nm and 650 to 700 nm.Figure 8
Distribution of selected bands based on the FI values for each plant.In theory, the spectra of the selected bands can provide 90% of the information of the total samples. The selected bands were included as independent variables to establish an estimation model for DRC.


#### 3.2.2. Dust Retention Model

The total sample set was divided into two subsets randomly, with the 70% part used to train the model and the 30% part set aside for testing. Models were established for each plant independently based on the selected bands. Moreover, models were also established using the total bands for comparison purposes. Table2 summarizes the training and test results for each plant using the CART, SVM, and RF methods, respectively. Figures 9 and 10 show the scatter plots between the estimated and measured dust amount by model using the selected bands and total bands, respectively.Table 2
Training and testing results for three plants using the different regression algorithms.
Plants
Algorithms
Number of bands
Training
Testing
R
2
MAE (g/m2)
RMSE (g/m2)
Bias
Number of samples
R
2
MAE (g/m2)
RMSE (g/m2)
Bias
Number of samples
GL
CART
1000
0.98
0.04
0.08
0.00
99
0.78
0.17
0.26
0.05
42
94
0.95
0.08
0.13
0.00
0.76
0.18
0.26
0.04
RF
1000
0.98
0.07
0.10
0.00
0.88
0.14
0.19
0.05
94
0.98
0.06
0.08
0.00
0.92
0.11
0.15
0.03
SVM
1000
0.97
0.08
0.09
−0.01
0.89
0.14
0.19
0.05
94
0.92
0.13
0.16
0.00
0.89
0.16
0.19
0.07
LC
CART
1000
0.97
0.05
0.10
0.00
97
0.50
0.33
0.47
−0.06
41
167
0.95
0.07
0.12
0.00
0.50
0.29
0.46
−0.03
RF
1000
0.97
0.08
0.11
0.00
0.83
0.17
0.23
−0.03
167
0.98
0.07
0.10
0.00
0.87
0.14
0.20
−0.02
SVM
1000
0.97
0.09
0.10
−0.01
0.80
0.17
0.23
−0.02
167
0.95
0.11
0.13
0.00
0.77
0.20
0.25
−0.01
CF
CART
1000
0.93
0.08
0.13
0.00
94
0.64
0.20
0.31
0.00
41
73
0.98
0.04
0.07
0.00
0.70
0.17
0.29
0.03
RF
1000
0.97
0.06
0.09
0.00
0.80
0.16
0.23
0.02
73
0.98
0.05
0.08
0.00
0.84
0.14
0.21
0.02
SVM
1000
0.97
0.06
0.08
0.01
0.90
0.13
0.17
0.03
73
0.97
0.08
0.08
0.00
0.88
0.14
0.18
−0.01Figure 9
Scatter plots of estimated and measured DRC based on selected bands: (a) GL, (b) LC, and (c) CF.
(a)
(b)
(c)Figure 10
Scatter plots of estimated and measured DRC based on total bands: (a) GL, (b) LC, and (c) CF.
(a)
(b)
(c)In general, the models established based on selected and total bands both achieved high accuracy, with a similar coefficient of determination (R2), mean absolute error (MAE), and root mean square error (RMSE). The testing results also imply that the models implementing the selected bands produced comparable performance to that of the models considering total bands. The RF-based models for LC and GL using selected bands produced evidently higher R2 values than those using the total bands. This indicates that dimensionality reduction is necessary, and the selected bands preserve important and useful information that could express the spectral differences of the leaves caused by dust retention.For LC and GL, the RF-based model performed better than the other two algorithms, with a testingR2 of 0.87 and 0.92, respectively. The bias values for the models are all less than 0.08. For CF, the SVM-based model outperformed the other two algorithms. Overall, the CART-based model produced the least accurate estimation results. Figure 11 shows the Taylor diagrams of testing accuracy for the three plants. The Taylor diagram is helpful for comparative assessment of different models. It integrates four statistics on a diagram to quantify the degree of correspondence between the modeled and observed values. The four statistics are the Pearson correlation coefficient, normalized standard deviation, normalized error standard deviation, and normalized bias. The measured (observed) values serve as the reference. More details can be found in [47]. According to Figure 11, the estimated results produced by the CART-based model show the lowest correlations with the measured values. The results estimated using the SVM and RF models show similar standard deviations and correlations. In addition, the three algorithms all underestimated the measured dust contents of LC.Figure 11
Taylor diagrams showing the correlations between the estimated DRC of the different models and the measured values of (a) GL, (b) LC, and (c) CF.
(a)
(b)
(c)


## 3.1. Spectral Characteristics

Figure5 shows the temporal changes in the unit DRC of the three green plants. It was found that the unit DRC increases with time but tends to remain stable or decrease because of a saturation effect after a long time. In addition, it was also found that the dust retention capability of CF is the most significant among the three green plants, with a mean unit DRC of 2.23 g/m3, followed by that of LC (2.21 g/m3). The dust retention capability of GL was the lowest at 2.12 g/m3. The DRC of plant leaves, as a result, increased temporally and reached saturation after a certain time, without rainfall and wind disturbance.Figure 5
Temporal changes in unit DRC of the three green plants.In general, the reflectance of the three green plants with or without dust on the leaves showed a universal characteristic, which is similar to the reflectance of many other plants. Due to the pigment absorption of the plants, the reflectance of the three green plants in the visible wavelength is low (less than 20%) and they usually have a reflection peak (at approximately 550 nm for GL and LC and approximately 600 nm for CF). The reflectance in the infrared band is high (greater than 60%) as contributed by the structure of the plants’ leaves.For the same plant, the reflectance of the leaves with dust and those that are clean was significantly different, particularly in the visible-infrared wavelength (Figure6). Compared to the reflectance of clean leaves, that of the dust-covered leaves in the visible wavelength markedly increased by more than 70%. It is well known that the reflectance of plant leaves in the visible wavelength is dependent on the absorption and reflection of the leaves’ pigments. The dust retention on the leaves not only influences the pigment absorption but also increases the leaves’ reflection, which causes high reflectance in the visible wavelength.Figure 6
Feature importance of different bands calculated using RF for each plant: (a) GL, (b) LC, and (c) CF.
(a)
(b)
(c)However, the reflectance of dust-covered leaves in the infrared wavelength is significantly lower than that of the clean leaves. The main reason is that dust on the leaves can decrease multiple reflections in the leaves’ structure, particularly of CF (Figure7). The characteristic of the reflectance in the shortwave infrared wavelength of the three green plants with or without dust on the leaves is random, because the reflectance in the shortwave infrared wavelength of the leaves was mainly affected by leaf water. Dust retention had little impact on leaf water (Figure 7).Figure 7
Reflectance of dust-covered and clean leaves.Based on the aforementioned analysis, it was found that significant correlations between the reflectance in the visible-infrared wavelength of the plant leaves and dust retention exist. Thus, it is possible to establish a model for estimating the DRC on plant leaves by using spectral information.


## 3.2. Dust Retention Estimation Model

### 3.2.1. Band Selection Results

As in the aforementioned analysis, the reflectance in the shortwave infrared wavelength of the leaves was mainly affected by leaf water and only slightly influenced by dust retention. Therefore, we only included spectra between the wavelengths of 351 and 1350 nm. There is a total of 1000 bands from the 351 nm to 1350 nm wavelength with an interval of 1 nm. As a result, 1000 independent variables were provided in the sample datasets.The RF regression algorithm was run for the total samples for each plant, respectively. FI values of bands in a range of 351–1350 nm were then derived from the algorithm outputs. Figure6 presents the distribution of FI estimated using RF at different bands. It can be seen that FI values for the three plants show a different distribution pattern. Overall, the FI for the three plants all reach peak values between a wavelength of 750 nm and 800 nm, which are the near infrared bands that are sensitive to vegetation health [46]. However, for GL and CF, the high FI values are mainly concentrated between 750 nm and 800 nm, whereas the FI values of LC range from 550 to 600 nm and overwhelm those of the near infrared bands. In addition, FI values also occur at 460 nm and 630 nm for GL and CF, respectively.The FI values were then sorted from highest to lowest; we then accumulated the FI values from highest to lowest. The accumulating was stopped when the accumulated FI value reached 0.9. Then the bands that have been accumulated were considered as important variables and selected to establish the DRC model. Figure8 shows the selected bands for each plant based on the threshold of 0.9 for the cumulative FI value. The number of selected bands for GL, LC, and CF is 94, 167, and 73, respectively, much less than the total number of samples. Because the distribution of FI values for three plants is different, the number of selected bands is different. For GL and CF, the selected bands are mainly in the ranges of 350–500 nm, 750–900 nm, and 1100–1350 nm. For LC, except for the same ranges of GL and CF, many bands were also selected from 550 to 600 nm and 650 to 700 nm.Figure 8
Distribution of selected bands based on the FI values for each plant.In theory, the spectra of the selected bands can provide 90% of the information of the total samples. The selected bands were included as independent variables to establish an estimation model for DRC.


### 3.2.2. Dust Retention Model

The total sample set was divided into two subsets randomly, with the 70% part used to train the model and the 30% part set aside for testing. Models were established for each plant independently based on the selected bands. Moreover, models were also established using the total bands for comparison purposes. Table2 summarizes the training and test results for each plant using the CART, SVM, and RF methods, respectively. Figures 9 and 10 show the scatter plots between the estimated and measured dust amount by model using the selected bands and total bands, respectively.Table 2
Training and testing results for three plants using the different regression algorithms.
Plants
Algorithms
Number of bands
Training
Testing
R
2
MAE (g/m2)
RMSE (g/m2)
Bias
Number of samples
R
2
MAE (g/m2)
RMSE (g/m2)
Bias
Number of samples
GL
CART
1000
0.98
0.04
0.08
0.00
99
0.78
0.17
0.26
0.05
42
94
0.95
0.08
0.13
0.00
0.76
0.18
0.26
0.04
RF
1000
0.98
0.07
0.10
0.00
0.88
0.14
0.19
0.05
94
0.98
0.06
0.08
0.00
0.92
0.11
0.15
0.03
SVM
1000
0.97
0.08
0.09
−0.01
0.89
0.14
0.19
0.05
94
0.92
0.13
0.16
0.00
0.89
0.16
0.19
0.07
LC
CART
1000
0.97
0.05
0.10
0.00
97
0.50
0.33
0.47
−0.06
41
167
0.95
0.07
0.12
0.00
0.50
0.29
0.46
−0.03
RF
1000
0.97
0.08
0.11
0.00
0.83
0.17
0.23
−0.03
167
0.98
0.07
0.10
0.00
0.87
0.14
0.20
−0.02
SVM
1000
0.97
0.09
0.10
−0.01
0.80
0.17
0.23
−0.02
167
0.95
0.11
0.13
0.00
0.77
0.20
0.25
−0.01
CF
CART
1000
0.93
0.08
0.13
0.00
94
0.64
0.20
0.31
0.00
41
73
0.98
0.04
0.07
0.00
0.70
0.17
0.29
0.03
RF
1000
0.97
0.06
0.09
0.00
0.80
0.16
0.23
0.02
73
0.98
0.05
0.08
0.00
0.84
0.14
0.21
0.02
SVM
1000
0.97
0.06
0.08
0.01
0.90
0.13
0.17
0.03
73
0.97
0.08
0.08
0.00
0.88
0.14
0.18
−0.01Figure 9
Scatter plots of estimated and measured DRC based on selected bands: (a) GL, (b) LC, and (c) CF.
(a)
(b)
(c)Figure 10
Scatter plots of estimated and measured DRC based on total bands: (a) GL, (b) LC, and (c) CF.
(a)
(b)
(c)In general, the models established based on selected and total bands both achieved high accuracy, with a similar coefficient of determination (R2), mean absolute error (MAE), and root mean square error (RMSE). The testing results also imply that the models implementing the selected bands produced comparable performance to that of the models considering total bands. The RF-based models for LC and GL using selected bands produced evidently higher R2 values than those using the total bands. This indicates that dimensionality reduction is necessary, and the selected bands preserve important and useful information that could express the spectral differences of the leaves caused by dust retention.For LC and GL, the RF-based model performed better than the other two algorithms, with a testingR2 of 0.87 and 0.92, respectively. The bias values for the models are all less than 0.08. For CF, the SVM-based model outperformed the other two algorithms. Overall, the CART-based model produced the least accurate estimation results. Figure 11 shows the Taylor diagrams of testing accuracy for the three plants. The Taylor diagram is helpful for comparative assessment of different models. It integrates four statistics on a diagram to quantify the degree of correspondence between the modeled and observed values. The four statistics are the Pearson correlation coefficient, normalized standard deviation, normalized error standard deviation, and normalized bias. The measured (observed) values serve as the reference. More details can be found in [47]. According to Figure 11, the estimated results produced by the CART-based model show the lowest correlations with the measured values. The results estimated using the SVM and RF models show similar standard deviations and correlations. In addition, the three algorithms all underestimated the measured dust contents of LC.Figure 11
Taylor diagrams showing the correlations between the estimated DRC of the different models and the measured values of (a) GL, (b) LC, and (c) CF.
(a)
(b)
(c)


## 3.2.1. Band Selection Results

As in the aforementioned analysis, the reflectance in the shortwave infrared wavelength of the leaves was mainly affected by leaf water and only slightly influenced by dust retention. Therefore, we only included spectra between the wavelengths of 351 and 1350 nm. There is a total of 1000 bands from the 351 nm to 1350 nm wavelength with an interval of 1 nm. As a result, 1000 independent variables were provided in the sample datasets.The RF regression algorithm was run for the total samples for each plant, respectively. FI values of bands in a range of 351–1350 nm were then derived from the algorithm outputs. Figure6 presents the distribution of FI estimated using RF at different bands. It can be seen that FI values for the three plants show a different distribution pattern. Overall, the FI for the three plants all reach peak values between a wavelength of 750 nm and 800 nm, which are the near infrared bands that are sensitive to vegetation health [46]. However, for GL and CF, the high FI values are mainly concentrated between 750 nm and 800 nm, whereas the FI values of LC range from 550 to 600 nm and overwhelm those of the near infrared bands. In addition, FI values also occur at 460 nm and 630 nm for GL and CF, respectively.The FI values were then sorted from highest to lowest; we then accumulated the FI values from highest to lowest. The accumulating was stopped when the accumulated FI value reached 0.9. Then the bands that have been accumulated were considered as important variables and selected to establish the DRC model. Figure8 shows the selected bands for each plant based on the threshold of 0.9 for the cumulative FI value. The number of selected bands for GL, LC, and CF is 94, 167, and 73, respectively, much less than the total number of samples. Because the distribution of FI values for three plants is different, the number of selected bands is different. For GL and CF, the selected bands are mainly in the ranges of 350–500 nm, 750–900 nm, and 1100–1350 nm. For LC, except for the same ranges of GL and CF, many bands were also selected from 550 to 600 nm and 650 to 700 nm.Figure 8
Distribution of selected bands based on the FI values for each plant.In theory, the spectra of the selected bands can provide 90% of the information of the total samples. The selected bands were included as independent variables to establish an estimation model for DRC.


## 3.2.2. Dust Retention Model

The total sample set was divided into two subsets randomly, with the 70% part used to train the model and the 30% part set aside for testing. Models were established for each plant independently based on the selected bands. Moreover, models were also established using the total bands for comparison purposes. Table2 summarizes the training and test results for each plant using the CART, SVM, and RF methods, respectively. Figures 9 and 10 show the scatter plots between the estimated and measured dust amount by model using the selected bands and total bands, respectively.Table 2
Training and testing results for three plants using the different regression algorithms.
Plants
Algorithms
Number of bands
Training
Testing
R
2
MAE (g/m2)
RMSE (g/m2)
Bias
Number of samples
R
2
MAE (g/m2)
RMSE (g/m2)
Bias
Number of samples
GL
CART
1000
0.98
0.04
0.08
0.00
99
0.78
0.17
0.26
0.05
42
94
0.95
0.08
0.13
0.00
0.76
0.18
0.26
0.04
RF
1000
0.98
0.07
0.10
0.00
0.88
0.14
0.19
0.05
94
0.98
0.06
0.08
0.00
0.92
0.11
0.15
0.03
SVM
1000
0.97
0.08
0.09
−0.01
0.89
0.14
0.19
0.05
94
0.92
0.13
0.16
0.00
0.89
0.16
0.19
0.07
LC
CART
1000
0.97
0.05
0.10
0.00
97
0.50
0.33
0.47
−0.06
41
167
0.95
0.07
0.12
0.00
0.50
0.29
0.46
−0.03
RF
1000
0.97
0.08
0.11
0.00
0.83
0.17
0.23
−0.03
167
0.98
0.07
0.10
0.00
0.87
0.14
0.20
−0.02
SVM
1000
0.97
0.09
0.10
−0.01
0.80
0.17
0.23
−0.02
167
0.95
0.11
0.13
0.00
0.77
0.20
0.25
−0.01
CF
CART
1000
0.93
0.08
0.13
0.00
94
0.64
0.20
0.31
0.00
41
73
0.98
0.04
0.07
0.00
0.70
0.17
0.29
0.03
RF
1000
0.97
0.06
0.09
0.00
0.80
0.16
0.23
0.02
73
0.98
0.05
0.08
0.00
0.84
0.14
0.21
0.02
SVM
1000
0.97
0.06
0.08
0.01
0.90
0.13
0.17
0.03
73
0.97
0.08
0.08
0.00
0.88
0.14
0.18
−0.01Figure 9
Scatter plots of estimated and measured DRC based on selected bands: (a) GL, (b) LC, and (c) CF.
(a)
(b)
(c)Figure 10
Scatter plots of estimated and measured DRC based on total bands: (a) GL, (b) LC, and (c) CF.
(a)
(b)
(c)In general, the models established based on selected and total bands both achieved high accuracy, with a similar coefficient of determination (R2), mean absolute error (MAE), and root mean square error (RMSE). The testing results also imply that the models implementing the selected bands produced comparable performance to that of the models considering total bands. The RF-based models for LC and GL using selected bands produced evidently higher R2 values than those using the total bands. This indicates that dimensionality reduction is necessary, and the selected bands preserve important and useful information that could express the spectral differences of the leaves caused by dust retention.For LC and GL, the RF-based model performed better than the other two algorithms, with a testingR2 of 0.87 and 0.92, respectively. The bias values for the models are all less than 0.08. For CF, the SVM-based model outperformed the other two algorithms. Overall, the CART-based model produced the least accurate estimation results. Figure 11 shows the Taylor diagrams of testing accuracy for the three plants. The Taylor diagram is helpful for comparative assessment of different models. It integrates four statistics on a diagram to quantify the degree of correspondence between the modeled and observed values. The four statistics are the Pearson correlation coefficient, normalized standard deviation, normalized error standard deviation, and normalized bias. The measured (observed) values serve as the reference. More details can be found in [47]. According to Figure 11, the estimated results produced by the CART-based model show the lowest correlations with the measured values. The results estimated using the SVM and RF models show similar standard deviations and correlations. In addition, the three algorithms all underestimated the measured dust contents of LC.Figure 11
Taylor diagrams showing the correlations between the estimated DRC of the different models and the measured values of (a) GL, (b) LC, and (c) CF.
(a)
(b)
(c)


## 4. Conclusion

In this study, we investigated the effectiveness of using machine learning to estimate the DRC of leaves based on remotely sensed hyperspectral information. We conducted experiments on three green plants in southern China. The spectra were measured using an ASD FieldSpec 3. A feature selection process was implemented to reduce the high dimensions of the original spectra. Three commonly used machine learning algorithms, SVM, CART, and RF, were used to detect the possible relationships between the DRC and the first derivative spectra. The conclusions can be summarized as follows:(1)
Significant correlations exist between spectral reflection and the DRC of the plant leaves in the visible-infrared wavelength region: the reflectance of the plant leaves increases in the visible wavelength and decreases in the infrared wavelength with increase in DRC. The characteristic of the reflectance in the shortwave infrared wavelength of the three green plants with or without dust on the leaves is random because the reflectance at these wavelengths is mainly affected by leaf water content.(2)
Spectra from 450 to 500 nm, 550 to 600 nm, 750 to 1000 nm, and 1100 to 1300 nm are recommended for detecting and estimating the DRC of leaves. However, appropriate bands differ among plants. The experiments in this study were only conducted on three types of plants; a feature selection process is recommended in any other practical applications.(3)
The RF algorithm reduced the variable dimensions well. Testing results showed that the estimated values using the SVM and RF approaches had good agreement with the measured DRC. SVM and RF, as a result, are recommended for modeling DRC based on hyperspectral data. Optimal algorithms should be determined based on different situations.This study provided a technical approach for estimating DRC on plant leaves based on hyperspectral measurements. The validation results showed that the machine learning model proposed in this study efficiently reduced the variable dimensions and accurately estimated the DRC of different plants. Consequently, the results of this study can be applied to monitor the DRC on leaves of other plants and further be fused or integrated with other types of spectral data to measure the DRC at a regional scale based on airborne hyperspectral sensors or sensors onboard unmanned aerial vehicles (UAVs).



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*Source: 6026259-2018-09-06.xml*