Hyperspectral Remote Sensing Inversion and Monitoring of Organic Matter in Black Soil Based on Dynamic Fitness Inertia Weight Particle Swarm Optimization Neural Network

Abstract

Long-term degradation of black soil has led to reductions in soil fertility and ecological service functions, which have seriously threatened national food security and regional ecological security. This study is motivated by the UN’s Sustainable Development Goal (SDG) 2—Zero Hunger, specifically, SDG 2.4 Sustainable Food Production Systems. The aim was to monitor the soil organic matter (SOM) content of black soil and its dynamics via hyperspectral remote sensing inversion. This is of great significance to the effective utilization and sustainable development of black soil resources. Taking the typical black soil area of Northeast China as an example, the hyperspectral data of ground features were compared with SOM contents measured in soil samples to correlate SOM with spectral features. Based on their quantitative relationship, a dynamic fitness inertia weighted particle swarm optimization (DPSO) algorithm is proposed, which balances the global and local search abilities of a particle swarm optimization algorithm. The DPSO algorithm is applied to the parameter adjustment of an artificial neural network (BPNN), which is used instead of a traditional error back propagation algorithm, to build a DPSO-BPNN model. Then a global optimal analytical expression of hyperspectral inversion is obtained to improve the generalization ability and stability of the remote sensing quantitative inversion model. The results show that DPSO-BPNN model is more stable and accurate than existing models, such as multiple stepwise regression, partial least squares, and BP neural network models (adjust complex coefficient of determination = 0.89, root mean square error = 1.58, relative recent deviation = 2.93). The results of DPSO-BPNN inversion are basically consistent with the trend in SOM contents measured during surface geochemical exploration. As such, this study provides a basis for hyperspectral remote sensing inversion and monitoring of the SOM contents in black soil.

1. Introduction

Soil resources constitute the “living skin” of the earth and are considered to be the key driver of various global feedback cycles. “The 2030 Agenda for Sustainable Development” issued by the United Nations has officially incorporated the issue of improving soil quality, achieving food security, and promoting sustainable agriculture as part of Sustainable Development Goal (SDG) 2—Zero Hunger. Black soil is the most precious soil resource on the earth and can be found in four parts of the world, namely, the Ukrainian plain in Ukraine, the Mississippi plain in the United States, the Northeast Plain in China, and the Pampas grassland, which extends from Argentina to Uruguay in South America. Black soil has high fertility, making it very suitable for growing food crops. China has less arable land per capita than other countries, but has very important black soil resources in the Northeast that comprise a very important part of China’s major grain-producing areas. On 1 August 2022, the People’s Republic of China formally implemented a law protecting black soil. Soil organic matter (SOM) refers to the various carbon containing organic compounds in soil. The SOM content is an important indicator of soil fertility evaluation [1,2,3]. Its dynamics directly affect the stability of agricultural ecosystems. Due to long-term high-intensity utilization and soil erosion, the contents of SOM and nutrients in cultivated land in the black soil region of Northeast China have decreased. Accordingly, soil biological, physical, and chemical properties and ecological service functions have degraded, threatening national food security and regional ecological security. Therefore, strengthening research on SOM in black soil areas can provide a reliable basis for the scientific evaluation of black soil quality [4,5,6], which is of great significance to the protection and sustainable use of black soil arable land resources and China’s food security.

Soil remote sensing inversion data can be divided into two categories: (1) spaceborne and (2) non-spaceborne remote sensing data. Non-spaceborne data can be further divided into airborne remote sensing data and ground measured data. Ground non-imaging spectrometers are mainly used to measure soil spectral reflectance curves in the field or laboratory, such as: Avafile series ground object spectrometers (Avantes Company, Apeldoom, The Netherlands); SR series ground object spectrometers (SEI Company, Haverhill, MA, USA); GER and SVC series field spectrometers (SVC Company, Poughkeepsie, NY, USA); and FieldSpec series portable field spectral radiometers (ASD Company, Longmont, CO, USA). In situ measurement of soil reflectance spectra by spectrometers can provide real-time and high-quality hyperspectral data, which provides an important basis for high-precision soil inversion models.

Bowers and Hanks [7] proposed the earliest study on the relationship between soil organic matter and soil spectral characteristics. After oxidation treatment of SOM, the reflectance of soil increased by 8.2% compared with the original sample. Al Abbas et al. [8] found a clear negative correlation between SOM content and spectral reflectance after spectral analysis of soil. Dai Changda et al. [9] studied 100 samples of 23 types of main soils from different regions of China. According to the characteristics of the spectral reflection curves and slope changes, the soil reflection characteristics of China were divided into four categories, thereby laying a foundation for future soil spectral research. At present, most remote sensing quantitative inversion methods based on soil spectral analysis involve data-driven models. The standard paradigm is a process of spectral data processing, characteristic band selection, and statistical regression modelling. The most common modelling methods based on multiple empirical relationships include stepwise multiple linear regression [10], principal component regression [11], and partial least squares regression [12]. These models can be applied to highly collinear data to establish an effective relationship between target variables and reflectance spectra. With the development of machine learning, the support vector machine [13], random forest [14], gradient lifting tree [15], Gaussian process regression [16], cubic regression [17], and other data-mining technologies have emerged for modelling, and have good nonlinear modelling ability. In the field of geostatistics, geographically weighted regression [18,19,20] is also commonly used in digital soil mapping. Recently, artificial neural network technology has been introduced for the quantitative inversion of soil remote sensing data. It has the advantages of effectively mining complex data structures and decomposing and reconstructing the original reflectance and first-derivative reflectance of soil through discrete wavelet transformation using GF-5 data (China Land Environment Hyperspectral Observation Satellite). A BP neural network prediction model has been used to obtain SOC estimates with the highest prediction accuracy [21]. Pyo et al. [22] used deep learning methods to estimate the contents of heavy metals from the reflection spectra of soil samples. They combined this with principal component analysis to reduce the dimensions, using a convolution automatic encoder to separate the relevant spectral characteristics of various heavy metals, and established a random forest regression model to estimate concentrations of arsenic, copper and lead. Zhang et al. [23] used a genetic algorithm to extract the characteristic bands of organic matter and give the adsorption and retention characteristics of Cd in soil organic matter. They also predicted soil Cd contents in a mining area by using a partial least square model. Inversion algorithms such as deep neural networks [24], long-term and short-term memory networks [25], and transfer learning [26] also provide novel solutions for remote sensing quantitative inversion of SOM content. However, building a complex neural network structure increases the calculation amount exponentially, and the amount of soil sample data required to train such neural networks is enormous, which imposes limitations on such methods.

This paper uses dynamic fitness inertia weighted particle swarm optimization (DPSO) to optimize the parameters of an artificial neural network (BPNN), enhance its global search ability, and build a DPSO-BPNN SOM remote sensing quantitative inversion model. It aims to meet the need for the quality monitoring of typical black soil cultivated land in Northeast China; this is of great significance to the effective utilization and sustainable development of black soil resources.

2. Materials

2.1. Study Area

The study area was located northeast of Jiamusi City, Heilongjiang Province, Northeast China. It is the hinterland of the Sanjiang Alluvial Plain formed by the Wusuli, Songhua and Heilongjiang Rivers. The geographical coordinates were 47°12′00′′–47°7′30′′N, 132°35′17′′–132°46′48′′E. The black soil resources in the study area were rich and the soil types mainly include dark brown soil, albic soil, black soil, meadow soil, swamp soil, peat soil, and paddy soil. The soil surface layer was black humus with a mean thickness of 30–60 cm and a maximum thickness of >1 m, mostly with a cylindrical or granular structure. The lower part was a thick and sticky sedimentary layer with more brown ferromanganese nodules, and the lowest part was a brown-yellow, sticky, parent material layer. The study area was convenient for transportation, with the roads extended in all directions, making it convenient for ground sampling, spectral measurement, and field investigation. The average altitude of the working area was about 50 m, and the relative height difference was about 10 m. A remote sensing image map of the study area is synthesized from the true colour band of Landsat 8 OLI data. The sampling time was October 2019 (Figure 1).

2.2. Materials

2.2.1. Soil Sample Points

The soil sample collection methods were as follows: 135 sampling points (checkerboard sampling) were evenly distributed in the study area. The points were arranged to avoid interference, such as from fertilization points, ridges, and ditches. The sampling depth was 0–20 cm (Figure 2). Firstly, we removed plant residues, weeds, gravels, bricks, fertilizer blocks, etc., and mixed in the samples. To represent the area or soil sample, a single place was mainly used for sampling (as a fixed-point position), in each field and crop type. Samples were taken within 1 m of the sampling points, 3–5 sub-samples collected at multiple points and mixed to form a sample. After the soil at each sampling point was fully mixed, 2–2.5 kg of each sample was reserved and placed into a sample bag. The sample bag was a clean cotton cloth bag, and wet soil samples were lined with a plastic bag. Sample bag number record.

The FieldSpec^® 4 Std-Res hyperspectral spectrometer produced by American ASD company is used for the measurement of soil spectral data, with a wavelength range of 350–2500 nm, can capture visible and near-infrared (VNIR) and short-wave infrared (SWIR). In the range of 350–1000 nm, the spectral sampling interval is 1.4 nm and the spectral resolution is 3 nm, whereas in the range of 1000–2500 nm, the spectral sampling interval is 2 nm and the spectral resolution is 10 nm (Figure 3). The field measurement period is 9:30–15:30 (Beijing time) to ensure sufficient solar altitude angle, no cirrus and cumulus clouds, and the wind force is less than grade 3. If the outdoor environment of the day is not satisfied, use ASD illuminator 75 W halogen lamp as the light source in the dark indoor environment, 60 cm away from the sample, the irradiation angle forms an included angle of 60° with the horizontal line, and the measuring probe is located 15 cm above the vertical of the sample. Before formal measurement of the samples, in order to obtain the absolute reflectance, a white reference plate equipped with the instrument was used for correction. After correction, we measured 10 spectral curves for each sample to obtain its original spectral curve. After spectral data measurement, the soil samples were sent to a professional testing institution for the determination of SOM content.

2.2.2. Hyperspectral Data Processing

Spectral data measurement can be affected by many environmental factors. Measured hyperspectral data contains noise, which weakens the spectral information of soil samples. To reduce the errors caused by spectral fluctuation and improve the signal-to-noise ratio of the spectral data, the Savitzky–Golay function was used to smooth the spectral curves. This reduces the noise interference to a certain extent and effectively retains the original shape and trend of the spectral curve (Figure 4).

To reduce the influence of differences between soil samples on the modelling accuracy, box chart analysis (Figure 5) was carried out for the SOM contents measured in the chemical laboratory. To reduce the potential error caused by the data itself at the sample level, we eliminated five outliers and analysed the remaining 130 samples (Table 1) which included 105 modelling samples and 25 test samples.

2.2.3. Feature Band Extraction Based on the Correlation Coefficient Method

According to the measured soil spectral reflectance data, the diagnostic characteristic bands that can represent SOM content were selected. The central problem in such analysis is the correlation between the soil samples’ SOM contents and the reflectance of each band.

The correlation coefficient method is based on using multi-sample content data and multi-form spectral transformation data to conduct correlation analysis on each band. The correlation coefficient between the soil element content of a given sample and the reflectance of each band is calculated, and we select the band with the highest correlation coefficient as the feature band of SOM content according to the previously determined approximate range. The correlation coefficient is calculated as follows:

(1)$r_i=\frac{Cov(X,Y)}{\sqrt{D(\mathrm{X})}\sqrt{D(\mathrm{Y})}}=\frac{{\displaystyle \sum _{n=1}^N(x_{ni}-{\overline{x}}_i)(y_n-\overline{y})}}{\sqrt{{\displaystyle \sum _{n=1}^N{(x_{ni}-{\overline{x}}_i)}^2}{\displaystyle \sum _{n=1}^N{(y_n-\overline{y})}^2}}}$

where $r_i$ is the coefficient of the correlation between SOM content and the spectral reflectance value, $i$ is the band number, and $x_{ni}$ is the spectral reflectance value at the wavelength of $n$ points on the spectral curve corresponding to the soil sample, ${\overline{x}}_i$ represents the average spectral reflectance at point $i$ on the corresponding spectral curve of $n$ soil samples, $n$ represents the number of soil samples, $y_n$ represents the SOM content of the nth soil sample, and $\overline{y}$ represents the average SOM content of $n$ soil samples. The correlation coefficients of the original spectral reflectance data and their 14 transformation forms and the SOM contents of 105 modelling-group samples were calculated.

3. Methodology

3.1. Dynamic Fitness Inertia Weight Particle Swarm Optimization

Particle Swarm Optimization (PSO)mathematical description:

Suppose a group composed of m particles searches in a D-dimensional search space. Each particle will change its position according to its historical best and the historical best of the group. There are three parts to describing the state of the ith particle in the particle swarm:

Current location: $x_i=(x_{i1},x_{i2},\cdots ,x_{iD})$, where $x_{id}\in [{\mathrm{pop}}_{\min },{\mathrm{pop}}_{\max }]$,$d\in \left\{1,2,\cdots ,D\right\}$,

Historical best position: $p_i=(p_{i1},p_{i2},\cdots ,p_{iD})$,

Current speed: $v_i=(v_{i1},v_{i2},\cdots ,v_{iD})$, where $v_{id}\in (v_{\min },v_{\max })$.

The current position is evaluated by the fitness function in the algorithm. If the current position $x_i$ is better than the historical optimal position $p_i$, the current position coordinates are stored in $p_i$. The best position of all particles is recorded as $p_g=(p_{g1},p_{g2},\cdots ,p_{gD})$, so for each particle, its position and velocity are changed according to the following formula:

(2)$v_{id}(t+1)=w\cdot v_{id}(t)+c_1\cdot r_1\cdot (p_{id}(t)-x_{id}(t))+c_2\cdot r_2\cdot (p_{gd}(t)-x_{id}(t))$

(3)$x_{id}(t+1)=x_{id}(t)+v_{id}(t+1)$

where $w$ is the inertia weight, which adjusts the search ability for the solution space; $c_1,c_2$ is the learning factor, and the learning step length is adjusted, usually to two; $r_1,r_2$ are two random numbers with a range of $\left[0,1\right]$; and t is the current number of iterations.

One of the keys to the performance of the PSO algorithm is its ability to balance global search and local search throughout the iteration process, which is directly affected by the inertia weight [27,28,29,30,31,32,33,34,35,36]. This paper proposes an improved algorithm: dynamic fitness inertia weight particle swarm optimization (DPSO). This algorithm enables each particle to dynamically adjust the weight according to its own search status in the iteration process. In each iteration, different particles have different inertia weights to increase the diversity of inertia weights. The weight adjustment method is as follows:

(4)$w_i(t)=\frac{rand}{2}+\frac{fi{t}_{gbest}(t)}{{(fi{t}_{pbest})}_i(t)}$

where $w_i(t)$ is the weight of particle i in iteration t, $rand$ is a random number within $[0,1]$, $fi{t}_{gbest}(t)$ is the global optimal fitness value at iteration t, and ${(fi{t}_{pbest})}_i(t)$ is the individual optimal fitness value of particle i at iteration t. The range of the ratio of the two is $[0,1]$, and the value of $w_i(t)$ is $[0.5,1.5]$.

The improved algorithm flow is as follows (Algorithm 1):

Algorithm 1. DPSO algorithm flow.

Step1: Initialize the population containing m particles, and randomly generate the position and velocity of each particle;

Step2: Calculate and evaluate the fitness value of each particle;

Step3: For each particle, its fitness value is compared with its individual optimal value $pbest$. If it is better, it is taken as the current individual optimal position;

Step4: For each particle, its fitness value is compared with the overall optimal value $gbest$. If it is better, it will be taken as the current overall optimal position;Step5: Calculate the inertia weight of each particle according to Formula (4);

Step6: Calculate the particle velocity and update the particle position according to Formulas (2) and (3);

Step7: Judge whether the preset fitness threshold or the maximum number of iterations has been reached. If yes, terminate. Otherwise, continue to cycle to step 2 until the termination conditions are met.

3.2. Improved BP Neural Network

A BP neural network (BPNN) is composed of an input layer, hidden layer, and output layer (Figure 6). The hidden layer is divided into a single hidden layer and multiple hidden layers. The more hidden layers, the larger the network scale and the stronger the generalization ability but it requires more training calculations. The more free parameters, the longer the training time, and the phenomenon of over-fitting can easily occur. Generally speaking, the number of hidden layers needs to be determined according to the specific case, but research shows that a three-layer BPNN with only one hidden layer can approach any continuous function in the bounded region with any accuracy as long as the number of nodes in the hidden layer is sufficient. Therefore, in general, it is preferable to increase the number of nodes in the hidden layer rather than the number of hidden layers, so as to avoid network complexity caused by having too many hidden layers, increasing the number of training samples and requiring a large amount of training calculation [37,38,39,40,41,42,43].

A three-layer BP neural network model is established based on spectral data. The characteristic bands extracted by the correlation coefficient method are used as the input data of the neural network model, and the corresponding organic matter content is the output.

There are many different types of excitation functions in neurons, such as the Purelin type excitation function, Log-sigmod type excitation function, and Tan-sigmod type excitation function. Their expressions and curves are as follows (Figure 7):

Purelin type excitation function:

(5)$f(x)=kx$

Log-sigmod type excitation function:

(6)$f(x)=\frac{1}{1+e^{-x}}$

Tan-sigmod type excitation function:

(7)$f(x)=\tanh (x)$

According to the characteristics of the three excitation functions, in the BPNN, the network training function adopts the Tan-sigmod type excitation function, the neurons in the hidden layer adopt the Log-sigmod type excitation function, and the output layer adopts the Purelin type excitation function, so that the final output of the network can obtain any value.

However, only relying on error back-propagation to adjust the weights and offsets will slow down the network convergence speed, and it can easily fall into a local extreme value and deviate from the global extreme value. Therefore, using the DPSO algorithm instead of error back propagation to adjust the parameters will increase the speed of parameter evolution in the optimal direction. The algorithm flow is shown in Figure 8.

In the DPSO-BPNN, we take the prediction error of the model as the fitness function of the PSO, and take the weight and bias in the network as the position parameters of the particles. Through the DPSO, we find the particle position with the smallest fitness function value, so as to obtain the optimal weight and bias. The global search ability of the neural network is enhanced, and the prediction accuracy and generalization ability of the model are improved by this approach.

3.3. Model Accuracy Evaluation

For the evaluation of model accuracy, the fitting performance of the model is evaluated by the adjusted complex coefficient of determination, ${\overline{R}}^2$. Its calculation formula is as follows:

(8)${\overline{R}}^2=1-\frac{{\displaystyle \sum _{i=1}^n{(y_i-{\widehat{y}}_i)}^2}/(n-p-1)}{{\displaystyle \sum _{i=1}^n{(y_i-\overline{y})}^2}/(n-1)}$

where $y_i$ is the ith measured value, ${\widehat{y}}_i$ is the ith predicted value, $\overline{y}$ is the average measured value, n is the number of samples, and p is the number of independent variables. The closer ${\overline{R}}^2$ is to 1, the higher the predictive accuracy of the model.

The predictive accuracy can also be judged by the root mean-square error (RMSE), which is calculated as follows:

(9)$RMSE=\sqrt{\frac{{\displaystyle \sum _{i=1}^n{(y_i-{\widehat{y}}_i)}^2}}{n}}$

where $y_i$ is the measured value of the ith sample, ${\widehat{y}}_i$ is the predicted value of the ith sample, and n is the number of samples. The smaller the RMSE, the higher the predictive accuracy of the model.

The relative percentage deviation (RPD) is the ratio of the standard deviation of the predicted value to the RMSE of the predicted value. When RPD < 1.5, the model is inaccurate; when 1.5 < RPD < 2.0, the model can only make a rough estimation; when 2.0 < RPD < 2.5, the model has good prediction ability; when 2.5 < RPD < 3.0, the model has better prediction ability; and when RPD > 3.0, the model has the best prediction ability.

4. Results

4.1. Feature-Band Extraction Results

The correlation coefficients of the original spectral reflectance data and their 14 transformation forms and the SOM contents of 105 modelling-group samples were calculated. Taking a spectral curve as an example (Figure 9).

From the diagram of the coefficients of correlation between the original spectral reflectance and SOM content data, a negative correlation can be seen, which is consistent with the previous analysis. The correlation coefficients are between −0.22 and −0.39, and peak at −0.39 at 896 nm. This band can be used as the diagnostic feature of SOM. The $1/R$ transformation has a positive correlation with the content of SOM, which is opposite to the trend of the original reflectance correlation coefficient, and peaks 0.42 at 896 nm. However, the correlation coefficient curves transformed by $\lg R$, $1/\lg R$, $\sqrt{R}$ are basically consistent with the correlation coefficient of the original reflectance, and there is no substantial change. That is, compared with the correlation coefficient calculated with the original reflectance, the position of the characteristic band and the value of the correlation coefficient are basically the same. It can be seen that these spectral transformation methods cannot effectively improve the correlation between the SOM and the spectral curve.

In the five transformation forms of the first-order differential ($R^{\prime }$, $(1/R{)}^{\prime }$, $(\lg R{)}^{\prime }$, $(\sqrt{R}{)}^{\prime }$, $(1/\lg R{)}^{\prime }$), the correlation coefficient curve fluctuates greatly, and both positive and negative correlations exist. The correlation coefficient is between −0.71–0.80, Both the value of the correlation coefficient and the number of peak points increased, indicating that the first-order differential transformation has positive significance in improving the correlation between SOM content and spectral data. Among them, the peak correlation coefficient of SOM content at 1257 nm of the was 0.80, which is the maximum correlation coefficient of all transformation forms, and can be used for the diagnostic feature-band selection of SOM.

Among the five transformation forms of the second-order differential ($R^{″}$, $(1/R{)}^{″}$, $(\lg R{)}^{″}$, $(\sqrt{R}{)}^{″}$, $(1/\lg R{)}^{″}$), the change in the correlation coefficient curve is more intense than that of the first-order differential. It has more peak points but with lower peak values than the first-order differential. The value of the correlation coefficient is between −0.51 and 0.52, which is slightly higher than that of the original spectral curve. This shows that the second-order differential transformation can make a certain improvement in the correlation between SOM content and spectral data, but the effect is slightly worse than that of the first-order differential transformation. Finally, the reflectance after logarithmic first-order differential transformation with the highest correlation was selected as the research data.

Table 2 lists the peak values and band positions of the correlation coefficients according to different transformation forms and SOM contents.

It can be seen from Table 2 that for the different forms of spectral transformation, the band positions where the correlation coefficients peak also differ. Generally, the peaks are concentrated near wavelengths of 774 nm, 896 nm, 1184 nm, 1360 nm, 1713 nm, and 2203 nm, indicating that the spectral reflectance responds to SOM near these six wavelengths. They can be used as the diagnostic feature bands of SOM obtained by the correlation analysis.

To sum up, in the feature-extraction method based on correlation coefficients, the highest-correlated log first-order differential reflectance data were used for modelling and inversion of SOM content. The diagnostic feature bands are 774 nm, 896 nm, 1184 nm, 1360 nm, 1713 nm, and 2203 nm.

4.2. Model Accuracy Evaluation

Using the reflectance data after logarithmic first-order differentiation, the DPSO-BPNN network model is established according to the feature bands at 774 nm, 896 nm, 1184 nm, 1360 nm, 1713 nm, and 2203 nm, while 105 sample points selected by the correlation coefficient method are used to predict the SOM content. The main parameter settings are as follows (Table 3):

The accuracy of the DPSO-BPNN network model is evaluated according to the adjusted complex coefficient of determination ${\overline{R}}^2$, which is an indicator of the fitting performance of the model. The RMSE is used to evaluate the predictive accuracy of the model, and the RPD is used to evaluate the prediction ability of the model.

The DPSO-BPNN network model was tested using data from 25 soil sample points. The results are ${\overline{R}}^2$= 0.89, RMSE = 1.58, and RPD = 2.93. The results show that the model of SOM content based on hyperspectral data has high predictive accuracy, strong general-ization ability, and low predictive error.

4.3. Model Inversion Results

The inversion results of organic matter in the study area are shown in Figure 10.

The inversion results were also verified using 1:250,000 geochemical data from the study area. A geochemical contour map is shown in Figure 11, in which the geochemical data on SOM were derived from the results of a 1:250,000 multi-objective geochemical survey carried out in Northeast China. The threshold range of the original discrete data was set as the mean ± 3.5 times the mean-square deviation. The maximum and minimum values were eliminated iteratively to obtain data with an approximately normal distribution. Finally, Kriging interpolation was used for mapping.

Comparing Figure 10 and Figure 11, it can be seen that both show that the SOM is generally high in the east and low in the west. There is a cluster enrichment in the southeast of the study area, which proves that the inversion accuracy of the DPSO-BPNN network model is high and is in good agreement with the macro-trends of the geochemical contour map. The DPSO-BPNN network model inversion results can show more detailed features than the surface geochemical exploration results.

Based on the above results, the DPSO-BPNN network model shows good application value as a predictive model of black soil organic matter content based on hyperspectral data. It can provide technical support for the scientific evaluation of black soil quality and help to protect the sustainable use of black soil cultivated land resources.

5. Discussion

5.1. Influence of SOM Content on Spectral Reflectance

The spectral characteristics of soil are complex. Spectral curves can reflect the com-prehensive properties of soil. Although their shapes are generally the same, different SOM contents will cause changes in spectral reflectance (Figure 12). In general, the higher the SOM content, the lower the spectral reflectance. The reflectance differences are most obvious in the wavelength range of 450–1900 nm.

To further explore the influence of SOM content on spectral reflectance, we selected the two samples with the highest and lowest SOM contents. We subtracted their spectral reflectance curves to obtain spectral reflectance D-value curves at different SOM contents (Figure 13). The D-value curves can reflect the wavelengths sensitive to SOM. In the 450–1150 nm range, the slope of the reflectance curve is very steep and the influence of SOM content on spectral reflectance increases rapidly with wavelength. It peaks near 1150 nm and continues to 1300 nm, indicating that the spectral reflectance is most obviously affected by SOM content within this band. Therefore, 1150–1300 nm can be used as the main range for the selection of a wavelength sensitive to SOM. A trough is present near 1400 nm, which is mainly affected by water vapour absorption. At 1400–1600 nm, the curve shows an obvious increasing trend, until it begins to decline near 1800 nm. A wave trough is formed again near 1900 nm under the influence of water vapour absorption. Above 1900 nm, the curve increases obviously, then the influence of SOM content on the reflectance curve begins to decrease at 2100 nm.

To highlight the features of the soil spectral curve, a parametric analysis of spectral features was carried out. Fourteen mathematical transformations are performed on the original spectral reflectance curve R: first-order differential ($R^{\prime }$), second-order differential ($R^{″}$), reciprocal ($1/R$), reciprocal first-order differential ($(1/R{)}^{\prime }$), reciprocal second-order differential ($(1/R{)}^{″}$), logarithm ($\lg R$), logarithm first-order differential ($(\lg R{)}^{\prime }$), logarithm second-order differential ($(\lg R{)}^{″}$), square root ($\sqrt{R}$), square root first-order differential ($(\sqrt{R}{)}^{\prime }$), square root second-order differential ($(\sqrt{R}{)}^{″}$), logarithm reciprocal ($1/\lg R$), logarithm reciprocal first-order differential ($(1/\lg R{)}^{\prime }$), and logarithmic reciprocal second-order differential ($(1/\lg R{)}^{″}$). Taking an original soil spectral curve as an example, the results are shown for the original curve and the 14 transformations.

It is easy to see from Figure 14 that after five first-order differential transformations ($R^{\prime }$, $(1/R{)}^{\prime }$, $(\lg R{)}^{\prime }$, $(\sqrt{R}{)}^{\prime }$, $(1/\lg R{)}^{\prime }$), there are many large fluctuations in the curve, and the reflectivity no longer changes with increases in wavelength. After the second-order differential transformations ($R^{″}$, $(1/R{)}^{″}$, $(\lg R{)}^{″}$, $(\sqrt{R}{)}^{″}$, $(1/\lg R{)}^{″}$), the spectral curve shows large variations at both ends. The variation in the middle is small and there is an obvious step phenomenon near the two water vapour absorption bands. Compared with the original spectral curve and non-differential transformations, the spectral curve after first- and second-order differential transformations has more peak feature points. This improves the ability to identify small differences in spectral information, making it more suitable for extracting diagnostic feature bands of SOM content (Figure 14).

5.2. Comparison of Soil Organic Matter Inversion Models

A total of 105 of the field samples are used as modelling samples and 25 are used as test samples to predict the SOM content. The reflectance after logarithmic first-order differentiation is used as the research data. According to the feature bands of 774 nm, 896 nm, 1184 nm, 1360 nm, 1713 nm, 2203 nm screened by the correlation coefficient method, the multivariate stepwise regression, partial least squares, and neural network commonly used in the existing SOM content inversion research are compared (Table 4).

Compared with the other three models commonly used in the existing research, DPSO-BPNN network model has obvious performance improvement: the value of ${\overline{R}}^2$ reaches 0.89, indicating that the prediction accuracy of this model is high; the minimum value of RMSE indicates that the prediction accuracy of the model is high, and it is reduced from 3.50 of BPNN (hidden layer 11 nodes) to 1.58, indicating that the model enhances the global search ability of neural network and improves the prediction performance of neural network; the value of RPD is 2.93, more than 2.5, indicating that the model has good prediction ability (Figure 15).

By comparing the predicted value of SOM content with the real value, it can be seen that compared with the other three inversion models, the predicted value and the real value of SOM content of DPSO-BPNN network model are more closely distributed near the straight line $x=y$, and the predicted result of the test group is also closer to the real value, indicating that the algorithm has strong generalization ability.

In conclusion, the DPSO-BPNN network model based on hyperspectral data has higher accuracy, better prediction ability, and stronger generalization ability in retrieving black soil organic matter.

6. Conclusions

Focus on the demand for cultivated land quality monitoring in SDG 2.4 Sustainable food production system, taking the typical black soil area in the Northeast China as an example, the hyperspectral data of ground features and the SOM content data of soil samples are used to fully consider the correlation between spectral features and strengthen the difference between spectral features. Based on the correlation and quantitative relationship between SOM content and spectral reflectance, a dynamic fitness inertia weighted particle swarm optimization (DPSO) algorithm is proposed to be applied to the parameter adjustment process of artificial neural network (BPNN). The DPSO-BPNN network model is constructed, and then the global optimal remote sensing inversion model of black soil organic matter content is obtained. The main conclusions are as follows:

(1) The spectral index obtained by logarithmic first-order differential transformation of the spectral reflectance of black soil on the ground has the highest correlation with the content of SOM, and the diagnostic feature bands are 774 nm, 896 nm, 1184 nm, 1360 nm, 1713 nm, and 2203 nm.

(2) Starting with balancing the global search and local search ability of PSO algorithm, DPSO algorithm is proposed. The improved algorithm is applied to the parameter adjustment process of BPNN to replace the traditional error back propagation algorithm, and then the global optimal analytical expression of hyperspectral inversion is obtained, which is better than the multiple stepwise regression model, and the partial least square model DPSO-BPNN is more stable and accurate. The DPSO-BPNN network model improves the generalization ability and stability of the remote sensing quantitative inversion model.

(3) The inversion results of the DPSO-BPNN network model based on black soil organic matter content and soil hyperspectral information are basically consistent with the ground geochemical exploration trend, especially in areas with high SOM, and the inversion results reveal more details of SOM distribution. This laid a scientific foundation for the subsequent retrieval of organic matter content in black soil area using hyperspectral remote sensing images, and also provided technical support for large-scale and dynamic monitoring of soil organic matter.

(4) Compared with traditional soil element content measurement methods, the prediction of soil nutrients using hyperspectral data is fast and efficient. The next steps will focus on (i) making more effective use of the unique advantages of hyperspectral data, such as its high spectral resolution and high data availability, (ii) mining the feature mechanisms based on soil spectra, (iii) establishing a universal spectral feature model, (iv) further improving the ability of hyperspectral data to predict soil components, and (v) forming a novel hyper-spectral remote sensing soil retrieval method that meets the needs of black soil quality monitoring in Northeast China.

Author Contributions

R.C.: methodology, writing—original draft preparation and editing; Z.C.: validation and formal analysis; D.W.: resources and visualization; K.G.: supervision and project administration. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Not applicable.

Acknowledgments

The authors are grateful for helpful comments from many researchers and colleagues.

Conflicts of Interest

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

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Figures and Tables

Figure 1. Study area: (a) Landsat 8 OLI data, red dot and yellow dot on the figure are all sampling points, and the yellow dots are the test data randomly selected; (b) Photo of study area.

Figure 2. Field sampling: (a) Soil at sampling point (b) Sampling work photo.

Figure 3. FieldSpec® 4 Std-Res hyperspectral spectrometer: (a) Hyperspectral spectrometer, (b) Working photos of spectrometer.

Figure 4. S-G smoothing of soil spectral curve (The colored lines are reflectance curves of some soil samples).

Figure 5. Box chart analysis result (The circle indicates the sample number mark).

Figure 6. Three-layer BP neural network with one hidden layer.

Figure 7. Three common excitation functions. (a) purelin; (b) log-sigmoid; (c) tan-sigmod.

Figure 8. DPSO-BPNN.

Figure 9. Original spectral curve and 14 transformation correlation coefficients: (a) Original reflectance; (b) First order differential; (c) Second order differential; (d) Reciprocal; (e) Reciprocal first order differential; (f) Reciprocal second order differential; (g) Logarithm; (h) Logarithmic first order differential; (i) Logarithmic second order differential; (j) Square root; (k) Square root first order differential; (l) Square root second order differential; (m) Logarithmic reciprocal; (n) Logarithmic reciprocal first order differential; (o) Logarithmic reciprocal second order differential.

Figure 9. Original spectral curve and 14 transformation correlation coefficients: (a) Original reflectance; (b) First order differential; (c) Second order differential; (d) Reciprocal; (e) Reciprocal first order differential; (f) Reciprocal second order differential; (g) Logarithm; (h) Logarithmic first order differential; (i) Logarithmic second order differential; (j) Square root; (k) Square root first order differential; (l) Square root second order differential; (m) Logarithmic reciprocal; (n) Logarithmic reciprocal first order differential; (o) Logarithmic reciprocal second order differential.

Figure 9. Original spectral curve and 14 transformation correlation coefficients: (a) Original reflectance; (b) First order differential; (c) Second order differential; (d) Reciprocal; (e) Reciprocal first order differential; (f) Reciprocal second order differential; (g) Logarithm; (h) Logarithmic first order differential; (i) Logarithmic second order differential; (j) Square root; (k) Square root first order differential; (l) Square root second order differential; (m) Logarithmic reciprocal; (n) Logarithmic reciprocal first order differential; (o) Logarithmic reciprocal second order differential.

Figure 10. Inversion results of SOM (%).

Figure 11. Surface geochemical exploration results (%).

Figure 12. Spectral curves for different SOM contents.

Figure 13. Spectral reflectance D-value curves at different SOM contents.

Figure 14. Original soil reflectance curve and 14 transformation forms: (a) Original reflectance; (b) First-order differential; (c)Second-order differential; (d) Reciprocal; (e) Reciprocal first-order differential; (f) Reciprocal second-order differential; (g) Logarithm; (h) Logarithmic first-order differential; (i) Logarithmic second-order differential; (j) Square root; (k) Square root first-order differential; (l) Square root second-order differential; (m) Logarithmic reciprocal; (n) Logarithmic reciprocal first-order differential; (o) Logarithmic reciprocal second-order differential.

Figure 14. Original soil reflectance curve and 14 transformation forms: (a) Original reflectance; (b) First-order differential; (c)Second-order differential; (d) Reciprocal; (e) Reciprocal first-order differential; (f) Reciprocal second-order differential; (g) Logarithm; (h) Logarithmic first-order differential; (i) Logarithmic second-order differential; (j) Square root; (k) Square root first-order differential; (l) Square root second-order differential; (m) Logarithmic reciprocal; (n) Logarithmic reciprocal first-order differential; (o) Logarithmic reciprocal second-order differential.

Figure 14. Original soil reflectance curve and 14 transformation forms: (a) Original reflectance; (b) First-order differential; (c)Second-order differential; (d) Reciprocal; (e) Reciprocal first-order differential; (f) Reciprocal second-order differential; (g) Logarithm; (h) Logarithmic first-order differential; (i) Logarithmic second-order differential; (j) Square root; (k) Square root first-order differential; (l) Square root second-order differential; (m) Logarithmic reciprocal; (n) Logarithmic reciprocal first-order differential; (o) Logarithmic reciprocal second-order differential.

Figure 14. Original soil reflectance curve and 14 transformation forms: (a) Original reflectance; (b) First-order differential; (c)Second-order differential; (d) Reciprocal; (e) Reciprocal first-order differential; (f) Reciprocal second-order differential; (g) Logarithm; (h) Logarithmic first-order differential; (i) Logarithmic second-order differential; (j) Square root; (k) Square root first-order differential; (l) Square root second-order differential; (m) Logarithmic reciprocal; (n) Logarithmic reciprocal first-order differential; (o) Logarithmic reciprocal second-order differential.

Figure 15. Comparison diagram of measured value and predicted value of SOM content: (a) Mul tiple stepwise regression; (b) Partial least squares regression; (c) BP neural network (hidden layer (5 nodes); (d) DPSO-BPNN network model.

Table 1

Statistical analysis of sample sizes before and after outlier elimination.

	Content Range	Mean Value	Standard Deviation	Kurtosis	Skewness	Coefficient of Variation
Before culling	34–71.7 g/kg	48.89 g/kg	6.92 g/kg	4.598	0.823	14.2%
After elimination	37.4–59.9 g/kg	47.9 g/kg	4.90 g/kg	2.867	−0.086	10.24%

Table 2

Correlation coefficient peaks and feature bands of different transformation forms.

Spectral Transformation Form	Feature Bands/nm	Correlation Coefficient	Spectral Transformation Form	Feature Bands/nm	Correlation Coefficient
$R$	896	−0.39	$$(\sqrt{R}{)}^{\prime }$$	774137517312203	−0.580.670.600.45
$$1/R$$	896	0.42	$$(1/\lg R{)}^{\prime }$$	774136016992203	−0.530.670.500.44
$\lg R$	896	−0.41	$$R^{″}$$	839118415031696	−0.50−0.490.510.51
$$\sqrt{R}$$	896	−0.40	$(1/R{)}^{″}$	839118412032196	0.51−0.510.50−0.48
$$1/\lg R$$	896	−0.39	$(\lg R{)}^{″}$	839120315032331	−0.510.510.460.41
$$R^{\prime }$$	774136117132203	−0.540.690.550.45	$$(\sqrt{R}{)}^{″}$$	8391184150316961913	−0.50−0.510.490.47−0.44
$$(1/R{)}^{\prime }$$	564114316622381	0.48−0.71−0.600.45	$$(1/\lg R{)}^{″}$$	8391184150316961913	−0.49−0.490.490.52−0.42
$(\lg R{)}^{\prime }$	685125717652381	−0.610.800.51−0.45

Table 3

Main parameter settings of the DPSO-BPNN algorithm.

Algorithm Parameters	Settings	Network Parameters	Settings
Maximum iterations	1000	Maximum training times	100
Learning factor C1	2	Input layer node	3
Learning factor C2	2	Hidden layer node	5
Particle swarm size	100	Output layer node	1
Speed range	[−5, 5]

Table 4

Comparison of SOM prediction model accuracy.

	${\overline{\mathit{R}}}^2$	RMSE	RPD
Multiple stepwise regression	0.58	3.13	1.21
Partial least squares regression	0.79	2.17	2.06
BP neural network(hidden layer 5 nodes)	0.79	2.04	2.14
BP neural network(hidden layer 7 nodes)	0.77	2.27	2.02
BP neural network(hidden layer 11 nodes)	0.46	3.50	1.41
DPSO-BPNNnetwork model	0.89	1.58	2.93

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