Estimation of Soil Moisture during Different Growth Stages of Summer Maize under Various Water Conditions Using UAV Multispectral Data and Machine Learning

Abstract

Accurate estimation of soil moisture content (SMC) is vital for effective farmland water management and informed irrigation decision-making. The utilization of unmanned aerial vehicle (UAV)-based remote sensing technology to monitor SMC offers advantages such as mobility, high timeliness, and high spatial resolution, thereby compensating for the limitations of in-situ observations and satellite remote sensing. However, previous research has primarily focused on SMC diagnostics for the entire crop growth period, often neglecting the development of targeted soil moisture modeling paradigms that account for the specific characteristics of the canopy and root zone at different growth stages. Furthermore, the variations in soil moisture status between fields, resulting from the hysteresis of water flow in irrigation channels at different levels, may influence the development of soil moisture modeling schemes, an area that has been seldom explored. In this study, SMC models based on UAV spectral information were constructed using Random Forest (RF) and Particle Swarm Optimization-Support Vector Machine (PSO-SVM) algorithms. The soil moisture modeling paradigms (i.e., input–output mapping) under different growth stages and soil moisture conditions of summer maize were systematically compared and discussed, along with the corresponding physical interpretability. Our results showed that (1) the SMC modeling schemes differ significantly across the various growth stages, with distinct input–output mappings recommended for the early (i.e., jointing, tasselling, and silking stages), middle (i.e., blister and milk stages), and late (i.e., maturing stage) periods. (2) these machine learning-based models performed best at the jointing stage, while subsequently, their accuracy generally exhibited a downward trend as the maize grew. (3) the RF model demonstrates superior robustness in estimating soil moisture status across different fields (moisture conditions), achieving optimal estimation accuracy in fields with overall higher SMC in line with the PSO-SVM model. (4) unlike the RF model’s robustness in spatial SMC diagnostics, the PSO-SVM model more reliably captured the temporal dynamics of SMC across different growth stages of summer maize. This study offers technical references for future modelers in UAV-based SMC modeling across various spatial and temporal conditions, addressing both the types of models as well as their input features.

1. Introduction

In agriculture, accurate estimation of soil moisture content (SMC) is essential for effective water management and informed irrigation decision-making [1,2]. Traditional in-situ observation methods, such as weighing soil samples before and after drying, time-domain reflectometry (TDR), and neutron probe measurements, offer high accuracy. However, these approaches suffer from many limitations, including small-scale monitoring and high costs, which hinder their performance in large-scale agricultural applications. Therefore, it is necessary to develop a more efficient and scalable method for SMC monitoring at the regional scale.

Nowadays, the application of remote sensing technology in the field of agriculture provides a new direction for SMC monitoring [3,4]. Satellite remote sensing technology boasts the advantages of extensive coverage and relatively high precision, enabling it to excel in large-scale SMC estimation. However, it falls short of small-scale and high-frequency SMC prediction in farmland [5,6]. In contrast, unmanned aerial vehicle (UAV) remote sensing technology demonstrates remarkable performance in predicting soil moisture content (SMC) in small-scale farmland. Firstly, the UAV platform boasts low operational costs and the capability to fly at high frequencies. Moreover, UAVs are equipped to capture images with a spatial resolution of 1–2 cm per pixel, a feature that significantly enhances their suitability for monitoring SMC in small-scale farmland [6,7]. The approach of monitoring SMC using UAVs equipped with thermal infrared, visible light, and multispectral sensors holds a wide application prospect [8,9,10,11,12]. Many previous studies utilized UAVs to acquire spectral information, then analyzed the correlation between spectral characteristics and SMC under various conditions and constructed physical or statistical models to estimate SMC. For instance, Zhang et al. [13] employed a UAV-based remote sensing system to obtain multispectral images of the canopy during the critical growth stages of maize. A relationship model between sensitive vegetation index and SMC at different growth stages based on machine learning method and multiple linear regression was constructed, which had high accuracy and stability. Tan et al. [14] captured multispectral images of summer maize at the jointing, tasselling, silking, and maturing stages. They utilized a combination of full subset screening and machine learning to enhance the accuracy and robustness of SMC estimation models, providing theoretical support for accurate monitoring of soil moisture and precision irrigation. Araya et al. [12] utilized UAVs to obtain multispectral information about prairie areas. By integrating topographic information with hydrological data on precipitation and evaporation, they fully characterized and predicted the dynamic soil moisture status in the heterogeneous terrain of grassland. Zhu et al. [15] obtained spectral information on the kiwifruit canopy with a multispectral camera carried by UAV and achieved SMC monitoring in the kiwifruit root region through an integrated learning framework.

Furthermore, traditional linear regression methods encounter challenges in capturing the intricate, nonlinear interactions between remote sensing indices and SMC, leading to suboptimal estimation accuracy [16]. Secondly, the variability in environmental conditions, such as soil type, vegetation cover, and weather patterns, can introduce substantial noise and uncertainty into the remote sensing measurements, further complicating the estimation process. Consequently, achieving ideal results in estimating SMC through traditional linear regression methods is a formidable task. The advantage of machine learning (ML) to learn and approximate complex nonlinear mappings has garnered increasing attention in soil moisture modeling. Machine learning methods such as Artificial Neural Networks (ANN) [17], Convolutional Neural Networks (CNN) [18], Support Vector Machines (SVM) [19], Extreme Learning Machines (ELM) [20] and Random Forests (RF) [21] have been widely applied to soil moisture estimation, demonstrating that ML can construct a comprehensive, multi-feature variable SMC-estimation model and improve the accuracy of it. For example, in 2010, Ahmad et al. [22] proposed a regression technique called support vector machine (SVM) and applied it to remote sensing SMC estimation. Zhang et al. [23] quantified SMC in a maize field under various irrigation conditions with UAV-based multimodal data based on three machine learning algorithms: partial least squares regression (PLSR), K nearest neighbor (KNN), and random forest regression (RFR). Li et al. [24] evaluated the importance of polarization features in wheat SMC retrieval using random forest regression and selected optimized feature combinations to construct a high-precision SMC estimation model.

Notably, owing to the scarcity of data, previous researchers have tended to construct mappings between spectral information and soil moisture dynamics over the entire growth period of crops. Nevertheless, from both physical and physiological perspectives, it is evident that the dominant factors affecting soil moisture dynamics vary with the development of the crop canopy and root system. For example, in the early growth stage, crop canopy is not fully developed. Compared with canopy spectral information, the information brought by bare soil may better reflect the condition of soil moisture. With the growth and development of crops, the spectral information of the crop canopy gradually gains the capability to reflect soil moisture conditions. Therefore, one innovative aspect of this study is exploring the discrepancy in input-output mappings for UAV-based SMC models at various growth stages. An SMC modeling paradigm for maize is established, which attempts to explain its feasibility from a physical perspective. In addition, prior research frequently employs artificial moisture gradients in field experimental plots as a foundational basis. However, soil moisture conditions in actual irrigated regions differ significantly from ideal settings and are largely influenced by the hysteresis of water flow at different levels of irrigation canals, such as branch canals, lateral canals, and sublateral canals. Therefore, another innovative point of this study is to investigate how varying moisture conditions induced by the irrigation canal system affect the structure and accuracy of SMC estimation models in actual irrigated areas.

In this study, summer maize grown from July to September 2023 at Haiwu Farm, Wugong, Shaanxi Province, China, was selected as the study area. Four fields with different moisture conditions were chosen as experimental plots. Utilizing a UAV equipped with a multispectral sensor, we obtained the spectral reflectance of the maize canopy, calculated various vegetation indexes, and collected ground data simultaneously. Random Forest (RF) and Particle Swarm Optimization-Support Vector Machine (PSO-SVM) algorithms are introduced to construct SMC models for different growth stages and moisture conditions at four soil depths, respectively. It should be emphasized that the primary goal of this study is not to attain state-of-the-art accuracy in SWC estimation through spectral information but rather to develop a UAV-based soil moisture modeling paradigm suitable for summer maize in China’s arid and semi-arid regions. We attempt to answer the following questions with the aid of this field-scale experiment: (1) How do the key input features of UAV-based soil moisture models vary across different growth stages due to the development of the canopy and root system throughout the entire growth period? What impact does this variation have on the accuracy of ML-based models? (2) How do moisture differences between fields within an irrigated area influence the construction of UAV-based SMC models? (3) Can the effects of temporal variability (across different growth stages) and spatial variability (across different moisture conditions) on the accuracy of UAV-based SMC models be elucidated from a physical perspective? It is hoped that this study can provide guidance for modelers on the design of UAV-based SMC modeling across various spatial and temporal conditions.

2. Materials and Methods

2.1. Experimental Area

In this study, field experiments were conducted at Haiwu Farm, located in Wugong County, Xianyang, Shaanxi Province. The farm is situated in the western part of the Guanzhong Plain (108°05′ E, 34°35′ N) within the Baojixia Irrigation Area. At an average altitude of 471 m, this region falls within the temperate semi-humid monsoon climate zone, with an annual average temperature of 12.9 °C and an annual average rainfall of approximately 600 mm, which is mainly concentrated from July to September. The annual sunshine duration is 2163.4 h, and the frost-free period spans 210 days. The soil in the study area is loam, with a bulk density of 1.36 g/cm³ at a depth of 0–20 cm. The soil pH is 8, and the organic matter content is 12.5 g/kg. The conditions of precipitation and temperature in the study area during the experiment are shown in Figure 1.

2.2. Experimental Design

The maize variety is Yanke 288 (Yan’an, China) sown on 15 June. The row spacing is 0.6 m, the plant spacing is 0.24 m, and the planting density is 4600 plants per hectare. To reflect the applicability of this research method in the Guanzhong Plain region of Shaanxi Province, crop fertilization, irrigation, and pest control management were conducted in accordance with local farming practices during the experiment. More precisely, the typical irrigation strategy for summer maize is as follows: During the sowing period, sufficient irrigation should be applied to ensure the field’s seedling emergence rate. When the moisture content of the topsoil falls below 65% during the jointing and tasseling stages, timely irrigation should be implemented. At the blistering and milk stages, the rainy season arrives, and precipitation can fulfill the maize’s growth requirements. Irrigation throughout the entire growth period is concentrated in June and July, occurring approximately 2 to 4 times, and the irrigation quota is around 450 to 600 m³ per mu. Given the local technical limitations in measuring water, the specific irrigation amount in each field was not accurately measured in this study. The differences in soil moisture between fields could be clearly observed (see the article below).

Four fields, A, B, C, and D, were selected for the experiment. Fields A and B are located along the east-west direction of the branch canal, while fields C and D are situated on one side of lateral canals (since the study area is relatively small, the soil texture of the four fields is the same, which is loam). The flow direction of the branch canal is from west to east. Fields A, B, C, and D are approximately 12,167 m², 12,920 m², 7040 m², and 10,764 m², respectively. The location of the experimental area, along with the distribution of fields and canals in the field, is shown in Figure 2 (GCS_WGS_1984).

2.3. Acquisition of Field Data

The multispectral images and ground data of this experiment were collected on 20 July 2023 (jointing stage, V6), 2 August (tasselling stage, VT), 10 August (silking stage, R1), 19 August (blistering stage, R2), 30 August (milk stage, R3), and 7 September (maturing stage, R4), totaling six stages.

2.3.1. Acquisition of Multispectral Image

Using the UAV (DJI Mavic 3M, Shenzhen, China), equipped with both a visible light camera and a multispectral camera, we obtained visible light images and multispectral images of crops at each growth stage. The visible light camera sensor is a 4/3-inch CMOS from DJI, featuring an effective pixel count of 20 million. The multispectral camera sensor, also from DJI, is a 1/2.8-inch CMOS with an effective pixel count of 5 million. The multispectral camera includes 4 spectral acquisition channels: 560 nm ± 16 nm (Red, R), 650 nm ± 16 nm (Green, G), 730 nm ± 16 nm (Red Edge, RE) and 860 nm ± 26 nm (Near Infrared, NIR). The red and green channels were calculated from the multispectral camera channels. The UAV platform and reflectivity calibration board are shown in Figure 3.

During the critical stages of maize growth, we selected clear weather conditions at noon with uniform wind speeds to capture images. We used a calibration board (25% reflection of the reference target) to achieve multispectral radiation calibration. The UAV took pictures along the preset fixed route. The UAV flew at an altitude of 50 m with a speed of 3 m/s, maintaining 85% heading overlap and 75% side overlap. During the flight and photography, the multispectral camera lens shot vertically downwards at regular time intervals. The flight was georeferenced with RTK technology to guarantee accurate positioning data and provide high-precision geographic reference. The GSD of the images captured by UAV was 2.31 cm/pixel, and the reprojection error was 1.06 pixels.

2.3.2. Acquisition of Ground Data

• Leaf Area Index (LAI)

At each sampling stage of summer maize, we selected 3 plants from each sampling point for the determination of LAI (Figure 4). We measured the length and width of each leaf using a ruler, and the LAI of maize was calculated using Formula (1).

$$\mathrm{LAI}={\displaystyle \frac{\sum 0.75\times {\mathrm{l}}_{\mathrm{i}}\times {\mathrm{w}}_{\mathrm{i}}}{\mathrm{A}}}$$

(1)

where LAI is the leaf area index (m²·m⁻²), l_i is the length of one leaf (m), w_i is the width of one leaf (m), and A is the floor space of one plant (m²).

2.

Soil Moisture Content (SMC)

After the UAV image collection is completed, the soil moisture content (SMC) is measured by the drying method with a three-point sampling approach. Each test field has three points on the diagonal as sampling points for field sampling. At each sampling point, we collect the soil sample every 10 cm, with depths of 0–10 cm, 10–20 cm, 20–30 cm, and 30–40 cm. Once a soil sample is taken, it will be immediately placed in an aluminum box and weighed. Subsequently, the soil sample is baked at a constant temperature of 105 °C for 8–10 h, drying it to a constant weight. After drying, we weigh the dry soil and calculate the SMC. The calculation formula of SMC is shown in Formula (2).

$$\mathrm{SWC}={\displaystyle \frac{{\mathrm{m}}_1-{\mathrm{m}}_2}{{\mathrm{m}}_2-{\mathrm{m}}_0}}\times 100$$

(2)

where SWC is soil moisture content (%), m₁ is wet soil plus aluminum box weight (g), m₂ is dry soil plus aluminum box weight (g), and m₀ is the aluminum box weight (g).

2.4. Acquisition of Spectral Information

2.4.1. Image Processing

The original multispectral images from the four bands, along with the visible light images captured by the UAV, were spliced together, and three-dimensional reconstruction was achieved based on the SFM algorithm within the DJI Modify V3.9.4 software, resulting in the complete multispectral images (.tif) of the fields. After that, the calibration reflector (25% reflection reference target) was used for multispectral radiation correction to obtain accurate spectral information. Then, we used the band synthesis function of ENVI5.6 software, synthesizing the reflectance image of four bands into a multi-band reflectance image, which was convenient for image processing and reflectance extraction. A region of interest was created in visible light images, and a selection of soil and vegetation image samples was made to classify soil and vegetation canopy using the support vector machine method in the image classification function. Finally, we created a grid mask to remove the soil background from multispectral images and extracted the reflectance of each sampling point after the background had been removed (Figure 5).

2.4.2. Vegetation Index

Vegetation index is a simple, effective and empirical measure to reflect vegetation status. It can enhance vegetation information and reduce the interference of non-vegetation information. In the field of remote sensing applications, the vegetation index has been widely used to qualitatively and quantitatively evaluate vegetation growth activity. In this study, based on the spectral band range of the camera, the vegetation indexes shown in

Table 1. Selected vegetation indexes and calculation formulas.

Vegetation Indexes	Formula	References
NDVI	$\mathrm{NDVI}={\displaystyle \frac{\mathrm{NIR} - \mathrm{R}}{\mathrm{NIR}+\mathrm{R}}}$	Haboudane et al., 2004 [25]
RVI	$\mathrm{RVI}={\displaystyle \frac{\mathrm{NIR}}{\mathrm{R}}}$	Sims and Gamon 2002 [26]
GNDVI	$\mathrm{GNDVI}={\displaystyle \frac{\mathrm{NIR}-\mathrm{G}}{\mathrm{NIR}+\mathrm{G}}}$	Yao et al., 2017 [27]
OSAVI	$\mathrm{OSAVI}={\displaystyle \frac{\mathrm{NIR}- \mathrm{R}}{\mathrm{NIR}+\mathrm{R}+0.16}}$	Haboudane et al., 2002 [28]
TVI	$\mathrm{TVI}=\sqrt{\mathrm{NDVI}+0.5}$	Broge and Leblanc 2001 [29]
MSAVI	$\mathrm{MSAVI}=0.5\times [2\mathrm{NIR}+1$ $-\sqrt{{(2\mathrm{NIR}+1)}^2 - 8(\mathrm{NIR}-\mathrm{R})}]$	Tian et al., 2011 [30]

Note: G, R, RE, and NIR are the spectral reflectance at 560 nm, 650 nm, 730 nm, and 860 nm, respectively.

are intended to be selected.

2.5. Data Processing

2.5.1. Grey Relational Analysis

Grey Relational Analysis (GRA) is a method used to analyze the “grey relational grade (GRG)” between two vectors. It determines the relational grade between two vectors by calculating the grey relational coefficient of the grey value between them, allowing factors involved in the analysis and evaluation to be categorized as “main factors” or “secondary factors”. In GRA, each element in two vectors is treated as a grey value, which can represent pixels in an image or other features in a dataset. The higher the grey value, the greater the weight of the element within the vector. Grey relational analysis places all evaluation indicators within a unified system for comparison rather than relying on pairwise comparisons and analyses, making this method widely applicable across various fields. The specific methodologies of grey relational analysis are as follows:

Let the reference sequence be ${\mathrm{X}}_0=\left\{{\mathrm{x}}_0\left(\mathrm{k}\right),\mathrm{k}=1,2···,\mathrm{n}\right\}$, the comparison sequence is ${\mathrm{X}}_{\mathrm{i}}=\left\{{\mathrm{x}}_{\mathrm{i}}\left(\mathrm{k}\right),\mathrm{k}=1,2···,\mathrm{n}\right\}$, Then the grey relational grade (GRG) between X0 and Xi can be calculated according to Formulas (3) and (4):

$$\mathrm{GRG}={\displaystyle \frac{1}{\mathrm{n}}}{\sum }_{\mathrm{k}=1}^{\mathrm{n}}\mathsf{\gamma }({\mathrm{x}}_0(\mathrm{k},{\mathrm{x}}_{\mathrm{i}}\left(\mathrm{k}\right)\left)\right)$$

(3)

$$\mathsf{\gamma }({\mathrm{x}}_0\left(\mathrm{k}\right),{\mathrm{x}}_{\mathrm{i}}\left(\mathrm{k}\right))={\displaystyle \frac{\frac{\min }{\mathrm{i}}\frac{\min }{\mathrm{k}}\left|{\mathrm{x}}_0\left(\mathrm{k}\right)-{\mathrm{x}}_{\mathrm{i}}\left(\mathrm{k}\right)\right|+\mathsf{\rho }\frac{\max }{\mathrm{i}}\frac{\max }{\mathrm{k}}\left|{\mathrm{x}}_0\left(\mathrm{k}\right)-{\mathrm{x}}_{\mathrm{i}}\left(\mathrm{k}\right)\right|}{\left|{\mathrm{x}}_0\left(\mathrm{k}\right)-{\mathrm{x}}_{\mathrm{i}}\left(\mathrm{k}\right)\right|+\mathsf{\rho }\frac{\max }{\mathrm{i}}\frac{\max }{\mathrm{k}}\left|{\mathrm{x}}_0\left(\mathrm{k}\right)-{\mathrm{x}}_{\mathrm{i}}\left(\mathrm{k}\right)\right|}}$$

(4)

where $\mathsf{\rho }$ is the resolution coefficient, 0.5.

We sorted the grey relational grades of each factor, and the degree of correlation among factors is indicated by their order, thus achieving the purpose of selecting variables.

A total of 11 indexes, including reflectance from 4 bands, 6 vegetation indexes, and the leaf area index (LAI), were selected for this study. These 11 indicators will be evaluated using GRA to form the optimal input variable combination, comprising six indicators that exhibit a strong relationship with soil moisture. This combination will subsequently be utilized as the input for the machine learning model. The proposed model inputs are listed in

Table 2. Proposed inputs.

Input Variable	Remarks
G	560 nm ± 16 nm
R	650 nm ± 16 nm
RE	730 nm ± 16 nm
NIR	860 nm ± 26 nm
LAI	$\mathrm{LAI}={\displaystyle \frac{\sum 0.75\times {\mathrm{l}}_{\mathrm{i}}\times {\mathrm{w}}_{\mathrm{i}}}{\mathrm{A}}}$
NDVI	$\mathrm{NDVI}={\displaystyle \frac{\mathrm{NIR} - \mathrm{R}}{\mathrm{NIR}+\mathrm{R}}}$
RVI	$\mathrm{RVI}={\displaystyle \frac{\mathrm{NIR}}{\mathrm{R}}}$
GNDVI	$\mathrm{GNDVI}={\displaystyle \frac{\mathrm{NIR}- \mathrm{G}}{\mathrm{NIR}+\mathrm{G}}}$
OSAVI	$\mathrm{OSAVI}={\displaystyle \frac{\mathrm{NIR} - \mathrm{R}}{\mathrm{NIR}+\mathrm{R}+0.16}}$
TVI	$\mathrm{TVI}=\sqrt{\mathrm{NDVI}+0.5}$
MSAVI	$\mathrm{MSAVI}=0.5\times [2\mathrm{NIR}+1$ $-\sqrt{{(2\mathrm{NIR}+1)}^2-8(\mathrm{NIR}-\mathrm{R})}]$

.

2.5.2. Sample Set Partitioning Based on Joint X–Y Distance

Using the sample set partitioning based on the joint X–Y distance (SPXY) algorithm to divide the training set and test set of the model, we utilize two-thirds of the data for training and one-third for testing. The SPXY algorithm is a sample set partitioning method rooted in a statistical perspective, which is an extension of the Kennard–Stone (KS) algorithm. This method aims to mitigate potential deviations between the training set and the test set, thereby enhancing the stability of the model. The calculation formulas are shown in Formulas (5)–(7).

$${\mathrm{d}}_{\mathrm{x}}(\mathrm{p}, \mathrm{q})=\sqrt{{\sum }_{j=1}^N{[{\mathrm{x}}_{\mathrm{p}}\left(\mathrm{j}\right)-{\mathrm{x}}_{\mathrm{q}}\left(\mathrm{j}\right)]}^2}$$

(5)

$${\mathrm{d}}_{\mathrm{y}}\left(\mathrm{p}, \mathrm{q}\right)=\sqrt{{({\mathrm{y}}_{\mathrm{p}}-{\mathrm{y}}_{\mathrm{q}})}^2}=\left|{\mathrm{y}}_{\mathrm{p}}-{\mathrm{y}}_{\mathrm{q}}\right|$$

(6)

The standardized formula is as follows:

$${\mathrm{d}}_{\mathrm{x}\mathrm{y}}(\mathrm{p}, \mathrm{q})={\displaystyle \frac{{\mathrm{d}}_{\mathrm{x}}(\mathrm{p}, \mathrm{q})}{\underset{\mathrm{p}, \mathrm{q}\in \left[1, \mathrm{N}\right]}{\max }{\mathrm{d}}_{\mathrm{x}}(\mathrm{p}, \mathrm{q})}}+{\displaystyle \frac{{\mathrm{d}}_{\mathrm{y}}(\mathrm{p}, \mathrm{q})}{\underset{\mathrm{p}, \mathrm{q}\in \left[1, \mathrm{N}\right]}{\max }{\mathrm{d}}_{\mathrm{y}}(\mathrm{p}, \mathrm{q})}}$$

(7)

where N is the sample number, ${\mathrm{x}}_{\mathrm{p}}\left(\mathrm{j}\right)$ and ${\mathrm{x}}_{\mathrm{q}}\left(\mathrm{j}\right)$ are the spectral values of samples p and q, respectively, $y_{\mathrm{p}}\left(\mathrm{j}\right)$ and ${\mathrm{y}}_{\mathrm{q}}\left(\mathrm{j}\right)$ are the feature vectors of samples p and q, respectively, ${\mathrm{d}}_{\mathrm{x}}(\mathrm{p}, \mathrm{q})$ is the Euclidean distance of x variables for samples p and q, ${\mathrm{d}}_{\mathrm{y}}(\mathrm{p}, \mathrm{q})$ is the Euclidean distance of y variables for samples p and q.

2.6. Modeling Methods

Using MATLAB R2016a software for Random Forest (RF) Regression modeling and Particle Swarm Optimization-Support Vector Machine (PSO-SVM) regression modeling. RF regression is a commonly used ensemble learning method. This method employs decision trees as base learners, generating multiple decision trees to vote and obtain the regression result through the “bootstrap sampling” and “random feature selection” strategies. RF exhibits a strong tolerance to noise and outliers, which can effectively prevent overfitting of the decision trees. PSO-SVM regression is a strategy that combines a global optimization algorithm with a machine learning model. The PSO algorithm can automatically discover the optimal combination of hyperparameters for SVM model performance, thus addressing the issue that SVM performance is overly dependent on parameter selection. PSO-SVM can handle high-dimensional data, boasting a simple structure and strong adaptability. It has distinct advantages in solving small sample and high-dimensional problems.

2.7. Statistical Analysis

In this study, the Coefficient of Determination (R²) and Root Mean Squared Error (RMSE) are selected as evaluation indicators to evaluate the estimation accuracy of the models. The calculation formulas are as follows:

$${\mathrm{R}}^2={\displaystyle \frac{{\sum }_{\mathrm{i}=1}^{\mathrm{N}}{({\mathrm{P}}_{\mathrm{i}}-\stackrel{\mathrm{-}}{\mathrm{O} })}^2}{\sum _{\mathrm{i}=1}^{\mathrm{N}}{({\mathrm{O}}_{\mathrm{i}}-\stackrel{\mathrm{-}}{\mathrm{O}})}^2}}$$

(8)

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{\sum _{\mathrm{i}=1}^{\mathrm{N}}{\left({\mathrm{O}}_{\mathrm{i} }-{\mathrm{P}}_{\mathrm{i}}\right)}^2}{\mathrm{N}}}}$$

(9)

where ${\mathrm{O}}_{\mathrm{i}}$ and ${\mathrm{P}}_{\mathrm{i}}$ are the measured value and test value, respectively, $\stackrel{\mathrm{-}}{\mathrm{O}}$ and $\stackrel{\mathrm{-}}{\mathrm{P}}$ are the measured mean value and test mean value, respectively, and N is the number of the test set sample.

3. Results

3.1. Temporal and Spatial Characteristics Analysis of Soil Moisture Data

Initially, we analyzed soil moisture data from three sampling points (marked as 1, 2, and 3) at a depth of 10–40 cm in four fields (A, B, C, and D) and at different growth stages. A heat map illustrating SMC under these diverse conditions is shown in Figure 6. It can be discerned from the Figure that SMC exhibits significant spatial and temporal variations.

Figure 7 illustrates the time series characteristics of soil moisture at varying depths during various growth stages. It can be observed that throughout the six growth stages of maize from July to September, the SMC at the same depth fluctuates with time, and the trend is similar: SMC gradually increases from the jointing stage to the tasselling stage, reaching its peak at the tasselling stage. It then gradually decreases as the maize progresses from the tasseling stage to the blister stage. Following that, soil moisture increases gradually from the blister stage to the milk stage, and ultimately, it decreases continuously from the milk stage to the maturing stage. Overall, SMC remains at a high level during the tasselling, silking, and milk stages, which largely aligns with the moisture sensitivity pattern of maize at its middle growth stages.

Figure 8 showcases the statistical analysis outcomes of SMC data gathered from four distinct fields. Notably, there exists a notable variation in SMC among these fields: Fields A and B consistently demonstrate lower SMC levels, with Field A exhibiting a relatively lower average and greater fluctuations in SMC. Conversely, Field C displays a generally higher SMC at each measured depth compared to A and B, and the SMC of this field is more concentrated and uniform. Field D stands out as having the highest SMC across all depths, accompanied by a lower standard deviation, suggesting that this field boasts the highest and most stable SMC among the four. This stability can likely be traced to the abundant lateral and sublateral irrigation canals encircling Field D, which contribute to more optimal and consistent irrigation conditions. Consequently, we can deduce that the dense network of irrigation canals aids in sustaining a stable and elevated soil moisture content within the fields. Such favorable moisture conditions are advantageous for crop growth and development, potentially indicative of optimal soil texture, structure, and irrigation management strategies. In the context of estimating SMC, Field D, with its uniform and consistent moisture profile, is poised to yield a more precise and ideal estimation. Furthermore, when compared to SMC variations across various growth stages, the SMC data within individual fields tends to exhibit greater dispersion.

In addition, there are significant variations in SMC under different depths. At a depth of 10 cm, the SMC is usually lower than that at other depths. At 20 cm and 30 cm depth, the soil moisture remains at a relatively high level. After that, the soil moisture gradually decreases as the depth increases. It can be observed that soil moisture at a depth of 10 cm is lower because surface moisture seeps down faster; the moisture in the surface soil is more susceptible to evaporation and infiltration. Therefore, compared to the surface soil, the retention ability of soil moisture is stronger at a depth of 20–30 cm, keeping SMC at a relatively high level.

3.2. SMC Modeling at Different Growth Stages

In this section, we constructed SMC-estimation models for different growth stages of maize, comparing the differences in accuracy between the two models (fields will not be classified when comparing the results of various growth stages). Additionally, we also discussed the rules of modeling paradigms among various growth stages.

3.2.1. Screening Variables for Various Stages Based on GRA (Grey Relational Analysis)

After utilizing grey relational analysis (GRA) to compute the grey relational grade (GRG) between each index and SMC across different growth stages, we determined that a higher GRG signifies a greater influence of that particular index on SMC. Based on the GRG, sorted from high to low, we selected six independent variables as the optimal combination of input variables for the model. The calculation results of GRG at different growth stages and depths are presented in Figure 9 below; the optimal combinations of variables are shown in Figure 10 below.

According to the charts above, it can be observed that there are differences in the optimal combinations of input variables selected among different growth stages. At the jointing, tasselling, and silking stages, the relational grades of vegetation indexes are generally higher than those of reflectance indexes. Therefore, vegetation indexes (NDVI, GNDVI, OSAVI, TVI) and NIR comprise the optimal combinations of input variables for these three growth stages. At the blister and milk stages, the relational grades of reflectance indexes (such as G, R, RE) and vegetation indexes (such as NDVI, GNDVI, OSAVI, and TVI) are at a similar level. The optimal combinations at these stages primarily consist of reflectance indexes (G, R, RE) combined with vegetation indexes (NDVI, GNDVI, OSAVI, TVI) and LAI. Finally, the green (G) and red (R) bands, along with vegetation indexes (NDVI, GNDVI, OSAVI, TVI), are preferred at the maturing stage.

Significantly, the relational grades of NIR at the two earlier growth stages, the jointing stage and the tasseling stage, are generally higher than those of other band reflectance (G, R, RE). However, they decrease with the progression of the growth stages and eventually drop out of the variable combinations. On the contrary, the relational grades of LAI at the jointing and tasselling stages are lower than those of other variables but then increase and begin to appear frequently in the combinations from the silking stage to the milk stage. At the maturing stage, its relational grade turns out to be lower than other variables and gradually withdraws from the combination. This may be attributed to the fact that LAI, as an important index reflecting the growth status of maize, typically reaches its highest level around the blister stage, at which time LAI may be more sensitive to changes in soil moisture. After the blister stage, LAI begins to decrease gradually, and its sensitivity to SMC decreases, rendering it less suitable for participating in SMC prediction.

In summary, we can divide the entire growth period of summer maize into three main stages based on GRA: It is more suitable to use vegetation indexes (NDVI, GNDVI, OSAVI, TVI) and NIR to make predictions at the jointing, tasselling, and silking stages. At the blister and milk stages, it is more suitable to predict with the combination of reflectance (G, R, RE), vegetation indexes (NDVI, GNDVI, OSAVI, TVI), and LAI. Finally, it is better to use reflectance (G, R) and vegetation indexes (NDVI, GNDVI, OSAVI, TVI) to estimate SMC at the maturing stage.

3.2.2. Establishment and Verification of RF Model for Various Stages

The variables screened by GRA are utilized as inputs for the model and employed to construct SMC-estimation models at each depth for different stages based on the RF model. The evaluation of the RF model’s performance under different depths at each growth stage is shown in Figure 11.

As evident from the Figure, the model’s estimation effectiveness varies across growth stages. The accuracy of the RF model at the jointing stage is significantly higher than at other growth stages, with R² values of the test set at 10 cm and 20 cm depths being 0.757 and 0.590, respectively. The accuracy of the model at the milk stage is slightly lower than that at the jointing stage, achieving R² values of 0.515, 0.677, and 0.814 for the test set at 10 cm, 30 cm, and 40 cm depths, respectively. These results indicate that the model performs satisfactorily at these two stages. In contrast, the models at the other four growth stages exhibit relatively poorer accuracy.

In addition, the model’s performance in estimating SMC at various depths also differs. In the test set, the RF model’s ability to estimate SMC for surface soil is generally superior to that for deeper soil layers, and the model generally performs better at the jointing stage. This can be attributed to the absorption and utilization of soil moisture by maize roots are concentrated in the surface layer at this stage. At this time, maize requires a significant amount of soil nutrients and moisture; thus, the surface moisture exerts a considerable influence on the canopy spectrum. Therefore, the model, with vegetation indexes and reflectivity as input variables, is able to adequately capture the changes in surface soil moisture at the jointing stage.

3.2.3. Establishment and Verification of PSO-SVM Model for Various Stages

The variables screened by GRA are utilized as inputs for the model and employed to construct SMC-estimation models at each depth for different stages based on the PSO-SVM model. The evaluation of the PSO-SVM model’s performance under different depths at each growth stage is shown in Figure 12.

The Figure clearly demonstrates that the model’s accuracy undergoes fluctuations at varying growth stages and depths. Firstly, the estimation accuracy at the jointing stage is the peak, with R² values for the test sets at surface soil depths (10 cm and 20 cm) reaching 0.973 and 0.828, respectively. The R² values for the test sets at other depths remain above 0.5, suggesting that the models at the jointing stage exhibit excellent fitting effects and generalization capabilities. The model’s accuracy at the tasselling, silking, blister, and maturing stages follows closely behind, with R² values for the test sets in the surface soil (10 cm and 20 cm) generally exceeding 0.6. Conversely, the estimation model’s accuracy at the milk stage is the lowest, with R² values for the test set at depths of 10 cm, 30 cm, and 40 cm falling below 0.5.

The model’s performance in estimating SMC at various depths differs. The model’s ability to estimate SMC for surface soil is generally superior to that for deeper soil layers, and the model generally performs better at the jointing stage. These results are similar to the trend observed in the RF model: Both methodologies attain their highest level of SMC estimation accuracy during the jointing stage, with the accuracy generally declining as maize grows through its growth stages and the soil depth increases. This can be attributed to the absorption and utilization of soil moisture by maize roots are concentrated in the surface layer at this stage. At this time, maize requires a significant amount of soil nutrients and moisture; thus, the surface moisture exerts a considerable influence on the canopy spectrum. Therefore, the model, with vegetation indexes and reflectivity as input variables, is able to adequately capture the changes in surface soil moisture at the jointing stage.

In addition, when comparing the estimation results between the RF model and the PSO-SVM model, it is apparent that there is a notable difference in estimation accuracy between the two models. Specifically, the PSO-SVM model demonstrates a significant improvement in accuracy compared to the RF model. The RF model’s accuracy is relatively lower at growth stages other than the jointing stage, whereas the PSO-SVM model consistently outperforms the RF model at all growth stages. Therefore, the PSO-SVM model is more suitable for estimating SMC across multiple growth stages of maize relative to the RF model. This superiority can potentially be attributed to the fact that SVM is more adept at handling small-scale datasets and possesses superior generalization capabilities than RF, thereby achieving more favorable estimation outcomes.

3.3. SMC Modeling in Different Fields

In this section, we constructed SMC-estimation models for different fields, comparing the differences in accuracy between the two models (growth stages will not be classified when comparing the results of fields). Additionally, we also discussed the rules of modeling paradigms among various fields.

3.3.1. Screening Variables for Various Fields Based on GRA (Grey Relational Analysis)

After utilizing grey relational analysis (GRA) to compute the grey relational grade (GRG) between each index and SMC in various fields, we selected six independent variables as the optimal combination of input variables for the model based on the GRG ranking from high to low. The calculation results of the GRG in different fields at each depth are presented in Figure 13 below, and the optimal combinations of variables are shown in Figure 14 below.

After reviewing the charts, it becomes evident that there is little variation among the optimal combinations chosen across different fields. The combinations for the four fields, A, B, C, and D, predominantly comprise vegetation indexes (NDVI, GNDVI, OSAVI, TVI), supplemented by spectral reflectance of specific bands (G, RE, NIR). Red reflectance (R), LAI, and other vegetation indexes (RVI, MSAVI) generally display a lower correlation with SMC; hence, they seldom appear in these combinations.

3.3.2. Establishment and Verification of RF Model for Various Fields

The variables screened by GRA are utilized as inputs for the model and employed to construct SMC-estimation models at each depth for different fields using the RF model. The evaluation of the RF model’s performance at different depths in each field is shown in Figure 15.

After scrutinizing the Figure, it can be discerned that the estimation accuracy of the RF model fluctuates across various fields. There is little difference in the accuracy among fields: the R² values of the test sets for the surface models (10 cm, 20 cm) in the four fields A, B, C, and D generally remain above 0.5 or even surpass 0.7. The differences in accuracy among fields are primarily evident in deeper soil layers (30 cm, 40 cm): Field D generally achieves the highest accuracy, with R² values of 0.624 and 0.603 for the test sets at 30 cm and 40 cm, respectively, accompanied by RMSE values of 0.874 and 0.806, respectively. This result indicates that the model exhibits better fitting and generalization capabilities in Field D. Fields B and C follow closely with the second-highest accuracies, both maintaining test set R² values exceeding 0.5 from 10 cm to 30 cm depth. The lowest accuracy is observed in Field A, where the test set R² values at 30 cm and 40 cm depth fall below 0.2.

In addition, the estimation accuracy in the four fields also exhibits certain variation patterns at each depth: The estimation accuracy of the RF model in surface soil (10 cm, 20 cm) is significantly better than that in deeper soil (30 cm, 40 cm). The SMC estimation accuracy in each field generally decreases with the increase in depth.

3.3.3. Establishment and Verification of PSO-SVM Model for Various Fields

The variables screened by GRA are utilized as inputs for the model, and SMC-estimation models are constructed at each depth for various fields based on the PSO-SVM model. The evaluation of SMC results for different depths in each field is presented in Figure 16.

There are differences in the estimation accuracy among models across various fields. Field D has the highest and most stable estimation accuracy. The R² values of the test set at each depth in Field D are 0.613, 0.524, 0.449, and 0.827, respectively, indicating good fitting effect and generalization ability at each depth. Secondly, the R² values of the test set in Field A consistently remain above 0.5 at depths of 10 cm to 20 cm. The estimation accuracy of Fields B and C is the worst, with a test set R² values below 0.5 at every depth, accompanied by a relatively high RMSE. In addition, the estimation accuracy of SMC in each field also exhibits a decreasing trend with an increase in depth.

Comparing the estimation results of the RF model and the PSO-SVM model, it can be observed that there are differences and similarities between the two models. Specifically, the estimation accuracy of the RF model is generally superior to that of the PSO-SVM model. This disparity can potentially be attributed to the high variability of soil moisture data in different fields, coupled with the presence of increased data noise and outliers. The RF model exhibits a robust tolerance for noise and outliers and is not susceptible to overfitting, ensuring it can demonstrate superior accuracy in estimating SMC in multiple fields. In addition, both models achieve their optimal performance in field D with an overall higher SMC.

4. Discussion

Soil moisture content (SMC) is a crucial parameter in irrigated agriculture, and accurate estimation of SMC is significant for water management and irrigation decision-making in irrigated areas. Nowadays, the approach of using s equipped with sensors to acquire remote sensing information for soil moisture monitoring has been extensively studied by scholars both domestically and internationally. In this research, we utilized a UAV-based platform with a multispectral sensor to acquire the spectral reflectance of the maize canopy, calculated vegetation indexes, and collected ground data. We employed grey relational analysis to select the optimal combinations of input variables and SMC models based on UAV spectral information were constructed using Random Forest (RF) and Particle Swarm Optimization-Support Vector Machine (PSO-SVM) algorithms. The soil moisture modeling paradigms (i.e., input–output mapping) under different growth stages and soil moisture conditions of summer maize were systematically compared and discussed, along with the corresponding physical interpretability. The results can provide a scientific reference for irrigation management in irrigated areas.

Nowadays, many studies have failed to explore the paradigm of SMC modeling for each growth stage of maize. In this study, we screened the combinations of input variables using the grey relational analysis algorithm to establish paradigms for SMC estimation modeling under various conditions and attempted to explain them. When soil moisture conditions change, the canopy spectrum of vegetation is affected. Generally speaking, compared to the reflectance of bands (G, R, NIR, and RE), vegetation indexes (NDVI, GNDVI, OSAVI, and TVI) can more sensitively reflect a change in SMC under different conditions. The advantage of the vegetation indexes is that they can comprehensively consider the information from multiple spectral bands, exhibiting higher sensitivity and accuracy in the estimation process of soil moisture [31,32,33]. In addition, among the four bands, G, RE, and NIR are more suitable for SMC estimation. Among them, the green band (G) can effectively reflect the chlorophyll content of vegetation. And chlorophyll content is closely related to the growth, development, and nutritional status of crops, which can effectively reflect their moisture stress and growth status. Therefore, the green band plays a crucial role in SMC estimation [34,35]. The two bands of RE and NIR are located near the significant absorption bands of vegetation chlorophyll, which are closely related to physiological parameters such as growth status and health condition [36,37,38]. Therefore, in the process of SMC modeling, G, RE, and NIR are often included as sensitive bands for estimation. This result is similar to the sensitive bands selected by Ge [36] to estimate soil moisture using UAVs and machine learning, confirming the rationality of the variable combinations established in this research. In addition, during the early growth stages, soil moisture exhibits a high degree of correlation with various vegetation indices, including NDVI, GNDVI, OSAVI, and TVI. Conversely, the correlation between band reflectance, LAI, and soil moisture is relatively low. However, as the maize canopy grows and develops, the correlation between LAI and soil moisture increases, and LAI gradually becomes a significant factor in predicting soil moisture levels.

The estimation accuracy is also significantly influenced by different modeling methods, with the accuracy varying significantly between two models under the same condition. The results of this study indicate that the estimation accuracy of the PSO-SVM model is generally higher than that of the RF model across multiple growth stages. This superiority stems from SVM’s robust generalization capabilities and stability in handling small-scale datasets, making it well-suited for complex nonlinear problems involving small sample sizes [16]. When estimating SMC in different fields (moisture conditions), the RF model typically exhibits higher accuracy compared to the PSO-SVM model. At this time, the spatial variability of soil moisture in the field is more pronounced, and the dataset contains greater amounts of data noise and outliers. SVM has a relatively weaker anti-interference ability and struggles to achieve high performance on noisy, overlapping datasets [39]. Conversely, the RF model demonstrates a high tolerance for data noise and outliers, and it is not prone to overfitting [40,41]. Therefore, the RF model is more suitable for soil moisture estimation under various moisture conditions.

At the same time, the estimation results reveal that the accuracy generally decreases with the increase of soil depth. This situation is particularly obvious in the early growth stage, such as the jointing stage, tasselling stage, and silking stage. The reason is that at the early stages, the root system of maize is relatively shallow, and maize primarily utilizes shallow soil moisture. Consequently, the canopy spectrum of maize at this period can better reflect the soil moisture conditions of the surface layers (10 cm and 20 cm). However, at the later stages, such as the blister stage and milk stage, the roots gradually extend downwards, and the utilization of soil moisture gradually shifts towards deeper layers (>30 cm). As a result, the advantage in prediction accuracy for surface soil moisture gradually diminishes as the maize grows [14,42].

There are some shortcomings in this study. To start with, we failed to emphasize the differences in modeling paradigms among various fields (moisture conditions). This may stem from the fact that the moisture variations between fields are not obvious enough. Additionally, the method of utilizing multispectral sensors is relatively simple, overlooking thermal infrared information, meteorological data, and other factors. Nowadays, numerous studies have demonstrated the feasibility and advantages of monitoring soil moisture based on multimodal data [2,43,44]. Therefore, we should explore the integration of multispectral sensors with other sensors, and meteorological information should also be incorporated into our considerations in the future. By integrating multimodal information, we can enhance the precision of soil moisture monitoring, thereby offering a stronger theoretical foundation and technical backing for water management and irrigation decision-making in irrigated regions.

5. Conclusions

In this study, UAV-based multispectral data and point-scale soil moisture profile observations were integrated to develop regional-scale soil moisture models. The performance of RF and PSO-SVM algorithms was evaluated in diagnosing soil moisture status across various growth stages of summer maize and under differing moisture conditions within the irrigation canal system, with corresponding modeling paradigms subsequently proposed. We demonstrated the ability and the challenge of UAV-based SMC models. Our research led to the following major conclusions:

(1)

The soil moisture fluctuated in the shape of an “M” during the maize growth period. Temporally, the SMC is relatively higher at the tasselling, silking, and milk stages but relatively lower at the jointing, blister, and maturing stages, which is essentially in line with the fact that maize is moisture-sensitive during the middle time of its growth period;

(2)

The modeling paradigms for UAV-based SMC estimation were recommended: In the early growth stages of maize (jointing, tasselling, and silking stages), the optimal combinations of input features comprise vegetation indexes (NDVI, GNDVI, OSAVI, TVI) and NIR reflectance; At the blister and milk stages, a combination of spectral reflectance (G, R, RE), vegetation indexes (NDVI, GNDVI, OSAVI, TVI), and LAI is more suitable. At the maturing stage, the green (G) and red (R) bands, along with vegetation indexes (NDVI, GNDVI, OSAVI, TVI), are preferred. Across multiple fields with varying moisture conditions, vegetation indexes (NDVI, GNDVI, OSAVI, TVI) and spectral reflectance (G, RE, NIR) are suggested;

(3)

Both RF and PSO-SVM models performed best at the jointing stage, while subsequently, their accuracy gradually deteriorated as the maize grew. Overall, RF performed better at capturing soil moisture differences across different growth stages, while PSO-SVM has a distinct advantage in reproducing the spatial variability of soil moisture.