Machine Learning Modelling for Soil Moisture Retrieval from Simulated NASA-ISRO SAR (NISAR) L-Band Data

Abstract

Soil moisture is a critical factor that supports plant growth, improves crop yields, and reduces erosion. Therefore, obtaining accurate and timely information about soil moisture across large regions is crucial. Remote sensing techniques, such as microwave remote sensing, have emerged as powerful tools for monitoring and mapping soil moisture. Synthetic aperture radar (SAR) is beneficial for estimating soil moisture at both global and local levels. This study aimed to assess soil moisture and dielectric constant retrieval over agricultural land using machine learning (ML) algorithms and decomposition techniques. Three polarimetric decomposition models were used to extract features from simulated NASA-ISRO SAR (NISAR) L-Band radar images. Machine learning techniques such as random forest regression, decision tree regression, stochastic gradient descent (SGD), XGBoost, K-nearest neighbors (KNN) regression, neural network regression, and multilinear regression were used to retrieve soil moisture from three different crop fields: wheat, soybean, and corn. The study found that the random forest regression technique produced the most precise soil moisture estimations for soybean fields, with an R² of 0.89 and RMSE of 0.050 without considering vegetation effects and an R² of 0.92 and RMSE of 0.042 considering vegetation effects. The results for real dielectric constant retrieval for the soybean field were an R² of 0.89 and RMSE of 6.79 without considering vegetation effects and an R² of 0.89 and RMSE of 6.78 with considering vegetation effects. These findings suggest that machine learning algorithms and decomposition techniques, along with a semi-empirical technique like Water Cloud Model (WCM), can be effective tools for estimating soil moisture and dielectric constant values precisely. The methodology applied in the current research contributes essential insights that could benefit upcoming missions, such as the Radar Observing System for Europe in L-band (ROSE-L) and the collaborative NASA-ISRO SAR (NISAR) mission, for future data analysis in soil moisture applications.

1. Introduction

Soil moisture (SM) plays an important role in the hydrologic event that connects the earth’s surface and atmospheric processes [1,2]. An in-depth understanding of soil moisture dynamics is essential for a wide range of meteorological, climatologic, and hydrologic applications [1,3,4]. Soil Moisture is an influencing component in crop growth and development in agricultural applications and an early warning indicator of agricultural drought emergencies [5,6]. Manual soil moisture content (SWC) mapping through field surveys is difficult as it consumes time and labour and provides limited data due to sampling constraints [7,8]. Temporal mapping of large areas is also challenging, as surface soil moisture is dynamic in nature and changes frequently over time.

Airborne and spaceborne remote sensing techniques keep track of the soil on a large scale and provide detailed data at reasonable temporal and spatial resolutions, allowing us to study soil moisture dynamics over a large area more effectively [1]. Soil moisture can be obtained from optical and microwave remote sensing [9]. Optical remote sensing is mainly sensitive to the topsoil surface as it relies on the reflection of light from the earth’s surface [10]. Microwave remote sensing provides a unique capability and has shown great potential for soil moisture estimation as it removes most of the constraints of optical remote sensing over retrieving soil moisture [11]. Active and passive microwave remote sensing has shown the capability to attain observations from a regional level to a global level [12]. Due to the spatial resolution limits of passive radiometers, which are often coarse, active microwave remote sensing is frequently utilised to estimate soil moisture [13]. Although active microwave remote sensing provides high spatial resolution, it is more sensitive to dielectric characteristics, surface parameters, vegetation, soil texture and sensor parameters [14]. The scattering behaviour of a surface is influenced by its geometric and dielectric properties concerning incident radiation [15]. The presence of vegetation canopy and surface roughness can modify the radar backscatter’s sensitivity to soil moisture. As a result, research efforts focused on estimating soil moisture generally prioritise examining bare surfaces where these factors are minimised. Polarimetric SAR provides polarised information on the targets, which enhances the radar capability in the scattering mechanism. Polarimetric decomposition is a useful technique to separate microwave scattering resulting from different targets and can distinguish between the scattering from the surface and volume targets, this method could be useful for measuring soil moisture in both bare and cropped conditions.

To estimate the dielectric constant values, various models have been developed in the microwave region of the electromagnetic spectrum to simulate the dielectric behaviour of soil [16,17]. The empirical model enhances our understanding of how soil–water mixtures behave. The model provides a way to estimate soil properties at different frequencies based on soil texture and water dielectric constants [18]. One notable example is Dobson’s work [19]. In that study, an empirical relationship was developed to estimate the real and imaginary parts of the dielectric constant at frequencies of 1.4 and 5 GHz [20]. Similarly, Hallikainen later proposed an empirical relationship for the dielectric constant of soil samples measured at frequencies ranging from 1.4 to 18 GHz [21]. While these models have their advantages and disadvantages, it is worth noting that some are site-specific, require several parameters, and are mainly developed for the dual pol dataset. The Dobson and Hallikainen models are limited to specific frequency ranges and require several sensor and target parameters to estimate the permittivity. The semi-empirical models, like the modified Dubois models, which are widely used to estimate the dielectric constant from dual-pol data, have limitations, such as being site-specific, usable only in bare or sparsely vegetated fields, and mainly developed for dual-pol datasets. A new mineralogy-based dielectric model (MBSDM) was developed using clay content as the input, which showed lower prediction errors compared to the semi-empirical mixing dielectric model (SMDM). The MBSDM balances predictions with the application, making it an excellent choice for estimating moist soil dielectric properties [22]. A frequency dielectric model designed for tundra organic soil at 1.4 GHz effectively forecasts the soil’s dielectric features under different moisture levels, densities, and temperatures. The model’s accuracy is comparable to the measurement error, ensuring performance [23]. Integrating matter (OM) into mixing models enhances the precision of microwave radiative transfer modeling by minimising errors in brightness temperature (TB) calculations. This adjustment improves the soil moisture readings from sensors like Soil Moisture Active Passive (SMAP), Soil Moisture and Ocean Salinity (SMOS), and Advanced Microwave Scanning Radiometer 2 (AMSR2) by lowering the constant with higher organic matter content. The enhanced model decreased the root mean square error (RMSE) of SMAP observed brightness temperature by 11%, showcasing its effectiveness in regions with matter [24]. The new dielectric mixing model for phase soil significantly enhances the precision of microwave remote sensing and portable soil sensors, reducing RMSE by 23–35% for SMAP, SMOS, and Advanced Microwave Scanning Radiometer for EOS (AMSR-E) and up to 53% for time domain reflectometer (TDR) and ground penetrating radar (GPR). It offers a fit to data without the need for nonphysical parameters and accurately forecasts dielectric constants in both saturated and unsaturated conditions. This model is expected to improve flood monitoring accuracy via satellite [25].

Several Studies have been conducted to estimate the soil moisture using L-band data. The research showcased how L-band quad-polarised data and decomposition methods effectively determined surface soil moisture in a small field. The Van Zyl decomposition revealed the surface scattering element, while the Yamaguchi decomposition displayed a correlation with field-measured soil moisture and demonstrated high accuracy. Tien-Hao Liao et al., 2021 [26] studied UAVSAR data combined with a radar scattering model based on physics that effectively calculates near-surface soil moisture in an area affected by grassland landslides, achieving an RMSE of 0.058 m³/m³. The Freeman Durden decomposition indicates relationships between soil moisture, surface scattering, and double bounce. This technique can be applied to grassland landslide areas to monitor soil moisture. The utilization of data and multiple incidence angles significantly improves the alpha approximation method for estimating soil moisture, reducing RMSE by 0.4% to 5% compared to single pol and single incidence data. This enhanced approach demonstrates accuracy when applied to corn, soybean, and wheat crops [27]. Burgin et al., 2017 [28] introduce a method that minimises the reliance on data by modeling radar reflections as a linear relationship with soil moisture utilizing coefficients obtained from Aquarius radar and radiometer information. This approach showcases soil moisture estimation based on SMAP radar data, which has been verified against the SMAP Level 2 radiometer-only soil moisture dataset.

Vegetation influences the soil moisture; thus, quantifying the vegetation contribution is sometimes important in the agriculture area. Using SAR data to estimate soil properties and vegetation presents challenges due to the interactions between vegetation water content and electromagnetic radiation, which affect scattering and absorption phenomena. The radar signals wavelength-dependent nature adds another layer of complexity, making it difficult to separate soil and vegetation contributions. Remote sensing models encounter difficulties in determining these properties, recommending the need for techniques in SAR data analysis [29,30,31,32]. A vegetation descriptor called Dual-pol Radar Vegetation Index (DpRVI_c) in a dual-pol L-band SAR setup was introduced, which effectively accounts for vegetation influences to estimate soil moisture using the Water Cloud Model (WCM). The proposed descriptor has shown accuracy, followed by NDVI and RVI_dp across types of crops and test locations. These results underscore the potential of using dual pol GRD SAR L band data for soil moisture estimation for upcoming missions like NISAR [33]. In regions with dense vegetation cover, the L-band SAR data can effectively predict the soil moisture by incorporating the semi-empirical water cloud model parameterised with Leaf Area Index [34]. Integrating the water cloud model and machine learning model like neural network algorithms suggests that SAR data can be effectively used for soil moisture estimation and improves the model’s overall accuracy [35]. Therefore, physical models inform and justify the application of ML algorithms

To utilise the potential of fully polarimetric datasets, Machine Learning can be employed. Using machine learning techniques, it is possible to accurately model the complex relationships between different factors and input data to estimate soil moisture levels. When it comes to this task, many people rely on two popular techniques: neural network and random forest algorithms. Hajj et al., 2017 [36] and their team successfully trained a neural network algorithm by utilising a simulated database. High-accuracy soil moisture estimations were achieved successfully. Carranza et al., 2021 [37] utilised a random forest algorithm to examine the correlation between ground-based soil moisture measurements and remotely sensed variables. They were able to achieve strong performance and capture the nonlinear relationship between the two. The first thorough assessment of twelve sophisticated statistical and machine learning (ML) methods for the estimate of soil moisture (SM) using dual-pol sentinel 1 data was conducted. The top three models with similar and promising SM estimates, according to the study, were the random forest (RF), subtractive clustering (SBC), and Adaptive Neuro Fuzzy Inference System (ANFIS). To assess the resilience of these top models (RF, SBC, and ANFIS), further performance study was conducted on different datasets. The results show that all three models performed consistently, with SBC being the most recommended model for SM estimation [38]. These studies show that machine learning techniques have the potential to estimate soil moisture accurately and efficiently.

The primary aim of this investigation is to assess the capacity of fully polarimetric synthetic aperture radar data to examine L-Band for estimating soil moisture using polarimetric decomposition technique and Machine Learning modelling. The study employed three different decompositions, namely Freeman-Durden three-component, Van Zyl, and H/A/Alpha, to identify different scattering mechanisms along with additional input polarimetric features to estimate soil moisture and soil dielectric constant in three different crop fields (i.e., corn, wheat, and soybean). Multiple machine learning algorithms were assessed to determine the optimal method for estimating soil dielectric constant and soil moisture.

2. Materials and Methods

2.1. Study Area and Dataset

The Soil Moisture Active Passive Experiment 2012 (SMAPVEX12) was a field campaign established to develop soil moisture retrieval algorithms and support the early adopter project of the Soil Moisture Active Passive (SMAP) mission. The campaign was conducted in a region of Manitoba, Canada (98°00′23″W, 49°40′48″N) situated within the Red River Watershed, and the Assiniboine River flows through the northern part of the area [39]. The field data collected in the region covers approximately 6 weeks in-situ soil dielectric constant and soil moisture data, which was the main reason to consider it as the study area. It covers a distance of 12.8 km × 70 km and demonstrates substantial changes in surface soil moisture as a result of varying soil textures.

The region experiences a notable variation in surface soil moisture due to the transition from dense clay to light, loamy sands from the east to the west. Microwave soil moisture techniques have been extensively employed to study this region due to the significance of agriculture in the area and the spatial variability of soil moisture [15]. The SMAPVEX12 site has a heterogeneous crop distribution, with cereals encompassing 23.4% of the crop acreage, trailed by canola at 16.0%, corn at 9.1%, soybeans at 18.5%, and perennial cover at 14.6%. Figure 1 Illustrate the position of crop fields and the field data point distribution strategy.

During the SMAPVEX12 campaign, field staff collected soil and vegetation data from 55 farmland fields and 4 forest locations between 7 June and 19 July 2012. In-flight days, soil moisture readings were taken on both the farmland and forest sites, while surface roughness measurements were taken on non-flight days. According to Figure 1b, there were 16 sample points per farmland pitch, with crews gathering three replicate soil moisture readings at each sample site to record regional heterogeneity caused by soil characteristics or management approaches [40]. The in-situ soil dielectric constant and soil moisture data from farmland were utilised alongside the QuadPol SAR (simulated NISAR) dataset for the same date, as detailed in Section 2.2.

2.2. Simulated NISAR Dataset

The data used in this study were provided by Jet Propulsion Laboratory (JPL), NASA. The data was acquired through the UAVSAR sensor, which utilises L-band frequencies it was then converted into a Simulated NISAR product. Its descriptive information about the conversion of UAVSAR data into simulated NISAR products is provided at this link: https://uavsar.jpl.nasa.gov/science/documents.html (accessed on 29 June 2024). The purpose of simulating NISAR data is to help the scientific community test algorithms and assess the quality of NISAR products before the NISAR launch. The QuadPol simulated NISAR 138A mode of 1.253 GHz Frequency and a (Ground Range Detected) resolution of 7.3 m × 7.3 m was used. The angle of incidence was 33.88 in the near range and 47.2 in the far range. A total number of 12 NISAR Simulated datasets were used from Flight Line ID: 31606 provided in

Table 1. Soil Moisture Measurement Available Dates.

Date	(Flight Line ID: 31606) Flight ID	Soil Moisture and Soil Dielectric Constant In-Situ Measurement Available	Surface Roughness In-Situ Measurement Available	QuadPol SAR Simulated NISAR Products Availabale
7th June	--	Yes	--	--
10th June	--	--	Yes	--
11th June	--	--	Yes	--
12th June	--	Yes	Yes	--
13th June	--	--	Yes	--
15th June	--	Yes	Yes	--
16th June	--	--	Yes	--
17th June	Flight 12044	Yes	Yes	Yes
18th June	--	--	Yes	--
19th June	--	--	Yes	Yes
21st June	--	--	Yes	--
22nd June	Flight 12046	Yes	--	Yes
23rd June	Flight 12047	Yes	--	Yes
24th June	--	--	Yes	--
25th June	Flight 12048	Yes	--	--
27th June	Flight 12049	Yes	--	Yes
29th June	Flight 12050	Yes	--	Yes
30th June	--	--	Yes	Yes
3rd July	Flight 12055	Yes	--	Yes
5th July	Flight 12056	Yes	--	Yes
7th July	--	--	Yes	--
8th July	Flight 12057	Yes	--	Yes
10th July	--	Yes	--	Yes
13th July	Flight 12059	Yes	--	Yes
14th July	Flight 12060	Yes	--	Yes
17th July	Flight 12061	Yes	--	Yes
19th July	--	Yes	--	--

with their respective acquisition dates, in-situ soil moisture measurement, and roughness availability. The data is available in a multi-looked complex format on the website https://uavsar.jpl.nasa.gov/ accessed on 29 June 2024.

2.3. Methodology

This study aims to retrieve soil moisture and soil dielectric constant using various Machine Learning algorithms. The flowchart in Figure 2 illustrates the process of machine learning. The covariance matrix, denoted as [C3], was extracted from the QuadPol Simulated NISAR orthorectified product. Polarimetric parameters were extracted using both model-based and eigenvalue-eigenvector-based decompositions. The model was trained using the following polarimetric input parameters: Alpha, Anisotropy, Entropy, Freeman-Durden dihedral, Freeman-Durden surface, Freeman-Durden volume, Surface/Dihedral, Surface/(Surface +Dihedral +Volume), Van Zyl dihedral, Van Zyl surface, Van Zyl volume, Soil roughness parameters RMS-Height, Correlation Length, VH(dB), VV(dB), HH(dB), HV(dB), HV(dB)/HH(dB), HV(dB)/VV(dB), VH(dB)/HH(dB), and VH(dB)/HH(dB). The estimation of soil moisture and soil dielectric have been done in three ways in three different crop fields. The first model does not consider the vegetation effect, the second model considers the vegetation effect by incorporating two-way attenuation and RVI parameters, and the third model does not consider the RMS and correlation length.

Seven different machine learning algorithms, namely random forest regression, decision tree regression, stochastic gradient descent (SGD), XGBoost, K-nearest neighbors (KNN) regression, neural network regression, and multiple linear regression were trained on 70% and tested on 30% dataset which is a thumb rule in machine learning modelling. The in-situ soil moisture and soil dielectric constant data obtained from the SMAPVEX12 field campaign conducted in Manitoba, Canada, as mentioned in Section 2.1 was used to test and validate the results. The best model was used to retrieve the soil moisture and soil dielectric constant map.

2.3.1. Polarimetric Decomposition Technique

The Freeman-Durden decomposition model was used as an input parameter in the machine learning algorithm because it provides valuable insights into the scattering properties of different targets, such as vegetation, urban structures, and bare soil. This specification allows the algorithm to distinguish between these different land cover types effectively [41]. The scattering vector utilised in Freeman-Durden analysis is defined as in Equation (1).

$${\mathrm{k}}_{\mathrm{L}}={\left[{\mathrm{S}}_{\mathrm{H}\mathrm{H}}\sqrt{2{\mathrm{S}}_{\mathrm{H}\mathrm{V}}{\mathrm{S}}_{\mathrm{V}\mathrm{V}}}\right]}^{\mathrm{T}}$$

(1)

$$\left[\mathrm{C}\right]=\left[{\mathrm{C}}_{\mathrm{v}}\right]+\left[{\mathrm{C}}_{\mathrm{d}}\right]+\left[{\mathrm{C}}_{\mathrm{s}}\right]$$

(2)

$$\left[{\mathrm{C}}_{\mathrm{v}}\right]={\displaystyle \frac{{\mathrm{f}}_{\mathrm{v}}}{8}}\left[\begin{array}{ccc}3& 0& 1\\ 0& 2& 0\\ 1& 0& 3\end{array}\right]\hspace{1em}\hspace{1em}{\mathrm{P}}_{\mathrm{v}}={\mathrm{f}}_{\mathrm{v}}$$

(3)

$$\left[{\mathrm{C}}_{\mathrm{d}}\right]={\mathrm{f}}_{\mathrm{d}}\left[\begin{array}{ccc}{\left|\mathsf{\alpha }\right|}^2& 0& \mathsf{\alpha }\\ 0& 0& 0\\ {\mathsf{\alpha }}^{\ast }& 0& 1\end{array}\right]\hspace{1em}\hspace{1em}{\mathrm{P}}_{\mathrm{d}}={\mathrm{f}}_{\mathrm{d}}\left(1+{\left|\mathsf{\alpha }\right|}^2\right)$$

(4)

$$\left[{\mathrm{C}}_{\mathrm{s}}\right]={\mathrm{f}}_{\mathrm{s}}\left[\begin{array}{ccc}{\left|\mathsf{\beta }\right|}^2& 0& \mathsf{\beta }\\ 0& 0& 0\\ {\mathsf{\beta }}^{\ast }& 0& 1\end{array}\right]\hspace{1em}\hspace{1em}{\mathrm{P}}_{\mathrm{s}}={\mathrm{f}}_{\mathrm{s}}\left(1+{\left|\mathsf{\beta }\right|}^2\right)$$

(5)

Equation (2) is composed of three submatrices, where [C_v], [C_d], and [C_s] refers to the covariance matrix of the volume scattering (Equation (3)), dihedral (Equation (4)), and single scattering (Equation (5)) and f_v, f_d, and f_s represent the energy, respectively. Ps, P_d, and P_v are freeman attributes. The α and β represent the data of S_HH/S_VV for the dihedral scattering and the single bounce scattering respectively.

Another technique used as an input parameter to the ML model was the H/A/α decomposition method. The H/A/α decomposition approach is useful for characterising target scattering processes, such as surface scattering, double-bounce scattering, and volume scattering, which are associated with different types of land cover and man-made structures [42]. The coherency matrix can be written as Equation (6).

$$\left[\mathrm{T}\right]={\left[{\mathrm{u}}_3\right]\left[\mathsf{\Sigma }\right]\left[{\mathrm{u}}_3\right]}^{-1}={\sum }_{\mathrm{i}=1}^{\mathrm{i}=3}{\mathsf{\lambda }}_{\mathrm{i}}{\mathrm{u}}_{\mathrm{i}}{{\mathrm{u}}_{\mathrm{i}}}^{\ast \mathrm{T}}$$

(6)

$$\mathrm{H}=-\sum _{\mathrm{i}=1}^3{\mathrm{P}}_{\mathrm{i}}{\mathrm{l}\mathrm{o}\mathrm{g}}_3\left({\mathrm{P}}_{\mathrm{i}}\right)$$

(7)

$$\mathsf{\alpha }=\sum _{\mathrm{i}=1}^{\mathrm{i}=3}{\mathrm{P}}_{\mathrm{i}}{\mathsf{\alpha }}_{\mathrm{i}}$$

(8)

$${\mathrm{P}}_{\mathrm{i}}={\displaystyle \frac{{\mathsf{\lambda }}_{\mathrm{i}}}{{\mathsf{\Sigma }}_{\mathrm{j}=1}^3{\mathsf{\lambda }}_{\mathrm{j}}}}$$

(9)

$$\mathrm{A}={\displaystyle \frac{{\mathsf{\lambda }}_2-{\mathsf{\lambda }}_3}{{\mathsf{\lambda }}_2+{\mathsf{\lambda }}_3}}\hspace{1em}\hspace{1em}\mathrm{for} \mathrm{H}>0.7$$

(10)

where u₃ represents three unit orthogonal eigenvectors, Equation (7) represents the logarithmic sum of eigenvalue, Equation (8) represents α, where Pi is the probability obtained from the eigenvalues Equation (9). The third parameter extracted from the H/A/α, known as anisotropy, is given in Equation (10).

The Van Zyl decomposition was used to recover useful polarimetric information, particularly those covered in vegetation. It is intended particularly for estimating the volume backscattering component from vegetated regions [43]. It determines the volume contribution of backscattering and separates it from other components, allowing for a more accurate study of soil moisture in vegetated regions.

$$〈\left|\mathrm{C}\right|〉=\mathsf{\alpha }\left[{\mathrm{C}}_{\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}}\right]+\left[{\mathrm{C}}_{\mathrm{r}\mathrm{e}\mathrm{m}\mathrm{a}\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{r}}\right]$$

(11)

$$\left[{\mathrm{C}}_{\mathrm{r}\mathrm{e}\mathrm{m}\mathrm{a}\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{r}}\right]=\left(\begin{array}{ccc}\mathsf{\xi }& 0& \mathsf{\rho }\\ 0& \mathsf{\eta }& 0\\ {\mathsf{\rho }}^{\ast }& 0& \mathsf{\varsigma }\end{array}\right)-\mathsf{\alpha }\left(\begin{array}{ccc}{\mathsf{\xi }}_{\mathsf{\alpha }}& 0& {\mathsf{\rho }}_{\mathsf{\alpha }}\\ 0& {\mathsf{\eta }}_{\mathsf{\alpha }}& 0\\ {\mathsf{\rho }}_{\mathsf{\alpha }}^{\ast }& 0& {\mathsf{\varsigma }}_{\mathsf{\alpha }}\end{array}\right)$$

(12)

$$\begin{gathered} {\mathsf{\lambda }}_1={\displaystyle \frac{1}{2}}\{\mathrm{Y}+\mathrm{X}\} \\ {\mathsf{\lambda }}_2={\displaystyle \frac{1}{2}}\{\mathrm{Y}-\mathrm{X}\} \\ {\mathsf{\lambda }}_3=\mathsf{\eta }-{\mathrm{a}\mathsf{\eta }}_{\mathsf{\alpha }} \\ \mathrm{X}=\sqrt{{\mathrm{Y}}^2-4\left(\mathsf{\xi }-\mathrm{a}{\mathsf{\xi }}_{\mathsf{\alpha }}\right)\left(\mathsf{\varsigma }-{\mathrm{a}\mathsf{\varsigma }}_{\mathsf{\alpha }}\right)+4{\left|\mathsf{\rho }-{\mathrm{a}\mathsf{\rho }}_{\mathsf{\alpha }}\right|}^2} \\ \mathrm{Y}=\mathsf{\xi }+\mathsf{\varsigma }-\mathrm{a}{\mathsf{\xi }}_{\mathsf{\alpha }}-{\mathrm{a}\mathsf{\varsigma }}_{\mathsf{\alpha }} \end{gathered}$$

(13)

where [C_model] is the covariance matrix, [C_remainder] is symmetric in Equation (11). The average covariance matrix in Equation (12). The eigenvalues of this matrix are described by Equation (13). The $\mathsf{\xi }$ s, $\mathsf{\varsigma }$, and, $\mathsf{\rho }$, $\mathsf{\eta }$ all depend on the size, shape, and electrical properties of the scatterers, as well as their statistical angular distribution.

2.3.2. Vegetation Attenuation

The WCM technique estimates the backscattering coefficient obtained from the area with vegetation coverage as expressed in Equations (14)–(17). The expression given below describes the interaction process between radar signal and vegetation. In this model, the total backscattering coefficient is a sum of the normalised radar cross-section of the vegetation and the two-way attenuation coefficient of the vegetation from the soil. The variables V₁ and V₂ are vegetation descriptors and improve the overall performance of the WCM. Here, the Leaf Area Index (LAI) and Plant Water Content (PWC) given in Equation (18) have been used as V₁ and V₂, respectively. The LAI and PWC data collected from the field campaign are available at https://smapvex12.espaceweb.usherbrooke.ca/home.php accessed on 29 June 2024.

$${\mathsf{\sigma }}_{\mathrm{P}\mathrm{P}}^0={\mathsf{\sigma }}_{\mathrm{v}\mathrm{e}\mathrm{g}}^0+{\mathrm{L}}^2{\mathsf{\sigma }}_{\mathrm{s}\mathrm{o}\mathrm{i}\mathrm{l}}^0$$

(14)

$${\mathsf{\sigma }}_{\mathrm{v}\mathrm{e}\mathrm{g}}^0=\mathrm{A}{\mathrm{V}}_1\mathrm{c}\mathrm{o}\mathrm{s}{\mathsf{\theta }}_{\mathrm{i}}(1-{\mathrm{L}}^2)$$

(15)

$${\mathrm{L}}^2=\exp (-2\mathrm{B}{\mathrm{V}}_2\mathrm{s}\mathrm{e}\mathrm{c}{\mathsf{\theta }}_{\mathrm{i}})$$

(16)

$${\mathsf{\sigma }}_{\mathrm{s}\mathrm{o}\mathrm{i}\mathrm{l}}^0=\mathrm{C}+\mathrm{D}\times {\mathrm{M}}_{\mathrm{V}}$$

(17)

$$\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{t} \mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{t} (\mathrm{K}\mathrm{g}/{\mathrm{m}}^2)=\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{h}\mathrm{b}\mathrm{i}\mathrm{o}\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s} (\mathrm{K}\mathrm{g}/{\mathrm{m}}^2)-\mathrm{d}\mathrm{r}\mathrm{y}\mathrm{b}\mathrm{i}\mathrm{o}\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s} (\mathrm{K}\mathrm{g}/{\mathrm{m}}^2)$$

(18)

where A and B are vegetation parameters, C and D are bare soil parameters, θ_i is incidence angle, and M_V is the volumetric soil moisture.

The machine learning model receives the two-way attenuation that it derives from the WCM model. To increase overall accuracy, the ML model also incorporates the Radar Vegetation Index (RVI), which is obtained from radar observation as expressed in Equation (19).

$$\mathrm{R}\mathrm{V}\mathrm{I}={\displaystyle \frac{8{\mathsf{\sigma }}_{\mathrm{H}\mathrm{V}}}{{\mathsf{\sigma }}_{\mathrm{H}\mathrm{H}}+{\mathsf{\sigma }}_{\mathrm{V}\mathrm{V}}+{2\mathsf{\sigma }}_{\mathrm{H}\mathrm{V}}}}$$

(19)

2.3.3. Machine Learning (ML) Modelling

Random forest regression was utilised, and numerous input factors, such as polarimetric data, were employed. During the training phase, each tree is constructed by recursively splitting the data based on the characteristics that offer the greatest information gain, it has a lower risk of overfitting, and it can account for missing data [44].

When estimating soil moisture, multilinear regression is used to make predictions about the soil moisture content based on several polarimetric input variables. The data that are fed into the method are used to calibrate a linear equation that, when applied, provides the most accurate description of the connection between the independent variables and the dependent variable [45].

In decision tree regression, the method models the relationship between the input polarimetric factors and the output variable (in this case, the soil moisture content) by building a binary tree structure. The nodes of the tree structure stand for the decisions that were made based on the input variables, and the branches of the tree structure stand for the effects of those decisions [46]. Decision tree regression is prone to be affected by overfitting and noise in the data.

Another regression known as the Stochastic gradient descent (SGD) model is iteratively adjusted based on a randomly chosen part of the training data that is referred to as a mini-batch. Nevertheless, SGD regression can be sensitive to the choice of learning rate hyperparameter [47], which can affect the algorithm’s ability to converge and its accuracy. To guarantee that the model is accurate, it is necessary to make use of relevant strategies such as early halting and learning rate scheduling.

XGBoost combines the abilities of several weaker models to create a more powerful predictive model. It uses a technique called gradient boosting. This means that it creates a predictive model by repeatedly improving it in small steps [48].

KNN regression works with a wide range of metrics that measure distance. In addition to this, it is simple to construct and does not need any assumptions to be made about the data that is being used [49].

Another effective method used in this study is the neural network, which can learn complicated patterns and correlations between the polarimetric variables fed into it and the soil moisture it produces as an output [50].

3. Results

This section discusses the results obtained from the machine learning models. This section is divided into three parts. The first section shows the results obtained from the ML models without considering the vegetation effects (not including the WCM and RVI). The second section presents the results obtained after considering the vegetation effect (including the WCM and RVI as input parameters). The third section discusses the results without considering the roughness parameters (i.e., RMS height and correlation length).

3.1. Results without Considering Vegetation Effects

Before applying machine learning modelling, correlation matrixes were generated for all the crop fields, which shows the correlation between the soil moisture and other polarimetric features. The correlation analysis was conducted to examine the strength of the relationship between soil moisture and various polarimetric features, including surface roughness parameters provided in Figure 3.

Soil dielectric constant and soil moisture were estimated in three distinct agricultural fields (corn, wheat, and soybeans) using the polarimetric decomposition technique and machine learning. Radar backscattering and numerous soil-related characteristics were gathered as a collection of SAR polarimetric inputs. The model’s soil dielectric constant outputs were validated using field-measured values through statistical measures such as the coefficient of determination (R2), root mean square error (RMSE), and mean absolute error (MAE) shown in Figure 4. A confidence interval (CI) and prediction interval (PI) were plotted in addition to a regression line fitting the data. The confidence interval (CI) is represented graphically by a yellow line, whereas the prediction interval (PI) is illustrated as a continuous blue line. The regression line that provides the closest fit to the data is depicted in red. The yellow line represents the upper and lower limits of the best-fit line, which are determined by the 95% confidence interval (CI). This means there is a 95% probability that the true value of the best-fit line falls within these limits. It is important to acknowledge that despite having a 95% confidence interval, there is still a 5% chance that the actual linear regression line that best fits the data may fall outside of the boundaries of the confidence interval.

In Figure 4a, the random forest output for the soil dielectric constant estimation in the soybean field exhibits a coefficient of determination of 0.89, an RMSE of 6.79, and an MAE of 5.15. Except for two data points, all other points fall within the prediction interval. Moving on to the wheat field shown in Figure 5a, random forest outperforms other algorithms with a coefficient of determination of 0.73, an RMSE of 3.99, and an MAE of 2.64. However, one data point lies completely outside the 95% prediction interval, and another data point falls outside the prediction interval but remains relatively close to it. In Figure 6a, the random forest algorithm was not efficient in the corn field compared to other algorithms; however, it still outperformed them. The output shows a coefficient of determination of 0.72, an RMSE of 1.96, and an MAE of 1.62. Only one data point was observed outside the prediction interval.

Decision tree regression also showed better performance in the soybean field, as depicted in Figure 4b. The majority of the data points fall within the upper and lower bounds of the 95% prediction interval, with only two data points lying outside. The coefficient of determination is 0.84, the second highest after random forest, while the RMSE is 8.16 and the MAE is 6.05. The minimum accuracy for the decision tree was found in the Corn field, depicted in Figure 6b, where the data points are found within the upper and lower bounds of the 95% prediction interval, except for one data point. However, the coefficient of determination is only 0.30, with an RMSE of 3.10 and an MAE of 2.42. For the corn field, the lowest accuracy was also found in the multilinear regression. It seems that the model does not fit the data well.

In Figure 7a, the random forest output for the soil moisture estimation in the soybean field exhibits a coefficient of determination of 0.89, an RMSE of 0.05, and an MAE of 0.04. Except for two data points, all other points fall within the prediction interval. Moving on to the wheat field shown in Figure 8a, random forest outperforms other algorithms to estimate soil moisture with a coefficient of determination of 0.88, an RMSE of 0.03, and an MAE of 0.02. However, two data points fall outside the prediction interval but remain relatively close to it. In Figure 9a, the random forest algorithm was less efficient in corn than in soybeans and wheat fields. The output shows a coefficient of determination of 0.78, an RMSE of 0.03, and an MAE of 0.02. Only one data point was observed outside the prediction interval. Based on the results, it is evident that random forest outperformed the other algorithms.

Additionally, the decision tree regression showed better performance in estimating soil moisture from the soybean field, as depicted in Figure 7b. The majority of the data points fall within the upper and lower bounds of the 95% prediction interval, with only one data point lying near the lower prediction interval. The coefficient of determination for the decision tree was 0.88, the second highest after random forest, while the RMSE is 0.05 and the MAE is 0.04. The lowest accuracy for the decision tree was found in the corn field, depicted in Figure 9b, where the data points are found within the upper and lower bounds of the 95% prediction interval, except for two data points, the coefficient of determination for the decision tree was 0.34, with an RMSE of 0.05 and MAE of 0.04. For the corn field, the lowest accuracy was found in XGBoost and the multilinear regression with the coefficient of determination of −0.25 and −0.07. It seems that the model does not fit the data well. For other algorithms, such as XGBoost, KNN, MLR, Stochastic gradient descent, and multilinear regression, the analysis is given in

Table 2. Analysis of modelled output of soil dielectric constant and soil moisture.

		Soil Dielectric Constant			Soil Moisture			Soil Moisture without RMS-H and Correlation Length Variable
Algorithms	Field Type	R2	RMSE	MAE	R2	RMSE (m3/m3)	MAE (m3/m3)	R2	RMSE (m3/m3)	MAE (m3/m3)
Random Forest	Soybeans	0.89	6.79	5.15	0.89	0.050	0.04	0.45	0.111	0.09
	Wheat	0.73	4.01	2.67	0.88	0.031	0.02	0.87	0.032	0.02
	Corn	0.72	1.96	1.62	0.78	0.030	0.02	0.75	0.032	0.03
Decision Tree	Soybeans	0.84	8.16	6.05	0.88	0.051	0.04	0.36	0.119	0.08
	Wheat	0.58	4.98	3.53	0.77	0.044	0.03	0.66	0.053	0.44
	Corn	0.30	3.10	2.42	0.34	0.052	0.04	0.45	0.048	0.04
XGBoost	Soybeans	0.65	12.05	8.28	0.77	0.072	0.05	0.36	0.119	0.09
	Wheat	0.54	5.21	3.45	0.58	0.059	0.05	0.54	0.061	0.05
	Corn	0.47	2.71	1.94	−0.25	0.072	0.06	−0.33	0.074	0.06
Stochastic Gradient Descent	Soybeans	0.58	13.11	10.92	0.62	0.092	0.08	0.41	0.115	0.09
	Wheat	0.62	4.71	3.23	0.68	0.052	0.04	0.66	0.054	0.04
	Corn	0.41	2.86	2.28	0.50	0.045	0.04	0.48	0.046	0.04
KNN	Soybeans	0.64	12.17	9.01	0.65	0.089	0.06	0.43	0.113	0.08
	Wheat	0.53	5.28	3.79	0.66	0.053	0.04	0.68	0.051	0.04
	Corn	0.65	2.22	1.86	0.68	0.036	0.03	0.56	0.043	0.03
Multilinear Regression	Soybeans	0.45	15.06	11.92	0.58	0.096	0.08	0.45	0.11	0.09
	Wheat	0.50	5.40	3.85	0.62	0.056	0.05	0.60	0.058	0.05
	Corn	−0.52	4.58	3.77	−0.07	0.067	0.06	0.22	0.057	0.05
Neural Network	Soybeans	0.60	12.79	8.84	0.51	0.100	0.08	0.25	0.138	0.12
	Wheat	0.40	5.94	4.65	0.45	0.075	0.05	0.27	0.081	0.06
	Corn	0.38	2.93	2.26	0.36	0.054	0.04	−0.63	0.078	0.07

.

The lowest accuracy was found for the corn field, where the coefficient of determination in both multilinear regression and XGboost was negative. This could be due to problems with the data or the model itself, as it is unable to capture any significant relationship between the independent and dependent variables—that is, it is unable to explain or predict the variation. In such cases, the coefficient of determination becomes negative. One of the reasons for the best results in soybean corn was the soybean open canopy, which means that there is less vegetation cover and spacing between the plants. Also, there is less plant material above the ground, which creates a situation where SAR signals can more easily penetrate through the canopy and interact directly with the soil beneath. When the SAR signal interacts with the soil, the sensor gets sufficient backscattering, which provides valuable information on soil moisture content. In the case of corn, it has denser canopies with a large amount of above-ground biomass, making it more challenging for the SAR signals to penetrate through the canopy.

More than 20 polarimetric features were used to train the machine learning model. Certain features, such as surface roughness parameters like correlation length and RMS-H cannot be eliminated as they play a crucial role and affect the SAR backscattering. The Decomposition technique and machine learning–based modelling played a crucial role in estimating soil moisture without considering the RMS-H and correlation length. This type of experiment is useful where the surface roughness parameter is not available as input to the model and machine learning–based retrieval, which suffer from unavailability. The results are presented in Table 2, which shows the modelled output of soil moisture without considering the roughness parameter. It was observed that random forest performed very well on the wheat field, with a coefficient of determination of 0.87. For the corn field, the coefficient of determination was 0.75, while it was 0.45 for the soybean field, which is comparatively less compared to the other crop fields. Interestingly, XGBoost and the neural network were found to be ineffective in predicting the variations in the dependent variable.

3.2. Results with Consideration of Vegetation Effects

The vegetation effect was considered, and all seven machine learning models were re-modeled, incorporating the two attenuation factors from the water cloud model and the Radar Vegetation Index retrieved from the full polarimetric data. The parameters C and D were obtained through linear model fitting. Parameters V₁ and V₂ represent the LAI and PWC. Parameters A and B were calibrated using the vegetation descriptors along with the soil parameters. The dielectric constant retrieved from the machine learning for the soybean field is shown in Figure 10.

The random forest algorithm was the best performer in the soybean field, as shown in Figure 10a, and demonstrated good agreement with an R² of 0.89, RMSE of 6.78, and MAE of 4.38. The decision tree algorithm, shown in Figure 10b, performed as well as the random forest algorithm, showing the capability to estimate the dielectric values in the soybean field. The decision tree algorithm had an R² of 0.88, RMSE of 7.10, and MAE of 4.69. The XGBoost algorithm in Figure 10c and the neural network algorithm in Figure 10g provided the same R² of 0.74; however, the RMSE and MAE values for XGBoost were lower, at 10.27 and 7.40, respectively, whereas the RMSE and MAE of the neural network algorithm were 10.35 and 7.90. The performance of the SGD algorithm, shown in Figure 10d, was lower compared to the random forest, decision tree, XGBoost, and neural network algorithms. The SGD algorithm had an R² of 0.61, RMSE of 12.69, and MAE of 10.54. The KNN had an R² of 0.72 (Figure 10e). The lowest performance was observed in the multilinear regression algorithm (Figure 10f), where the R² was 0.47, RMSE was 14.77, and MAE was 11.90. All the machine learning algorithms performed well in the soybean field except the multilinear regression.

Figure 11 shows the dielectric constant estimated result from the machine learning in the wheat field. Here, the random forest shown in Figure 11a performed well with an R² of 0.82, RMSE of 3.21, and MAE of 2.08. The decision tree algorithm performance, as shown in Figure 11b, was not effective in the wheat field with an R² of 0.60, RMSE of 4.85, and MAE of 3.20. The XGBoost algorithm shown in Figure 11c performed better in estimating the dielectric constant from the wheat field with an R² of 0.66, RMSE of 4.46, and MAE of 2.90. The stochastic gradient descent performed better than the decision tree; the SGD shown in Figure 11d had an R² of 0.62, RMSE of 4.73, and MAE of 3.26. The KNN algorithm performance in the wheat field was not as effective; Figure 11e shows that the KNN had an R² of 0.56, RMSE of 5.07, and MAE of 3.66. The multilinear regression did not perform well, having an R² of 0.48, RMSE of 5.53, and MAE of 3.70 in Figure 11f. The neural network algorithm shown in Figure 11g shows an R² of 0.59, RMSE of 4.92, and MAE of 3.65. The neural network performance was better than the K-nearest neighbor and multilinear regression.

The ML results for the corn field are shown in Figure 12. The random forest (Figure 12a) has shown good results with an R² of 0.77, RMSE of 1.77, and MAE of 1.45. In contrast, the decision tree algorithm in Figure 12b drastically changed to negative, showing an R² of −0.20, RMSE of 4.08, and MAE of 3.10. The XGBoost algorithm (Figure 12c) shows an R² of 0.45, RMSE of 2.77, and MAE of 2.07, and it performed better than the decision tree, multilinear regression, and neural network. The stochastic gradient descent algorithm shown in Figure 12d shows an R² of 0.43, RMSE of 2.62, and MAE of 2.24, which is better than the multilinear regression and neural network. The K-nearest neighbor performed better than the XGBoost, decision tree, SGD, MLR, and NN. The KNN was the second-best performer in estimating the dielectric constant in the corn field with an R² of 0.64, RMSE of 2.23, and MAE of 1.76, as shown in Figure 12e.

The MLR model did not perform well with the corn data and provided an R² of −0.24, RMSE of 4.14, and MAE of 3.49, as shown in Figure 12f. The neural network model performance was better than the decision tree and multilinear regression, with an R² of 0.42, RMSE of 2.82, and MAE of 2.18, as shown in Figure 12g.

The estimation of soil moisture in the soybean field is shown in Figure 13. Here, the random forest (Figure 13a) performed extensively well, with an R² of 0.92, RMSE of 0.042, and MAE of 0.03. The decision tree (Figure 13b) performed well but not as much, with an R² of 0.83, RMSE of 0.061, and MAE of 0.04. The XGBoost performance was outstanding, with an R² of 0.91, RMSE of 0.046, and MAE of 0.03. It performed well compared to all the algorithms except random forest, as shown in Figure 13c. The SGD estimated the soil moisture with an R² of 0.65, RMSE of 0.088, and MAE of 0.07. The SGD performance is better than the MLR model in this case, as shown in Figure 13d. The KNN performance was better than the SGD, MLR, and NN. The KNN shows an R² of 0.72, RMSE of 0.078, and MAE of 0.05, as shown in Figure 13e. The MLR in Figure 13f shows an R² of 0.62, RMSE of 0.092, and MAE of 0.07, which is not significant compared to other models. The least performer in the soybean field is the neural network, with an R² of 0.61, RMSE of 0.093, and MAE of 0.07, as shown in Figure 13g.

The random forest performed very well in the estimation of soil moisture in the wheat field with an R² of 0.91, RMSE of 0.027, and MAE of 0.02, as shown in Figure 14a. The second-best performing algorithm is the decision tree (Figure 14b), with an R² of 0.85, RMSE of 0.035, and MAE of 0.03. The XGBoost model did not perform very well, showing an R² of 0.62, RMSE of 0.056, and MAE of 0.05 in Figure 14c, but the XGBoost model performed better than the neural network. The SGD algorithm (Figure 14d) had an R² of 0.69, RMSE of 0.051, and MAE of 0.04, performing similarly to KNN but better than XGBoost. The KNN results shown in Figure 14e demonstrate an R² of 0.69, RMSE of 0.050, and MAE of 0.04, which are better results than the MLR, NN, and XGB models. The MLR algorithm also performed well in estimating the soil moisture in the wheat field with an R² of 0.65, RMSE of 0.054, and MAE of 0.04, as shown in Figure 14f, better than XGB and NN.

The neural network performed the least in this case, with an R² of 0.40, RMSE of 0.070, and MAE of 0.06, as shown in Figure 14g. In estimating soil moisture in the wheat field, the random forest again performed better without underfitting or overfitting the model.

The ML results from the corn field are shown in Figure 15. The random forest in Figure 15a had an R² of 0.80, RMSE of 0.028, and MAE of 0.02, which means the performance is again good and satisfactory compared to all other algorithms. The decision tree modeled the soil moisture in the corn field with an R² of 0.73, RMSE of 0.033, and MAE of 0.03, as shown in Figure 15b. The XGBoost (Figure 15c) performance was not satisfactory, with a negative value of R² of −0.07, RMSE of 0.067, and MAE of 0.06. Here, the performance of the SGD algorithm was better than that of the XGBoost, as well as the MLR and NN. The SGD had an R² of 0.52, RMSE of 0.045, and MAE of 0.03, as shown in Figure 15d. The KNN model performed well, better than the XGBoost, SGD, MLR, and neural network. The KNN had an R² of 0.68, RMSE of 0.038, and MAE of 0.03, as shown in Figure 15e. The MLR (Figure 15f) modeling for soil moisture in the corn field was the least effective, with an R² of −0.11, RMSE of 0.061, and MAE of 0.05. The neural network modeling, as shown in Figure 15g, was the second least effective in soil moisture estimation with an R² of 0.37, RMSE of 0.051, and MAE of 0.04. All the analyses of the modelled output of soil dielectric constant and soil moisture (considering vegetation effect in the model) are combined in

Table 3. Analysis of modelled output of soil dielectric constant and soil moisture (considering vegetation effect in the model).

		Soil Dielectric Constant			Soil Moisture
Algorithms	Field Type	R2	RMSE	MAE	R2	RMSE (m3/m3)	MAE (m3/m3)
Random Forest	Soybeans	0.89	6.78	4.38	0.92	0.042	0.03
	Wheat	0.82	3.21	2.08	0.91	0.027	0.02
	Corn	0.77	1.77	1.45	0.80	0.028	0.02
Decision Tree	Soybeans	0.88	7.10	4.69	0.83	0.061	0.04
	Wheat	0.60	4.85	3.20	0.85	0.035	0.03
	Corn	−0.20	4.08	3.10	0.73	0.033	0.03
XGBoost	Soybeans	0.74	10.27	7.40	0.91	0.046	0.03
	Wheat	0.66	4.46	2.90	0.62	0.056	0.05
	Corn	0.45	2.77	2.07	−0.07	0.067	0.06
Stochastic Gradient Descent	Soybeans	0.61	12.69	10.54	0.65	0.088	0.07
	Wheat	0.62	4.73	3.26	0.69	0.051	0.04
	Corn	0.43	2.82	2.24	0.52	0.045	0.03
KNN	Soybeans	0.72	10.72	7.80	0.72	0.078	0.05
	Wheat	0.56	5.07	3.66	0.69	0050	0.04
	Corn	0.64	2.23	1.76	0.66	0.038	0.03
Multilinear Regression	Soybeans	0.47	14.77	11.90	0.62	0.092	0.07
	Wheat	0.48	5.53	3.70	0.65	0.054	0.04
	Corn	−0.24	4.14	3.49	0.11	0.061	0.05
Neural Network	Soybeans	0.74	10.35	7.90	0.61	0.093	0.07
	Wheat	0.59	4.92	3.65	0.40	0.070	0.06
	Corn	0.42	2.82	2.18	0.37	0.051	0.04

.

4. Discussion

It is significant to highlight that the models’ effectiveness varied depending on the agricultural fields and machine learning techniques used. The findings imply that certain models could be more appropriate for particular crops or datasets. Further investigation, validation, and comparison with other models are required to determine if the machine learning techniques for estimating soil dielectric constant are robust and generalizable. The choice of features, model improvement, and possible errors caused during data collecting should all be considered.

The analysis of feature importance derived from the random forest model provides valuable insights into the relative significance of various features in predicting the target variable, as shown in Figure 16. The feature that holds the most significant influence is the Van Zyl dihedral, as indicated by its high importance score of 0.294013. The score of 0.213926 is closely associated with anisotropy, signifying its significant influence on the predictions. Soil roughness RMS and correlation length are notable contributors, with respective scores of 0.136134 and 0.13075. These four characteristics are identified as the principal factors that propel the model’s prediction. The features of entropy, Van Zyl surface, Freeman-Durden volume, and Freeman-Durden dihedral exhibit a moderate level of significance, whereas the remaining features demonstrate comparatively lower importance scores. In general, comprehending the relative significance of these characteristics offers valuable perspectives for subsequent investigation and decision-making pertaining to the given dataset.

The random forest performance was best in all the scenarios. The soil dielectric constant and soil moisture map was generated using the random forest in Figure 17, which provides the spatial distribution of soil dielectric constant and soil moisture across the study area. The model combines the information from various polarimetric input features to predict the soil moisture values at unsampled locations. The darker shades denote the lower soil moisture, and the lighter shades denote the higher soil moisture. It is important to highlight that the accuracy and reliability of the soil moisture map are dependent on the quality and representativeness of the input data, as well as the random forest model’s success in capturing the underlying relationships. Validation and comparison with ground-truth measurements or other reference data sources improved the resulting map’s accuracy.

The study aimed to assess the potential of fully polarimetric synthetic aperture radar data to estimate soil dielectric constant and moisture values at L-band. It also demonstrated the usefulness of decomposition techniques and machine learning models in estimating soil moisture with or without the surface roughness parameter. The study was conducted in Winnipeg, Canada, using simulated NISAR data, which sets it apart from prior studies. Over 20 input features, such as Freeman-Durden decomposition, Van Zyl decomposition, H/A/alpha, polarization ratio, and surface parameter, were used to train seven different machine learning algorithms. Akhavan et al., 2021 [39] conducted a study on airborne UAVSAR data and used a feature selection approach to choose input variables for the machine learning model. They used random forest and neural network algorithms to model soil moisture and found that random forests performed better than neural networks. The best accuracy was achieved in the soybean field with R2 = 0.86, while the lowest accuracy was seen in a corn field with R² = 0.40. The study concluded that the number of input features doesn’t necessarily lead to better accuracy and that the surface roughness parameter is an important variable for soil moisture modeling. Wang et al., 2017 [41] compared the Freeman-Durden, Hajnsek, and An decomposition techniques for soil moisture retrieval over corn, canola, soybean, and wheat fields. They removed the volume scattering component and normalised the incidence angle. The best result had an RMSE of 0.06 m3/m3, while the lowest was an RMSE of 0.11 m³/m³. Wang et al., 2016 [51] removed the volume scattering contribution and focused on surface scattering to estimate soil moisture. They used airborne UAVSAR and Sampex12 data for various crop phenology stages. Using a simplified polarimetric decomposition, they found an inversion rate of 26–38% and an RMSE of 0.06–0.12 m³/m³ for soil moisture retrieval.

The present study examines the previous literature and understands that the impact of decomposition techniques and machine learning algorithms is crucial in estimating the soil dielectric constant and soil moisture. Thus, these techniques are implemented in the current study. All three scattering components (surface, dihedral, and volume) were used without removing any of them in the model, and no feature selection approach (such as trial and error, backward feature selection, or forward feature selection) was utilised, as previous authors have shown that it does not affect the overall accuracy of the model. The lack of effect on the results was observed with the feature selection method because it performs the same process of selecting the best features iteratively, which already exists in ML models, adding nothing new to the results. The feature selection method might select features that work well with the training dataset but not for unseen data, which can lead to overfitting. Conversely, removing too many features might lead to underfitting. Some features, even if they are not strongly predictive individually, can significantly contribute when combined with other features. One of the main reasons for not considering the feature selection method was that machine learning is capable on its own of prioritizing or ranking the best features without discarding any features, maximising model performance. One example is the random forest, which provides feature importance. The study estimated soil dielectric constant and soil moisture values, identifying the Van Zyl dihedral, anisotropy, RMS-H, and correlation length as the most significant features. The results were evaluated both with and without the surface roughness parameter.

The incorporation of vegetation correction using the Water Cloud Model (WCM) has consistently yielded better results compared to those obtained without this correction. The WCM integrates parameters such as Leaf Area Index (LAI) and Plant Water Content (PWC). It is found that the Water Cloud Model is highly suitable for incorporating these parameters, making it ideal for soil moisture studies. The results of our random forest analysis show significant improvements after implementing the WCM. For the soybean field, the R² increased from 0.89 to 0.92; for the wheat field, from 0.88 to 0.91; and for the corn field, from 0.78 to 0.80. Similarly, the root mean square error (RMSE) values decreased across these fields, from 0.050 to 0.042 for soybean, from 0.031 to 0.027 for wheat, and from 0.030 to 0.028 for corn. These improvements highlight the consistent enhancement of results post-WCM implementation.

All the algorithms demonstrated better consistent results. However, a few algorithms did not exhibit uniform improvements. Specifically, the decision tree algorithm for the soybean field saw a decrease in R² from 0.88 to 0.83, the KNN algorithm for the corn field decreased from an R² of 0.68 to 0.66, and the neural network for the wheat field showed an R² drop from 0.75 to 0.40. These exceptions are attributed to the inherent limitations of certain algorithms in handling the complexity added by the vegetation correction parameters. Decision trees, for instance, are sensitive to noise and prone to overfitting; a very deep decision tree might be overfitted to noise in the training data, explaining the decreased performance in the soybean field. The KNN algorithm, known for its simplicity, struggled with the additional dimensions introduced by the WCM and RVI, leading to reduced accuracy in the corn field. Additionally, the limited data for the corn field may have resulted in underfitting. On the other hand, neural networks, which require extensive training data and fine-tuning, may also be impacted by the choice of activation functions and overfitting, which can lead to learning noise in the training data and result in artifacts in the predictions. This explains the drop in performance for the wheat field.

The implementation of the Water Cloud Model has proven to be beneficial, significantly improving the performance of most algorithms in soil dielectric constant and soil moisture estimation by effectively accounting for vegetation attenuation.

The simulated NISAR L-band data (provided by the NASA-JPL) used in this study replicate future NISAR data characteristics and help to understand the quality of future NISAR products. The future NISAR quad-polarization data will be available for regions like India and the United States [52], with an L-band frequency of 1.257 GHz. The L-SAR system provides a 7-m resolution along its direction of travel (along a track) and a resolution between 2 and 8 m across the track, depending on the viewing mode [53]. On the other hand, the future European Space Agency ROSE-L mission has a spatial resolution of 5–10 m, which will use advanced radar techniques, including full polarimetry, with a frequency of 1.257 GHz for soil moisture and forestry applications [54]. The current study aims to provide essential insights that will be helpful for researchers in the data analysis of the upcoming mission.

5. Conclusions

The results were obtained for three crop types: wheat, soybean, and corn fields. Random forest showed the best results for the soybean field with a coefficient of determination of 0.89, RMS of 0.033 m³/m³, MAE of 0.001 m³/m³, and MBE of 0.023 m³/m³. For the wheat field, a coefficient of determination of 0.87 was observed. Random forest performed better in the soybean field compared to the wheat field, but it still outperformed the other machine learning algorithms. Adverse performance was reported for neural networks, XGBoost, and multilinear regression. For soil dielectric constant estimation, the random forest again provided better results in the soybean crop field with an R² of 0.89, RMSE of 6.79, and MAE of 5.15. Decision trees, SGD, and KNN also worked better in corn and wheat fields. The results were good in the soybean field due to the lower amount of vegetation present. The corn field model performed less accurately than the other fields due to vegetation and a lower amount of in-situ soil moisture than the other fields. To analyse the effect of vegetation, two-way attenuation from WCM and RVI parameters were incorporated into the ML model. The results observed while considering the vegetation effects were better as compared with the results without considering the vegetation effect. The random forest again showed the best results for the soybean with a coefficient of determination of 0.92 m³/m³, RMSE of 0.042 m³/m^3, and MAE of 0.03 m³/m³. The random forest algorithm demonstrates the best overall performance for predicting soil moisture even without considering RMS-H and correlation length surface roughness parameters, particularly for wheat with an R² of 0.87 and a low RMSE of 0.032 m³/m³. Other Algorithms also performed well. One of the reasons the random forest performed better than other ML algorithms was its ability to handle a larger number of input variables without overfitting. The most important input parameters for soil moisture estimation identified by random forest were Van Zyl dihedral, anisotropy, surface roughness, correlation length, entropy, Van Zyl surface, and Freeman-Durden volume. The soil moisture was predicted for the whole study area, and a range between 0.10 to 0.50 m³/m³ soil moisture is estimated using the random forest model. Dielectric and soil moisture maps were generated for the study area. The methodology applied in the current research contributes essential insights that could benefit upcoming missions, such as the Radar Observing System for Europe in L-band (ROSE-L) and the collaborative NASA-ISRO SAR (NISAR) mission, for future data analysis in soil moisture applications. The datasets from these NISAR and ROSE-L missions, when available in the future, can be used in a similar way for the soil moisture estimation as presented in the study. Future researchers can benefit from our study when handling the actual NISAR or ROSE-L datasets. The following points illustrate how the findings of this study assist researchers in the analysis of future datasets:

• To retrieve the dielectric constant and soil moisture in different types of crop fields using seven different ML algorithms incorporated by the SAR decomposition models from fully polarimetric L-band data.
• The random forest algorithm performed better than the decision tree, XGBoost, SGD, KNN, NN, and MLR algorithms in handling complex nonlinear data.
• The incorporation of vegetation correction using the Water Cloud Model (WCM) has consistently yielded better results than those obtained without this correction.
• The Water Cloud Model is highly suitable for incorporating Leaf Area Index (LAI) and Plant Water Content (PWC) parameters, making it ideal for soil moisture studies within vegetated areas using the L-band data.
• The surface roughness parameter significantly plays an important role when modelling SAR-based soil moisture. The study estimates soil moisture with and without the incorporation of the surface roughness parameter in the model.