A Review of Root Zone Soil Moisture Estimation Methods Based on Remote Sensing

Abstract

Root zone soil moisture (RZSM) controls vegetation transpiration and hydraulic distribution processes and plays a key role in energy and water exchange between land surface and atmosphere; hence, accurate estimation of RZSM is crucial for agricultural irrigation management practices. Traditional methods to measure soil moisture at stations are laborious and spatially uneven, making it difficult to obtain soil moisture data on a large scale. Remote sensing techniques can provide soil moisture in a large-scale range, but they can only provide surface soil moisture (SSM) with a depth of approximately 5–10 cm. In order to obtain a large range of soil moisture for deeper soil layers, especially the crop root zone with a depth of about 100–200 cm, numerous methods based on remote sensing inversion have been proposed. This paper analyzes and summarizes the research progress of remote sensing-based RZSM estimation methods in the past few decades and classifies these methods into four categories: empirical methods, semi-empirical methods, physics-based methods, and machine learning methods. Then, the advantages and disadvantages of various methods are outlined. Additionally an outlook on the future development of RZSM estimation methods is made and discussed.

1. Introduction

Soil moisture is a crucial Essential Climate Variable (ECV) that plays a crucial role in regulating the exchange of water, energy, and carbon between the land surface and atmosphere [1,2]. RZSM is a significant variable in plant growth, drought monitoring, agricultural water management, hydrological cycling, and so on. Generally, it specifically refers to the moisture content of the soil layer where plant roots predominantly extract water and nutrients, and it is measured at a depth of 100 cm from the surface [3]. Therefore, it is necessary to accurately estimate RZSM in agricultural production and ecological environmental management.

Traditionally, RZSM can be obtained by in situ measurements, such as time-domain reflectometry [4], the cosmic ray neutron method [5,6], and the gravimetric method [7]. However, due to the sparse site distribution and weak representative sampling, these methods could not fully reflect the spatial variability of regional soil moisture. Additionally, the installation, calibration, and maintenance of monitoring equipment are time-consuming and costly [8,9]. Relatively, satellite remote sensing technology can quickly obtain large-scale spatial distribution of soil moisture information. Depending on the wavelength band in which the remote sensing sensor operates, the main satellite remote sensing observation techniques to monitor soil moisture mainly include optical remote sensing and microwave remote sensing. Optical remote sensing technology typically utilizes the reflective or emissive properties of the earth’s surface in the optical spectrum (visible and infrared bands) to estimate soil moisture. This is based on the assumption that soil moisture affects the spectral reflectance and emissivity of the soil surface and thus can be inferred from the observed radiance or temperature of the soil pixels. While optical remote sensing offers high resolution and is well-established, it is prone to interference from cloudy and rainy conditions, and it does not effectively penetrate dense vegetation. In contrast, microwave remote sensing operates at longer wavelengths, has superior penetration capabilities, and is largely unaffected by clouds and atmospheric conditions. Consequently, microwave remote sensing technology, with its ability to penetrate vegetation cover and conduct all-weather observations, finds extensive applications in soil moisture detection [10,11,12,13,14]. However, the current development of microwave remote sensing is limited by its restriction to C-band and L-band measurements, which can only detect soil moisture information up to a depth of 10 cm below the surface.

Therefore, in order to estimate soil moisture in deeper soil layers over a large area using remote sensing observations, researchers have developed various hybrid methods to address this issue. Kostov et al. [15] provide a detailed overview of RZSM estimate methods and classify them into four major categories: regression, knowledge-based, inversion, and soil water modeling techniques. They also indicate that the method of assimilating remote sensing data into physical models may be the best approach to solve the problem of RZSM estimation. Subsequently, various data assimilation methods have been proposed for estimating soil moisture. Entekhabi et al. [16] employed an extended Kalman filter (EKF) algorithm to assimilate microwave and thermal infrared observations into the soil heat and moisture diffusion system equation to infer soil moisture and temperature profiles. Houser et al. [17] utilized a four-dimensional data assimilation method (4Dvar), along with other optimization techniques, to assimilate the push broom microwave radiometer into the Topmodel-based Land–Atmosphere Transfer Scheme to estimate the temporal continuity of regional-scale soil moisture data. Vereecken et al. [18] reviewed the approach of combining remote sensing data with soil water balance models and pointed out that the success of retrieving profile soil moisture from remote sensing soil moisture data mainly depends on the type of assimilation method. They also suggested that combining a Kalman filter with the Markov chain Monte Carlo method to simultaneously estimate state variables and system parameters appears to be the most promising. Recently, Khandan et al. [19] conducted a comprehensive review of soil water data assimilation techniques, emphasizing that assimilating remote sensing data into land surface models (LSMs) can significantly improve the accuracy of soil moisture estimation. Overall, data assimilation methods have been the optimal approach for soil moisture estimation for a long time. However, given the complexity and uncertainty of data assimilation methods, some scholars have proposed semi-empirical methods based on simplified physical equations. Wagner et al. [20] proposed the exponential filter based on the two-layer soil water balance equation to estimate RZSM from SSM. Additionally, machine learning techniques have been applied to RZSM estimation studies [21,22], which can achieve high accuracy inversion of RZSM by training and optimizing large amounts of remotely sensed data, as well as improve the efficiency and automation of data processing and analysis.

In summary, there have been numerous studies and reviews on estimating soil moisture using data assimilation methods in the past few decades. However, comprehensive reviews specifically focused on RZSM estimation methods are relatively limited, especially concerning newly developed techniques. Therefore, this paper aims to systematically review and compare various RZSM estimation methods from empirical, semi-empirical, physical mechanism-based, and machine learning perspectives. It will also discuss the limitations and challenges of these methods and propose future research directions. The objective is to assist in the development of large-scale, high-accuracy RZSM products, leading to more sustainable agricultural and water management practices.

2. Methods for Estimating Root Zone Soil Moisture

The principle to estimate RZSM using remotely sensed data is to establish a statistical or physical–mechanistic relationship between remotely sensed data and RZSM. This section describes four broad categories of methods for RZSM estimation, including empirical methods, semi-empirical methods, physics-based methods, and machine learning methods.

2.1. Empirical Methods

Empirical methods for estimating RZSM rely on prior observations, knowledge, or experience to construct models without a clear physical mechanism. These methods typically establish statistical relationships between SSM estimated from remote sensing or remote sensing-derived indices and RZSM. Statistical regression, cross-correlation regression, and cumulative distribution function matching are commonly used empirical statistical models.

2.1.1. Statistical Regression

The more common empirical RZSM inversion methods mostly use statistical regression relationships as the RZSM inversion model, as shown in Equation (1):

$$SM=f\left(RSindex\right)$$

(1)

where SM denotes RZSM, f denotes function, and RSindex denotes the remote sensing index.

In the above regression method, the RSindex used for inversion of RZSM usually includes surface parameters such as land surface temperature (LST), the vegetation index (VI), the spectral index, and thermal inertia. Among these, the combination of VI and LST can effectively elucidate differences in land surface water heat exchange processes, particularly the interaction between soil moisture, evapotranspiration, and surface temperature under varying vegetation cover conditions. Consequently, a range of remote sensing indices derived from the combined LST and VI data have been widely used for soil moisture inversion. Noteworthy methods in this regard include the Temperature Vegetation Dryness Index (TVDI) [23], the Vegetation Temperature Condition Index (VTCI) [24], and the Vegetation Supplication Water Index (VSWI) [25]. Sandholt et al. [23] established a strong correlation between the TVDI and RZSM (with R² ranging from 0.61 to 0.83). In a study by Yuan et al. [26], the performance of an apparent thermal inertia (ATI)-based model, a TVDI-based model, and a combined ATI/TVDI model to invert 20 cm depth soil moisture inversion on the Loess Plateau in China was compared and analyzed. The results demonstrated that the combined ATI/TVDI model exhibited greater applicability compared to the ATI-based and TVDI-based models, yielding a maximum R value of 0.73 ± 0.011, a minimum RMSE value of 3.43 ± 0.071%, and a minimum MAE value of 0.05 ± 0.025 compared to the measured values. Zhao et al. [27] proposed an improved version of the TVDI called the temperature vegetation quantification index (TVQI) based on the dry and wet edge theory for the TVDI. It was shown that the TVQI improved the R², RMSE, and NSE of the TVDI for estimating soil moisture at 10 cm of depth by 0.2, 0.03, and 4.6, respectively. Additionally, Patel et al. [28] conducted RZSM inversion in Rajasthan using the VTCI method, which demonstrated a good correlation (R² = 0.63) with the average profile soil moisture at a depth of 50 cm below the surface.

The crop water stress index (CWSI), which considers canopy temperature, is also commonly used to invert soil moisture. Akuraju et al. [29] used the CWSI to invert the RZSM of Dookie farm, which was the average of soil moisture measured at four layers of 0–30 cm, 30–60 cm, 60–90 cm, and 90–120 cm, and the results showed that the estimated RZSM had errors of 3.9% and 5.3% for the two cropping seasons, respectively. Saeidi et al. [30] constructed the correlation between the CWSI and RZSM using five regression models: linear, exponential, logarithmic, polynomial, and power exponential, and the results showed that the regression models with polynomial (R = 0.987) and power exponential (R = 0.65) estimated the soil moisture with relatively best accuracy.

In addition, the topographic moisture index (TWI) can be used to quantitatively model the wet and dry conditions of soil at each point under ideal conditions, and more and more studies have applied the topographic moisture index to the description of the spatial distribution of soil moisture. The physical meaning of the TWI can be expressed as a composite function that combines unit sink area and slope [31]. The index is defined as follows:

$$TWI=\ln \frac{SCA}{\tan \beta }$$

(2)

where $SCA$ is the sink area and $\beta$ is the local slope angle.

Buchanan et al. [32] calculated the TWI using more than 400 unique formulas and found a good correlation with soil moisture at a depth of 12 cm. In their best case, the R² and R values between the TWI and soil moisture were 0.61 and 0.78, respectively. Raduła et al. [33] analyzed the correlation between the TWI and soil moisture at a depth of 6 cm and found that it outperformed Ellenberg’s indicator values (EIVs). Their study also showed that EIVs can be used instead of the TWI to invert soil moisture under complex topography and relatively stable climatic conditions. Furthermore, they compared and assessed the accuracy of 10 different TWI algorithms in predicting soil moisture. The findings indicated that the Multiple Flow Direction (MFD) algorithm [34], particularly the MFD-md algorithm, demonstrated the highest accuracy. However, it is important to note that the TWI has limited explanatory power in predicting soil moisture distribution due to its dependence on factors such as soil moisture redistribution, radiation, soil properties, and vegetation cover heterogeneity [35,36].

In summary, the surface parameters or spectral indices may not reflect the soil moisture at different depths, especially for deeper layers, and may be affected by other factors such as vegetation, soil texture, and surface roughness. These methods may have low spatial accuracy and poor evaluation for different soil depths, particularly for the topographic wetness index. In addition, remote sensing data employed in these methods are frequently optical remote sensing data and are, therefore, also influenced by weather conditions and vegetation, which in turn affect the estimation of RZSM.

2.1.2. Cross-Correlation Analysis

A cross-correlation analysis is commonly used to characterize the lag relationship between SSM and RZSM [37,38,39,40]. The coupling relationship between SSM and RZSM was analyzed by calculating the maximum delayed correlation coefficient (Lag-R) and the corresponding lag time (days) between the SSM and RZSM time series. A high number of correlations indicates a strong coupling between SSM and RZSM, indicating a higher potential for inversion of RZSM from SSM, and vice versa [39,41].

Corresponding studies showed that Lag-R decreased with increasing depth, and lag time increased with increasing depth. The strength of coupling between SSM and RZSM decreases with increasing soil depth. Ford et al. [39] showed that the mean values of Lag-R between SSM and 25, 50, and 100 cm were 0.79, 0.57, and 0.41, respectively, with mean lag times of 2, 8, and 38 days, in that order. Tian et al. [41] showed that the Lag-R of a 15 cm soil layer varied from 0.91 at a lag time of 0.5 days to 0.57 at a lag time of 7 days for a 60 cm soil layer. Xu et al. [42] showed that the Lag-R of SSM (5 cm) and RZSM (10, 20, and 40 cm) varied from 0.79, 0.57, and 0.41, respectively. The mean Lag-R decreased from 0.88 to 0.71, while the mean lag time increased from 0.08 to 0.43 days.

The coupling strength between soil moisture in different soil layers is primarily influenced by rainfall conditions; regions with higher rainfall exhibit a stronger coupling between SSM and RZSM. Ford et al. [39] identified a significant relationship between Lag-R and rainfall between surface (5 cm) and deep (25 cm) soil moisture in Oklahoma. Additionally, Tian et al. [41] established a significant correlation between Lag-R and rainfall for surface (5 cm) and deep (25, 50 cm) soil moisture, reporting correlation coefficients of 0.33, 0.43, 0.33, and 0.38, respectively, while also noting that there was no significant linear correlation between Lag-R and either soil parameter or vegetation parameter LAI.

A cross-correlation analysis usually aims to assess the strength of the lagged linear correlation between two variables. However, considering that soil infiltration processes are nonlinear, the lagged dependence between SSM and RZSM may not be linear. The coupling relationship between SSM and RZSM is influenced by factors such as geographic location, climatic conditions, vegetation type, and soil moisture content [37,43]. Another method to characterize the temporal evolution of the subsurface soil moisture at different depths is the Dynamic Time Warp (DTW) technique, which can align two time series that have different lengths or speeds [44]. Herbert et al. [45] used DTW to analyze the temporal patterns of SSM from SMOS, in situ soil moisture from the REMEDHUS network, rain rate, and other variables. They found that DTW could capture the temporal dynamics of soil moisture at different depths and reveal the effects of rainfall events and soil texture on soil moisture variability.

The method is simple and easy to implement, but the accuracy of estimating RZSM is often poor and is often used as a simple assessment to determine the suitability of an area for inversion of RZSM using SSM.

2.1.3. Cumulative Distribution Function Matching

The cumulative distribution function matching (CDF) method is commonly used in hydrological studies, including bias correction [46] and scale conversion of different observations [47,48]. It has been successfully applied to invert RZSM from SSM [40,42,49] and to establish the relationship between the difference between SSM minus RZSM and SSM to achieve RZSM. The specific calculation steps are as follows:

(i)

The time series data for SSM and RZSM were ranked based on the duration of the study.

(ii)

The difference ($\Delta$) between the ranked SSM and RZSM was calculated as follows:

$$\Delta ={\theta }_s-{\theta }_{SF}$$

(3)

where ${\theta }_s$ refers to SSM and ${\theta }_{SF}$ represents RZSM.

(iii)

Next, the relationship between $\Delta$ and ${\theta }_s$ is expressed as a third-order polynomial in the following way:

$${\Delta }_p=A+B\times {{\theta }_S}^3+c\times {{\theta }_S}^2+D\times {\theta }_S$$

(4)

where ${\Delta }_p$ is the difference between predicted SSM and RZSM, while A, B, C, and D are fitted parameters.

(iv)

Finally, RZSM was calculated using CDF as follows:

$${\theta }_{CDF}={\theta }_s-{\Delta }_p$$

(5)

where ${\theta }_{CDF}$ is the predicted RZSM.

The CDF method has been used as a benchmark method for estimating RZSM in numerous studies. Tian et al. [41] used CDF to estimate soil moisture in 5 cm, 15 cm, 25 cm, 40 cm, and 60 cm soils, and the results showed that the estimated soil moisture compared with the measured values had a mean R of 0.84, 0.66, 0.44, 0.3, and 0.83, respectively. Xu et al. [42] compared the performance of CDF with the cross-correlation analysis and vertical variability methods for estimating RZSM, respectively, and showed that CDF and the other two methods exhibited a strong linear relationship in NSE, RMSE, and R, which also indicated that the simulation accuracy of the CDF method was significantly affected by the coupling strength and the vertical variability between SSM and RZSM. The study also found that the decoupling of SSM and RZSM significantly reduced the accuracy of soil moisture simulations. The R² value before decoupling was 0.912, while after decoupling it was 0.610. Gao et al. [40] verified the performance of the CDF matching method in estimating RZSM in three different climatic regions in the continental United States. The study found that the prediction accuracy was highest in wet regions and lowest in semi-arid regions, mainly due to poor coupling between SSM and RZSM in dry regions.

The accuracy of estimating RZSM using the CDF method depends entirely on the correlation between SSM and RZSM. When there is a strong coupling between the surface and root zone, the estimation accuracy is high; however, when there is poor coupling, the estimation results are not well.

2.2. Semi-Empirical Methods

Semi-empirical approaches for determining RZSM rely on simplified physical model mechanisms, which use experimental or simulated data to derive estimates. As such, this approach offers a trade-off between the complexity of physical models and the simplicity of empirical models. Among the semi-empirical techniques typically used for RZSM estimation are the exponential filter method and the SMAR model.

2.2.1. Exponential Filter Method

The exponential filter method (ExpF) is a widely used semi-empirical approach for estimating RZSM. It is a classic method that has been used extensively in research studies. The ExpF model was originally proposed by Wagner et al. [20] and later modified by Albergel et al. [50]. The ExpF model determines soil moisture dynamics based on SSM, using a recursive exponential filter function to estimate the soil water index (SWI). The formula for the SWI and the recursive exponential filter function are given below:

$$SW{I}_i=\frac{{\theta }_i-{\theta }_{i,min}}{{\theta }_{i,max}-{\theta }_{i,min}}$$

(6)

$${SWI}_{m,t_n}={SWI}_{m,t_{n-1}}+K_{t_n}\left({ms}_{t_n}-{SWI}_{m,t_{n-1}}\right)$$

(7)

where ${\theta }_i$ is the soil moisture of the i layer and ${\theta }_{i,min}$ and ${\theta }_{i,max}$ are the minimum and maximum values (cm³/cm³) of the time series of soil moisture content for the i layer, respectively. ${SWI}_{m,t_n}$ and ${SWI}_{m,t_{n-1}}$ are the predicted RZSM indices of layer i at time $t_n$ and $t_{n-1}$, respectively. ${ms}_{t_n}$ is the actual measured SSM at time $t_n$. $K_{t_n}$ represents the change in SSM at time $t_n$, and it can be calculated as follows:

$$K_{t_n}=\frac{K_{t_{n-1}}}{K_{t_{n-1}}+e^{-\frac{t_n-t_{n-1}}{T}}}$$

(8)

where $K_{t_{n-1}}$ represents the change in SSM at time $t_{n-1}$ and T is a time constant in days. The initial values of the parameters in the above equation are ${SWI}_{m,t_1}={ms}_{t_1}$, $K_{t_1}=1$.

In the above equation, T is the only unknown parameter required by the ExpF method when SSM is given. The parameter T reflects the degree of migration and retention of near-surface water content to the root zone layer over a period of time. A larger T value implies that RZSM changes more slowly and is less influenced by SSM. A smaller T value implies that RZSM changes more rapidly and follows the variation of SSM. The choice of T value is crucial for the ExpF method, as it directly affects the accuracy and reliability of RZSM estimation. Generally, the optimal T value ($T_{opt}$) for each layer at each site was the one that gave the highest Nash–Sutcliffe Efficiency (NSE) coefficient by comparing the simulated and measured SWI.

Many regions and sites lack sufficient and reliable measured data, making it impossible to directly calculate $T_{opt}$ for each site. Therefore, some studies proposed the method of using regional generalized $T_{opt}$; that is, using a fixed or regional $T_{opt}$ to replace the $T_{opt}$ of each site within a region. Albergel et al. [50] and Ford et al. [39] have found that there is no significant difference in the accuracy of RZSM estimation between using site-specific T values and using regional generalized T values, so a fixed T value can be used instead of the T values of each site. For example, Wagner et al. [20] proposed a generalized T = 20 days to estimate the RZSM of a 0~100 cm soil layer, which has been widely used in studies worldwide [51,52]. The method of using regional fixed T values is simple and easy to implement, but it does not consider the spatial heterogeneity of soil moisture at the catchment scale, as well as the effects of soil, climate, and vegetation factors on T values. Therefore, many studies explored how to determine $T_{opt}$ based on these factors. Qiu et al. [53] proposed a method to estimate $T_{opt}$ of a 0~70 cm soil layer based on long-term NDVI values, using the formula $T_{opt}$ = −75.263 × NDVI + 68.171. This method was also adopted by another study [54]. Tian et al. [41] proposed a method to estimate $T_{opt}$ in a 0~70 cm soil layer by constructing a multiple regression model with soil, vegetation, and meteorological variables, and it has been applied in the alpine cold region of China. Bouaziz et al. [55] found a strong positive correlation between $T_{opt}$ and catchment-scale vegetation accessible water storage capacities, which allows inferring $T_{opt}$ from the root zone storage capacity estimated by hydrological models in temperate climate regions. Grillakis et al. [56] used an artificial neural network (ANN) method to regionalize $T_{opt}$ values at a global scale. This method first calibrated $T_{opt}$ values with in situ observations from the International Soil Moisture Network (ISMN) using CCI soil moisture data and then regionalized the calibrated results using global descriptors of soil, climate, and vegetation, thus achieving global regionalization of RZSM estimation values. Tian et al. [57] used the random forest (RF) method to classify $T_{opt}$ values in different regions of China. This method determined $T_{opt}$ values according to the relationship between $T_{opt}$ and soil, climate, and vegetation characteristics based on the spatial distribution of these characteristics.

Overall, the Expf method can estimate RZSM with high accuracy by determining only a single parameter T value. This method is simple, easy to implement, and fast. However, this method has some limitations. Although it considers the attenuation effect of soil moisture, it does not incorporate the relevant physical processes that control soil moisture changes. In addition, the parameter T value depends on various physical factors that influence the dynamics of soil moisture, such as soil texture, vegetation, terrain, and climatic conditions. These factors make the T value spatially variable, which increases the difficulty of finding a suitable T value at the regional scale and limits the applicability of this method.

2.2.2. SMAR Model

Considering that the physical mechanism of the Expf method is not well understood, Manfreda et al. [58] extended the model of Wagner et al. [20] into a two-layer physically based infiltration model, which is the SMAR model. The SMAR model links SSM and RZSM based on a simplified soil water balance equation with a physical basis and is a semi-empirical RZSM assessment method.

It is assumed that the soil consists of two layers, the first one being the surface layer a few centimeters deep (corresponding to the depth range that can be monitored by remote sensing satellites) and the second one located below the first layer and extending to the rooting depth of the vegetation (about 60–150 cm). The most important water exchange between the two soil layers is infiltration, while processes such as lateral flow and capillary rise are neglected. The two soil moisture layers are linked by a simplified soil moisture balance equation, as shown in Equation (9):

$$n_1{Z}_{r1}y\left(t\right)=n_1{Z}_{r1}\left[s_1\left(t\right),\right.\left.t\right]=n_1{Z}_{r1}\left\{\begin{array}{c}\left(s_1\left(t\right)-s_{c1}\right),{ s}_1\left(t\right)\ge s_{c1}\\ 0, s_1\left(t\right)<s_{c1}\end{array}\right.$$

(9)

where $y\left(t\right)$ denotes the saturated infiltration fraction of the lower soil layer, $n_1$ denotes the first soil porosity, $Z_{r1}$ denotes the depth of the first soil layer, $s_1\left({\theta }_1/n_1\right)$ denotes the relative saturation of the first layer (obtained by dividing the water content ${\theta }_1$ by the porosity $n_1$ of the first layer of soil), and $s_{c1}$ denotes the relative saturation of the first field water content. This equation implies that the permeability of the soil is infinite when the relative saturation is higher than any value of the field water content, and the model does not take into account the saturation effect in the lower layer. All parameters of the model can be estimated from soil texture, soil depth, and soil water loss. The specific detailed physical derivation equations of the model are detailed in Manfreda et al. [58].

Manfreda et al. [58] compared SMAR with Expf and demonstrated that SMAR outperformed Expf in arid regions. This is because the SMAR model incorporated the physical relationship of soil moisture between different layers, while Expf only considered the ‘decay effect’ of soil moisture. However, the SMAR method also had some drawbacks. First, it was assumed that when SSM was higher than the field capacity, the lower soil moisture reached saturation, and the possible saturation effect of the lower soil moisture was ignored. Second, it was assumed that the soil water loss function was linear, which might lead to approximation errors for the lower soil moisture estimation. To enhance these defects, Faridani et al. [59] introduced a nonlinear soil water loss function, proposed an improved SMAR model (MSMAR), and found that the model could improve RZSM estimation accuracy. In addition, Baldwin et al. [60] used a neural network to optimize the parameters of the SMAR model regionally and also achieved some effects. However, these improvements also increased the complexity and uncertainty of the model, and in some seasonally wet areas, the SMAR model still performed poorly.

Overall, the SMAR model attempts to establish the relationship between SSM and RZSM through a simple soil physics equation for semi-arid environments, which is to some extent more physically meaningful than the exponential filtering method, although it is based on a physical equation that is more applicable to arid regions, which leads to a significant limitation in its application.

2.3. Physics-Based Methods

Recently, data assimilation, which combines measured or remote sensing data with physical models to continuously update and correct soil moisture state parameters in the model, has emerged as one of the most promising methods for estimating RZSM. As a result, it can estimate RZSM with relative accuracy.

2.3.1. Data Assimilation Methods

Data assimilation methods to estimate soil moisture include direct insertion, statistical correction, optimal interpolation, variational constraint, and sequential data assimilation methods. Among them, variational and sequential data assimilation methods are the most widely used in soil moisture simulation [19].

Variational methods transform the data assimilation problem into a function minimization problem. By controlling variables/parameters, this method can find an optimal solution that minimizes the distance cost function between predicted and observed values while satisfying dynamic constraint limitations. Common variational algorithms include three-dimensional variational data assimilation (3Dvar) [61] and 4Dvar [62]. 4Dvar improves on 3Dvar by considering background field information that changes with time and better captures complex nonlinear constraint relationships. Some business operational data assimilation products generated using the 4Dvar algorithm include the Europe Land Data Assimilation System (ELDAS) [63] and ECMWF Reanalysis v5 (ERA5) [64]. Variational methods are suitable for high-dimensional, nonlinear, and non-Gaussian problems and can use prior information to weight and reduce the impact of observation errors. However, linearizing nonlinear functions can lead to errors, and solving complex models can be computationally expensive.

Sequential data assimilation methods mainly include Kalman filters (KFs) and particle filters (PFs). KFs use the system model and measurements to progressively calculate the probability distribution of the system state, thus obtaining an optimal state estimate [65]. However, in practical applications, many systems are nonlinear and do not satisfy the assumptions of linear systems. In this context, the EKF was proposed Entekhabi et al. [16]. It extends the linear system model of the KF to the nonlinear case and approximates the nonlinear system model using Taylor expansions and linearization. However, the EKF increases computational costs, and its full forward covariance matrix performs poorly in large-scale problems. By comparison, the ensemble Kalman filter (EnKF) can overcome this limitation [66]. The EnKF decomposes the state vector into multiple random variables and uses Monte Carlo methods to solve the probability distribution, making it suitable for high-dimensional nonlinear system problems. Currently, the EnKF is the most popular algorithm in soil moisture data assimilation and has derived a series of EnKF variants such as the augmented ensemble Kalman filter (AenKF) [67,68], the local ensemble transform Kalman filter (LETKF) [69,70], the unscented weighted ensemble Kalman filter (UWEnKF) [71,72], and the error subspace transform Kalman filter (ESTKF) [73]. The advantages of the EnKF algorithm are its computational efficiency, its ability to deal with nonlinear and non-Gaussian problems, and its ability to update model parameters using observed data. However, the EnKF algorithm also has some drawbacks, such as sensitivity to the initial ensemble and the problem that resampling methods may lead to the loss of ensemble diversity and filtering divergence. To solve these problems, some improved resampling methods have been proposed, such as the stratified sampling method [74], the bootstrap sampling method [75], and the hidden parameter ensemble resampling method [76]. These methods can maintain the diversity of the ensemble and improve the stability and accuracy of assimilation.

The KF and its variant algorithms require observation and model errors to be normally distributed, which almost all hydrological applications do not assume. This assumption limits the application of these algorithms to a great extent. To overcome this limitation, PFs [77] have been recommended as alternative methods in hydrological applications. The PF uses discrete particle states to approximate continuous state distributions and updates particle states step by step through importance sampling, resampling, and other methods, making it suitable for various nonlinear and non-Gaussian situations. However, the PF also suffers from problems with particle degeneracy and lack of diversity. Resampling operations can minimize particle degeneracy, and various resampling methods have been developed to overcome particle degeneracy, such as residual resampling, multilinear resampling, weighted random resampling, stratified resampling, and covariance resampling. All of these methods have been proven effective in establishing posterior density, but there are still subtle differences in implementation. To further reduce weight degradation issues in large-scale applications, ref [78] used a variable variance multiplier and Markov chain Monte Carlo method to improve parameter search and developed the Particle Filter–Markov Chain Monte Carlo (PF-MCMC) method. Although the PF-MCMC method can accurately estimate states and parameters, its implementation requires considerable computational resources, which leads to decreased efficiency. Recently, the Evolutionary Particle Filter Method (EPFM), based on genetic algorithms (GAs) and MCMC, was proposed [79]. The EPFM method uses GAs to optimize parameter selection in the PF and uses MCMC to accurately estimate the system state, improving computational efficiency and accuracy. Studies have already demonstrated that the PF and its variants are superior to the EnFF and its variants in simulating soil moisture. Lei et al. [80] demonstrated that the PF yielded better results than the EnKF for most multi-layer soil moisture states and at different depths. Xu et al. [81] compared the accuracy of soil moisture estimation by assimilating SMAP data into a hydrologic model of the Variable Infiltration Capacity (VIC) using two assimilation techniques: the EnKF and EPFM. The results revealed that the EPFM exhibited better correlation and unbiased root-mean-square error (ubRMSE) than the EnKF across most of the validation sites throughout the contiguous United States.

2.3.2. Physical Model of Data Assimilation

There are two main physical models for estimating soil moisture: land surface odels (LSMs) and hydrological models. LSMs simulate the physical, biogeochemical, and radiative processes at the land surface, including vegetation dynamics and boundary layer turbulence transport. LSMs predict interactions between the land and atmosphere and are typically used for large-scale global or regional studies. Hydrological models approximate hydrological phenomena such as evapotranspiration, soil water transport, and surface runoff at a smaller scale than LSMs, typically at the watershed level.

Currently, land surface models (LSMs) are widely used in research on assimilating soil moisture data [19]. Business-oriented, operational assimilation datasets of remote sensing data for soil moisture have been derived from these LSMs [82,83]. Reichle et al. [84] utilized an EnKF to assimilate scanning multichannel microwave radiometer and AMSR-E SSM data into the NASA catchment land surface model, resulting in global estimates of surface and deep soil moisture. Martens et al. [85] incorporated CCI SSM and SMOS SSM data into the Global Land Evaporation Amsterdam Model (GLEAM) using the Newtonian nudging scheme, resulting in multiple versions of global-scale soil moisture products (GLEAM V3). This method can utilize two different SSM data to improve the consistency and comparability of soil moisture estimation. Lievens et al. [86] assimilated Sentinel-1 SAR and SMAP passive microwave brightness temperature data into GLEAM using an ensemble Kalman filter, resulting in global estimates of SMAP passive and active soil moisture at a spatial resolution of 9 km. This method can utilize the advantages of SAR and SMAP data to compensate for their respective deficiencies and improve the accuracy and resolution of soil moisture estimation. Following Lievens et al. [86], the National Aeronautics and Space Administration (NASA) assimilated SMAP brightness temperature data along with land cover, vegetation, and terrain information into GLEAM. This effort resulted in global estimates of SSM and RZSM every three hours (SMAP L4) [87].

The spatial resolution of the data products derived from LSMs assimilation ranges from 3 km to 25 km. This carries valuable insights for studying water cycle dynamics at regional or larger watershed scales, yet it falls short of the scale requirements for precision agriculture. In order to enhance the resolution of the soil moisture assimilation data, two methods are chiefly employed: (1) incorporating downscaled high-resolution soil moisture remotely sensed data. Dumedah et al. [88] utilized Disaggregation based on Physical and Theoretical scale Change (DisPATCh) to downscale SMOS data, before assimilating them into the Joint UK Land Environment Simulator (JULES), effectively generating RZSM data with a spatial resolution of 1 km; (2) assimilating high-resolution remote sensing data such as optical, thermal infrared, or active radar into field-scale hydrological models to estimate high-resolution RZSM. Ahmadi et al. [89] assimilated MODIS and LANDSAT-8 land surface temperature (LST) data into the Hydrus-1D model using the EnKF algorithm to estimate farm-scale vertical soil moisture profiles. Despite apparent bias in the MODIS-LST data, the results show that the RMSE remains within the range of 0.012 to 0.013 cm³/cm³ compared to observed data. The use of different data sources to provide different parameters in the data assimilation process can increase the input variables and constraints of the model and improve the adaptability and stability of the model. Lei et al. [80] used $f_{PET}$, the ratio of actual-to-potential ET or fractional potential ET, derived from thermal infrared (TIR) data to represent the comprehensive availability of root zone water, used SAR to invert SSM, and used KF and PF techniques to assimilate both into the Soil–Vegetation–Atmosphere–Transfer (SVAT) model, obtaining a RZSM dataset with a spatial resolution of 30 m. The study showed that the simultaneous assimilation of $f_{PET}$ and SSM bivariate can achieve higher accuracy than the assimilation of $f_{PET}$ or SSM univariate. Similarly, Chen et al. [90] used SAR-based SSM retrieval and TIR-based ET estimation as data sources and used ET as an indicator variable for RZSM. They combined these data with the EnKF technique and simultaneously assimilated them into a soil moisture balance model. This method produced high-resolution (30 m) daily RZSM data.

In general, the estimation of RZSM has been achieved by assimilating multi-source remote sensing data into physical models, resulting in a series of operational remote sensing products. However, data assimilation is often associated with high computational costs and complexity, and its accuracy is largely dependent on the quality of numerous physical model parameters (such as soil properties, atmospheric forcing, and vegetation cover) [19,91]. Moreover, the mismatch of scale between remote sensing soil moisture data or land surface assimilation soil moisture simulation data and ground-based observation data can also result in significant errors in assessing RZSM [92,93]. Due to the different regionalization methods of different parameters in hydrological models, the spatial scales of regional parameters are inconsistent, which also leads to some difficulties in the spatial scale extension of local models [94].

2.4. Machine Learning Methods

In recent years, with the continuous development of computer science, a series of machine learning algorithms have been applied in the inversion of RZSM [95]. These algorithms have the ability to learn and identify nonlinear relationships between SSM or environmental factors and RZSM, even in the case of discontinuous data. This provides convenience for integrating information from different data sources and processing large amounts of data.

We conducted a thorough literature review of 20 recent publications on machine learning-based estimation of RZSM. In Table 1, we classified and summarized the various methods utilized, the input variables used, the feature extraction techniques employed, the depths considered, and the study areas investigated. Our analysis indicates that the most frequently used machine learning algorithms for RZSM inversion are random forest (RF) and artificial neural networks (ANNs). Bertalan et al. [96] compared the abilities of RF, Elastic Net Regression (ENR), the Generalized Linear Model (GLM), and the Robust Linear Model (RLM) for estimating RZSM, and found that RF had the highest accuracy, followed by ENR, while the GLM had the lowest accuracy. Based on optical and thermal infrared remote sensing data provided by Landsat-8, Cheng et al. [97] employed RF to estimate the multi-layer soil moisture in Beijing, China, and the results showed that RF achieved higher accuracy, with R² ranging from 0.67 to 0.81, and relative root-mean-square error (rRMSE) ranging from 8.74% to 14.68%. Zhu et al. [98] found that the ANN outperformed RF and linear models in RZSM estimation, and they constructed a simple model with only five input variables, which achieved high accuracy (RMSE was 0.039 cm³/cm³, and R² was 0.697). Liu et al. [99] utilized an ANN to estimate the multi-layer (0–50 cm) soil moisture in China, and they achieved an R² ranging from 0.64 to 0.69.

Feature extraction is one of the most crucial steps in data pre-processing. It helps to reduce noise and redundancy in the data, as well as improve both the accuracy and speed of the model. There are three primary classes of feature selection methods: filter, wrapper, and embedded. The filter method selects the most relevant features based on statistical properties, such as correlation with the target variable. Common examples include variance thresholding, Pearson correlation, and mutual information. On the other hand, wrapper methods evaluate different subsets of features by training a model on each subset and selecting the best-performing set based on a specific evaluation metric. Common examples include forward selection, backward elimination, and recursive feature elimination. Embedded methods integrate feature selection into the model training process itself, using feature importance provided by models such as tree models or tree-based ensemble algorithms. The goal is to improve model accuracy by selecting or eliminating features based on their level of importance. Currently, wrapper methods are the most popular feature selection technique for estimating RZSM through machine learning. Babaeian et al. [100] analyzed the impacts of different variable combinations on RZSM estimation. The results showed that the combination of the NDVI, NTR, and physical and hydraulic soil information had the highest accuracy in the model. Furthermore, the addition of SSM to the aforementioned combination as a model input significantly improved the estimation of RZSM. Carranza et al. [101] used a permutation method to study the impact of covariates on RZSM estimation. The results indicated that SSM, soil properties, and land cover type had a significant impact on the accuracy of the RF model, while the influence of meteorological variables was relatively small. Similarly, Yu et al. [102], using the importance function of CatBoost, found that latitude, soil pH, bulk density, DEM, and dew point had high feature importance scores for modeling RZSM, while meteorological variables had low scores.

In summary, machine learning algorithms have significant advantages in processing large amounts of data and establishing surface-to-root zone soil moisture relationship models. They can quickly capture and adapt to complex data features, improving the model's accuracy and efficiency. However, their applicability is affected by the selection of training data, environmental factors, and specific characteristics of the study area, which weakens their ability to extrapolate the results to unobserved regions and predict extreme values. For example, Zeng et al. [103] used an RF model trained based on data from known sites and validated on unsampled sites. They found that the model performs poorly in spatial extrapolation, with an RMSE of 0.052 m³/m³. Especially under extreme drought conditions, the model significantly overestimates soil moisture content. In addition, the physical mechanism of machine learning algorithms is yet to be further clarified.

Table 1. Summary of machine learning methods for RZSM estimation.

Reference	Approach	Input Variables	Spatial and Temporal	Feature Selection Method	Metric	Study Area
[21]	ANN + Hydrus-1D	SSM, T, RH, SR, WS, ET, API, silt, clay, LAI	10 cm, 20 cm, 50 cm	wrapper	R, RMSE	The Lower Great Lakes Basin
[104]	SVM-EnKF	P, T, Rh, Rn, Ws, PET	5 cm, 10 cm, 40 cm, 100 cm	filter	R, RMSE, ubRMSE, bias	The Xiang River Basin
[105]	ANN	NDVI, T, ET, SWI, SSM	30 cm, 40 cm, 50 cm	wrapper	R, RMSE	Global
[106]	EnKF-GP	P, T, Rh, solar radiation	5 cm, 10 cm, 20 cm, 50 cm, 100 cm	/	NSE, MARE, Bias	USA
[22]	ANN	SH, P, S, AT, SR, WS, ET	20 cm, 50 cm	wrapper	R, RMSE, ubRMSE	The United States
[107]	Bay-ANNs	Red, green, blue, NIR, NDVI, EVI, VHI, field capacity	15 cm, 30 cm	wrapper	R, R2, RMSE, MAE	The agricultural field located in Scipio, Millard County, in central Utah
[108]	ANN	SSM	30 cm, 60 cm	/	NSE	Global
[99]	ANN	Climate, soil, topography, cropping pattern	10 cm, 20 cm, 30 cm, 40 cm, 50 cm	wrapper	R2	China
[100]	AutoML	NTR, NDVI, text, BD, OC, θFC, θPWP, Ksat, φ	2 cm, 10 cm, 50 cm	wrapper	NSE, RMSE, rRMSE,	The University of Arizona Maricopa Agricultural Center
[101]	RF, Hydrus-1D	RG, Q, rd, SQ, TN, TX, UG, EV24, LAI, LAI_lag, RG_lag, Q_lag, rd_lag, SQ_lag, TN_lag, TX_lag, UG_lag, E24_lag, DOY, crop	10 cm, 20 cm, 40 cm	wrapper	R2, RMSE, rRMSE, bias	Raam catchment
[109]	XGB	P, LST, NDVI, EVI, GPP, sand, silt, clay, BD, elevation, SSM	10 cm, 20 cm, 50 cm	filter, wrapper	R, ubRMSE, bias	The United States
[110]	SVM-SWOA	T, RH, solar, P, sped, ST, growing degree days	30 cm, 60 cm, 120 cm	filter	MAE, RMSE, MAPE, and MBE	Iowa, USA
[102]	CatBoost	Meteorology, soil physical and chemical properties, DEM, lng, lat	10 cm, 20 cm, 30 cm, 40 cm, 50 cm	wrapper, embedded	R2, RMSE, MAE, MSE, MAPE	The main maize production areas in China
[97]	RF	Multispectral, thermal	10 cm, 20 cm, 40 cm, 60 cm, 80 cm	wrapper	R2, RMSE, rRMSE	Beijing, China
[95]	Hydrus-1D + ConvLSTM	P, T, soil BD, SOM content, ET, NDVI, LAI, and upper soil moisture	10–40 cm	filter	R2: 0.31	The Hailar river basin, China
[111]	ANFIS-WOA, ANFIS-KHA, ANFIS-FA	T, RH, WS, ST	20 cm, 30 cm	wrapper	RMSE, MAPE	The northwest of Turkey and the Strait of Istanbul
[98]	MLR, RF, ANN	Ts × lnd, ET, PET, A, NDVI, BD, Ks, clay, sand, SOC	0~5 m	filter, wrapper	R2, RMSE, MAPE	Loess Plateau
[112]	PLSR, KNN, RF	RGB, multispectral, thermal	10 cm, 20 cm	wrapper	R2, RMSE, rRMSE	Ordos, Inner Mongolia Autonomous Region, China
[113]	RF, ANN, DBN, RNN, LSTM, attention-LSTM	P, LST, NDVI, sand, silt, clay, elevation, albedo	10 cm, 20 cm, 40 cm	wrapper	R, RMSE, ubRMSE, MAE, bias	Tibetan
[114]	RF, SVM, ELM	Vegetation indices	10 cm, 20 cm, 30 cm, 40 cm, 60 cm	embedded	R2, rRMSE, RMSE, MAE, GPI	Wugong County, Xianyang City, Shaanxi Province, NW China

Table 1. Summary of machine learning methods for RZSM estimation.

Reference	Approach	Input Variables	Spatial and Temporal	Feature Selection Method	Metric	Study Area
[21]	ANN + Hydrus-1D	SSM, T, RH, SR, WS, ET, API, silt, clay, LAI	10 cm, 20 cm, 50 cm	wrapper	R, RMSE	The Lower Great Lakes Basin
[104]	SVM-EnKF	P, T, Rh, Rn, Ws, PET	5 cm, 10 cm, 40 cm, 100 cm	filter	R, RMSE, ubRMSE, bias	The Xiang River Basin
[105]	ANN	NDVI, T, ET, SWI, SSM	30 cm, 40 cm, 50 cm	wrapper	R, RMSE	Global
[106]	EnKF-GP	P, T, Rh, solar radiation	5 cm, 10 cm, 20 cm, 50 cm, 100 cm	/	NSE, MARE, Bias	USA
[22]	ANN	SH, P, S, AT, SR, WS, ET	20 cm, 50 cm	wrapper	R, RMSE, ubRMSE	The United States
[107]	Bay-ANNs	Red, green, blue, NIR, NDVI, EVI, VHI, field capacity	15 cm, 30 cm	wrapper	R, R2, RMSE, MAE	The agricultural field located in Scipio, Millard County, in central Utah
[108]	ANN	SSM	30 cm, 60 cm	/	NSE	Global
[99]	ANN	Climate, soil, topography, cropping pattern	10 cm, 20 cm, 30 cm, 40 cm, 50 cm	wrapper	R2	China
[100]	AutoML	NTR, NDVI, text, BD, OC, θFC, θPWP, Ksat, φ	2 cm, 10 cm, 50 cm	wrapper	NSE, RMSE, rRMSE,	The University of Arizona Maricopa Agricultural Center
[101]	RF, Hydrus-1D	RG, Q, rd, SQ, TN, TX, UG, EV24, LAI, LAI_lag, RG_lag, Q_lag, rd_lag, SQ_lag, TN_lag, TX_lag, UG_lag, E24_lag, DOY, crop	10 cm, 20 cm, 40 cm	wrapper	R2, RMSE, rRMSE, bias	Raam catchment
[109]	XGB	P, LST, NDVI, EVI, GPP, sand, silt, clay, BD, elevation, SSM	10 cm, 20 cm, 50 cm	filter, wrapper	R, ubRMSE, bias	The United States
[110]	SVM-SWOA	T, RH, solar, P, sped, ST, growing degree days	30 cm, 60 cm, 120 cm	filter	MAE, RMSE, MAPE, and MBE	Iowa, USA
[102]	CatBoost	Meteorology, soil physical and chemical properties, DEM, lng, lat	10 cm, 20 cm, 30 cm, 40 cm, 50 cm	wrapper, embedded	R2, RMSE, MAE, MSE, MAPE	The main maize production areas in China
[97]	RF	Multispectral, thermal	10 cm, 20 cm, 40 cm, 60 cm, 80 cm	wrapper	R2, RMSE, rRMSE	Beijing, China
[95]	Hydrus-1D + ConvLSTM	P, T, soil BD, SOM content, ET, NDVI, LAI, and upper soil moisture	10–40 cm	filter	R2: 0.31	The Hailar river basin, China
[111]	ANFIS-WOA, ANFIS-KHA, ANFIS-FA	T, RH, WS, ST	20 cm, 30 cm	wrapper	RMSE, MAPE	The northwest of Turkey and the Strait of Istanbul
[98]	MLR, RF, ANN	Ts × lnd, ET, PET, A, NDVI, BD, Ks, clay, sand, SOC	0~5 m	filter, wrapper	R2, RMSE, MAPE	Loess Plateau
[112]	PLSR, KNN, RF	RGB, multispectral, thermal	10 cm, 20 cm	wrapper	R2, RMSE, rRMSE	Ordos, Inner Mongolia Autonomous Region, China
[113]	RF, ANN, DBN, RNN, LSTM, attention-LSTM	P, LST, NDVI, sand, silt, clay, elevation, albedo	10 cm, 20 cm, 40 cm	wrapper	R, RMSE, ubRMSE, MAE, bias	Tibetan
[114]	RF, SVM, ELM	Vegetation indices	10 cm, 20 cm, 30 cm, 40 cm, 60 cm	embedded	R2, rRMSE, RMSE, MAE, GPI	Wugong County, Xianyang City, Shaanxi Province, NW China

3. Discussion

3.1. Comparison of RZSM Estimate Methods

We selected four typical referenced methods for estimating RZSM and summarized the input remote sensing data, spatial resolution, temporal resolution, depth, accuracy, and study area for each method in Table 2. And, in the following, the differences in accuracy, efficiency, complexity, and RZSM estimation depth are fully discussed.

3.1.1. Accuracy

Among the four methods, the empirical statistical method has the worst accuracy. Compared with multiple linear regression, machine learning (RF and ANN) showed better accuracy in predicting RZSM in the Loess Plateau, China, but the study also pointed out that multiple linear regression could provide more explicit equations with relatively acceptable accuracy (RMSE = 0.043, R² = 0.625, MAPE = 25.9), making it more conducive to widespread application [98]. In cold mountainous areas, it was found that CDF exhibited lower performance compared to machine learning and ExPF, and the gap in accuracy between CDF and the latter two methods increased with soil depth [41].

Compared with physical models, machine learning methods can easily describe the relationship between SSM and RZSM and provide higher estimation accuracy. Carranza et al. [101] demonstrated that the overall accuracy of RF in estimating RZSM was superior to the overall accuracy of the physical model (Hydrus-1D), but RF had inferior prediction accuracy in extreme values compared to the physical model. Kornelsen et al. [21] estimated the soil moisture in the 10, 20, and 50 cm soil layers of the study area using SSM and meteorological information as ANN input variables, and Hydrus-1D generated soil moisture as output variables. The results showed that the ANN could represent well the simulated soil moisture by Hydrus-1D, but the ANN had weaker transferability and poorer accuracy in untrained stations.

Compared to existing data assimilation products, ExpF has demonstrated superior performance in different regions. Yang et al. [115] used SSM from SMAP L3 and applied an exponential filter to estimate RZSM in agricultural areas of eastern China. The study indicated that the estimated soil moisture exhibited higher accuracy than the RZSM provided by ERA5, with an NSE of 0.78 and an RMSE of 0.1 m³/m³. Grillakis et al. [56] used the ESA CCI soil moisture product, soil properties, climate characteristics, and vegetation index to calibrate the regional soil water index (SWI) and generate soil moisture in the root zone using artificial neural networks (ANNs). The results showed good consistency compared to the soil moisture products provided by the European Center for Medium-Range Weather Forecasts (ECMWFs), ERA5 Land, and the Famine Early Warning Systems Network land data assimilation system.

Moreover, machine learning methods also showed certain advantages compared to existing data assimilation products. Pan et al. [22] used an ANN to estimate soil moisture at 20 cm and 50 cm soil depths in the continental United States, and the overall accuracy of this method is comparable to the root zone soil moisture products derived from SMOS and Noah Joint Inversion. Karthikeyan et al. [109] predicted multi-layer (5 cm, 10 cm, 20 cm, 50 cm, and 100 cm) soil moisture in the continental United States using SSM, soil properties, vegetation indices, temperature, and terrain as input variables for XGBoost. The results indicated that most sites had an estimated root zone soil moisture accuracy with an RMSE of less than 0.04 cm³/cm³, which is better than the existing remote sensing root zone soil moisture product (SMAP L4 SM).

However, ExpF showed better performance than machine learning methods. Tian et al. [41] conducted a study in high-altitude cold areas, which demonstrated that ExpF can best capture the temporal variation of soil moisture in the root zone compared to machine learning approaches. Zhang et al. [116] compared three methods (ANN, LR, and ExpF) for vertically extrapolating SSM and estimating RZSM. They found that ExpF was better than ANN and LR in capturing the relative variability and correlation between soil moisture at different depths.

To sum up, the accuracy of different RZSM estimation methods varies depending on the region and condition, but in general, semi-empirical methods (ExpF) > machine learning methods > physics-based methods > empirical methods is a fair accuracy order.

3.1.2. Efficiency and Complexity

Empirical statistical methods only consider the statistical relationship between RZSM and SSM or between multiple atmospheric forcing variables. This approach is simple to calculate and shows the lowest complexity and the highest efficiency. Machine learning methods establish a relationship model between data and soil moisture achieve inversion through a large amount of data training and do not require complex physical models. However, reliable data are needed for training and validation, and the complexity is relatively low, but the calculation time is relatively long. Semi-empirical methods are based on empirical statistical methods and introduce some simplified physical equations or assumptions to simulate the physical processes of soil moisture movement, such as water diffusion from the surface layer to the root zone and water loss in the root zone. The semi-empirical method has a higher complexity than the empirical statistical method due to the consideration of some physical processes of soil moisture movement, but its computational efficiency is higher than the physical model due to the simplification of the complex physical processes. Data assimilation is a method of fusing multiple data sources, which can integrate the advantages of physical models and empirical statistical methods to improve the accuracy and reliability of inversion. But this method has the highest complexity, and consideration should be given to multiple factors, such as data quality and fusion algorithms with a relatively large amount of computation and lower efficiency. Therefore, efficiency is ranked as experience-based statistical > semi-empirical > machine learning > data assimilation, while complexity is ranked as data assimilation > semi-empirical > machine learning > experience-based statistical.

3.1.3. Depth

Compared to other methods, the estimation of RZSM based on physical models has certain limitations. Physical models rely on the soil moisture conservation equation and soil moisture transport theory, which limit the depth of estimation. Most physical models can estimate soil moisture depths of up to 2–3 m. However, empirical and machine learning methods do not involve soil moisture transfer processes in the estimation process and rely solely on statistical relationships. As such, the depth of soil moisture estimation primarily depends on the given depth of soil moisture and can be unlimited.

Table 2. Summary of methods for RZSM estimation.

Reference	Method	Remote Sensing Data	Spatial Resolution	Time Scale	Depth	Accuracy	Study Area
[26]	Statistical regression	MODIS	500 m	2017	20 cm	R: 0.73; RMSE: 0.034; MAE: 0.025	The Chinese Loess Plateau
[27]	Statistical regression	MODIS	500 m	2013–2014	40 cm	R: 0.77	Beijing
[117]	Data assimilation	SMAP L4	9 km	2015–present; daily	100 cm	ubRMSD: 0.027 m3/m3	Global
[118]	Data assimilation	GLEAM 3.5b	0.25°	1980–present;1 day	0–10, 10–100 cm	ubRMSE: 0.026 m3/m3	Tibetan Plateau
		GLDAS 2.2	0.25°	2003–present;1 day	0–10, 10–40, 40–100, 100–200 cm	ubRMSE: 0.021 m3/m3	Tibetan Plateau
		ERA5	0.25	1979–present; 1 h	0–7, 7–28, 28–100, 100–289 cm	ubRMSE: 0.015 m3/m3	Tibetan Plateau
[119]	ExpF	ESA CCI	0.25°	2015–2018, 2019–2021	0–100 cm	ubRMSE: 0.05 m3/m3	Jiangsu province, China
	Data assimilation	SMAP-L4	9 km			ubRMSE: 0.01 m3/m3
[120]	ExpF	SMOS-BEC SWI (TSMAP)	1 km	2015–2016; 1 daily	100 cm	Coordinate root-mean-square deviation (cRMSD): 0.039	The Soil Moisture Measurements Station Network of the University of Salamanca
		SMOS-BEC SWI (TSMOS)				cRMSD: 0.037
		MODIS ATI SWI (TSMAP)				cRMSD: 0.022
		MODIS ATI SWI (TSMOS)				cRMSD: 0.021
		SMAP L4 RZSM				cRMSD: 0.020
		SMOS-CESBIO L4 RZSM				cRMSD: 0.028
[88]	Data assimilation	SMOS	1 km	2010	0–30 cm; 30–60 cm; 60–90 cm	RMSE: 0.071; 0.058; 0.067 m3/m3	The western plains of New South Wales, Australia
[100]	Machine learning	UAS multispectral	1280 × 960 pixels	2017	2 cm, 10 cm, 50 cm	RMSE: 0.02 m3/m3; R: 0.9	The University of Arizona Maricopa Agricultural Center

Table 2. Summary of methods for RZSM estimation.

Reference	Method	Remote Sensing Data	Spatial Resolution	Time Scale	Depth	Accuracy	Study Area
[26]	Statistical regression	MODIS	500 m	2017	20 cm	R: 0.73; RMSE: 0.034; MAE: 0.025	The Chinese Loess Plateau
[27]	Statistical regression	MODIS	500 m	2013–2014	40 cm	R: 0.77	Beijing
[117]	Data assimilation	SMAP L4	9 km	2015–present; daily	100 cm	ubRMSD: 0.027 m3/m3	Global
[118]	Data assimilation	GLEAM 3.5b	0.25°	1980–present;1 day	0–10, 10–100 cm	ubRMSE: 0.026 m3/m3	Tibetan Plateau
		GLDAS 2.2	0.25°	2003–present;1 day	0–10, 10–40, 40–100, 100–200 cm	ubRMSE: 0.021 m3/m3	Tibetan Plateau
		ERA5	0.25	1979–present; 1 h	0–7, 7–28, 28–100, 100–289 cm	ubRMSE: 0.015 m3/m3	Tibetan Plateau
[119]	ExpF	ESA CCI	0.25°	2015–2018, 2019–2021	0–100 cm	ubRMSE: 0.05 m3/m3	Jiangsu province, China
	Data assimilation	SMAP-L4	9 km			ubRMSE: 0.01 m3/m3
[120]	ExpF	SMOS-BEC SWI (TSMAP)	1 km	2015–2016; 1 daily	100 cm	Coordinate root-mean-square deviation (cRMSD): 0.039	The Soil Moisture Measurements Station Network of the University of Salamanca
		SMOS-BEC SWI (TSMOS)				cRMSD: 0.037
		MODIS ATI SWI (TSMAP)				cRMSD: 0.022
		MODIS ATI SWI (TSMOS)				cRMSD: 0.021
		SMAP L4 RZSM				cRMSD: 0.020
		SMOS-CESBIO L4 RZSM				cRMSD: 0.028
[88]	Data assimilation	SMOS	1 km	2010	0–30 cm; 30–60 cm; 60–90 cm	RMSE: 0.071; 0.058; 0.067 m3/m3	The western plains of New South Wales, Australia
[100]	Machine learning	UAS multispectral	1280 × 960 pixels	2017	2 cm, 10 cm, 50 cm	RMSE: 0.02 m3/m3; R: 0.9	The University of Arizona Maricopa Agricultural Center

3.2. Limitations of the Current Methods

3.2.1. Limitations of Remote Sensing Data

Remote sensing technology provides measurements of SSM but cannot directly measure RZSM. Indirect measurement of RZSM can be achieved through the inversion of SSM obtained using optical and microwave remote sensing. However, SSM measurements derived from remote sensing are influenced by various factors. The inversion method based on optical remote sensing is mainly affected by vegetation cover, light conditions, and vegetation type, impacting the accuracy of RZSM inversion. In contrast, the inversion method based on microwave remote sensing is not affected by factors, such as vegetation cover and light conditions, and is suitable for highly vegetated areas. Nevertheless, the low spatial resolution of microwave remote sensing hinders the accurate capturing of small-scale soil moisture changes, introducing uncertainty into the inversion. These uncertainties in data sources contribute to errors in the accuracy of RZSM inversion.

3.2.2. Uncertainty of In Situ Observation

Although there are limitations in the accuracy and representativeness of in situ observation, in situ observation of soil moisture is essential for modeling and validation of RZSM inversion. However, there are various uncertainties in in situ observation of soil moisture such as spatial and temporal variability, sampling error, measurement error, data processing error, and the influence of soil depth and root distribution. These factors make it difficult for in situ measurements to accurately reflect the soil moisture situation in the whole region and limit the accuracy and reliability of the measured data.

3.2.3. Uncertainty of the RZSM Estimation Method

Remote sensing-based inversion of RZSM is a very complex process, and its quantification process may have errors. The parameters and assumptions of these models described in the paper may have uncertainties, thus introducing model errors. Model errors may arise from aspects such as imperfect model parameterization and uncertainty in model input data. For example, under extreme drought events, SSM is decoupled from RZSM, and the method of estimating RZSM by relying only on the statistical relationship between the surface layer and the root zone will no longer be practical.

4. Conclusions and Outlook

RZSM is a crucial environmental variable that impacts climate-related hydrological processes in agriculture. Remote sensing technology can provide spatiotemporal continuous SSM, but it cannot reflect the changes of RZSM. Even RZSM remote sensing products produced by data assimilation or data fusion still suffer from low spatial resolution (ranging from several kilometers to tens of kilometers). This limitation greatly restricts their application in agriculture, ecology, and hydrology. In order to obtain high-resolution and high-precision RZSM remote sensing products, several methods have been developed and evaluated, which estimate RZSM by inverting surface information derived from remote sensing data. In this paper, we provide a comprehensive review of these methods, highlighting their respective advantages and disadvantages. Despite the progress made over the past decades, it is crucial to address the limitations and uncertainties of these methods in future research.

(1) Regional agricultural applications require soil moisture products with high spatial and temporal resolution in the root zone. To obtain at least daily frequencies, temporal extrapolation methods are needed to avoid the influence of clouds on optical/thermal observations and the low temporal resolution of microwave data.

(2) The fusion of multi-source remote sensing data and multiple algorithms to improve the accuracy and reliability of remote sensing inversion of RZSM. The joint multi-sensor inversion algorithm can integrate data from different sensors and effectively use various information sources, thus improving the accuracy and robustness of remote sensing inversion of RZSM, especially for areas with complex topography and land cover. In addition, to further improve the performance of remote sensing inversion of RZSM, the strategy of fusing different models and methods can be used. For example, physically guided machine learning models based on physical mechanisms can be developed by fusing physical mechanism models with machine learning [105], and machine learning can also be combined with data assimilation methods [121,122,123] to achieve an improvement of RZSM prediction accuracy.

(3) The accuracy of RZSM depends on the input satellite data and the estimation method. On the one hand, the accuracy of input data, such as satellite-based soil moisture products, needs to be improved. On the other hand, the uncertainty of RZSM estimation needs to be quantified by in situ soil moisture observations. Intercomparison of different RZSM estimation methods based on constructed synthetic datasets that are rich in variability in spatial and temporal heterogeneity and patterns of soil moisture will help to determine the applicability of each method under certain conditions.

(4) The P-band wavelengths (250–500 MHz) are capable of penetrating the ground to a depth of 40 cm or even deeper into the soil layer. This characteristic allows for better circumvention of the effects of vegetation cover and increases the likelihood of obtaining accurate soil moisture measurements in forested areas. Two notable initiatives that contribute to this field are the ESA’s P-band SAR BIO MASS [124], which is set to be launched in 2023, and NASA’s SNoOPI (Signals of Opportunity) program [125]. These programs aim to provide direct access to RZSM opportunities through remote sensing techniques. With the increasing number of satellites and in situ measurements, there is a growing opportunity for advancements in RZSM estimation methods and the establishment of synergies with new satellite data. These developments are crucial for the creation of actionable and high-quality RZSM products.

In conclusion, a combination of all available data sources is needed in order to generate highly accurate RZSM products. Future research in this field could generate long-term, time continuous, and operational RZSM datasets with high spatial and temporal resolution.