An AI-Based Nested Large–Small Model for Passive Microwave Soil Moisture and Land Surface Temperature Retrieval Method

Abstract

Retrieving soil moisture (SM) and land surface temperature (LST) provides crucial environmental data for smart agriculture, enabling precise irrigation, crop health monitoring, and yield optimization. The rapid advancement of Artificial intelligence (AI) hardware offers new opportunities to overcome the limitations of traditional geophysical parameter retrieval methods. We propose a nested large–small model method that uses AI techniques for the joint iterative retrieval of passive microwave SM and LST. This method retains the strengths of traditional physical and statistical methods while incorporating spatiotemporal factors influencing surface emissivity for multi-hierarchical classification. The method preserves the physical significance and interpretability of traditional methods while significantly improving the accuracy of passive microwave SM and LST retrieval. With the use of the terrestrial area of China as a case, multi-hierarchical classification was applied to verify the feasibility of the method. Experimental data show a significant improvement in retrieval accuracy after hierarchical classification. In ground-based validation, the ascending and descending orbit SM retrieval models 5 achieved MAEs of 0.026 m³/m³ and 0.030 m³/m³, respectively, improving by 0.015 m³/m³ and 0.012 m³/m³ over the large model, and 0.032 m³/m³ and 0.028 m³/m³ over AMSR2 SM products. The ascending and descending orbit LST retrieval models 5 achieved MAEs of 1.67 K and 1.72 K, respectively, with improvements of 0.67 K and 0.49 K over the large model, and 0.57 K and 0.56 K over the MODIS LST products. The retrieval model can theoretically be enhanced to the pixel level, potentially maximizing retrieval accuracy, which provides a theoretical and technical basis for the parameter retrieval of AI passive microwave large models.

1. Introduction

In the rapidly evolving technological landscape, generative AI technologies, like ChatGPT 4, are driving unprecedented advancements and introducing innovative methods for geophysical parameter retrieval. The integration of AI with remote sensing provides novel solutions. This fusion of technologies heralds not only novel products but also a fundamental transformation in geophysical retrieval models, greatly enhancing retrieval accuracy. In agricultural ecosystems, soil moisture and surface temperature are key factors that directly affect crop growth and yield. Studying the dynamic changes in these parameters and their effects on agricultural production is crucial for creating effective management strategies, improving crop resilience, and safeguarding food security. Despite advancements, considerable room remains for improving the accuracy of soil moisture and land surface temperature retrieval through passive microwave remote sensing. Thus, integrating AI with passive microwave remote sensing undoubtedly represents a new breakthrough, deserving ongoing focus and in-depth research.

In recent decades, satellite remote sensing, with global coverage and high-precision monitoring, has become essential for observing soil moisture and land surface temperature over large spatial scales and extended time periods. It meets the demand for both spatial and temporal measurements, offering broader applications compared to point-based measurements. Algorithms using thermal infrared and visible light for surface parameter retrieval are heavily affected by weather conditions. For example, analysis of NASA’s land surface temperature products shows that over 60% of the data are affected by cloud cover, significantly limiting practical applications. In contrast, microwave remote sensing, with its ability to penetrate clouds, rain, and the atmosphere, has distinct advantages over visible light and infrared sensing, which are more vulnerable to atmospheric interference. As a result, passive microwave technology is widely used for monitoring and retrieving soil moisture and land surface temperature [1,2]. In the microwave band, the dielectric constant is crucial for controlling emissivity, with soil moisture having the greatest impact on it [3]. Therefore, passive microwave technology, highly sensitive to soil moisture, has been successfully applied in its monitoring [3,4,5]. Passive microwave soil moisture retrieval methods are currently classified into three categories. The first category includes empirical models, such as the Normalized Polarization Difference (NPD) for approximating soil moisture, and more comprehensive multi-parameter algorithms considering soil, vegetation, and atmospheric conditions [6,7]. The second category includes physical models and statistical methods, such as the τ-ω model based on microwave radiative transfer equations, which accounts for soil dielectric constant, surface roughness, and vegetation effects [8]. Additionally, the Single-Channel Algorithm (SCA) focuses on the frequency/polarization channel most sensitive to soil moisture [9,10], while the Land Parameter Retrieval Model (LPRM) includes atmospheric contributions to enhance accuracy under varying conditions [11,12]. The SMRFM model integrates MODIS optical/thermal infrared data with passive microwave data, using a least squares method for spatiotemporal soil moisture fusion [13]. Additionally, the use of EnKF to assimilate passive microwave soil moisture data improves the estimation accuracy of land surface variables [14]. The third category consists of neural network algorithms, evolving from neural network models based on microwave radiation transfer [15] to the use of CNN, GRNN, and BPNN models for high-precision soil moisture retrieval [16,17,18].

Passive microwave technology encounters major challenges in retrieving land surface temperature, primarily due to complex surface thermal radiation mechanisms and the low spatial resolution inherent to microwave sensors. Compared to soil moisture, satellite-based brightness temperature from passive microwaves is less sensitive to surface temperature variations, leaving significant room for improving retrieval accuracy [1,19,20]. Methods for retrieving land surface temperature via passive microwave technology are broadly classified into three categories. The first category includes empirical models that use multiple regression to establish relationships between brightness temperature data and land surface temperatures observed on the ground [21]. The second category consists of physical and statistical models, including single-channel [22] and multi-channel [23] algorithms, which estimate emissivity via simplified radiative transfer and empirical equations. The third category involves neural network algorithms, which mainly use brightness temperature data as input for models like ANNs, CNNs, and DBNs [24,25,26,27]. These algorithms have evolved by incorporating vegetation, surface parameters, and atmospheric water vapor as prior knowledge to improve land surface temperature retrieval accuracy [28,29,30]. Neural network algorithms, with powerful computational capabilities, handle nonlinear calculations and achieve near-optimal solutions. However, the relationships between input variables and output parameters, as well as the computational processes in hidden layers, need further clarification. While incorporating prior knowledge theoretically improves retrieval accuracy, it may introduce new sources of error. Moreover, the training and testing data for these models rely mainly on statistical sampling, limiting their general applicability.

These methods provide a variety of options for retrieving soil moisture and land surface temperature. Each algorithm has distinct advantages in simplicity, comprehensiveness, and adaptability to different conditions, but also has specific limitations due to assumptions about atmospheric contributions, vegetation effects, and computational demands. Empirical equations often become inaccurate when applied to large datasets, leading to reduced retrieval capabilities [31]. Additionally, statistical methods are typically limited to specific localized regions [32]. Traditional algorithms mainly rely on the relationship between input variables and output parameters from empirical equations to solve the Radiative Transfer Equation (RTE), ensuring interpretability and physical consistency in the retrieval process. Mao et al. introduced a geophysical parameter retrieval theory that integrates deep learning with physical and statistical methods, based on physical logic derivation [19,33,34]. Their MDK-CR algorithm, which jointly retrieves soil moisture and land surface temperature by treating them as mutual prior knowledge, represents a major technical breakthrough. This fully coupled method addresses the limitations of previous algorithms while effectively combining the strengths of physical methods and neural networks, enabling deep learning with physical interpretability.

Although passive microwave technology is relatively unaffected by clouds and rain, its low spatial resolution and complex internal structure remain challenging. As a result, the accuracy of AI-based soil moisture (SM) and land surface temperature (LST) retrieval using passive microwave data still needs improvement. This study used a tree structure for the multi-hierarchy classification of the study area, based on the spatiotemporal characteristics of geographic factors influencing surface emissivity. Additionally, in adopting the fine-tuning strategy, small models were generated at each node in every hierarchy. Based on this approach, we propose a nested large–small model method for retrieving soil moisture and land surface temperature from passive microwave data. In this method, we use neural networks coupled with physical and statistical methods to jointly retrieve SM and LST, treating them as mutual prior knowledge. Simultaneously, factors like topography, seasonality, vegetation, and soil type, which influence surface emissivity, were used as control conditions to divide the study area into a multi-level hierarchical tree structure. The small models in each hierarchy were fine-tuned or retrained using corresponding multi-source data to ensure accuracy. These small models adjust surface emissivity within specific regions, improving retrieval accuracy while ensuring regional applicability and generalization.

2. Methodology

The soil moisture and land surface temperature joint retrieval method integrates artificial intelligence, physical, and statistical methods, creating a closed system of equations that describe the relationships between input variables and output parameters. Physical methods form functional relationships using simulated data from physical models to solve specific scenarios. However, simulated data have limitations, and multi-source data from statistical methods can complement the analysis of more complex situations. Neural networks, as optimization tools, can efficiently combine physical and statistical methods to update and refine these functional relationships. By the radiative transfer equation, the relationships between SM, LST, and land surface emissivity (LSE) are clarified, providing a theoretical basis for retrieval. LSE accuracy is influenced by various surface and spatiotemporal factors and is critical for SM and LST retrieval. Considering the factors affecting LSE, the study area is classified into hierarchical levels using a tree structure, with the secondary study areas at each hierarchical level constructing a multi-source database for training and testing iterative models in neural networks. Through fine-tuning or retraining, an effective nested large–small model structure is developed. This hierarchical approach to prior knowledge effectively reduces roughness interference in SM and LST retrieval and prevents new errors from direct prior knowledge input. This method improves retrieval accuracy while retaining the advantages of physical and statistical methods, enhancing the neural network’s physical significance and interpretability.

The specific steps are shown in Figure 1. Firstly, expert knowledge (including physical theoretical models, semi-empirical physical models, and empirical statistical models.) was used to derive soil moisture and surface temperature retrieval mechanisms from radiation transfer processes in soil, vegetation, atmosphere, and satellites. Secondly, a generalized statistical method was constructed through the radiative transfer pathway to link brightness temperature with soil moisture (SM) and land surface temperature (LST). Remote sensing, assimilation, and ground-based observation data were compiled into a multi-source statistical dataset, which provided training and testing samples for the neural network, integrating physical and statistical methods through big data fusion. Thirdly, factors affecting surface emissivity were used to develop a hierarchical classification system, forming a multi-level, tree-structured classification across the study area. Based on Parts 1 and 2 in Figure 1, multi-source databases were created in part 3 in each sub-region as neural network training and testing sets. The hierarchical models form a nested large-small model structure. Fourthly, a joint iterative retrieval model in part 4 for SM and LST was built using neural networks, with each model employing the other as prior knowledge. Iteration continues until retrieval accuracy reaches a threshold, achieving optimal soil moisture and surface temperature values. Finally, retrieval results are evaluated in part 5 by comparing them to product data and ground observations. If requirements are met, the model is retained; otherwise, part 4 is repeated for retraining.

3. Data and Method

3.1. Data

The training and testing datasets were generated through the fusion of multi-source data.

Table 1. Multi-source data information.

Data Type	Name	Source	Resolution
Remote Sensing Data	AMSR 2 BTs	Aqua (JAXA)	0.1 Deg
	AMSR 2 SMC	Aqua (JAXA)	0.1 Deg
	MYD11C1	Aqua (MODIS)	0.05 Deg
Simulation Data	AIEM Simulation Data	Advanced Integral Equation Model
	M-D Simulation Data	Matrix Doubling Model
Assimilation Data	ERA5	ECMWF	0.1 Deg
	CLDAS	China Land Data Assimilation System	0.0625 Deg
Ground Data	Meteorological Station Data	National Meteorological Science Data Center	Point Data

lists the multi-source data used, including simulated data from physical models, remote sensing imagery, ground observation data, and assimilation products. Multi-source data fusion is crucial to this study, utilizing these multi-source datasets provides more complete and accurate information, enhancing the understanding and retrieval capabilities of soil moisture and land surface temperature. The following is a detailed explanation of the multi-source data used.

3.1.1. Remote Sensing Data

In the passive microwave retrieval method for soil moisture and land surface temperature, AMSR 2 brightness temperature was used as an independent variable (input). AMSR 2 (Advanced Microwave Scanning Radiometer 2) is mounted on the Japan Aerospace Exploration Agency (JAXA) satellite, “Global Change Observation Mission-Water (GCOM-W1)”, which was successfully launched in 2012 to acquire surface microwave brightness temperature data. Currently, two main types of AMSR 2 SM products are available: the official soil moisture product generated by JAXA using a lookup table algorithm and the product created by the University of Amsterdam using the Land Parameter Retrieval Model (LPRM) algorithm. We obtained JAXA L3 brightness temperature data and soil moisture data with a spatial resolution of approximately 10 km (0.1°) from JAXA’s official website (gportal.jaxa.jp). The AMSR 2 brightness temperature data include observation frequencies of 6.9 GHz, 10.65 GHz, 18.7 GHz, 23.8 GHz, 36.5 GHz, 89 GHz, and the newly added 7.3 GHz, totaling 14 channels in both horizontal (H) and vertical (V) polarizations. These data have been widely recognized and used [35,36].

The land surface temperature data used in the retrieval method were sourced from the Moderate Resolution Imaging Spectroradiometer (MODIS) (MYD11C1), with a spatial resolution of 0.05°. MODIS is mounted on the Terra and Aqua satellites [37], which orbit the Earth at fixed times. Terra crosses the equator north to south at 10:30 AM local time, while Aqua crosses south to north at 1:30 PM local time. Both satellites update their ascending and descending orbits twice daily. MODIS land surface temperature data include quality indicators, and their accuracy is widely recognized and applied in various fields [38,39].

Since AMSR 2 is also mounted on the Aqua satellite, using its data alongside MYD11C1 for training and testing can effectively avoid errors caused by differences in temporal scale, requiring only consideration of differences in spatial resolution. Upscaling the MYD11C1 data to a 0.1° spatial resolution enables the daily retrieval of remote sensing data with consistent brightness temperature, soil moisture, and land surface temperature at the same time and spatial resolution.

3.1.2. Simulation Data of AIEM and M-D

The Advanced Integral Equation Model (AIEM) [40,41] and the Matrix Doubling (M-D) model [42] were employed to generate simulated data for soil moisture and land surface temperature. The AIEM was developed from the Integral Equation Model (IEM), while the M-D model provides high accuracy in simulating soil moisture, as its retrieval algorithm accounts for multiple scattering within vegetation and between vegetation and the surface. In this study, both models were applied under specific conditions (0.5 cm < $sig$ < 3.5 cm, 3 cm < $cl$ < 35 cm, 0.02 < $SM$ < 0.45, 270 K < $LST$ < 325 K) to simulate the relationship between brightness temperature, soil moisture, and land surface temperature. The simulation data are primarily used to assist in the collection of remote sensing data and to generate statistical data, thereby helping to validate and calibrate the accuracy of the remote sensing data. Comparing simulated data with remote sensing data allows for the assessment of remote sensing data quality and the study of relationships between soil moisture and land surface temperature under different conditions. This improves the understanding of soil moisture and land surface temperature while providing reliable statistical data for further research and applications.

3.1.3. Assimilation Data and Ground Data

The assimilation data include the Fifth-Generation ECMWF Reanalysis (ERA5) and China Land Data Assimilation System (CLDAS) data. ERA5 is the fifth-generation global atmospheric reanalysis dataset released by the European Centre for Medium-Range Weather Forecasts (ECMWF). This dataset spans from January 1950 to the present and provides hourly estimates of atmospheric, land, and ocean climate variables. Most data have a spatial resolution of 30 km, while certain land parameters have a resolution of 0.1°. In recent years, the ERA5 dataset has been widely used, with improved accuracy compared to earlier versions [43,44,45]. In this study, soil moisture (SWVL1) and land surface temperature (LSTL1) data from the first level of ERA5 were used, covering a depth range of 0–7 cm with a resolution of 0.1°.

The China Meteorological Administration’s CLDAS (China Land Data Assimilation System) product covers the Asian region (0–65°N, 60–160°E) [46]. CLDAS employs data fusion and assimilation techniques, integrating multi-source data such as ground observations, satellite remote sensing, and numerical model outputs to generate meteorological variables like air temperature, LST, SM, air pressure, humidity, wind speed, precipitation, and radiation. SM and LST data are sourced from the CLDAS-V1.0 operational system provided by the China Meteorological Data Service Center. The CLDAS dataset includes hourly soil moisture and temperature data for East Asia at depth ranges of 0–5, 0–10, 10–40, 40–100, and 100–200 cm, with a spatial resolution of 0.0625°. In this study, surface temperature and soil moisture data from the 0–5 cm depth range were used. To match AMSR 2 resolution, CLDAS soil moisture and land surface temperature data were resampled to 0.1°. During data collection, only ground observation data close to ERA 5 and CLDAS values were used, and outliers or unrepresentative data were excluded to ensure that the selected data reflected diverse physical conditions.

The ground observation data in this study were sourced from hourly observations provided by the National Meteorological Science Data Center, including data from national meteorological stations in China. The data include hourly observations of air temperature, air pressure, relative humidity, vapor pressure, wind, and precipitation, and are classified as point data.

3.2. Geophysical Logic Derivation

The SM and LST retrieval method is based on the radiative transfer process, linking ground and atmospheric variables to brightness temperature observations. SM and LST retrieval rely on thermal radiation models of bare soil, vegetated soil, and canopy. Figure 2 illustrates the radiative transfer derivation linked to brightness temperature measurements. This process identifies the unknowns related to SM and LST, guiding the construction of statistical methods and neural networks.

For bare soil, LSE is mainly influenced by SM and surface roughness, while atmospheric water vapor affects satellite radiative measurements at specific frequencies. The satellite brightness temperature ($T_{Bi}$) in channel $i$ and the surface state variables (i.e., $SM$ and $LST$) are expressed as in Equation (1).

$$T_{Bi}={\mathsf{\Phi }}_i\left(SM,LST,Roughness\right)$$

(1)

To improve the retrieval accuracy of LST and SM, the effect of atmospheric water vapor on the satellite’s brightness temperature is considered. Within the satellite coverage area, the temperatures of the soil and vegetation layers are considered to be the averaged value of a single effective surface temperature. Depending on surface roughness, there are three main surface radiation models.

3.2.1. Smooth Surface Radiative Model

In a smooth surface, the brightness temperature ($T_{Bp}$) is related to the true surface temperature as in Equation (2):

$$T_{Bp}\left(\theta \right)=e_{sp}\left(\theta \right)\cdot T_s$$

(2)

where ($p$) represents the polarization in either H or V, $T_s$ is the effective land surface temperature, $\theta$ is the incident angle relative to the lowest point, and $e_{sp}\left(\theta \right)$ is the land surface emissivity, which can be calculated from the land surface reflectance ${\Gamma }_{Bp}\left(\theta \right)$ using Equation (3).

$$e_{sp}\left(\theta \right)=1-{\Gamma }_{Bp}\left(\theta \right)$$

(3)

With the use of the Fresnel equations for a smooth surface, the surface reflectance ${\Gamma }_{Bp}\left(\theta \right)$ can be calculated from the soil dielectric constant ($\epsilon$) and the incident angle ($\theta$) using Equations (4) and (5). The dielectric constant depends on the SM at specific frequencies and, to a lesser extent, on soil density and the percentages of sand and clay. According to the relationship between brightness temperature and land surface state variables, there are three unknowns: $T_S$, $\theta$, and $\epsilon$ (which is also a function of $SM$).

$${\Gamma }_{B_H}^{*}={\left|{\displaystyle \frac{cos\theta -{\left(\epsilon -si{n}^2\theta \right)}^{0.5}}{cos\theta +{\left(\epsilon -si{n}^2\theta \right)}^{0.5}}}\right|}^2$$

(4)

$${\Gamma }_{B_V}^{*}={\left|{\displaystyle \frac{\epsilon cos\theta -{\left(\epsilon -si{n}^2\theta \right)}^{0.5}}{\epsilon cos\theta +{\left(\epsilon -si{n}^2\theta \right)}^{0.5}}}\right|}^2$$

(5)

The Dobson dielectric model is used to estimate the soil dielectric constant [47].

3.2.2. Rough Surface Radiation Model

A smooth surface is a specific case of a rough surface, so roughness effects must be considered in surface radiation models. Additionally, since microwave radiation penetrates the surface, volume scattering (caused by uneven soil properties) must be considered. Semi-empirical and physical models are used to calculate rough surface emissivity. The semi-empirical L-MEB model [48] is applied to analyze rough surfaces. The rough surface reflectivity (${\Gamma }_{Bp}$) can be written as Equation (6):

$${\Gamma }_{B_p}\left(\theta \right)=\left(\left(1-Q_R\left(\theta \right)\right){\Gamma }_{B_{p}1}^{*}\left(\theta \right)+Q_R\left(\theta \right){\Gamma }_{B_{p}2}^{*}\left(\theta \right)\right)\exp -H_{RP}\left(\theta \right)co{s}^{N_{PR}}\left(\theta \right)$$

(6)

Here, ${\Gamma }_{B_{p}1}^{*}$ and ${\Gamma }_{B_{p}2}^{*}$ (where ($p_1=H$) and ($p_2=V$)) represent the specular reflectance of a smooth surface for horizontal and vertical polarizations, respectively. Meanwhile, $H_{RP}$, $Q_R$, and $N_{PR}$ are roughness parameters, which are defined in Equation (7):

$$HQN=f\left(s,l,\dots \right)$$

(7)

Here, $HQN$ represents the roughness model, while $s$ and $l$ denote the root mean square height and the correlation length, respectively, which are used to describe surface roughness. Therefore, when considering the brightness temperature measurement ($T_{Bp}$), there are five main unknown parameters for a rough surface: SM, LST, $\theta$, $s$, and $l$, another parameter. Consequently, at least five equations are required to solve for the SM and LST parameters.

3.2.3. Vegetation Radiation Model

As shown in Figure 2, the brightness temperature of the vegetation surface can be approximated as the sum of five radiation components: (1) atmospheric upward radiation; (2) atmospheric downward radiation and cosmic background radiation attenuated by vegetation, surface reflection, and atmospheric attenuation; (3) downward radiation from vegetation reflected by the surface and attenuated by vegetation and the atmosphere; (4) atmospheric attenuation of upward radiation from vegetation; (5) soil radiation attenuated by vegetation and the atmosphere.

The impact of the atmosphere ($T_A$) on the brightness temperature can be expressed as Equation (8):

$$T_A=T_u+\exp \left(-{\tau }_a\right)r_p{T}_d$$

(8)

Here, $T_u$ and $T_d$ represent the energy of the atmospheric upward radiation and atmospheric downward radiation, respectively. ${\tau }_a$ is the atmospheric opacity along the viewing path, which depends on the WVC (Water Vapor Content), and $r_p$ denotes the surface reflectivity. Considering the atmospheric effects, the entire radiative transfer (RT) process on the vegetation surface can be described by Equation (9):

$$\begin{array}{c}{T}_{bp}=T_u+exp\left(-{\tau }_a\right)\left\{r_p{T}_d+T_s\left(1-r_{sp}\right)\exp \left(-{\tau }_c\right)\right.+T_c\left(1-{\omega }_p\right)\left[1-\exp \left(-{\tau }_c\right)\right]\\ +T_c\left(1-{\omega }_p\right)\left[1-\exp \left(-{\tau }_c\right)\right]\left.r_{sp}\exp \left(-{\tau }_c\right)\right\}\end{array}$$

(9)

Here, LSE ($e_{sp}$) is correlated with the reflectivity ($r_{sp}$), expressed as ($e_{sp}=1-r_{sp}$). ${\tau }_c$ is the vegetation opacity along the viewing path, and ${\omega }_p$ denotes the single scattering albedo of the vegetation. It is worth noting that the constructed radiative transfer process neglects multiple scattering within the vegetation layer and assumes that the soil and vegetation temperature, $T_s$, are approximately equal. The relationship between opacity along the observation path and vegetation water content can be expressed as Equation (10):

$${\tau }_c=b{w}_e/cos\theta$$

(10)

Here, $b$ is the statistical coefficient, and ${\omega }_e$ represents the vegetation water content.

Therefore, for vegetation-covered surfaces, there are nine unknowns, namely $SM$, $LST$, $e_{sp}$, ${\omega }_p$, ${\omega }_e$, $\theta$, $s$, $l$, and $WVC$. Bare surfaces are considered a special case of the vegetated surface. Based on this, retrieving both SM and LST for vegetated surfaces requires nine equations to solve for these nine unknown variables. Due to inherent relationships between different physical parameters, Mao et al. compared retrieval accuracies across different frequencies by constructing various combinations of eight to fourteen radiative transfer equations. They concluded that using at least ten low-frequency channels (6.9, 7.3, 10.65, 18.7, and 23.8 GHz in vertical/horizontal polarization) to build ten theoretical equations for neural networks yielded optimal retrieval accuracy for SM. In contrast, high-frequency channels are more sensitive to LST, and using at least ten high-frequency channels (10.65, 18.7, 23.8, 36.5, and 89 GHz in vertical/horizontal polarization) yields better accuracy for LST retrieval [19]. When fewer than ten microwave channels are used, the retrieval accuracy of SM and LST may slightly decrease. Additionally, SM and LST are interrelated and mutually constrained [49]. In summary, we retrieved the initial SM by solving for the nine unknowns using brightness temperatures from ten channels. To improve the accuracy of LST retrieval, SM is used as an input for the deep learning model. On the other hand, LST is a key variable for calculating land surface emissivity. Therefore, using LST as an input for the deep learning network can also enhance the accuracy of SM retrieval. A joint iterative retrieval model was constructed to continuously improve the accuracy of both SM and LST retrievals.

3.3. Multi-Hierarchy Classification and Establishment of a Multi-Source Database

Based on the sensitivity of the microwave low-frequency channel to soil moisture and the high-frequency channel to surface temperature, and the determination of the number of unknowns in radiative transfer Equations (1)–(10), the equation can be solved to obtain the soil moisture and surface temperature values. In deriving the relationship between the input and output variables through the radiative transfer equation and using neural networks to efficiently solve the complex scenarios of nonlinear equations, the solutions for soil moisture and surface temperature are obtained. In reality, Earth’s surface comprises more than just bare soil and vegetation, and with AMSR 2’s 0.1° spatial resolution, a single pixel may cover multiple surface types. Therefore, simulated data from physical methods lack sufficient representativeness for low-resolution real pixels. In order to accurately retrieve soil moisture (SM) and land surface temperature (LST), generalized statistical methods are used to guide data collection, forming a multi-source training and testing database. This multi-source database includes known variables (brightness temperatures at each frequency from the satellite) and corresponding unknowns (SM and LST at the ground). It ensures temporal and spatial synchronization between AMSR 2 brightness temperatures from Aqua and the corresponding SM and LST data. Additionally, data are only included in the database when AMSR 2’s SM products and MODIS’s LST products closely match SM and LST data from ERA5 and CLDAS (the difference is less than 0.03 m³/m³ and 0.5 K). The multi-source database can be used to solve the radiative transfer equation through neural networks, and the trained model retrieves daily ascending and descending SM and LST values for the study area.

When selecting a study area with diverse landscapes and climates, the neural network model trained on the area’s database may be influenced by spatiotemporal geographic factors, affecting SM and LST retrieval accuracy in specific regions. To address this, the spatial and temporal characteristics of geographical factors affecting surface emissivity are considered, and a multi-level hierarchical division of the study area is implemented. At each level, the same factors are used to further divide the study area into multiple sub-regions, forming a hierarchical tree-structured classification. Part 3 in Figure 1 shows the hierarchical classification process of the study area, incorporating spatiotemporal geographical characteristics. The study area is classified into multiple levels based on roughness, season, vegetation, snow cover, water bodies, soil type, precipitation, and other factors. A multi-source database is built for each sub-region, and neural network models are fine-tuned or retrained for each sub-region.

In hierarchical classification, DEM data represents large-scale surface roughness and is used in various terrain analysis and environmental research fields [50,51]. The DEM data was sourced from the GEBCO_2022 Grid. Due to the variability in terrain elevation, only a rough classification was based on differences between large-scale terrains. Seasonal classification was defined as follows: March to May as spring; June to August as summer; September to November as autumn; December to February as winter. Vegetation classification used MVIs (Passive Microwave Vegetation Indices) of Equation (11) [52]. These indices were cross-validated with the NDVI for more than ten types of terrestrial vegetation, showing that 6.9 GHz and 10.65 GHz performed best across various global vegetation types. Snow classification was based on the Snow Water Equivalent (SWE) of Equation (12) [53]. An $SWE$ extracts snow signals and serves as a physically based snow emission model. Soil type classification used a dataset from the National Glacial and Frozen Soil Desert Scientific Data Center. Precipitation data come from the daily precipitation datasets of ERA5 Land.

$$MVIs\left(f_1,f_2\right)={\displaystyle \frac{T_{Bv}\left(f_2\right)-T_{Bh}\left(f_2\right)}{T_{Bv}\left(f_1\right)-T_{Bh}\left(f1\right)}}$$

(11)

$$SWE=f\left(SD\right)=f\left(T_{B}18.7-T_{B}37\right)$$

(12)

In Equation (11), $T_{Bv}$ and $T_{Bh}$ represent the vertical and horizontal polarization of the brightness temperature channels, respectively. In Equation (12), $f\left(SD\right)$ is related to the snow grain radius and snow density, and $SD$ represents snow depth, which is related to the 18.7 and 37 GHz frequencies in passive microwaves.

3.4. Neural Network Models with Mutually Prior Knowledge

After determining the input parameters through the derivation of radiative transfer equations and building multi-source databases for sub-regions, the corresponding input and output parameters are used to train the neural network to solve the radiative transfer equations. In total, 80% of the multi-source database was used for training, and 20% for testing. This approach allows the neural network to serve as an optimization tool while retaining physical significance and interpretability.

3.4.1. Construct an Iterative Retrieval Model

We selected the Fully Connected Neural Network (FCNN) as the primary model architecture for retrieving SM and LST. The reasoning is as follows: First, the FCNN has strong expressive power, allowing it to effectively model complex nonlinear relationships. SM and LST retrieval involve the interactions of multiple nonlinear features, which traditional methods struggle to capture fully. The FCNN, with its layer-by-layer neuron structure, efficiently handles these complex patterns, achieving high-precision retrievals. Second, the FCNN is flexible in structure and can adapt to different datasets through the adjustment of the number of hidden layers and nodes per layer. This flexibility allows it to meet SM and LST retrieval needs across different regions, seasons, and environmental conditions. The architecture can be dynamically adjusted based on specific data distributions and problem scales, improving the model’s applicability and accuracy. Moreover, the FCNN has no sequence dependence, making it suitable for handling independently and identically distributed (IID) data. In SM and LST retrieval, each data pixel is independent, and the FCNN directly models these samples, simplifying the retrieval process. Finally, the FCNN is simple to build and train, performing exceptionally well in handling feature engineering.

As deep learning expands across various fields, constructing neural networks becomes increasingly important. Traditional manual tuning methods are time-consuming and heavily dependent on experience. To optimize the FCNN’s structural parameters, we used the Tree-structured Parzen Estimator (TPE) algorithm in Hyperopt to systematically explore the optimal network architecture. The TPE is a hyperparameter optimization technique based on Bayesian optimization. It guides the hyperparameter search by constructing two probability distributions: one representing areas with lower objective function values, and the other representing areas with higher objective function values. The TPE uses a ratio to direct the search, prioritizing hyperparameter combinations with higher probabilities in areas with lower objective function values. After evaluating a new hyperparameter combination, the TPE updates the model and adjusts the hyperparameters for the next sampling based on the results. Compared to traditional grid search and random search methods, the TPE efficiently guides the search, avoiding ineffective areas and enabling the discovery of better hyperparameter combinations with fewer evaluations. We defined the search space to include 3–10 hidden layers, 16–1000 nodes per layer, and activation functions like ReLU, Sigmoid, and Tanh. Dropout rates for each layer, ranging from 0.1 to 0.5, were also considered. The objective function aimed to maximize model performance on the validation set using MAE and R. The Adam optimizer and binary cross-entropy loss function were used during training. After 50 iterations, the TPE algorithm identified the optimal parameter set for the network architecture of the retrieval model. This approach significantly reduced manual tuning time and improved model performance systematically.

After applying the TPE algorithm to search for the optimal FCNN grid structure across the multi-source database, we selected the hyperparameter combination with the lowest error to build the iterative retrieval model for SM and LST. The iterative retrieval model, serving as a solver for the radiative transfer equations, is illustrated in Figure 3. The FCNN comprises three main components: an input layer, hidden layers, and an output layer. Neuronal connections in the hidden layers are represented by synaptic weights, and interlayer connections are described by four equation sets (Equations (13)–(16)).

$$V_k={\displaystyle \sum }_{j=1}^n{x}_j{W}_{k,j}$$

(13)

$$H_z=f\left(U_z\right)$$

(14)

$$O_m={\displaystyle \sum }_{z=1}^n{H}_z{W}_{m,z}$$

(15)

$$y_m=f\left(O_m\right)$$

(16)

The input layer $x$ consists of $j$ neurons, the first hidden layer $V$ has $k$ neurons, the final hidden layer $U$ has $z$ neurons, and the output layer $O$ has $m$ neurons. $W_{k,j}$ and $W_{m,z}$ are the synaptic weights of the neurons, and $U$ and $H$ represent the net values and outputs of the final hidden layer neurons, respectively, while $O$ and $y$ represent the net values and outputs of the output layer neurons. $f\left(U\right)$ and $f\left(O\right)$ are kernel functions used as activation functions for the neurons. Each layer of neurons contributes to the overall functionality of radiative transfer through the aggregation of their outputs. As shown in Figure 3, the input parameters for the initial retrieval model consist of 10 brightness temperatures, while the input parameters for the iterative retrieval model include 10 brightness temperatures and one iteration parameter. The output parameter is either SM or LST.

When input and output parameters are strongly correlated, neural networks can be used directly for retrieval. However, when the correlation is weak, introducing prior knowledge can significantly improve retrieval accuracy, establishing a more effective physical relationship between input and output parameters. In the passive microwave SM and LST retrieval method, when the retrieval value from the previous SM model is used as an input parameter for the LST model, and the retrieval value from the previous LST model is used as an input for the SM model, it forms an SM and LST retrieval model with mutual prior knowledge. Repeating this process continuously constitutes the iterative process, updating SM and LST values. The iteration stops when all training data reach the global optimum (i.e., when the difference in LST/SM retrieval values between two consecutive iterations is less than 0.01 K/0.001 m³/m³). Combining the fitting ability of neural networks with the introduction of prior knowledge allows the model to more accurately retrieve SM and LST, enhancing its practicality and applicability.

3.4.2. The SM and LST Retrieval Method with Nested Large–Small Models

For the entire study area, we separately constructed SM and LST joint retrieval models for ascending and descending orbits. In these models, SM and LST are treated as prior knowledge for each other. Through iterative training, a joint retrieval model for the entire study area was obtained, referred to as the “large model”. To refine the retrieval process, we established a tree-structured, multi-hierarchy classification system for the study area. Each hierarchy contains several sub-regions, derived from the parent node (study area) and inheriting the multi-source database from the previous node. Model training for each sub-region can therefore use a fine-tuning strategy, significantly reducing time and computational cost. As shown in the red section of Figure 3, the fine-tuning process allows for the selective locking of layers (freezing layer weights) without changing the number of hidden layers or neurons, adjusting only specific parameters. The adjustment process involves modifying parameters in Equations (13)–(16). In Equations (13) and (15), the weights connecting the input and hidden layers are modified as $W_{k,j}\prime$ and $W_{m,z}’$, adjusting each input feature’s contribution to the hidden and output layer neurons. Additionally, bias terms $b_k$ and $b_m$ are added to adjust the baseline activation levels of the hidden and output layer neurons, resulting in Equations (17) and (18), which subsequently affect the results of the entire forward propagation and the final output. In Equations (14) and (16), the activation functions of the hidden/output layers, $f$, are adjusted or changed, altering the nonlinear transformations, which affect the network’s learning ability and output performance. The fine-tuning process is conducted through backpropagation, combined with optimization algorithms (such as gradient descent, Adam, etc.) for training. The model parameters are continuously updated based on the training data to minimize the loss function.

$$V_k={\displaystyle \sum }_{j=1}^n{x}_{j}W{\prime }_{k,j}+b_k$$

(17)

$$O_m={\displaystyle \sum }_{z=1}^n{H}_{z}W{\prime }_{m,z}+b_m$$

(18)

Fine-tuning can greatly reduce time and computational costs. The fine-tuning strategy is applied first for sub-region retrieval model training. If fine-tuning fails to achieve the expected results on the test set, we use the sub-region’s multi-source database to retrain the model using the same method as for the “large model”. The model fine-tuned from the large model or retrained for the sub-region is referred to as the “small model” in the retrieval method. Through fine-tuning and retraining strategies, we developed a nested large-small model for SM and LST retrieval method to meet the specific needs of both the entire study area and its sub-regions. This approach leverages the large model’s learning capability while quickly adapting to sub-regions’ specific conditions, improving retrieval accuracy and optimizing computational resources.

3.5. Validation Method

To validate the results from the nested large–small model for SM and LST retrieval, we assess the accuracy of retrieval values against satellite remote sensing pixels and ground truth measurements. The applicability of SM and LST retrieval results depends on the quality of validation. The pixel area of passive microwave remote sensing products (AMSR2) is relatively large, while land surfaces often show heterogeneous features. The high heterogeneity of surface types within a single pixel complicates validation. Passive microwave remote sensing satellite data represent area data, covering a certain depth and thickness, while ground station measurements provide point data. This difference in data dimensionality further complicates validation, making it difficult to obtain field measurements that match the AMSR2 pixel size. We adopted a comprehensive validation strategy to assess SM and LST retrievals from two perspectives. First, we cross-validated the retrievals with established remote sensing products (such as AMSR2 SM and MODIS LST data) to evaluate consistency and applicability on a large spatial scale. Second, we compared the retrievals with ground observation data. To ensure the representativeness of ground observation data, we established observation networks in pixels with flat terrain and minimal surface variation. The average of the observation network represents the actual ground observation value for the pixel. High-precision data from the observation network serve as the reference standard for validating the retrievals. These two methods comprehensively evaluate the accuracy and reliability of the retrievals, supporting more precise surface feature analysis.

4. Results and Discussion

4.1. Case Study and Retrieval Scheme

To validate the feasibility and accuracy of the soil moisture (SM) and land surface temperature (LST) retrieval method, we selected the terrestrial area of China as the case study. We chose China due to its complex geography and diverse climatic conditions, making it an ideal testing environment. China spans a vast territory, with latitudes from 3°31′00″ to 53°33′00″N and longitudes from 73°29′59″ to 135°2′30″E. The terrain is higher in the west and lower in the east, featuring five main landforms: plateaus, mountains, hills, basins, and plains. China’s geographical location and diverse terrain create a variety of climates, including tropical, subtropical monsoon, temperate monsoon, temperate grassland, and plateau mountain climates. The diverse climates affect surface water cycling, energy balance, vegetation growth seasons, SM evaporation, and the spatial and temporal distribution of SM and LST. This results in rainfall being high in the southeast and low in the northwest. The variety of vegetation and soil types across China’s land area makes it an excellent region for retrieving soil moisture and land surface temperature. This not only aids in understanding how these variables behave under complex topography and diverse climatic conditions but also enhances the applicability and generalization of the model in other regions with similar geographic and climatic characteristics. Additionally, the extensive prior knowledge we possess for this region has greatly facilitated the advancement of this research.

When this retrieval method is applied to jointly retrieve soil moisture and land surface temperature over China, the first step is to determine nine unknowns based on the radiation transfer equation and establish a complete closed-form system of equations that describes the relationship between the input variables and output parameters. Ten low-frequency brightness temperature values are used to retrieve soil moisture, while ten high-frequency brightness temperature values are used to retrieve land surface temperature. Statistical methods are then applied to guide the collection of multi-source data for the land area of China, ensuring the standardization of both temporal and spatial resolutions. The multi-source data consist of brightness temperature values from seven channels, covering a total of 14 frequencies, as well as AMSR 2 SM, MYD11C1, simulated data, assimilation data, and ground-based data. The study area is divided into five hierarchies, from Hierarchy 1 to Hierarchy 5. Hierarchy 1 encompasses the entire region of China without further hierarchical classification. After quality control is applied to the multi-source data, a multi-source database for Hierarchy 1 is created. Data will only be included in the database if the differences between AMSR 2 SM products and MODIS LST products, as well as the SM and LST data from ERA5 and CLDAS, are both less than 0.03 m³/m³ and 0.5 K, respectively. The data selected from the database were used to apply the TPE algorithm to identify the optimal hyperparameters, after which an iterative neural network training model, referred to as the “large model (Model 1)”, was constructed. Hierarchies 2 to 5 represent the subdivided regions following classification. The multi-source database of Hierarchy 1 is used to generate multi-source databases for the subdivided regions. The neural network model, fine-tuned or retrained using the multi-source database of the subdivided regions, is referred to as the "small model (Models 2–5)", establishing a nested relationship between the large and small models. The surface emissivity factors used for multi-hierarchy classification include roughness (DEM), season, vegetation, snow, and soil type.

Roughness and soil type show little dynamic change and are considered constant, while vegetation and snow vary seasonally. For example, in the eastern plains, the microwave vegetation index is much higher in summer than in winter. Thus, sub-regions in Hierarchies 4 and 5 are dynamic. The multi-hierarchy structural framework of this application case is shown in Figure 4. After applying multi-hierarchy classification, the number of nodes in Hierarchies 1 to 5 are 1, 6, 24, 48, and 96, respectively. In each hierarchy, a research area related to the previous one is selected to test and validate the retrieval method’s feasibility. As selected by the red dashed box in Figure 4. To capture varying climate, vegetation, and hydrological conditions, multi-source data from China were collected from June 2020 to June 2022, and classification criteria were applied. A multi-source database was established in each hierarchy’s study area following the retrieval method. Joint retrieval models of SM and LST, using each selected node as prior knowledge, were constructed. SM and LST were iteratively retrieved, and the results were compared with product and station data to evaluate the retrieval method’s feasibility.

4.2. Large–Small Model Training and Testing

This study used the TPE algorithm in Hyperopt to determine the optimal neural network structure for the hierarchical data, as shown in

Table 2. Optimal neural network hyperparameters for SM and LST retrieval are determined with TPE.

	Asc.SM Model (AF)	Asc.LST Model (AF)	Des.SM Model (AF)	Des.LST Model (AF)
1	32 (relu)	64 (relu)	32 (relu)	64 (relu)
2	416 (relu)	648 (relu)	448 (relu)	680 (relu)
3	880 (relu)	612 (relu)	624 (relu)	688 (relu)
4	640 (sigmoid)	820 (relu)	992 (sigmoid)	804 (relu)
5	1 (linear)	982 (relu)	1 (linear)	992 (relu)
6		748 (relu)		970 (relu)
7		820 (relu)		860 (relu)
8		1 (linear)		1 (linear)

. Through this optimization, we constructed a joint retrieval model in which SM and LST serve as prior knowledge for each other. Training and fine-tuning the models using the established multi-source database led to the development of a nested large–small model for joint SM and LST retrieval method, addressing the needs of both the entire study area and its sub-regions. The retrieval performance of the model for SM and LST was evaluated using two metrics: Mean Absolute Error (MAE) and correlation coefficient (R).

4.2.1. Ascending Orbit Iterative Retrieval Based on LST and SM as Prior Knowledge

The ascending orbit SM retrieval models for the multi-source database of each hierarchy were trained and tested using a neural network, as illustrated with density scatter plots (Figure 5) and heatmaps (Figure 6). The LST retrieval models are illustrated in the density scatter plots (Figure 7) and heatmaps (Figure 8). In the density scatter plots, each subplot, "(h1), (h2), (h3), (h4), (h5)", corresponds to Hierarchies 1 through 5. The training and testing data for each hierarchy consist of 450,000, 45,000, 100,000, 50,000, and 20,000 samples, with 20% used for testing. Since models 2, 4, and 5 were fine-tuned, the data volume was smaller.

The test results for the ascending orbit SM retrieval model are shown in Figure 5 and Figure 6. Models 1 through 5 show low error levels and high correlations at each hierarchical level, with MAEs of 0.013, 0.011, 0.010, 0.009, and 0.008 m³/m³, and R values of 0.844, 0.876, 0.903, 0.910, and 0.916. Model 2’s MAE at Hierarchy 2 decreased by 0.004 m³/m³, and R increased by 0.122; Model 3’s MAE at Hierarchy 3 decreased by 0.009 m³/m³, and R increased by 0.136; Model 4’s MAE at Hierarchy 4 decreased by 0.012 m³/m³, and R increased by 0.112; Model 5’s MAE at Hierarchy 5 decreased by 0.012 m³/m³, and R increased by 0.118. The density scatter plots show that when SM values are below 0.07 m³/m³, the model overestimates the retrieval values, while for SM values above 0.07 m³/m³, it underestimates them. This occurs because most SM values are concentrated below 0.1 m³/m³. Pixels with high SM values often contain large water bodies or were not collected due to cloud and rain conditions during the generation of the multi-source database. Although this phenomenon appears in all scatter plots, the trained models at each level converge better than those at previous levels.

The test results for the ascending orbit LST retrieval model are illustrated in Figure 7 and Figure 8. Models 1 to 5 show low error levels and high correlations across hierarchical levels, with MAEs of 2.10 K, 1.77 K, 1.50 K, 1.54 K, and 1.59 K, and R values of 0.959, 0.966, 0.973, 0.974, and 0.969, respectively. Model 2’s MAE at Hierarchy 2 decreased by 0.36 K, and R increased by 0.018; Model 3’s MAE at Hierarchy 3 decreased by 0.80 K, and R increased by 0.087; Model 4’s MAE at Hierarchy 4 decreased by 0.92 K, and R increased by 0.074; Model 5’s MAE at Hierarchy 5 decreased by 0.74 K, and R increased by 0.071. Due to regional and climatic differences, the data range varies across levels: 261 K to 330 K in Hierarchy 1, 271 K to 323 K in Hierarchy 2, and 294 K to 323 K in Hierarchies 3 to 5. This causes models 1 and 2 to show larger errors when applied to data from other hierarchical levels. Notably, the test results show that model 2 has the lowest accuracy when applied to other hierarchical levels.

4.2.2. Descending Orbit Iterative Retrieval Based on LST and SM as Prior Knowledge

The descending orbit SM retrieval models for the multi-source database of each hierarchy were trained and tested using a neural network, as illustrated in the density scatter plots (Figure 9) and heatmaps (Figure 10). The LST retrieval models are illustrated in the density scatter plots (Figure 11) and heatmaps (Figure 12). In the density scatter plots, each subplot "(h1), (h2), (h3), (h4), (h5)" corresponds to Hierarchies 1 through 5. The training and testing data for each hierarchy consist of 550,000, 80,000, 130,000, 80,000, and 30,000 samples, with 20% used for testing.

The test results for the descending orbit SM retrieval model are illustrated in Figure 9 and Figure 10. Models 1 to 5 show low error levels and high correlations at each hierarchical level, with MAEs of 0.017, 0.014, 0.012, 0.012, and 0.011 m³/m³, and R values of 0.875, 0.898, 0.917, 0.924, and 0.936. Model 2’s MAE at Hierarchy 2 decreased by 0.012 m³/m³, and R increased by 0.107; Model 3’s MAE at Hierarchy 3 decreased by 0.017 m³/m³, and R increased by 0.106; Model 4’s MAE at Hierarchy 4 decreased by 0.018 m³/m³, and R increased by 0.099; Model 5’s MAE at Hierarchy 5 decreased by 0.018 m³/m³, and R increased by 0.111. The density scatter plots show the regression line intersecting the 1:1 line at an SM value of approximately 0.12. When the SM value is below 0.12, the model overestimates retrieval values, and when the SM value is above 0.12, the retrieval values are underestimated. The farther the data points are from the intersection, the larger the deviation. Notably, model 2 shows relatively lower retrieval accuracy at Hierarchies 3 through 5.

The test results for the descending orbit LST retrieval model are illustrated in Figure 11 and Figure 12. Models 1 to 5 show low error levels and high correlations across hierarchical levels, with MAEs of 2.11 K, 1.73 K, 1.47 K, 1.50 K, and 1.51 K, and R values of 0.958, 0.970, 0.981, 0.973, and 0.965. At Hierarchy 2, model 2’s MAE decreased by 0.17 K, and R increased by 0.015; at Hierarchy 3, model 3’s MAE decreased by 0.33 K, and R increased by 0.068; at Hierarchy 4, model 4’s MAE decreased by 0.42 K, and R increased by 0.086; at Hierarchy 5, model 5’s MAE decreased by 0.39 K, and R increased by 0.080. The data range varies across hierarchical levels: 252 K to 305 K in Hierarchy 1, 258 K to 303 K in Hierarchy 2, and 283 K to 303 K in Hierarchies 3 to 5. This causes models 1 and 2 to show lower accuracy when applied to data from the last three hierarchical levels.

Overall, the retrieval models trained at each hierarchical level achieved satisfactory accuracy. The higher proportion of high SM values in the descending orbit data leads to a higher MAE for the descending orbit SM large model compared to the ascending orbit large model. However, the correlation coefficients of the descending orbit small models at Hierarchies 2 to 5 are higher than those of the ascending orbit small models. Since SM serves as prior knowledge for the LST retrieval model, the retrieval errors of the ascending and descending orbit LST large–small models are similar to those of SM. The neural network’s strong learning capability, combined with the effective introduction of prior knowledge, enables the model to achieve higher retrieval accuracy across various input–output correlations, enhancing its practicality and applicability. During the training of the iterative retrieval models, where SM and LST serve as prior knowledge for each other, the large–small ascending and descending orbit models reached the set threshold after 5–8 iterations, at which point they were considered to have achieved global optimization, and the iteration was stopped.

4.3. Application and Validation

Cross-validation is a crucial step before algorithm application. We compared the retrieved SM and LST with AMSR 2 SM products and MODIS LST products, respectively. To demonstrate the algorithm’s practical feasibility, ascending and descending orbit AMSR 2 images from 1 August 2022 were selected for validation. These images had to meet the temporal requirements of the case study while avoiding spatial issues from AMSR 2’s dynamic swath gaps and cloud interference in the MYD11C1 images used for cross-validation.

4.3.1. Application and Cross-Validation of SM Retrieval

Figure 13a,b display the SM images retrieved by the large model for the ascending and descending orbits, respectively, while Figure 13A,B show the corresponding AMSR 2 SM products from the Japan Aerospace Exploration Agency (JAXA, Tokyo, Japan). By comparing Figure 13a,A,b,B, we found that the soil moisture retrieval results of the model are generally consistent with the spatial distribution trend of the AMSR2 soil moisture product and effectively capture regions with higher soil moisture. In the southwest, east, and northeast of the study area, where forest cover is extensive, AMSR2 soil moisture estimates are overestimated, with many pixels displaying peak values that deviate from ground observation data. In the semi-arid regions of the central and northwestern study areas, AMSR2 soil moisture values are lower than those observed on the ground. In contrast, the retrieval values from our soil moisture model closely match ground observations, demonstrating more reasonable performance in both forest and semi-arid regions.

Figure 14a–d display the SM images retrieved by small models 2 and 3 for the ascending and descending orbits, while Figure 14A–D show the corresponding AMSR 2 SM products from the Japan Aerospace Exploration Agency (JAXA). Comparing the retrieval results in Figure 14 with the AMSR 2 products shows that the SM retrievals of small models 2 and 3 are similar to those of the large model. Notably, in this study area, the deviation between AMSR 2 SM product values and ground observation data is smaller. After model optimization, the Hierarchy 3 retrieval model aligns more closely with the AMSR 2 SM products than the Hierarchy 2 model. Figure 15a–d display the SM images retrieved by small models 4 and 5 for the ascending and descending orbits, while Figure 15A–D show the corresponding AMSR 2 SM products from JAXA. Comparing the retrieval results in Figure 15 with the AMSR 2 products shows that the SM retrievals of small models 4 and 5 exhibit better consistency with the AMSR 2 SM products. However, in coastal and lake regions, the AMSR 2 product values peak higher than the ground measurement data. Our algorithm cannot entirely avoid this issue but is closer to actual conditions.

Overall, the spatial agreement is good. Specifically, all pixels were cross-validated except those lacking brightness temperature data due to swath gaps or containing a high proportion of water bodies. Cross-validation results for the ascending orbit are shown in Figure 16. With AMSR 2 SM products as a reference, the MAE and RMSE for SM estimation are as follows: model 1 (MAE 0.024 m³/m³, RMSE 0.029 m³/m³), model 2 (MAE 0.024 m³/m³, RMSE 0.031 m³/m³), model 3 (MAE 0.019 m³/m³, RMSE 0.029 m³/m³), model 4 (MAE 0.017 m³/m³, RMSE 0.028 m³/m³), and model 5 (MAE 0.016 m³/m³, RMSE 0.025 m³/m³). Cross-validation results for the descending orbit are shown in Figure 17. For the descending orbit, the SM estimation results are as follows: model 1 (MAE 0.023 m³/m³, RMSE 0.032 m³/m³), model 2 (MAE 0.032 m³/m³, RMSE 0.046 m³/m³), model 3 (MAE 0.023 m³/m³, RMSE 0.032 m³/m³), model 4 (MAE 0.021 m³/m³, RMSE 0.033 m³/m³), and model 5 (MAE 0.022 m³/m³, RMSE 0.035 m³/m³). The validation results are consistent with the training data. The descending orbit has a higher proportion of high SM values, leading to a greater MAE compared to the ascending orbit model.

4.3.2. Application and Cross-Validation of LST Retrieval

Figure 18a displays the daytime (13:30) LST retrieved by the model, revealing a reasonable surface temperature distribution trend across China. The highest surface temperatures occur in the Badain Jaran, Tengger, and Taklamakan Deserts in Xinjiang, whereas the Tibetan Plateau shows the lowest temperatures. In general, land surface temperatures in northern China are lower than in the south. However, in summer, higher land surface temperatures in the north are primarily due to longer daylight hours and increased solar radiation. In contrast, the south has denser vegetation, which lowers surface temperatures through evapotranspiration. Northern regions experience fewer clouds, promoting rapid heat dissipation, while the south is more cloud-covered, offering better insulation. Furthermore, the humid climate and increased cloud cover in the south enhance atmospheric reflection, reducing the solar radiation reaching the surface. The corresponding MODIS LST product data (Figure 18A) show clear skies in the north, with direct sunlight reaching the surface, leading to relatively higher surface temperatures. In the north, the absence of clouds allows rapid surface heat dissipation, whereas the cloudier south provides better insulation. Consequently, nighttime temperatures in the south are relatively higher, as demonstrated in Figure 18B,b. Comparing Figure 18A,a,B,b reveals that under cloud-free conditions, the model’s LST retrieval results align with the general trends of the MODIS LST product, but significant deviations were observed in certain regions. Under cloudy conditions, retrieving surface temperature with passive microwave remote sensing demonstrates the unique advantage of this technology.

Figure 19a–d show the LST images retrieved by small models 2 and 3 for the ascending and descending orbits, respectively. Figure 19A–D depict the corresponding MODIS LST products for the same orbits. Comparing the retrieval results in Figure 19 with the MODIS LST products, small model 2’s LST values show some deviation, whereas small model 3 shows significant improvement in accuracy. This is consistent with the model’s training results and may be related to the scope of the training data. Figure 20a–d show the LST images retrieved by small models 4 and 5 for the ascending and descending orbits, respectively. Figure 20A–D show the corresponding MODIS LST products for the same orbits. In comparing the retrieval results in Figure 20 with the MODIS LST products, small models 4 and 5 show a high degree of consistency with MODIS LST values. In coastal areas, both the LST retrieval values and MODIS LST are lower, which is related to the high soil moisture values and the excessive proportion of water bodies within the pixels. Model 5’s LST retrieval values show smaller deviations from ground-based measurements, indicating a closer approximation to actual surface temperatures.

Cross-validation results for LST in the ascending orbit are shown in Figure 21. With MODIS LST as a reference, the LST estimates are as follows: model 1 (MAE 2.35 K, RMSE 3.23 K), model 2 (MAE 1.97 K, RMSE 2.28 K), model 3 (MAE 1.75 K, RMSE 2.01 K), model 4 (MAE 1.82 K, RMSE 2.16 K), and model 5 (MAE 1.84 K, RMSE 2.23 K). Cross-validation results for the descending orbit are shown in Figure 22. With MODIS LST as a reference, the LST estimates for the descending orbit are as follows: model 1 (MAE 2.31 K, RMSE 3.16 K), model 2 (MAE 1.99 K, RMSE 2.24 K), model 3 (MAE 1.68 K, RMSE 1.81 K), model 4 (MAE 1.85 K, RMSE 1.98 K), and model 5 (MAE 1.84 K, RMSE 1.95 K). Notably, in the ascending orbit, MODIS LST is generally higher than passive microwave LST, whereas in the descending orbit, passive microwave LST is usually higher than MODIS LST.

4.3.3. Ground Validation

We selected optimal pixels based on the meteorological station distribution to establish a ground observation network for validation. In the ground validation process for ascending and descending orbit retrieval models, models 1–5 used 300, 100, 100, 50, and 25 ground observation networks, respectively. The mean value of each observation network can best represent the ground observation value of the pixel, allowing for the evaluation of the model’s performance and reliability at different hierarchies, and providing a basis for subsequent model optimization. The SM ground validation results (Figure 23 and Figure 24) show that, in both ascending and descending orbits, the deviation between AMSR 2 SM product values and ground observation data is greater than that between model retrieval values and ground observation data. Similarly, the deviation between small-model retrieval values and ground observation data is smaller than that of higher-hierarchy models. The LST ground validation results (Figure 25 and Figure 26) indicate that, in both ascending and descending orbits, the deviation between MODIS LST product values and ground observation data is greater than that between model retrieval values and ground observation data. Similarly, the deviation between small-model retrieval values and ground observation data is smaller than that of higher-hierarchy models. During ground validation, it was observed that MODIS LST was generally higher than passive microwave LST in ascending orbits, while passive microwave LST was higher in descending orbits. This difference is more pronounced in descending orbits, determined by the characteristics of microwave remote sensing.

Although the mean values from the ground observation network represent ground data, data attribute differences exist between ground data and passive microwave remote sensing data, resulting in discrepancies between the two. Ground data were selected from pixels in flat terrain with minimal surface variation, forming a network that represents true surface SM and land LST values. However, the number of available ground observation data for any given day is limited. We used MAE as the evaluation metric for the validation results.

Table 3. MAE (m³/m³) of soil moisture ground observation validation.

	Ascending Orbits					Descending Orbits
	h1	h2	h3	h4	h5	h1	h2	h3	h4	h5
Model 1	0.045	0.046	0.046	0.053	0.041	0.057	0.047	0.047	0.041	0.042
Model 2	\	0.046	0.046	0.045	0.035	\	0.044	0.044	0.038	0.038
Model 3	\	\	0.034	0.034	0.026	\	\	0.039	0.033	0.033
Model 4	\	\	\	0.031	0.027	\	\	\	0.030	0.031
Model 5	\	\	\	\	0.026	\	\	\	\	0.030
AMSR 2 SM	0.064	0.077	0.077	0.075	0.058	0.076	0.063	0.063	0.056	0.058

and

Table 4. MAE (K) of surface temperature ground observation validation.

	Ascending Orbits					Descending Orbits
	h1	h2	h3	h4	h5	h1	h2	h3	h4	h5
Model 1	2.30	2.03	2.03	2.10	2.34	2.12	2.04	2.04	2.07	2.21
Model 2	\	1.83	1.83	1.92	1.98	\	1.95	1.95	1.96	1.96
Model 3	\	\	1.71	1.70	1.72	\	\	1.79	1.84	1.78
Model 4	\	\	\	1.69	1.69	\	\	\	1.79	1.76
Model 5	\	\	\	\	1.67	\	\	\	\	1.72
MYD11C1	2.61	2.34	2.34	2.33	2.24	2.56	2.38	2.38	2.34	2.28

show that the retrieved SM and LST values from both the ascending and descending models trained under our method outperformed the AMSR 2 SM and MODIS LST products. For SM, the ascending retrieval model 5 achieved an MAE of 0.026 m³/m³, improving by 0.015 m³/m³ and 0.032 m³/m³ compared to the larger model and AMSR 2 SM product, respectively. The descending SM retrieval model 5 achieved an MAE of 0.030 m³/m³, with improvements of 0.012 m³/m³ and 0.028 m³/m³ compared to the larger model and AMSR 2 SM product, respectively. For LST, the ascending retrieval model 5 achieved an MAE of 1.67 K, improving by 0.67 K and 0.57 K compared to the larger model and MODIS LST product, respectively. The descending LST retrieval model 5 achieved an MAE of 1.72 K, improving by 0.49 K and 0.56 K compared to the larger model and MODIS LST product, respectively. Comparative analysis shows that our retrieval method is highly consistent with other algorithm products, and the multi-hierarchy classified model retrieval values are closer to the ground observation data.

5. Conclusions and Future Prospects

To improve the retrieval accuracy of soil moisture and land surface temperature, we proposed a nested large-small model joint retrieval method based on artificial intelligence. Through the hierarchical strategy of large–small model nesting, the small model can accurately invert soil moisture and land surface temperature with relatively fewer training data. Compared to traditional deep learning methods, this approach not only improves accuracy but also offers better interpretability and generalization ability. We combined physical, statistical, and deep learning methods, using neural networks to optimize physical and statistical models, successfully solving the coupling problem between soil moisture and land surface temperature. By constructing a multi-source database with physical and statistical methods, we trained the neural network, forming a nested large–small model retrieval framework that significantly improved the passive microwave retrieval accuracy. Case studies show that the method is feasible. The retrieval results for soil moisture and land surface temperature demonstrate that all-weather retrieval is feasible. Validation results show that the ascending soil moisture retrieval model 5 improves the Mean Absolute Error (MAE) by 0.015 m³/m³ compared to model 1, while the land surface temperature (LST) retrieval model 5 improves the MAE by 0.67 K. When the neural network’s output is highly dependent on the input, direct retrieval can be performed; however, when the output has weaker dependence, prior knowledge must be introduced. Since soil moisture is closely related to satellite brightness temperature, its retrieval does not require land surface temperature as prior knowledge, whereas land surface temperature retrieval requires soil moisture as prior knowledge.

Although the proposed retrieval method has achieved some success, there is still room for improvement. First, the distribution of soil moisture in the training data may affect the accuracy of the model. Additionally, discrepancies between ground-based data and remote sensing data can also influence the accuracy of the validation results. To further enhance the performance of the method, we propose the following improvements: (1) Improve data quality: Increase the amount of reliable, high-precision training data, especially more detailed soil moisture and land surface temperature data, to strengthen the training process. (2) Pixel-level models: Develop pixel-level nested models for the high-precision retrieval of soil moisture and land surface temperature, thereby improving spatial resolution performance. These improvements will not only enhance the retrieval accuracy and reliability but also expand the method’s applicability, providing stronger data support and theoretical foundations for geoscience research.