Effects of Deep Learning Observation Operators in Direct Radiance Assimilation of Microwave Radiation Imager on Land Surface Models

1. Introduction

Soil moisture plays a critical role in land–atmosphere interactions. By modulating the partitioning of surface sensible and latent heat fluxes, it alters evapotranspiration, runoff generation, and water–heat transport, thereby exerting substantial impacts on weather and climate predictions [1,2,3]. Land surface model simulations constitute a primary means of projecting future soil moisture states. Incorporating observational information into land surface models via data assimilation to optimize initial conditions represents an important approach for improving simulation and forecast accuracy [4,5,6,7].

Accurate observational information is the primary source of performance improvements in data assimilation. However, conventional in situ measurements are severely limited for land surface assimilation needs due to the high spatial heterogeneity of soil moisture. With the advancement of satellite remote sensing, assimilating remotely sensed data to optimize initial fields has become standard practice. Two main assimilation schemes are commonly used at present: indirect assimilation, which incorporates microwave-retrieved land surface products [8,9,10,11], and direct assimilation, which employs an observation operator to transform background state variables into brightness temperature and directly assimilates satellite brightness temperature observations [1,12,13,14,15]. Indirect assimilation, valued for its simplicity and directness [14,16,17,18], was the first scheme to gain widespread application and substantially improved the forecast performance of land surface models. However, with the refinement of land surface models and advances in data assimilation techniques, the limitations of indirect assimilation have gradually become apparent: the retrieval process introduces errors originating from auxiliary datasets, which markedly amplifies uncertainties in retrieval errors and impairs the stability of assimilation performance [5,19]. Meanwhile, processing delays associated with retrieved products degrade the timeliness of operational data assimilation. In contrast, the direct assimilation of brightness temperature skips the complex retrieval process and thus allows for more effective control of observational errors [20]. Given this merit, studies concerning the direct assimilation of satellite radiance observations have attracted extensive attention [1,5,7,21,22,23]. Numerous scientists have further improved the assimilation performance of brightness temperature data via key technical optimizations [24,25] and the synergistic assimilation of multi-satellite datasets [26].

Although assimilating satellite brightness temperature data can refine the initial states of land surface models, substantial uncertainties still persist [14]. In direct radiance assimilation, the observation operator serves as a critical link between model state variables and observed brightness temperature [13] , and its accuracy directly determines assimilation performance. Observation operators are generally built upon physical radiative transfer models, such as CMEM, CRTM, RTTOV, and ARMS [7,22,27,28,29,30]. Nevertheless, conventional physical radiative transfer models require abundant ancillary data, among which the uncertainties associated with land surface emissivity stand out most prominently. Direct observational measurements of surface emissivity are lacking [27]. Although numerous studies have developed surface emissivity estimation models [31,32] , significant biases remain in simulated emissivity values owing to the intricate, variable nature of land surface media and the absence of key input parameters including vegetation conditions, soil moisture and surface roughness [33].

The advancement of deep learning techniques provides more optional observation operators for data assimilation [34,35,36]. To mitigate biases induced by land surface emissivity errors, Li et al. [37] developed an observation operator for assimilation built on a Multilayer Perceptron (MLP), which avoids explicitly incorporating land surface emissivity. By learning the inherent statistical correlations between variables characterizing land surface radiative properties, this model indirectly captures emissivity’s effects on brightness temperature. It effectively suppresses errors caused by uncertainties in land surface emissivity and markedly enhances the accuracy of brightness temperature simulations. Based on this, this study introduces the MLP-based observation operator into the Simplified Extended Kalman Filter (SEKF) framework to boost the performance of direct radiance assimilation. An integrated assimilation system coupling the Common Land Model (CoLM), the MLP module and the SEKF algorithm is constructed to quantify how direct assimilation of FY-3D Microwave Radiation Imager (MWRI) brightness temperature observations improves CoLM simulation outputs.

The remainder of this paper is organized as follows: Section 2 introduces the data used in this study and their preprocessing procedures. Section 3 describes the models employed, including the MLP model, the CMEM model used for comparison, and the assimilation system framework. Section 4 details the experimental design, outlining the specific construction details of the assimilation system and the configuration of different experimental schemes. Section 5 systematically analyzes the assimilation impact, focusing on evaluating the overall effectiveness of the MLP assimilation system and comparing the simulation performance of MLP and CMEM as observation operators. Section 6 presents the assimilation results through typical case studies and statistical analysis. Section 7 summarizes the main conclusions and discusses future research directions.

2. Data Description

2.1. FY-3D/MWRI Brightness Temperature Data

This study uses brightness temperature (TB) observations from the Microwave Radiation Imager (MWRI) aboard the Fengyun-3D (FY-3D) meteorological satellite. FY-3D is a Chinese second-generation polar-orbiting meteorological satellite operating in an afternoon orbit. Its primary passive microwave sensor, the MWRI, is a conically scanning, multi-frequency, dual-polarized radiometer with a swath width of approximately 1400 km. It measures at five frequencies: 10.65, 18.7, 23.8, 36.5, and 89.0 GHz. The TB data are preprocessed and calibrated to meet operational standards, with absolute calibration accuracy better than 2.0 K.

This study focuses on the vertically polarized (V-pol) channel at 10.65 GHz. Compared to its horizontal counterpart, V-pol microwaves are less sensitive to land surface roughness and are relatively less affected by vegetation and complex terrain, thereby providing a more stable representation of the target’s intrinsic radiation characteristics [21]. For this preliminary analysis, this study prioritizes the assimilation of daytime observations. Daytime solar radiation enhances the surface thermal emission signal, allowing the MLP model to more clearly capture the nonlinear relationships between TB and land surface parameters and achieve higher TB simulation accuracy [37]. Daytime samples are identified by converting the observation UTC time to Local Solar Time (LST) using the formula $\mathrm{L}\mathrm{S}\mathrm{T}=\mathrm{U}\mathrm{T}\mathrm{C}+{\displaystyle \frac{\mathrm{Longitude}}{{15}^{°}}}$ ; samples with LST between 6:00 and 18:00 are classified as daytime.

2.2. ERA5 Reanalysis Datasets

Forcing data for this study are obtained from two ERA5 products: total column cloud liquid water, vegetation type, vegetation cover, and soil type are drawn from the global ERA5 reanalysis (spatial resolution: 0.25° × 0.25°); 2 m air temperature, 10 m wind components, land surface temperature, and surface soil temperature (0 to 7 cm) are taken from the ERA5-Land reanalysis. ERA5-Land provides high-resolution land surface fields at a spatial resolution of 0.1° × 0.1°, achieved through an advanced land surface model configuration explicitly optimized to represent key land surface processes. From the ERA5 soil type classification, we derive volumetric sand and clay fractions to characterize soil texture. All forcing variables are spatially interpolated to the FY-3D/MWRI observation pixel centers using nearest-neighbor interpolation before assimilation.

To categorize the underlying surface, we aggregate the original ERA5 vegetation types into nine primary classes based on the provided global vegetation labels (Table 1). High vegetation types are merged as follows: evergreen and deciduous needleleaf forests into “Needleleaf Forest”; evergreen and deciduous broadleaf forests into “Broadleaf Forest”; and wetland forest/woodland and broken forest into “Mixed Forest”. For low vegetation types, grassland and tall grass are combined into “Grassland”; crops and irrigated crops are merged into “Agricultural Lands”; while semidesert, tundra, and Bogs and marshes remain as independent categories. Evergreen and deciduous shrubs are merged into “Shrubs”. This classification scheme is used to input observation data into the pre-trained MLP model by land cover type for type-specific brightness temperature (TB) simulations.

2.3. In-Situ Soil Moisture Observations

To objectively evaluate the performance of the soil moisture assimilation system, this study employs in-situ soil moisture observations from ground-based stations that are temporally and spatially coincident with satellite overpasses as an independent validation benchmark. Hourly volumetric soil moisture measurements at the 0–10 cm depth layer from 2,878 automatic soil moisture monitoring stations—operated by the National Meteorological Information Center (NMIC) of the China Meteorological Administration (CMA)—were used; soil moisture values extracted from these data serve as quantitative references for validation. The spatial distribution of these stations is illustrated in Figure 1. Classification of the observation stations based on ERA5 vegetation types reveals that the underlying surface across China’s land domain is predominantly characterized by four types: agricultural Land, grassland, shemidesert, and shrubland (Figure 1). For systematic validation and analysis, this study primarily utilizes observations from June to July 2022.

2.4. Data Preprocessing

To construct the input dataset for the assimilation system, this study conducted systematic preprocessing of multi-source data, including FY-3D/MWRI satellite brightness temperatures. First, land-based observations were extracted using the land mask provided by the FY-3D satellite. Subsequently, rigorous geolocation quality control was performed: data from the five edge pixels of each scanning swath and all pixels within 50 km inland from land-water boundaries were excluded to mitigate edge effects and interference from mixed land-water pixels. Based on this, the nearest neighbor interpolation method was employed to match variables from the ERA5 reanalysis data—including 2 m air temperature, wind speed, liquid water content, and vegetation type—to the screened FY-3D observations. Furthermore, to eliminate the influence of clouds on surface microwave radiative transfer, the interpolated ERA5 cloud liquid water path (LWP) was used as a cloud detection indicator. Observations with LWP values exceeding 0.01 kg/m² were identified as cloud-affected and excluded from assimilation [38].

According to the design of the assimilation system, assimilation was performed over the Chinese land domain at 0600 UTC daily. To align with this scheme, input datasets within a 6-hour window centered on each assimilation time were aggregated into a single analysis sample.

3. Model Description

3.1. The Common Land Model (CoLM)

Land surface process models provide a mathematical framework for simulating the physical exchanges of water and energy between the land surface and the atmosphere [39]. The Common Land Model (CoLM) adopted in this study is widely regarded as one of the most reliable and comprehensive land surface models [40,41]. CoLM discretizes the soil column into multiple vertical layers, enabling high-resolution representation of soil moisture profiles. It explicitly represents key hydrological and biophysical processes—including precipitation infiltration, surface evaporation, vegetation transpiration, and surface and subsurface runoff. Furthermore, through an improved soil parameterization scheme that accounts for soil organic matter content, CoLM refines the estimation of soil hydraulic and thermal properties, thereby improving simulation fidelity.

CoLM requires high-quality meteorological forcing data and static soil parameters for reliable operation. Meteorological forcing data are typically derived from atmospheric reanalysis products or in situ observations and include near-surface wind speed, 2 m air temperature, 2 m specific humidity, surface pressure, precipitation rate, and downward shortwave and longwave radiation [40,42]. In offline model evaluation, global reanalysis datasets—including ERA-Interim and ERA5—as well as high-resolution regional products such as the China Meteorological Forcing Dataset (CMFD), are commonly used as meteorological forcing [40,43]. Static soil parameters are drawn from global soil databases, notably the Global Soil Data Set for Earth System Modeling (GSDE) [44], to ensure physical realism and cross-study comparability of simulations. In this study, CoLM is forced exclusively by the ERA5 global atmospheric reanalysis dataset.

Figure 2 shows the 30 day average spatial distribution of volumetric soil moisture in the 0–10 cm soil layer, simulated by the Community Land Model (CoLM), compared with in situ observations from 2,878 national meteorological stations. Observations reveal a spatial pattern characterized by “wet conditions in southern China and dry conditions in northern China, with wetter conditions in eastern regions and drier conditions in western regions”: soil moisture is generally high in southern regions such as the middle and lower reaches of the Yangtze River and South China (frequently exceeding 0.30 m³/m³), while northern regions such as western Inner Mongolia and Tibet are relatively dry (often below 0.15 m³/m³, with local areas below 0.05 m³/m³). CoLM not only reproduces this wet–dry spatial pattern with reasonable fidelity but also captures the pronounced east–west gradient in soil moisture—from humid eastern regions to arid western regions—thereby demonstrating its capability to represent the large-scale spatial structure of soil moisture. However, localized biases persist in magnitude: simulated values are systematically higher in North China (115°E, 37°N) and the eastern Tibetan Plateau (94°E, 33°N), while underestimations occur at stations in East China (118°E, 30°N) and parts of South China (112°E, 25°N).

3.2. CMEM Radiative Transfer Model

This study employs the Community Microwave Emission Modeling platform (CMEM), a land surface microwave radiative transfer model developed under the leadership of the European Centre for Medium-Range Weather Forecasts (ECMWF), as the observation operator for comparative experiments [14]. CMEM is specifically designed to simulate brightness temperature (TB) across the 1–20 GHz frequency range for diverse land surface conditions, under varying polarization states (vertical/horizontal) and observation geometries (e.g., incidence angle, azimuth). As one of the most widely adopted and physically comprehensive radiative transfer models in soil moisture and land surface remote sensing, CMEM explicitly represents radiative transfer processes over heterogeneous surfaces—including bare soil, vegetated canopies, snow, ice, and open water—while rigorously accounting for the coupled effects of atmospheric attenuation, sensor frequency, polarization, and viewing geometry on the simulated TB signal.

CMEM employs a modular architecture that enables flexible selection of parameterization schemes for atmospheric contributions, soil emissivity, and vegetation emissivity. Given the focus of this study on summer-season surface soil moisture, snow-related processes are explicitly disabled in the model configuration. The specific setup is as follows: (i) the Dobson dielectric mixing model (Dobson et al., 1985) is applied to compute the complex dielectric constant of moist soil, consistent with the satellite observation frequency; (ii) the Fresnel reflectivity model (Njoku and Kong, 1977) is used to derive surface emissivity under the assumption of a smooth, homogeneous interface; (iii) surface roughness effects are corrected using the semi-empirical Wegmueller model (Wegmueller and Matzler, 1999); (iv) vegetation opacity is estimated via the geometric-optics-based Wegmueller model (Wegmueller et al., 1995); (v) atmospheric attenuation and emission are simulated using the Ulaby radiative transfer formulation (Ulaby et al., 1986); and (vi) surface soil temperature is adopted as the effective physical temperature of the soil layer, while near-surface air temperature is used as a physically justified proxy for canopy temperature.

3.3. MLP Model

Uncertainty in land surface emissivity is a critical factor constraining the effectiveness of land surface radiance brightness temperature assimilation. Conventional observation operators, which heavily rely on this uncertain parameter, suffer from limited simulation accuracy. To overcome this dependency, Li et al. [37] developed an observation operator based on a Multi-Layer Perceptron (MLP) that achieves efficient and high-accuracy simulation of brightness temperature across different vegetation types without requiring explicit land surface emissivity.

This observation operator employs a modeling strategy that groups data by vegetation type and classifies observations into daytime and nighttime categories. Leveraging the strong nonlinear mapping capability of MLP networks, it directly learns the implicit physical relationships between brightness temperature and a suite of surface and environmental variables—including land surface temperature, wind speed, soil moisture, and satellite geometric parameters—thereby circumventing explicit emissivity parameterization.Furthermore, to tackle the issue of large errors in traditional models caused by complex daytime radiative processes, this MLP model effectively captures the synergistic effects of solar radiation and surface parameters on brightness temperature via its deep learning mechanism.

Evaluation using simulations of the FY-3D/MWRI 10.65 GHz vertically polarized channel shows that the MLP model achieves significantly higher simulation accuracy than the traditional CMEM model for most vegetation types during daytime, with the overall RMSE reduced from 6.94 K to 4.34 K (As shown in Figure 3). Notably, the improvement is most pronounced over bare soil regions—areas highly sensitive to emissivity and where traditional models exhibit the largest errors—in which the RMSE decreases from 10.35 K to 4.07 K. In the following experiments, the mean bias under different vegetation types will be adopted as the bias correction term.

3.4. SEKF Assimilation Method

The Simplified Extended Kalman Filter (SEKF) is a computationally efficient variant of the Extended Kalman Filter (EKF) that links observations to prognostic variables via the observation operator H, thereby supporting point-wise data assimilation. The state variable update is formulated as:

$$x^a=x^b+\mathbf{K}\left[y^o-H\left(x^b\right)\right]$$

(1)

where x denotes the state variable; $x^a$ and $x^b$ represent the analysis and background fields, respectively; $y^o$ is the observation vector; H is the nonlinear observation operator mapping state variables from model space to observation space; and $H\left(x^b\right)$ represents the simulated observation vector. The Kalman gain matrix K weights the contributions of the model state and observations:

$$\mathbf{K}=\mathbf{B}{\mathbf{H}}^T{\left(\mathbf{H}\mathbf{B}{\mathbf{H}}^T+\mathbf{R}\right)}^{-1}$$

(2)

where H is the Jacobian matrix of the observation operator and Hᵀ its transpose; B and R denote the background and observation error covariance matrices, respectively, quantifying their respective uncertainties. The Jacobian matrix H reflects the sensitivity of brightness temperature to infinitesimal perturbations in soil moisture within the top three soil layers. In this study, H is computed numerically using the finite difference method:

$$\mathbf{H}={\displaystyle \frac{H\left(x+\delta x\right)-H\left(x\right)}{\delta x}}$$

(3)

That is, H is derived by applying an infinitesimal perturbation δx to the soil moisture in the background state vector and computing the resulting change in simulated brightness temperature via the observation operator.

3.5. Land Surface Data Assimilation System

Built upon the CoLM and SEKF assimilation framework, this study implements two land surface data assimilation systems: one employing the MLP observation operator and the other the CMEM observation operator (hereinafter referred to as the MLP and CMEM schemes, respectively). Both systems use CoLM-simulated fields as the background state and assimilate satellite observations via SEKF to update soil moisture.

During the assimilation process, model-simulated soil moisture is first interpolated to satellite observation points. The difference between observed and simulated brightness temperatures is then calculated to derive the observation increment. Subsequently, a regional averaging method is used to re-interpolate this increment field back to the model grid—i.e., for each model grid cell as the center, all observation points within a range of twice the grid spacing are searched, and the arithmetic mean of their observation increments is computed for assimilation updates. This method effectively reduces errors introduced by directly interpolating observed brightness temperatures to the model grid and better preserves the original observation information.

4. Numerical Experiments

4.1. Sensitivity Test of Observation Operator

In SEKF assimilation systems, it is necessary to define the adjoint matrix of the observation operator, which is usually obtained by transposing the observation operator matrix. Therefore, the observation operator matrix must be computed first. The observation operator is a nonlinear function, and its matrix representation can only capture its linearized component. Here, the linearized operator matrix is typically obtained via perturbation experiments involving two perturbed versions of the observation operator [5]. The experiment uses the model simulation output at 0600 UTC on 2 June 2022 as the reference state (denoted as $x_b$) and applies a suite of small, symmetric positive and negative perturbations—ranging in amplitude from ${10}^{-7}$ to ${10}^{-2}$—to the soil moisture variable, thereby generating the corresponding perturbed states $x_b^{+}$ and $x_b^{-}$. After inputting these states into both the CMEM model and the MLP surrogate model, respectively, the reference brightness temperature, the positively perturbed brightness temperature $T{B}_{pert}^{+}$, and the negatively perturbed brightness temperature $T{B}_{pert}^{-}$ are obtained for each model. Based on these results, the forward difference $H^{+}$ and the backward difference $H^{-}$ of this observation operator are computed as approximations of the tangent-linear operator:

$$H^{+}=[{TB}_{pert}^{+}-{TB}_{no}]/pert$$

(4)

$$H^{-}=-[{TB}_{pert}^{-}-{TB}_{no}]/pert$$

(5)

where $H^{+}$ quantifies the output change rate of the observation operator after applying a positive perturbation to the background state, and $H^{-}$ measures that after applying a negative perturbation; $pert$ pert denotes the imposed perturbation magnitude. Mathematically, $H^{+}$ and $H^{-}$ are numerical approximations of the tangent-linear operator (i.e., the Jacobian matrix) of the observation operator at the reference state. If the MLP model is continuously differentiable in a neighborhood of the reference state, then its response gradients to perturbations along distinct directions must be consistent; this consistency implies that $H^{+}$ and $H^{-}$ are nearly identical. Stability is assessed against two core criteria: first, as the perturbation magnitude decreases, $\mid H^{+}-H^{-}\mid$ should approach 0, indicating differentiability; while $(H^{+}+H^{-})/2$ should converge to a stable value, ensuring a reliable tangent-linear approximation [5].

Figure 4 shows the sensitivity responses of the two observation operators to three typical underlying surfaces: agricultural land, grassland, and semidesert. The red and black solid lines correspond respectively to the curves of the mean $(H^{+}+H^{-})/2$and absolute difference $\mid H^{+}-H^{-}\mid$, respectively, as functions of perturbation magnitude (the same convention applies throughout). As shown in Figure 4, the perturbation responses of the CMEM model exhibit relatively consistent piecewise characteristics across the different underlying surfaces. At the minimal perturbation magnitude (${10}^{-7}$), the asymmetry curves all show high initial values and rapidly decay as the perturbation increases, then quickly approach 0. Within the range of ${10}^{-6}$ to ${10}^{-2}$, both the asymmetry and corresponding mean values of CMEM remain stabl, with no noticeable increase as perturbation magnitude grows. Among the three surfaces, semidesert exhibits significantly higher asymmetric response intensity under small perturbations than agricultural land or grassland, indicating the most pronounced nonlinear behavior; in contrast, the response curves for agricultural land and grassland are flatter, reflecting higher overall stability compared to semidesert. Moreover, the mean response (red solid line) for semidesert is significantly higher than that of the other two surface types and attains the highest response intensity overall. For the MLP observation operator, stability is well maintained over the moderate-perturbation interval: within the magnitude range ${10}^{-6}$ to ${10}^{-3}$, $\mid H^{+}-H^{-}\mid$ approaches zero and $(H^{+}+H^{-})/2$ converges to a stable value, —satisfying the stability criterion [5]. When the perturbation exceed ${10}^{-3}$, nonlinear effects become markedly enhanced; when it is too small (e.g., less than ${10}^{-6}$), numerical round-off errors may dominate. Across the full perturbation range, agricultural land and grassland demonstrate relatively strong overall stability, with minimal variation in their central response values; agricultural land also maintains stability under moderate and small perturbations, with only a sharp rise in sensitivity observed under strong disturbances; semidesert displays the highest perturbation sensitivity among the three surface types, showing the most significant asymmetric response intensity—yet still substantially lower than the corresponding values for the CMEM model.

Based on the above sensitivity analysis results, this study determines the optimal perturbation magnitude ranges for the two observation operators, tailored to each vegetation type. For the CMEM model, the perturbation magnitude is set to ${10}^{-3}$ for agricultural land and grassland (with good overall stability), and for semidesert, it is set to ${10}^{-4}$ (more sensitive to perturbations). For the MLP observation operator, the perturbation magnitude is set to ${10}^{-4}$ for agricultural land and grassland, where stability is maintained over the moderate-perturbation interval; for semidesert, it is set to ${10}^{-5}$, as this surface type exhibits the strongest perturbation sensitivity among the three and responds with pronounced nonlinear behavior under large perturbations.

4.2. Error Setting

Specifying the observation and background error covariance matrices is a core step governing the quality of the analysis field in a data assimilation system. The observation error covariance matrix R quantifies the uncertainty inherent in observational data, whereas the background error covariance matrix B characterizes the uncertainty associated with the model forecast state.

To objectively and quantitatively assess the error characteristics of the two observation operators, this study conducted systematic statistical validation of the biases between satellite-observed brightness temperatures and those simulated by the MLP and CMEM models—separately for each vegetation type. The results indicated that model errors varied across different vegetation types. To accurately reflect the total observational uncertainty under various scenarios, it is necessary to set observation errors separately for each vegetation type. Accounting for the combined contributions of instrumental noise, forward model approximation errors, and other unquantified sources, the MLP model’s observation errors were set to values slightly exceeding the standard deviation of the corresponding vegetation-type-specific bias (Table 2), thereby ensuring robust representation of observational uncertainty under diverse vegetation conditions. In contrast, the CMEM model employed a uniform observation error of 8 K—chosen to be marginally larger than the overall bias standard deviation—to facilitate direct comparison.

Meanwhile, this study uses the CoLM-simulated soil moisture from the top three model layers as the background state for assimilation. Based on the statistical characteristics of historical CoLM simulations, the background error standard deviations were set to 0.17 m³/m³ for the first layer and 0.16 m³/m³ for both the second and third layers. To ensure a fair performance comparison between the MLP and CMEM assimilation systems, identical background states and background error specifications were applied to both systems.

4.3. Quality Control

To ensure the reliability of assimilation system inputs, this study implemented an additional quality control step on the simulated brightness temperature data, building upon preliminary systematic preprocessing. The preliminary preprocessing had already removed contamination from observational edge effects, sea-land mixed pixels, and cloud-affected observations—achieved through geographic positioning screening, sea–land boundary masking, and cloud detection. Subsequently, a threshold-based outlier detection method was applied: samples for which the absolute observation increment (i.e., the difference between observed and background-simulated brightness temperatures) exceeded twice the standard deviation of all increments were flagged as outliers and excluded. This step effectively removed highly biased or high-variance samples that could otherwise degrade assimilation performance, thereby yielding a higher-quality observational dataset for assimilation.

The same unified quality control procedure was applied to both the MLP and CMEM assimilation systems to ensure consistent input data quality across experiments.

4.4. Experimental Design

The assimilation period spanned from 0000 UTC on 2 June 2022 to 0000 UTC on 2 July 2022, with assimilation cycles executed every 6 hours—yielding a total of 120 analysis times. Following this, one-week forecast experiments covering the period 02–09 July 2022 were conducted. Using soil moisture from the top three CoLM layers as the background state, the assimilation system first mapped it to radiometric brightness temperature via the respective observation operator, then fused satellite-observed brightness temperatures using the SEKF to achieve layer-resolved soil moisture updates.

Three comparative experiments were conducted (Table 3): (1) the control experiment (CTL), in which no data assimilation was performed and the CoLM model ran freely; (2) the MLP assimilation experiment, employing the MLP observation operator; and (3) the CMEM assimilation experiment, which substituted the CMEM observation operator for the MLP while retaining all other assimilation configurations—including background state, error specifications, quality control, and SEKF settings—identical to those in the MLP experiment.

5. Analysis of Numerical Results

5.1. Analysis of Assimilation Improvement Effects

Figure 5 shows the spatial distribution of the top three layers’ average soil moisture at the beginning and end of the assimilation period for the three experimental groups (CTL, MLP, CMEM) and the station observations. At the start of the assimilation period, observed soil moisture exhibits a distinct spatial gradient, with higher values in the southeast and lower values in the northwest. The Northeast Plain (127°E, 45°N) and southern regions (113°E, 27°N) are the main wet centers, with maximum volumetric soil moisture exceeding 0.4 m³/m³; the Tibetan Plateau (85°E, 32°N), Inner Mongolia Plateau (110°E, 41°N), Loess Plateau (107°E, 37°N), and the northern part of the North China Plain (117°E, 39°N) constitute extensive dry centers, with soil moisture generally below 0.15 m³/m³, and the driest areas on the Tibetan Plateau and Inner Mongolia Plateau even falling below 0.05 m³/m³. All three experimental groups reproduce the spatial locations of the main wet and dry areas, with deviations only in magnitude: for dry areas such as the Inner Mongolia Plateau, the simulated results are significantly higher than the actual observations; for wet areas such as the Northeast Plain, the simulated results are notably lower than the observed values, overall exhibiting a characteristic of “wetter in dry areas and drier in wet areas.”

At the end of the assimilation period, the spatial pattern of the observed values still maintains the overall distribution characteristics of wet southeast and dry northwest, but the specific structure has undergone significant adjustments: the extent of dry areas in the northern region has substantially reduced and contracted northward, with northern North China transitioning from dry to wet; the extent of the wet center in the Northeast Plain has increased, and its intensity has strengthened, while the humidity in the main wet areas of the south has weakened compared to the initial state. Compared with the CTL experiment, both assimilation experiments significantly improve the simulation of soil moisture spatial structure. In dry regions—including the Inner Mongolia Plateau and the Loess Plateau—the spatial extents simulated by all three experiments broadly agree with observations. However, the assimilation experiments better capture drought intensity: simulated values are consistently below 0.10 m³/m³, with local minima dropping below 0.05 m³/m³, whereas CTL overestimates soil moisture, yielding values predominantly between 0.10 and 0.20 m³/m³. In the humid Northeast Plain, both assimilation experiments successfully reproduce the spatial structure of the wet center.

5.2. Evaluation of Assimilation Improvement Effects Using MLP

To evaluate the effectiveness of the MLP-based assimilation system, this study compares the MLP experiment (with assimilation) against the CTL experiment (without assimilation). Soil moisture outputs from all experiments are vertically integrated into an equivalent 0 to 10 cm layer via thickness-weighted averaging to facilitate direct comparison against in-situ station observations.

Figure 6a shows the spatial distribution of RMSE differences (CTL minus MLP) for surface soil moisture during the assimilation period. Across most regions, the differences are positive, indicating that the assimilation system effectively reduced simulation errors over most regions. Areas with significant error reduction (i.e., positive RMSE differences) are mainly concentrated in the Tibetan Plateau (92°E, 32°N), Loess Plateau (107°E, 37°N), Henan Province (113°E, 33°N), and northern Anhui Province (116°E, 31°N). Among the evaluated regions, the Loess Plateau shows the most pronounced improvement: the RMSE in the MLP experiment decreases by more than 0.04 m³/m³ relative to CTL. In contrast, improvements are marginal in the Northeast Plain, North China, and South China, which may be related to regional vegetation coverage. To clarify the causes of these differences, Figure 6c presents the spatial distribution of the annual mean Normalized Difference Vegetation Index (NDVI) over China [45], with vegetation coverage classified into five categories: low [0, 0.2), moderately low [0.2, 0.4), moderate [0.4, 0.6), moderately high [0.6, 0.8), and high [0.8, 1]. Regions such as Northeast and Southeast China are predominantly characterized by high vegetation coverage, while the Inner Mongolia Plateau and Loess Plateau are mainly covered by moderately low vegetation, and areas such as the Taklamakan Desert and western Tibetan Plateau exhibit low vegetation coverage [45,46]. In the Loess Plateau and surrounding areas such as Henan, vegetation is relatively sparse, leading to a stronger direct sensitivity of brightness temperature to soil moisture and reduced microwave signal attenuation by the vegetation layer. Consequently, the assimilation system more effectively exploits observational information to correct the model state. In contrast, regions including Northeast China and the southeastern coastal areas are predominantly covered by dense forests in summer, where abundant vegetation enhances vegetation emission and diminishes the direct sensitivity of brightness temperature to soil moisture, thereby limiting the assimilation system’s ability to optimize soil moisture estimates.

To assess the persistence of assimilation effects, a one-week forecast evaluation was conducted immediately after the assimilation period (02–09 July 2022) (Table 3). Figure 6b shows the spatial distribution of RMSE differences in surface soil moisture between the two experimental groups during the forecast period. The results indicate that the positive impact of assimilation attenuates in both spatial extent and magnitude; however, the Loess Plateau, which exhibited the largest assimilation improvement, still maintains a statistically significant advantage. One week after assimilation ceased, the RMSE in the MLP experiment over this region remains more than 0.02 m³/m³ lower than that in the CTL experiment, indicating robust persistence of the assimilation benefit. Furthermore, the negative assimilation impacts observed in North China and South China are also alleviated. These spatial differences are closely linked to underlying surface vegetation and land surface conditions. In the Loess Plateau, where vegetation is sparse, soil moisture dynamics are dominated by slow physical processes such as evaporation, leading to low temporal variability and enabling the assimilated state to persist more effectively during the forecast period. In contrast, in regions such as South China, where vegetation is abundant, active energy and water exchange between vegetation and the atmosphere continuously modulates soil moisture, thereby diminishing the persistence of assimilation effects. Thus, the vegetation characteristics and land surface conditions of the underlying surface determine not only the magnitude of assimilation improvement during the analysis phase but also the persistence of its benefits during the forecast phase.

Figure 7 displays the vertical cross-sections of soil moisture from the two experiments (CTL and MLP) over the region 32–35°N, 106–110°E. As shown in the figure, two distinct events of significant surface soil moisture increase occurred in this region around 17 June and 27 June. The moistening signals propagated rapidly downward to soil layers above 30 cm as the model integrated, gradually extending their influence to deeper layers. Continuous land surface assimilation exerted an overall reducing effect on soil moisture in this region: in the CTL experiment (Figure 7b), the elevated soil moisture persisted and continued to affect the region, whereas in the MLP experiment (Figure 7a), the assimilation quickly introduced moisture adjustment information into the surface layer, effectively weakening the impact of the two surface moistening events on deep soil. Notably, this assimilation effect remained evident in the simulation of deep soil moisture after 1 July. While this analysis confirms the capacity of land surface assimilation to adjust deep soil moisture, the validity of the assimilation effects requires further verification with actual observational data in subsequent studies.

5.3. Comparison of Performance Between MLP and CMEM Observation Operators

Figure 8 shows the spatial distribution of RMSE differences (CMEM minus MLP) between the CMEM and MLP experiments during the assimilation phase (0600 UTC on 17 June 2022, Figure 8a) and the forecast phase (0000 UTC on 9 July 2022, Figure 8b). Here, a positive RMSE differenc indicates that the MLP scheme outperforms CMEM (i.e., MLP’s RMSE is lower than CMEM’s). During the assimilation phase (Figure 8a), the MLP scheme demonstrates a clear advantage: the mean RMSE difference between the two experiments is 0.0042 m³/m³, and statistical analysis of all observation sites shows that MLP outperforms CMEM at 52% of sites, while CMEM outperforms MLP at only 33% of sites. This indicates that the MLP model achieves performance comparable to that of a mature physical model in incorporating observational information. Spatially, regions with significant improvement in the MLP experiment (defined as areas with positive RMSE differences) are concentrated over most of Xinjiang, eastern Qinghai, northern Sichuan, the Loess Plateau, Henan, and Anhui. These regions are characterized by relatively sparse vegetation cover, under which soil moisture exhibits a more sensitive and direct response to variations in microwave brightness temperature. Moreover, the MLP model bypasses physical parameterization of land surface emissivity entirely, thereby avoiding errors arising from emissivity estimation uncertainty in CMEM. In contrast, the MLP and CMEM experiments show broadly comparable performance over the southern North China Plain and southeastern regions, primarily because dense and heterogeneous vegetation cover in these areas strongly emits and attenuates microwave signals.

During the forecast phase (Figure 8b), the robustness advantage of the MLP scheme becomes more pronounced, with the proportion of regions where MLP performs better expanding to 56%, while the proportion where CMEM outperforms MLP decreases to 29%. The regions where the MLP experiment continues to show improvement remain concentrated in areas with relatively simple underlying surface structures, such as the Loess Plateau and central Xinjiang, where the response of soil moisture to microwave signals is relatively stable, allowing the assimilation impact to maintain good persistence.

6. Analysis of Temporal Variations in Assimilation Impact

6.1. Case Analysis of Soil Moisture Stations

To systematically examine how assimilation effects vary with underlying surface types, three representative stations located on semidesert, grassland, and agricultural land (geographical locations shown in Figure 8b) were selected for case studies. Time series of observed and simulated soil moisture at each station are presented in Figure 9. Initially, the model-simulated soil moisture in all three experiments exhibited a wet bias relative to observations. In the CTL experiment, this bias persisted throughout the simulation period due to the absence of observational constraints, resulting in poor representation of temporal soil moisture dynamics. In contrast, after assimilation, the responses of the two experimental groups differed significantly across underlying surfaces.

At the semidesert station (Figure 9a), the initial soil moisture exhibited a wet bias of approximately 0.05 m³/m³ relative to observations. In the CMEM assimilation experiment, this bias was corrected within two days, achieving the closest agreement with observed values first. This indicates a rapid response to strong brightness temperature signals under dry-surface conditions. However, the system then continuously over-adjusted, causing soil moisture to remain persistently below the observations and form a stable dry bias with an average deviation of −0.03 m³/m³. This may be attributed to limited temporal responsiveness of the CMEM model to soil moisture changes, for example, the land surface emissivity model’s insensitivity to small soil moisture variations. In contrast, the MLP assimilation experiment adjusted more slowly initially but gradually converged toward the observed values during the second week of assimilation and subsequently fluctuated narrowly around the observations, maintaining a state closest to the observations even during the subsequent forecast period, thereby demonstrating superior long-term stability and adaptability.

Figure 9b presents results for the grassland site with relatively slow soil moisture changes. The initial soil moisture at this site showed a wet bias of approximately 0.14 m³/m³ relative to observations. Although the CMEM assimilation experiment slowly approached the observations, its adjustment magnitude was limited, and it ultimately failed to effectively correct the model’s inherent wet bias. In contrast, the MLP assimilation experiment gradually adjusted to near the observed values within about one week, then maintained stability while responding to short-term observational variations. This indicates that the statistical model retains a certain capacity for soil moisture information extraction and assimilation even under vegetation influence.

Figure 9c presents results for the agricultural land site with denser vegetation. The initial wet bias at this site was approximately 0.15 m³/m³ relative to observations. The CMEM assimilation experiment performed highly similarly to the control experiment at this site (blue and green lines overlapping), indicating weak assimilation influence and failure to correct the model’s wet bias. In contrast, after adjusting to near the observed values, the MLP assimilation experiment fluctuated more stably around the observations without systematic deviation. It also maintained assimilation influence for approximately one week during the subsequent forecast phase, demonstrating better state retention and adaptability.

6.2. Analysis of Mean Error Characteristics

Previous studies have shown that due to the complex underlying surface environment in high-altitude regions (e.g., the Tibetan Plateau) and the significant errors in the background field data used to train the MLP model in such areas, the MLP model exhibits noticeable biases and suboptimal performance in brightness temperature simulations [37]. To ensure the reliability and representativeness of quantitative statistical results and to avoid interference from systematic errors in high-altitude regions on the overall assessment, only stations east of 100°E were selected for the analysis in this section, enabling an objective comparison of the performance differences among the MLP assimilation scheme, the CMEM assimilation scheme, and the control experiment (CTL) in soil moisture simulation.

Figure 10 and Figure 11 show the temporal evolution of standard deviation and correlation coefficient, respectively, for soil moisture from the MLP assimilation experiment, CMEM assimilation experiment, and CTL experiment, all evaluated against observations under the three vegetation cover conditions described above. Land surface assimilation yielded the greatest improvement in semidesert regions (Figure 10a and Figure 11a). The CTL experiment maintained a relatively steady standard deviation within 0.1 to 0.13 m³/m³. In the CMEM experiment, the improvement effect is relatively obvious at the initial stage of assimilation, with both the standard deviation and the correlation coefficient being better than those of the CTL experiment. However, this improvement gradually diminishes as assimilation progresses, likely due to increasing background field accuracy, which reduces the relative benefit of assimilation. In contrast, MLP consistently achieved a lower standard deviation and higher correlation coefficient than CTL throughout assimilation and into the forecast period. This may be attributed to the fact that land surface emissivity in semidesert areas is highly susceptible to factors such as soil texture, surface roughness, and instantaneous water content, leading to substantial fluctuations and making errors difficult to control in the CMEM model, thereby preventing the assimilation advantage from being sustained or even manifested. The MLP model, however, does not require land surface emissivity as input and thus avoids error propagation from these sources entirely. Consequently, in semidesert regions, MLP-simulated soil moisture values demonstrate significantly better stability and spatial correlation than both the CMEM assimilation experiment and the CTL experiment, representing the most prominent improvement.

Compared to semidesert stations, the underlying surfaces at grassland and agricultural land stations are more heterogeneous. At grassland stations (Figure 10b and Figure 11b), overall dispersion was marginally higher than at semidesert stations. The CMEM experiment reduced standard deviation relative to CTL only sporadically—primarily during early assimilation—and showed negligible improvement in spatial structure, as indicated by the correlation coefficient. In contrast, the MLP experiment sustained a consistently lower standard deviation than both CTL and CMEM throughout the assimilation period; its correlation coefficient remained the highest across all time steps, and the assimilation-induced improvement persisted for approximately five days into the forecast period. Cropland stations (Figure 10c and Figure 11c) feature the most heterogeneous underlying surfaces. Here, the CTL experiment exhibited the largest dispersion and strongest temporal fluctuations. The CMEM standard deviation closely tracked that of CTL—with minimal separation—whereas MLP maintained a robustly lower standard deviation and achieved a substantially improved correlation coefficient. Critically, the assimilation benefit from MLP extended for nearly one week into the forecast period, underscoring its stable and reliable performance under complex vegetated conditions.

7. Conclusions

Soil moisture is a key parameter in land surface processes and holds significant importance for numerical weather prediction and climate forecasting. Direct assimilation based on microwave brightness temperature is an effective approach for optimizing the initial field of soil moisture. However, traditional methods rely on physical radiative transfer models, and the uncertainties inherent in their land surface parameterization limit the effectiveness of assimilation. To address this issue, this study introduced an observation operator based on the MLP method and another based on the CMEM model, respectively. Coupled with the SEKF assimilation method, two direct microwave brightness temperature assimilation systems applicable to the CoLM land surface model were constructed, and the improvements to the CoLM model background field through the assimilation of FY-3D/MWRI brightness temperature data were evaluated.

Evaluations based on in-situ station data indicate that the MLP assimilation scheme can effectively optimize the simulation of surface soil moisture under different vegetation covers across Chinese land areas, while also exerting positive adjustments on deeper soil moisture. By effectively circumventing the challenges associated with land surface emissivity estimation, the MLP model generally reduces simulation errors across the study region, with the most prominent optimization effects observed in bare soil and grassland areas, where errors decreased by 8.3% and 10.2%, respectively. Even in cropland areas characterized by more complex vegetation, the MLP scheme remains capable of effectively utilizing brightness temperature observations to achieve stable improvements in soil moisture simulation. Furthermore, following assimilation with the MLP scheme, the correlation coefficients with observed values increased across all cases, with the most significant enhancement occurring in bare soil regions, where improvements of 53.9% and 63.8% were achieved relative to the control experiment and the CMEM scheme, respectively.

The improvement effects of the MLP assimilation scheme decay with increasing forecast lead time, yet persist robustly within core influence regions. Over the one-week forecast period, both the magnitude and statistical significance of the improvements gradually diminished; however, the MLP scheme maintained a lower soil moisture standard deviation than the control experiment across key regions—including the Loess Plateau—indicating sustained stabilization of the initial soil moisture field. Furthermore, across all three vegetation types, the MLP experiment consistently yielded the highest correlation coefficients among the three experiments, confirming its superior ability to enhance the spatial coherence of soil moisture simulations and improve agreement between simulated fields and in situ observations.

However, notable regional differences exist in the assimilation effectiveness of the MLP scheme. Improvements are more evident in areas such as central Xinjiang, the Loess Plateau, Henan, and Anhui, while the effects are relatively limited in certain regions with complex underlying surfaces or high altitudes. Consequently, the universality of the current single-operator assimilation scheme remains insufficient. Future work will therefore focus on developing a multi-operator collaborative assimilation framework, aiming to achieve more stable and universally applicable improvements in soil moisture simulation across China by integrating the advantages of different observation operators.