Long-term TB observations are subjected to outlier detection. A quality identifier, denoted by the integer n1, is assigned to each record (see Table 1). The judgment criterion is based on the mean (μ) and standard deviation (σ) of TB within each season: if the TB at time n, denoted TB(n), satisfies |TB(n)-μ|≤3σ, the observation is considered valid; otherwise, it is flagged as anomalous. While this statistical 3σ threshold serves as an efficient gross error check, it has inherent limitations. Genuine extreme meteorological events may be flagged as outliers; however, such events typically involve precipitation and wet-radome conditions, which inherently invalidate standard MWR profiling. Conversely, undetected minor erroneous data (e.g., small instrumental drifts) remaining within the 3σ range are systematically identified and eliminated in the subsequent consistency checks to prevent long-term biases.

Because MWRs operate continuously in outdoor environments, the radome can accumulate dust, moisture, or other contaminants, which may degrade measurement sensitivity and accuracy. Regular cleaning of the radome with purified water under clear-sky conditions is necessary, but this procedure often induces temporary abnormal increases in TB, resembling precipitation signals. Although an active blower/heater system is deployed, sub-zero winter temperatures can slow evaporation. Following cleaning, TB values generally return to normal within 1–2 h, but this process can take up to 4 h in winter. Based on maintenance logs, TB observations recorded within 4 h after radome cleaning are flagged as abnormal (n1=1 in Table 1) to conservatively ensure data purity.

During precipitation events, residual water layers on the radome may cause large uncertainties in TB observations, directly affecting retrieval accuracy (Wei et al., 2021). Therefore, after removing anomalous values via the outlier detection, precipitation-related data are further screened. The LV1 TB data from the RPG-HATPRO MWR include a Rainflag provided by a collocated precipitation sensor, indicating precipitation conditions: Rainflag = 0 denotes no precipitation, and Rainflag = 1 denotes precipitation. Accordingly, precipitation conditions are represented by identifier n2, as defined in Table 1.

Two complementary methods were used to identify cloudy conditions. The first method exploits the high sensitivity of the 31.4 GHz water vapor channel (CH7) to liquid water in clouds, analyzing TB fluctuations to detect cloud presence. The second approach incorporates CBH information derived from co-located infrared radiometer measurements to refine the classification of cloud and clear periods.

Given that the high-frequency water vapor channel CH7 (31.4 GHz) is sensitive to liquid water in clouds, its observed TB exhibits noticeable fluctuations when clouds are present. Therefore, the variability of CH7 observations over a specific time period – quantified by the standard deviation within a given time window – can serve as a reference indicator for the presence of clouds during that period.

Following the approach of Turner et al. (2007), this study uses a 30 min time window to calculate the standard deviation of CH7 observed TB, denoted as σc. The stability of the 31.4 GHz channel is then assessed by comparing σc against a threshold defined as a+b⋅IWV, where IWV represents the total column water vapor, and the parameters are set as a=0.15 K and b=0.06 K cm⁻¹. Based on this method for identifying cloudy conditions, the observed TB data are classified using the identifier n3: n3=0 for clear sky and n3=1 for cloudy sky.

To further improve cloud detection accuracy, the CH7-based method is complemented with CBH information obtained from a zenith-view IRT. It should be noted that the CBH is directly provided as a standard product by the RPG built-in software, which estimates the cloud base by correlating the IRT-measured sky temperature with the ambient temperature profile. The CBH value itself provides a physical constraint for identifying clear-sky periods. In this study, cases with the CBH values lower than 500 m or larger than 8000 m were treated as clear-sky conditions (n4=0). Conversely, cases with CBH higher than approximately 6–8 km are typical cirrus altitudes, and 2–6 km are typical mid-level clouds, and lower than about 2 km is generally associated with low clouds, and all of them is classified as cloudy (n4=1).

To facilitate the correct use of ground-based microwave radiometer observations, a comprehensive classification identifier, nflag, was established by integrating all the aforementioned classification flags. Its values and corresponding meanings are listed in Table 1, where “Other” indicates data with additional quality uncertainties and is not recommended for use.

Thus, based on TB observations obtained from the ground-based microwave radiometer during 2013–2022, the raw data were first subjected to an initial quality screening to remove outliers. Weather conditions – including precipitation, clear sky, and cloudy sky – were then identified and classified using multiple criteria. The final result is a nearly ten-year, high-temporal-resolution (∼ 1 min) multichannel TB long-term dataset, providing a reliable foundation for analyzing observational TB characteristics under different weather conditions, performing radiative simulations, and conducting atmospheric temperature and humidity profile retrievals.

To assess the quality of observed TB data, the MWRT (Microwave Radiative Transfer) model (Liu, 1998) was employed. MWRT is based on the four-stream discrete ordinate method to solve the radiative transfer equation, achieving high computational efficiency while maintaining good accuracy. Previous studies have demonstrated that MWRT outperforms other commonly used radiative transfer models in simulating ground-based MWR observations (Zou et al., 2021).

To simulate MWR-observed TBs, MWRT requires input atmospheric profiles, including pressure, temperature, and humidity. As no local radiosonde data are available at XH and the nearest sounding station provides only two profiles per day (morning and evening), hourly ERA5 reanalysis data with a spatial resolution of 0.25° were used to provide the atmospheric state fields. The quality of MWR TB observations was then quantitatively assessed by comparing simulated and measured TBs using three statistical indicators: mean bias (MB), correlation coefficient (R), and standard deviation (SD). These metrics respectively characterize bias, correlation, and dispersion, thereby providing a comprehensive evaluation of observation accuracy and reliability.

Given the accuracy of radiative transfer simulations under clear-sky conditions, the TBs observed by the ground-based microwave radiometer are expected to be consistent with simulated TBs. In the comparison study, a spatiotemporal synchronization approach was applied. Specifically, to match the 1 min MWR observations with the hourly forward-modeled TBs, the single 1 min MWR measurement closest to the exact hour of the simulation was selected. Subsequently, data pairs with anomalous deviations were removed using the 3σ criterion based on the Root Mean Square Error (RMSE).

Figure 3 presents scatter plots comparing observed and simulated TBs under clear-sky conditions during 2013–2022. Statistics from ∼ 28 000 matched samples show that R values between simulated and observed TBs are close to 1.0 for most channels, with data points concentrated along the 1 : 1 line, indicating strong agreement. This result confirms both the physical reliability of the observed TBs and the long-term stability of the MWR instrument. Among the O₂ channels, the low-frequency oxygen channel at 51.26 GHz (CH8) shows a slightly lower correlation (∼ 0.98) and the largest mean bias (∼ 1.51 K), which can be attributed to its sensitivity to lower- and mid-tropospheric water vapor as well as residual uncertainties in oxygen absorption parameterizations within radiative transfer models (Zou et al., 2021).

To systematically evaluate the long-term performance of the ground-based MWR, statistical analyses of R, MB, and SD were conducted for multi-channel observed and simulated TBs over the 10-year period (2013–2022). As shown in Fig. 4, except for 2013 – when limited observation samples slightly reduced correlations in the water vapor channels – the correlation coefficients for all channels remain highly consistent across the remaining years. The water vapor channels (CH1–CH7) and temperature channels (CH10–CH14) both show R>0.98, indicating excellent consistency between simulated and observed TBs. For the low-frequency oxygen channels (CH8 and CH9), correlation coefficients are slightly reduced, consistent with the results in Fig. 3, likely due to channel sensitivity to water vapor and limitations in the radiative transfer model. In terms of MB, except for 2013, the water vapor channels show a decreasing MB with increasing frequency. The largest MB is observed for CH8 (51.26 GHz), while the high-frequency oxygen channels (CH10–CH14) remain relatively stable. For SD, CH1 shows the largest values among the water vapor channels, which decrease progressively with frequency, whereas the high-frequency oxygen channels (CH10–CH14) maintain small and stable SD values.

Overall, the 2013–2022 evaluation of the MWR TBs using MWRT simulations confirms the instrument's long-term stability and the reliability of its measurements. Based on this foundation, a multi-parameter dataset was constructed by integrating the quality-controlled, weather-classified, minute-resolution, multi-channel TB observations with corresponding IRTs, and manufacturer-provided CBHs, IWV and LWP. It should be noted that CBHs, IWV and LWP are standard products retrieved by the instrument's built-in software. No additional LWP offset correction was performed.

The OE method is grounded in Bayesian theory (Rodgers, 2000), which can be expressed as: 1Px|y=Py|xP(x)P(y), where P(y|x) represents the likelihood function describing uncertainties in the measurement process and forward model, P(x) defines the prior probability distribution of the atmospheric state, and P(y) is a normalization factor ensuring that the posterior probability integrates to one. The posterior probability P(x|y) thus quantifies the likelihood of a given atmospheric state x given the observation y.

In this study, the prior dataset for the OE retrieval was constructed using radiosonde profiles from the Beijing station during 2016–2019. The station, located approximately 50 km from XH, provides vertical profiles of atmospheric pressure, temperature, and humidity twice daily (around 08:00 and 20:00 local time). These radiosonde observations were used to construct the prior mean state and covariance matrix required in the OE framework and also serve as an independent reference for evaluating the retrieval accuracy.

In the OE framework, a forward operator is required to simulate TBs from a given atmospheric state. For the clear-sky retrievals, we utilized the non-scattering microwave radiative transfer model (nonScatMWRadTran; Löhnert and Crewell, 2003). Gas absorption follows Rosenkranz (1998), with updates to the 22.235 GHz water vapor line width (Liljegren et al., 2005) and continuum absorption (Turner et al., 2009). Since liquid water scattering is negligible under clear-sky conditions (screened via strict LWP thresholds), this non-scattering assumption is physically appropriate.

To evaluate the applicability of nonScatMWRadTran, we benchmarked it against the MWRT model (Liu, 1998), which has been previously validated against line-by-line simulations for XH observations (Zou et al., 2021), making it a highly reliable baseline. Using 212 collocated radiosonde profiles, the two models showed excellent agreement, with RMSEs below 0.12 K (R>0.9999) for the O2 channels (51–58 GHz) and below 1.5 K (R>0.9992) for the WV channels (22–31 GHz).

Because OE retrieval requires repeated forward-model evaluations for Jacobian estimation, computational efficiency is critical for long-term processing. Given the 34-element state vector, each OE iteration requires 2N+1 forward-model evaluations. Compared with MWRT, the in-process implementation of nonScatMWRadTran substantially reduces retrieval time while maintaining comparable simulation accuracy.

To configure the OE retrieval setup, the state vector comprises atmospheric temperature and humidity profiles. To ensure structural consistency with the operational RPG-LV2 product and facilitate comparative analyses, the OE retrieval adopts the 34-layer vertical grid (up to 10 km), resulting in a 68-element state vector including temperature and log₁₀-transformed specific humidity profiles. Additionally, the surface meteorological observations (surface temperature and humidity) are incorporated as the bottom layer, yielding a final dataset with 35 vertical levels (the surface level plus the 34 retrieval layers). It is important to note that the passive nature of ground-based microwave radiometry dictates that the vertical information content is most abundant in the lower troposphere. Consequently, the retrieval sensitivity is highest within the boundary layer (0–2 km) and decreases with altitude (Fu et al., 2026). Furthermore, the total effective observation error covariance matrix (Se) is constructed as a diagonal matrix, assuming uncorrelated observation errors among channels. In this setup, the diagonal elements represent the total effective observation variance, which comprehensively accounts for instrumental thermal noise, calibration uncertainties, and forward-model errors. Based on the clear-sky observation-minus-simulation (O-B) residual statistics and the quality assessment of TBs detailed in Sect. 3.2.2, the prescribed observation error standard deviations (the square root of the diagonal elements of Se) were specified as 2.0, 2.2, 1.8, 1.3, 1.4, 1.0, and 1.0 K for the seven K-band water vapor channels (22.24–31.40 GHz), and 1.5, 1.7, 1.2, 0.8, 1.0, 1.0, and 1.0 K for the seven V-band oxygen channels (51.26–58.00 GHz), respectively. In addition, the background error covariance matrix (Sa) was constructed separately for each season (DJF, MAM, JJA, and SON) using long-term statistics derived from collocated radiosonde observations during 2016–2019.

DNNs have been widely applied in remote sensing retrievals. Common neural network architectures include the backpropagation (BP) network, convolutional neural network (CNN), and recurrent neural network (RNN) (Guo et al., 2021; Malmgren-Hansen et al., 2019; Zhao et al., 2018). Among these, the BP neural network is well suited for nonlinear regression problems, as it can approximate complex functions without explicitly constructing a physical forward model. While a standard BP network typically includes only a single hidden layer, a DNN extends this structure by stacking multiple hidden layers, enhancing feature extraction and nonlinear representation capabilities.

A typical DNN consists of an input layer, multiple hidden layers, and an output layer. Each neuron in the input layer represents a feature (in this case, one microwave channel), and neurons in the hidden layers apply weighted transformations followed by nonlinear activation functions. The network is trained via forward and backward propagation, and regularization techniques such as Dropout are employed to prevent overfitting.

In this study, a DNN-based retrieval model was developed for MWR profile retrieval (Fig. 5). The input comprises 14-channel TBs, and the output corresponds to temperature and humidity profiles from 0–10 km. The training dataset was constructed using temporally matched actual MWR TB observations from 2019 and corresponding ERA5 temperature and humidity profiles as targets. Utilizing observed TBs rather than forward-simulated TBs allows the empirical model to inherently account for real-world instrumental noise and site-specific measurement characteristics. Furthermore, restricting the training dataset to a single representative year (capturing a full seasonal cycle) was a deliberate strategy. It ensures that the subsequent application of this model to the remaining 9 years of the decadal dataset serves as a strictly independent temporal evaluation, thereby rigorously demonstrating the model's true generalizability and the instrument's long-term stability. After removing missing values, all input features were normalized to ensure consistent data scaling. The dataset was randomly divided into training, validation, and test sets in a 6 : 2 : 2 ratio to maintain both randomness and reproducibility. The DNN architecture consists of three hidden layers, each using the LeakyReLU activation function and batch normalization to enhance nonlinearity and accelerate convergence. Dropout regularization was applied to each hidden layer to prevent overfitting, while a linear activation was used in the output layer for regression. The model was optimized using the mean squared error (MSE) loss function, with EarlyStopping and ReduceLROnPlateau strategies applied – training was terminated if no improvement was observed for 15 consecutive epochs, and the learning rate was halved if no improvement occurred for 5 epochs.

To quantitatively evaluate retrieval performance, radiosonde-measured temperature and humidity profiles from 2020 were used as the reference “truth”. Both the OE- and DNN-based retrievals, derived from 2020 MWR TB observations, were assessed against these independent profiles. Three statistical metrics were employed: MB, R, and SD. To further quantify improvements relative to the RPG-LV2 operational product, an accuracy improvement rate (Zhang et al., 2020) was introduced, calculated as: 2k=(sm+x‾m)-(sr+x‾r)(sm+x‾m), where k is the accuracy improvement rate, x‾m is the mean bias of the RPG-LV2 product, calculated as x‾m=1n∑i=1nxmi, and x‾r is the mean bias of the new model retrieval, x‾r=1n∑i=1nxri. The standard deviations are 3sm=1n∑i=1n(xmi-x‾m)2,sr=1n∑i=1n(xri-x‾r)2, where xmi=Xmi-Xsi, xri=Xri-Xsi; Xmi represents the RPG-LV2 product values, Xri represents the retrieval results from the new model, and Xsi is the reference truth (radiosonde observation or ERA5 data). Here, n is the sample size, with i=1,2,3,…,n. This evaluation framework enables a direct comparison of the two retrieval approaches (OE and DNN) against both the reference truth and the operational product, thereby quantifying the relative improvement achieved by the proposed methods.

Under clear-sky conditions, multi-channel TB observations from the MWR were used to retrieve atmospheric temperature and humidity profiles using the OE method. To directly evaluate the retrieval performance, the OE-retrieved profiles are compared against radiosonde measurements, rather than relying solely on the manufacturer-provided product. Figure 6 presents a comparison of the RPG-LV2 product and the OE-retrieved profiles against radiosonde measurements in 2020, in terms of MB and RMSE.

For temperature (Fig. 6a), the OE retrievals demonstrate consistently superior performance compared with the RPG-LV2 product across the full 0–10 km layer. The mean bias of OE-retrieved temperature relative to radiosonde data ranges from -0.83 to 0.50 K, while the RMSE varies from 0.96 to 3.56 K, increasing gradually with altitude and reaching its maximum at 10 km. For relative humidity (Fig. 6b), the OE retrievals also outperform the RPG-LV2 results across all altitudes, with mean biases between -6 % and 6 % and RMSE values ranging from 9 % to 20 %. These results indicate that the OE method provides physically consistent and robust retrievals under clear-sky conditions, where radiative transfer assumptions are well satisfied.

Further statistical analyses were conducted to quantify the differences between the retrieved profiles and radiosonde measurements across different altitude ranges, as well as to evaluate the accuracy improvement of the OE retrieval relative to the RPG-LV2 product (Table 2). Across all four altitude intervals ([0–2], [2–6], [6–10], and [0–10] km), the OE retrievals exhibit consistently higher accuracy. Over the full 0–10 km layer, the OE retrieval achieves a 35 % improvement in temperature accuracy relative to RPG-LV2, with particularly notable gains of up to 40 % within both the near-surface (0–2 km) and upper-tropospheric (6–10 km) layers. For relative humidity, the OE retrieval achieves a 25 % accuracy improvement over the full profile, with the highest enhancement (29 %) observed near the surface (0–2 km). These results confirm the robustness of the OE method under clear-sky conditions and highlight its capability to effectively reduce systematic biases in both temperature and humidity retrievals.

Similarly, under cloudy-sky conditions, multichannel MWR TBs at XH were used as input to the DNN-based retrieval model to obtain atmospheric temperature and humidity profiles. Given that cloud contamination violates the assumptions of traditional radiative transfer inversion, the DNN retrieval is directly evaluated against radiosonde observations to assess its capability under all-sky conditions. Figure 7 compares the DNN-retrieved profiles, RPG-LV2 product against radiosonde observations in 2020 in terms of MB and RMSE.

The DNN-retrieved temperature profiles exhibit markedly reduced mean biases across the entire altitude range compared to the RPG-LV2 results, with the overall mean bias of 0.38 K. The corresponding RMSE is significantly lower, particularly within the near-surface layer (below 2 km) and the mid-to-upper troposphere (above 4 km), typically ranging between 1 and 3.5 K. For relative humidity, the DNN retrievals also outperform the RPG-LV2 product throughout the entire 0–10 km range. Although both MB and RMSE increase with altitude, the mean bias remains within ±5 % below 6 km and reaches its maximum near 10 km. These results demonstrate that the DNN model effectively captures the nonlinear relationships between TB observations and atmospheric state variables.

Table 3 summarizes the MB and RMSE values of the DNN and RPG-LV2 retrievals relative to radiosonde profiles across different altitude ranges, along with the accuracy improvement rates of the DNN retrievals. Overall, the DNN model yields systematically lower MB and RMSE values than the RPG-LV2 product across all layers, indicating clear and consistent improvement. For temperature profiles, the DNN retrieval achieves an overall 39 % increase in accuracy over the 0–10 km layer relative to RPG-LV2, with the most pronounced improvements of 41 % in the near-surface layer (<2 km) and 56 % in the mid-to-upper layer (6–10 km). For humidity profiles, the DNN retrieval shows a 28 % overall accuracy improvement, with the highest enhancement (30 %) observed in the 0–6 km range.

From an application perspective, the OE and DNN approaches are employed as complementary rather than competing methods. The physically based OE method performs optimally under clear-sky conditions where forward radiative transfer modelling is highly reliable. Conversely, the DNN model demonstrates enhanced robustness under cloudy conditions by implicitly capturing the complex, nonlinear relationships between TBs and atmospheric states. By applying each method under its respective optimal conditions, this condition-dependent strategy yields retrieval results that are consistently closer to independent radiosonde observations than the generic operational RPG-LV2 product across all sky conditions.