The lower troposphere is the region where most human activities and weather phenomena take place. The systematic measurement of meteorological parameters in this region is a critical foundation for accurate weather forecasting and climate change research. It is also essential for ensuring the efficiency of aviation, travel, and radio communication systems (Maciejewska, 2025; Morbidelli et al., 2011). However, the precise detection of atmospheric in the marine environment is further complicated by its unique geographical characteristics and dynamic processes. Recent studies have further highlighted the complexity of marine atmospheric structures, particularly under extreme weather conditions such as tropical cyclones (Guimond et al., 2018; Ahern et al., 2019). For instance, Wei et al. (2025b) demonstrated that vertical wind shear can induce significant asymmetry in atmospheric duct distributions, underscoring the spatial and temporal variability of atmospheric properties in oceanic regions.

The primary bottlenecks are the sparse distribution of oceanic sounding stations and the inherent limitations of traditional atmospheric retrieval methods, contributing to a significant observational gap in the atmospheric boundary layer (Cimini et al., 2020). This sparse distribution of stations makes data acquisition in the marine environment extremely difficult. The limitations are particularly evident when dealing with marine dynamic environments. Specifically, data-driven retrieval methods such as statistical and neural-network-based approaches exhibit strong dependence on large historical datasets, which are difficult to obtain in marine environments. In addition, buoy-based platforms are subject to wave-induced motion, which leads to variations in the observation zenith angle and consequently introduces brightness temperature deviations. These attitude-related effects must be addressed through appropriate measurement preprocessing and correction procedures before the retrieval stage.

Currently, various mainstream methods are used for atmospheric parameter profiling retrieval. These include the Bayesian maximum probability estimation algorithm (Clough et al., 2005), one-dimensional variational retrieval methods (Hewison, 2007), physically based retrieval methods based on radiative transfer theory (Zhou et al., 2024; Liu et al., 2024; Gaffard and Hewison, 2003; Reinhardt et al., 2009), and statistical retrieval methods (Zheng, 2010). Neural-network algorithms have also gained increasing attention (Renju et al., 2023). While high computational accuracy can theoretically be achieved with physical retrieval methods, their inherently large computational requirements severely limit real-time performance. Statistical retrieval methods are effective in terrestrial environments where sufficient data is available. However, their strong reliance on historical data makes them struggle in marine regions with limited data. Neural-network algorithms demonstrate outstanding performance due to their powerful nonlinear mapping capabilities. However, traditional neural network models, such as the classic backpropagation (BP) neural network, generally require a large amount of training data (Hu et al., 2023; Jiménez and Eriksson, 2016). This high data requirement conflicts sharply with the limited ability to obtain field data in the unique environment of the ocean. As a result, their training effects and retrieval performance are significantly limited (Yao and Guan, 2022; Mahdianpari et al., 2021). Early pioneering studies established the fundamental capabilities of ground-based microwave radiometry. For instance, Decker et al. (1978) made significant progress in ground-based detection, and Guiraud et al. (1979) revealed the detection capabilities of absorption spectra at different frequencies. However, applying these traditional methods to complex marine environments presents significant challenges. More recently, Turner et al. (2007) noted that physical retrieval methods, while accurate, are computationally inefficient for real-time applications. Furthermore, in their Arctic region study, Candlish et al. (2012) explicitly pointed out that the accuracy of ship-based platform data is significantly reduced when using traditional neural-network-based retrieval of atmospheric profiles. This is due to changes in attitude and insufficient on-site data. Recent studies also suggest that even state-of-the-art reanalysis data like ERA5 may exhibit systematic biases under complex marine weather conditions such as tropical cyclones (Wei et al., 2025a), further emphasizing the need for observation-driven profiling methods in data-sparse oceanic environments. These studies collectively highlight a core issue: how to effectively overcome errors caused by platform attitude and improve the accuracy and efficiency of atmospheric parameter profiles. Although mechanical stabilization (Schnitt et al., 2024) can reduce platform motion, it introduces significant challenges for long-term autonomous buoy operation in terms of power consumption and maintenance complexity. Therefore, this study adopts a software-based approach using real-time zenith angle correction from attitude sensors. During field experiments, the buoy exhibited residual pitch and roll variations of approximately ±2.5° and ±3.2°, respectively. Our algorithm explicitly compensates for these residual pointing variations, enabling accurate retrieval of atmospheric parameters under dynamic marine conditions.

As discussed previously, ground-based microwave radiometers (MWR) provide a powerful remote sensing technology. They are capable of capturing atmospheric microwave radiation information in real-time and continuously. This enables the retrieval of key parameters, such as atmospheric temperature and humidity profiles, and atmospheric refractive index. On the other hand, buoys are flexible, real-time monitoring platforms. They can integrate multi-parameter measurement functions and offer the unique advantages of long-term, uninterrupted, and all-weather operation. This can effectively compensate for the observational deficiencies caused by the sparse distribution of traditional oceanic sounding stations (Roemmich et al., 2009; Cronin et al., 2023; Liu et al., 2019; Fang et al., 2018). Consequently, an effective approach to addressing the scarcity of tropospheric data in marine environments is the combination of advanced ground-based microwave radiometer technology with autonomous, multi-parameter buoy monitoring platforms. Industry initiatives have previously explored this potential, such as the deployment of the first floating microwave radiometer (Haun, 2017). In the academic field, several studies have also explored the application of microwave radiometers in marine environments. For instance, Schnitt et al. (2024) and Griesche et al. (2020) demonstrated ship-based profiling capabilities, while Yan et al. (2022) focused on improving retrieval algorithms for ocean-based platforms. More recently, Cimini et al. (2025) reviewed the capability of microwave radiometers for offshore wind energy applications, highlighting that while onshore retrievals show high correlation (>0.9) with radiosondes (Cimini et al., 2003), offshore retrievals are significantly challenged by platform motion and data sparsity, necessitating advanced calibration and elevation scanning strategies.

Therefore, this study deploys a ground-based microwave radiometer on an ocean buoy platform. Through incorporating platform attitude correction methods and applying multi-objective optimization algorithms, a history-independent retrieval model is constructed to address the challenges above. Through simulation experiments and field sea trials, the method's performance, retrieval accuracy, and applicability under the tested conditions are comprehensively evaluated. Its potential for application in real marine environments is also assessed.

To provide an intuitive overview of the proposed retrieval strategy, Fig. 5 illustrates the complete workflow of the buoy-based temperature and humidity profile retrieval. The procedure consists of four main parts: (1) preprocessing and attitude correction of microwave radiometer observations, (2) construction of the forward radiative transfer model and objective functions, (3) multi-objective optimization using the NSGA-II algorithm with physical constraints, and (4) systematic bias correction and final profile generation.

To comprehensively evaluate the performance and suitability of the proposed models for marine environments, microwave radiometer observation experiments were conducted on a buoy platform. This was done in the coastal waters of Jiaozhou Bay, Qingdao (36.0721540° N, 120.3047530° E). The models include the tropospheric temperature and humidity profile retrieval model and the buoy platform zenith compensation correction model. During the experiment, 38 sets of valid observational data were obtained. These data were compared with radio sounding data from the Qingdao Meteorological Observatory (Station ID: 54857) for validation. For each radiosonde launch time (00:00 and 12:00 UTC), the temporally co-located microwave radiometer retrieval record closest in time was selected for comparison. A matchup was considered valid only if the radiosonde profile passed quality control and was successfully interpolated onto the standard height grid of the microwave radiometer (0–10 km). This procedure ensures temporal consistency between the two observing systems and provides a reliable basis for profile-to-profile validation. The sounding data are from the Wyoming State University sounding database (36.0702040° N, 120.3331640° E). The two observation points are 2.5 km apart. Therefore, their data can be considered co-located observations. This provides reliable reference true values for model validation.

To quantitatively assess the performance of the proposed retrieval model, the retrieval accuracy is evaluated using the root mean square error (RMSE), which represents the statistical uncertainty of the retrieved profiles with respect to radiosonde observations.

Figure 7 presents the statistical comparison between the uncorrected NSGA-II retrievals and the collocated radiosonde observations for the 38 matched cases. Panels (a) and (b) show the mean temperature and relative humidity profiles, respectively, while panels (c) and (d) present the corresponding mean profile differences, defined as the difference between the mean retrieved profiles and the mean radiosonde profiles.

It should be emphasized that the profiles shown in Fig. 7 represent averaged vertical structures over all matched cases, and the difference panels reflect the bias between the mean profiles rather than sample-wise error statistics.

As shown in Fig. 7a and c, the retrieved temperature profile generally follows the radiosonde profile in terms of overall vertical structure. However, systematic deviations are still evident at certain altitude ranges. Near the surface, the retrieved temperature is slightly higher than the radiosonde observations, while in parts of the lower-to-middle troposphere it tends to be lower. The corresponding bias profile exhibits clear height-dependent variations, indicating the presence of structured systematic deviations prior to bias correction.

For relative humidity, as shown in Fig. 7b and d, the retrieved profile is generally lower than the radiosonde profile over a large portion of the troposphere. The negative bias is most pronounced in the mid-troposphere (approximately 2–6 km), suggesting a systematic underestimation in the mean humidity structure before correction.

Overall, Fig. 7 demonstrates that the uncorrected retrieval captures the general vertical structure of temperature and humidity, but exhibits clear height-dependent systematic deviations in the mean profiles. These results provide the basis for the subsequent systematic bias correction analysis.

The retrieval results shown in Fig. 7 already incorporate attitude correction in the forward modelling process. To further isolate and evaluate the effect of attitude correction, an additional comparison was conducted between retrievals with and without applying the attitude correction, prior to the introduction of systematic bias correction.

The overall improvement introduced by attitude correction is relatively limited for the present dataset. This behaviour is consistent with the characteristics of the buoy observations, where the platform attitude angles are generally small (typically within 1–3°), resulting in relatively weak perturbations to the observation geometry. Under such conditions, the influence of attitude-induced effects on brightness temperature is correspondingly modest.

A grouped statistical analysis based on the magnitude of the attitude angle is presented in Table 2. The results do not exhibit a strictly monotonic relationship between attitude magnitude and retrieval improvement. Across the three subsets, the mean changes in RMSE remain small for both temperature and relative humidity, indicating that the impact of attitude correction under the present observational conditions is limited and case-dependent.

It should be noted that the slightly positive mean ΔRMSE in the >2.5° subset does not necessarily imply a degradation of retrieval performance due to attitude correction. Instead, this result likely reflects the combined influence of multiple uncertainty sources in a limited-sample marine dataset. In practice, larger attitude angles are often associated with stronger platform motion and increased short-term atmospheric variability. As a result, the geometric improvement introduced by attitude correction may be partially offset by other sources of error, including instrument noise, temporal–spatial mismatch, and environmental variability.

Given that the magnitude of the mean ΔRMSE in this subset remains small, this result should be interpreted with caution and should not be generalized beyond the present dataset. Overall, these findings suggest that while the average impact of attitude correction is modest under weak-motion conditions, it remains physically necessary and is expected to become more important under conditions with larger viewing-angle deviations.

For a representative case with relatively large attitude variation, the quantitative comparison before and after attitude correction is summarized in Table 3. The temperature RMSE decreases from 3.69 to 2.99 K, while the relative humidity RMSE decreases from 18.95 % to 18.57 %. These results indicate that incorporating attitude information improves the physical consistency of the forward model and becomes increasingly important under conditions with stronger platform motion.

Nevertheless, sensitivity analysis indicates that variations in viewing angle can introduce systematic brightness temperature deviations across multiple channels, particularly in specific K-band and V-band frequencies (Fig. 8). This indicates that attitude-induced geometric effects can propagate into the retrieval process through the forward radiative transfer model. Therefore, even though the average improvement is limited for the present dataset, explicit attitude correction remains physically necessary for buoy-based microwave radiometer retrievals and is expected to become increasingly important under conditions with stronger platform motion and larger viewing-angle deviations.

Figure 8 was generated from a theoretical sensitivity experiment in which a standard atmospheric profile from ITU-R P.835 was combined with ITU-R P.676 gaseous absorption calculations to simulate channel brightness temperatures at different viewing angles; ΔTB was defined relative to the 0° nadir-view case.

To more clearly illustrate the effect of the systematic bias correction, Fig. 9 presents the average-profile comparison based on the 38 valid collocated cases on the common vertical grid. Panel (a) compares the mean corrected temperature profile with the mean observed temperature profile, while panel (c) shows the corresponding mean temperature bias profiles before and after correction. Similarly, panel (b) compares the mean corrected and mean observed relative humidity profiles, and panel (d) shows the corresponding mean relative humidity bias profiles before and after correction. In panels (c) and (d), the shaded regions represent ±1 standard deviation of the profile errors across the 38 matched cases.

Note: By mathematical construction of the LOOCV mean bias correction procedure, the mean residual of the corrected retrievals across all 38 folds is identically zero at every height level. This figure is presented solely to illustrate the magnitude and vertical structure of the pre-correction systematic bias, which motivates the need for bias correction. The effectiveness of the correction is quantified by the reduction in RMSE, as shown in Fig. 11.

Figure 9 illustrates the magnitude and vertical structure of the systematic bias present in the uncorrected retrievals. As shown in panels (c) and (d), both temperature and relative humidity exhibit significant height-dependent negative biases (underestimation). Specifically, the temperature bias reaches its maximum of approximately 8 K around the 7–8 km altitude, while the relative humidity bias generally increases with altitude, reaching approximately 28 % near 10 km. This strong and structured systematic bias provides the motivation for applying a height-dependent bias correction.

We intentionally omit plotting the mean residual of the corrected retrievals here because, by mathematical construction of the LOOCV mean bias correction procedure, the mean residual of the corrected retrievals across all 38 folds is identically zero at every height level. This is an inherent property of the leave-one-out approach for mean bias correction, not a limitation of the method. For this reason, the mean residual cannot be used as evidence of correction effectiveness.

Instead, the effectiveness of the bias correction is properly quantified by the reduction in root-mean-square error (RMSE), which measures the magnitude of the retrieval errors regardless of their sign. As shown in the newly added Fig. 11, the overall RMSE is significantly reduced after correction, from 4.11 to 2.13 K for temperature and from 24.09 % to 21.42 % for relative humidity.

To evaluate the variability between different bias correction models derived from the LOOCV procedure, Fig. 10 shows the individual bias correction profiles obtained from each of the 38 folds. The faint gray lines represent the bias profile calculated when each single sample is left out of the training set, while the thick blue line denotes the mean bias profile across all folds. The light blue shaded area indicates the ±1 standard deviation of the bias estimates.

It can be seen that all 38 individual bias profiles are highly consistent with the mean bias profile, forming a tight cluster around the mean. The standard deviation of the bias estimates is less than 0.3 K for temperature and less than 3 % for relative humidity across 92 % of the atmospheric layers below 10 km. The largest variability is observed near the surface (0–1 km) and at the top of the profile (9–10 km), which is consistent with the higher uncertainty in these regions due to boundary layer turbulence and reduced signal strength at higher altitudes. This remarkable consistency demonstrates that the systematic bias characteristics in the Jiaozhou Bay region are highly stable and not sensitive to the specific selection of training samples. Even when any single sample is removed from the training set, the resulting bias profile remains almost identical to the mean profile. For operational deployment, a single static bias correction profile, calculated as the mean of all 38 collocated samples, is used. This static profile has been validated to achieve nearly identical performance to the LOOCV results, with a difference in overall RMSE of less than 0.02 K for temperature and 0.1 % for relative humidity. This confirms that using a single static model does not compromise retrieval accuracy while greatly simplifying operational implementation.

Figure 11 quantifies the improvement in retrieval performance across all 38 LOOCV folds by comparing the RMSE distribution before and after bias correction. The boxplots show the spread of the overall RMSE values for temperature and relative humidity, respectively.

For temperature, the mean RMSE decreases significantly from 4.11 K before correction to 2.13 K after correction, representing a 48.2 % reduction. Although the standard deviation of the RMSE across all folds increases slightly from 0.52 to 0.62 K due to a few extreme atmospheric conditions, the substantial reduction in the mean RMSE (from 4.11 to 2.13 K) along with the high improvement rate (89.5 % of the folds exhibiting enhanced accuracy) demonstrates the robust and widespread effectiveness of the proposed correction scheme across varying conditions. For relative humidity, the mean RMSE decreases from 24.09 % to 21.42 %, a reduction of 11.1 %.

Importantly, 34 out of 38 folds (89.5 %) show improved retrieval accuracy for temperature after correction, and 32 out of 38 folds (84.2 %) show improved accuracy for relative humidity. The few cases where RMSE increased are associated with rare extreme atmospheric conditions that are underrepresented in the limited training dataset.

To further quantify the correction effectiveness and the overall retrieval performance, a detailed statistical summary of the 38 LOOCV-based held-out cases is provided in Table 4.

Temperature retrieval performance: As summarized in Table 4, the corrected temperature retrieval shows improved agreement with the radiosonde observations, with an overall RMSE of 2.13 K and a correlation coefficient of 0.99 over the 0–10 km layer. The correction effect is evident in both the lower troposphere and the middle-to-upper troposphere, although the magnitude of improvement is not entirely uniform with height. This result indicates that the retrieval contains a relatively stable height-dependent bias component that can be effectively mitigated through the present correction scheme. Nevertheless, after removal of the dominant systematic bias component, the residual temperature error is still influenced by case-dependent variability and observational uncertainty.

Relative humidity retrieval performance: For relative humidity, the overall RMSE after correction is 21.42 %, with a correlation coefficient of 0.69 over the 0–10 km layer, as shown in Table 4. Compared with temperature, the improvement in humidity retrieval is more limited and less vertically uniform. This behaviour is consistent with the stronger case-to-case variability of water-vapour structure, the reduced sensitivity of humidity-sensitive channels in the middle and upper troposphere, and the additional influence of spatial mismatch between the buoy and radiosonde observations. Therefore, although the systematic bias correction reduces the mean humidity error, the residual uncertainty in humidity retrieval remains comparatively larger than that in temperature retrieval.

The layered statistics further show that the corrected temperature retrieval remains more accurate in the 0–2 km layer than in the 2–10 km layer in terms of absolute RMSE, although both layers benefit from the reduction of systematic bias. For relative humidity, the retrieval uncertainty remains larger in the 2–10 km layer than in the 0–2 km layer, reflecting the decrease of water-vapour content and retrieval sensitivity with height.

This level of performance is broadly consistent with the error ranges reported in previous studies using ground-based microwave radiometers under comparable profiling conditions (e.g., Massaro et al., 2015; Yan et al., 2020; Cimini et al., 2011).

It should be noted, however, that the 38 matched radiosonde profiles used in this study were collected during a limited nearshore campaign period in Jiaozhou Bay. Therefore, the dataset does not provide seasonal or broad regional coverage and should not be interpreted as a comprehensive sampling of all marine atmospheric states. Although all matched cases were obtained within one month, they are not strictly identical repetitions, because they include both daytime and nighttime launches and still exhibit case-to-case variability in near-surface thermodynamic conditions as well as lower-tropospheric temperature and humidity stratification.

In summary, the sea-trial results support the effectiveness and feasibility of the proposed method under the present nearshore observational conditions. By constructing a small-scale prior experience database and integrating platform attitude information, the NSGA-II-based retrieval framework reduces the dependence on large historical training datasets. Under the LOOCV-based correction framework, the retrieval results after systematic bias correction should be interpreted primarily as evidence of retrieval feasibility and of the usefulness of height-dependent bias mitigation under the tested buoy-based nearshore conditions, rather than as a generalized validation across all marine environments.

To more directly illustrate the structural effect of the adjacent-layer continuity constraint on the retrieved temperature profile, Fig. 12 presents a representative case comparing retrievals obtained with and without the continuity constraint, together with the collocated radiosonde profile. It should be emphasized that the primary purpose of this constraint is not to guarantee a lower RMSE for every individual case, but to suppress non-physical layer-to-layer discontinuities and to maintain basic thermodynamic plausibility under limited observational constraint.

Note: In this particular case, the unconstrained retrieval achieves a lower RMSE with respect to the collocated radiosonde. However, the unconstrained profile exhibits larger non-physical layer-to-layer jumps, while the constrained profile maintains more physically reasonable vertical continuity.

As correctly observed by the reviewer, in this particular case, the unconstrained solution yields a lower RMSE with respect to the collocated radiosonde profile. However, this apparent improvement comes at the cost of introducing large, non-physical jumps between adjacent retrieval levels, as clearly visible in the enlarged view (panel b). These discrete jumps are not representative of real atmospheric structure, which exhibits continuous vertical variation.

Statistically, across all 38 matched cases, the constrained retrieval achieves a slightly lower overall RMSE (2.13 K for temperature and 21.42 % for relative humidity) compared to the unconstrained retrieval (2.27 K for temperature and 22.89 % for relative humidity). More importantly, the continuity constraint eliminates unphysical discontinuities in 100 % of the test cases, ensuring that all retrieved profiles are physically plausible.

The climatology profile derived from our local radiosonde data does not exhibit large oscillations, and the continuity constraint we applied is designed to maintain this basic physical smoothness. The constraint only limits the absolute magnitude of differences between neighbouring levels (δ1=8 K for temperature, δ2=60% for relative humidity) and does not enforce any specific lapse rate structure. Therefore, local inversions and gradient transitions are still fully allowed.

This behaviour reflects the fundamental trade-off between local profile fitting and structural continuity in ill-posed remote sensing retrieval problems. Under limited observational constraint, a less regularized solution may occasionally fit a specific collocated sample more closely, but it will generally produce less physically consistent results that are less robust to observational noise.

Under limited observational constraints, a less regularized solution may fit the collocated radiosonde profile more closely in an individual case, but such a profile may also contain stronger small-scale oscillations and weaker physical smoothness.

To further evaluate the performance of the proposed method, a quantitative comparison with the built-in retrieval algorithm of the microwave radiometer is conducted over the 0–10 km altitude range.

All methods are evaluated on the same matched samples and interpolated onto a common vertical grid to ensure consistency. The comparison results are summarized in Table 5.

For temperature retrieval, the built-in algorithm yields an RMSE of 4.13 K. The proposed method shows a comparable performance before correction (4.11 K), indicating that the baseline inversion framework is consistent with the operational product. After applying the proposed system error correction, the temperature RMSE is significantly reduced to 2.13 K, demonstrating a clear improvement. For relative humidity, the built-in algorithm exhibits an RMSE of 29.50 %, while the proposed method achieves lower errors both before (24.09 %) and after correction (21.42 %). This indicates that the proposed method provides a more accurate representation of humidity profiles throughout the troposphere.

Overall, the results indicate that the proposed method maintains a comparable baseline performance to the built-in algorithm and achieves improved retrieval accuracy after correction for the present matched dataset.

The sea-trial results obtained in Jiaozhou Bay support the effectiveness and feasibility of the proposed buoy-based retrieval framework under the present nearshore observational conditions. For temperature, the retrieval contains a relatively stable height-dependent bias component that can be effectively reduced through the present LOOCV-based systematic bias correction. For relative humidity, the improvement is more limited and less vertically uniform, indicating that the residual error is still strongly influenced by case-dependent variability, reduced channel sensitivity aloft, and spatial mismatch between the buoy and the radiosonde station.

The present results should be interpreted within the limits of the current dataset. The 38 matched radiosonde profiles were collected during a limited nearshore campaign period in Jiaozhou Bay and therefore do not provide seasonal or broad regional coverage. Although the matched cases include both daytime and nighttime launches, they still represent a relatively narrow observational sample and should not be interpreted as a comprehensive validation across all marine atmospheric conditions.

A further limitation is that the present retrieval framework is mainly validated under non-precipitating and relatively weak-cloud-liquid-water conditions. In the current study, liquid water path (LWP) is used only as an auxiliary diagnostic indicator for possible cloud contamination and residual retrieval uncertainty, rather than as an inversion variable. Therefore, the present results are more appropriately interpreted as demonstrating retrieval feasibility under the tested nearshore conditions, rather than as establishing the same level of accuracy for broader offshore or open-ocean applications under all weather conditions.

In addition, the current framework includes level-dependent physical bounds and adjacent-layer continuity constraints, which act mainly to suppress unrealistic layer-to-layer oscillations and to maintain basic profile continuity. The representative case comparison in Fig. 10 further shows that these constraints primarily affect the structural smoothness of the retrieved profile, rather than guaranteeing lower RMSE for every individual case. This reflects the trade-off between local profile fitting and structural continuity in the present inversion framework.

Future work should focus on three aspects. First, broader validation is required using marine observational datasets with extended temporal scales and environmental diversity. Specifically, while the single static bias correction profile proposed for operational use demonstrates highly stable performance matching the LOOCV results within our campaign, it has not yet been verified against a completely independent, external dataset. Future efforts will explicitly focus on deploying this static model under distinct offshore and open-ocean environments to rigorously evaluate its cross-regional transferability and eliminate any potential risk of local over-fitting. Second, the current retrieval framework may be improved by introducing more comprehensive physical constraints and by further optimizing the NSGA-II parameter settings. Third, multi-source data fusion, such as the combination of buoy-based microwave radiometry with satellite microwave observations, GNSS remote sensing, or other marine observing systems, may help alleviate data scarcity and improve the robustness and generalizability of marine atmospheric-profile retrieval.

This study proposed a buoy-based retrieval framework for marine atmospheric temperature and humidity profiles using a ground-based microwave radiometer, attitude correction, a small-sample prior database, and NSGA-II optimization. The results from the Jiaozhou Bay field campaign show that the proposed method can achieve good retrieval accuracy under the present nearshore observational conditions.

The analysis indicates that the retrieval contains a stable height-dependent bias component, particularly for temperature, which can be reduced through the present LOOCV-based systematic bias correction. After correction, the overall retrieval performance over the 0–10 km layer reaches an RMSE of 2.13 K for temperature and 21.42 % for relative humidity for the 38 matched cases, compared to 4.11 K and 24.09 % before correction.

Overall, the present study demonstrates the feasibility of buoy-based continuous remote retrieval of marine atmospheric profiles under sparse-data and dynamically varying observational conditions. However, the current results should be interpreted within the limits of the tested nearshore dataset and should not be generalized directly to broader offshore or open-ocean environments without further validation.