Aviation contributes to climate change through both carbon dioxide (CO2) emission and non-CO2 effects. The latter may have accounted for 66 % of aviation's total net Effective Radiative Forcing (ERF) in 2018 . The largest contributor to non-CO2 ERF is the radiative forcing from condensation trails – contrails – which are linear ice clouds formed behind aircraft as hot exhaust gases mix with cold ambient air. The physical processes governing contrail formation are well understood . While most contrails dissipate quickly and have a negligible climatic impact, those that form within Ice Supersaturated Regions (ISSRs) can persist for hours , eventually developing into contrail cirrus clouds with microphysical and optical properties similar to those of natural cirrus .

ISSRs are regions of the atmosphere where the Relative Humidity with respect to ice is supersaturated, RHi > 100 %, which is a meta-stable thermodynamic state. The size of ISSRs has been estimated based on the distance flown within such regions by Measurement of Ozone and Water Vapor by Airbus In-Service Aircraft (MOZAIC) aircraft, showing that they can extend over O(10–100) km . ISSRs are typically located at the tropopause level and are rather frequent across the globe . Their formation is facilitated by the presence of upward winds and the meeting of cold and warm air streams . The dynamics of ISSRs also present complex patterns as it has been determined that ISSRs' displacement may be slower than the surrounding wind field's .

On average, it is estimated that aircraft spends 13.5 % of their flight time in ISSRs and that only a small proportion of flights might be responsible for the majority of persistent contrail formation. For instance, it has been estimated that only 2.7 % of total flights are responsible for 80 % of the total contrail RF in 2019 . These findings have motivated flight rerouting as a short-term mitigation strategy, e.g. . Being able to meteorologically forecast ISSRs with enough accuracy would allow a slight deviation of the flight route to avoid the formation of persistent contrails, at the cost of a small amount of additional CO2 emissions.

Global ISSR forecasts are generally derived from Numerical Weather Prediction (NWP) models, informed by in-situ and satellite observations. However, detecting ISSRs remains challenging, particularly through satellite observations due to their relatively narrow vertical extent . The tropopause region, where ISSRs typically occur, also features steep vertical gradients in humidity , necessitating high vertical resolution for accurate characterization. Both remote measurements with lidar and in-situ observations, such as those made with balloon-borne instruments and with on-flight sensors , provide accurate measurements of RHi, but are spatially and temporally limited.

Hence we must rely on NWP models to obtain RHi values across the global atmosphere. NWP models contribute in two ways: forecasts, which predict atmospheric conditions in real time and are required for operational contrail avoidance, and reanalysis, which retrospectively reconstruct past atmospheric states by assimilating all historical observations. While forecasts are necessary for live avoidance decisions, reanalysis data is well-suited for retrospective studies such as this one. We therefore use the ERA5 reanalysis dataset , which is widely regarded as a highly trusted reconstruction of the global atmosphere. However, as other NWP products, ERA5 is known to suffer from a dry bias in the Upper Troposphere (UT) and Lower Stratosphere (LS) , which means that the model often predicts lower relative humidity values compared to the observed values. This bias, as well as significant random errors, can lead to considerable errors in RHi estimates, particularly in regions where contrails are likely to form. Previous work on the correction of humidity bias in ERA5 have shown potential for improvement of the ISSR detection in the UTLS. applied a bivariate Quantile Mapping (QM) correction to ERA5 temperature and relative humidity fields, significantly reducing the dry bias. They report a reduction of the RHi bias from approximately -4.5 % to -1.2 % on average at pressure levels of 250, 225, and 200 hPa. This bias reduction leads to an improved classification of different contrail categories. proposed a machine learning (ML) approach to improve ERA5's RHi estimates in the UT using an Artificial Neural Network (ANN).

In this study, we present a hybrid ensemble machine learning approach to correct the dry bias in ERA5's RHi in the UTLS. We combine an XGBoost regressor and an ANN, leveraging the complementary strengths of both models. ANNs are well-suited for modeling complex, non-linear relationships in multivariate data , while tree-based models like XGBoost excel in handling structured data and often deliver state-of-the-art performance . We dynamically chose the model based on the initial RHi value provided by ERA5: the XGBoost is used for prediction in drier conditions (RHi < 85 %), while the ANN is used for more humid cases (RHi > 85 %). ISSR formation involves more complex and non-linear atmospheric dynamics , which are better captured by ANNs due to their flexibility and non-linear representation capabilities. Effectively, the ANN captures subtle variations relevant to ISSR classification, while the XGBoost model is used to correct bias under simpler thermodynamic conditions.

This paper is organized as follows. In Sect.  we describe the IAGOS and ERA5 datasets, the collocation procedure, filtering, and feature engineering. Sect.  details the ANN and XGBoost architectures, training procedures, and the hybrid model. Sect.  presents our results, showing improvements in regression and classification scores under different meteorological conditions.

In this study, we will use two complementary datasets. The ERA5 reanalysis data from the European Centre for Medium-Range Weather Forecasts (ECMWF, ), and the in-situ observations from the In-service Aircraft for a Global Observing System (IAGOS, ) program. ERA5 provides a global and consistent estimate of atmospheric conditions through a wide range of variables, while IAGOS offers direct measurements of RHi at cruise altitudes. Combining these datasets enables a supervised learning approach where the ERA5 features serve as model inputs, while the estimation of RHi from IAGOS from temperature and relative humidity measurements serve as the target variable. The following subsections describe each dataset, along with our preprocessing and feature engineering methodology.

Unlike , we focus on the North Atlantic region, spanning latitudes from 40 to 70° N and longitudes from 65° W to 5° E (Fig. ). This region shows a relatively uniform distribution of the IAGOS data and is known for frequent contrail formation due to high air traffic and favorable atmospheric conditions. For these reasons, it is thought to be a potential region for contrail avoidance trials. We selected the year 2022 as our study period as it offers recent atmospheric conditions and comes after the maximum COVID disruption of international flights in 2020 and 2021. Our data processing is implemented based on methodology from , with some modifications to ensure proper separation of the training and test datasets to avoid temporal leakage.

Correcting the dry bias in ERA5's RHi estimates in the UTLS presents a significant challenge due to the inherently non-linear nature of atmospheric processes. To address this, we propose a hybrid machine learning approach that combines two complementary models: an ANN and an XGBoost. The ANN is well-suited for capturing complex, non-linear dependencies, particularly under high humidity conditions, while XGBoost performs robustly in drier regimes.

The hybrid strategy dynamically selects the appropriate model for prediction based on the ERA5-estimated RHi value. Specifically, for samples where ERA5 RHi is below 85 %, predictions are taken from the XGBoost model, which has demonstrated superior performance in lower-humidity environments. Conversely, for RHi values exceeding 85 %, the ANN model is employed, leveraging its capacity to extract highly non-linear patterns, such as those associated with ISSRs. The 85 % threshold was chosen based on two key considerations. First, ERA5 is known to exhibit a MAE of approximately 15 % in humid conditions. By subtracting this from the 100 % threshold typically used to identify ISSRs, we ensure that the ANN model is prioritized in critical high-humidity cases. Second, validation dataset performance confirmed that this hybrid architecture consistently outperforms either model used in isolation.

Firstly, the ANN component is trained to predict RHi using the input features summarized in Table 1. Data are normalized using min–max scaling, with the RHi range extended to 200 % to reduce sensitivity to outliers and mitigate dry bias. The final network architecture includes three hidden layers with 100 neurons each, employing He initialization and ReLU activation functions. Batch normalization and dropout regularization are applied between layers to stabilize training and reduce overfitting. The output layer uses a linear activation function to predict RHi , denoted as RHi_ANN.

Training is conducted using the Adam optimizer with a learning rate of 0.001, decay rate of 5 × 10⁻³, and momentum of 0.98. The model is trained over 150 epochs with a batch size of 1024, and early stopping is employed to halt training if validation loss does not improve over 20 consecutive epochs. A custom loss function, based on the Mean Squared Error (MSE), is used to emphasize accuracy in high-RHi conditions. The loss function is defined as: 3L(y,y^)=1n∑i=1nwi⋅(yi-y^i)2, with wi=1+yiα.

In Eq. (), yi is the target value at index i, y^i is the predicted value at index i, n is the number of samples, and α is a weight factor. The weight parameter (α) that defines the weight of the RHi value is denoted WEIGHT_FACTOR. This weighted approach prioritizes performance in ISSRs, addressing the ERA5 dry bias. Hyperparameters were optimized via grid search on the train dataset as detailed in Table .

Secondly, the XGBoost model uses the same input feature set as the ANN, including engineered variables. XGBoost is an efficient implementation of gradient boosting known for its scalability, accuracy, and interpretability. The final model was trained with 100 estimators, a learning rate of 0.1, a maximum tree depth of 4, a subsampling ratio of 0.9, and a column sampling ratio per tree of 0.8. In Table , we report the performance comparison for a set of ML models.

The hybrid model achieved an ETS of 0.44 and a MAE of 11.37 %. Compared to ERA5, it showed an improvement of +0.08 in ETS and -2.33 % in MAE. Fig.  compares scatter plots of our different models predictions on the test dataset to the baseline ERA5 estimates, see Fig. a. Figure c shows that the XGBoost model was able to correct low RHi values with great accuracy, consequently showing strong MAE improvement. However, it struggles with higher RHi values, resulting in poor ETS. The ANN, Fig. b, shows a strong ETS, indicating its ability to classify ISSRs, but it overestimates the lower RHi values leading to a higher MAE. The hybrid model shown in Fig. d combines the strengths of both models, achieving a good balance between ETS and MAE.

The RHi estimates are effectively improved by combining the strengths of both models, leveraging the ANN's ability to capture non-linear relationships and the XGBoost's robustness in handling drier conditions. The hybrid model achieves a higher ETS comparable to the ANN's while maintaining a lower MAE than both models. This hybrid approach demonstrates the potential of combining different machine learning techniques to improve predictions in complex atmospheric conditions. Table  summarizes the performance of all models in terms of ETS and MAE.

Table  presents the most important features used by the ANN and XGBoost models. As expected we find RHi_ERA5 as the most important feature. This table shows that the models relied on different features for predictions: the XGBoost model relies more heavily on features with stronger linear relationships to the target, such as the vertical temperature gradients, while the ANN is able to exploit more complex, non-linear patterns, like the time embeddings. This observation highlights the complementary nature of the two models, with the ANN capturing complex relationships (often associated with more humid regions) and the XGBoost focusing on more linear patterns.

The performance of the hybrid model relative to the baseline ERA5 are assessed for both UT and LS under clear- and cloudy-sky conditions. Results are shown in Fig. . The best improvement in MAE is observable in the LS, from 13.19 % to 10.71 %. This is explained because the model performs a better correction on lower RHi values and the LS counts significantly less ISSRs (see Fig. ). In Table , we report the predictions performance for each of the cases. In comparison, while QM successfully removes bias from the distribution, it does not improve point-wise predictive accuracy. explicitly report that after applying QM, the “RMSE, MAE, and MSE increase unnoticeably”. In contrast, our model significantly reduces the MAE from 13.70 % to 11.37 %.

Finally, Fig.  presents the number of correctly predicted ISSRs for the various cases. We observe that the hybrid model correctly predicts significantly more ISSRs than ERA5 in the LS, 92 out of 204, compared to 54 out of 204 for ERA5. Overall, the hybrid model improves ISSR detection by approximately 10 % across all conditions. In the UT, the improvement is less significant, with only 4 additional ISSRs correctly classified.

In this study, we used a hybrid ensemble model to improve RHi from ERA5 reanalysis in the UTLS using in-situ measurement from IAGOS. The dry bias of ERA5 is considerably reduced and the number of correctly predicted ISSRs is increased, especially in the LS where it nearly doubles.

The hybrid model is built on two complementary models: an XGBoost regressor that excels in dry conditions (RHi < 85 %), and an ANN that performs better in more humid regions (RHi > 85 %). The hybrid model demonstrated significant improvements compared to the initial ERA5 estimates, both in terms of MAE and ETS. It achieved an MAE of 11.37 %, compared to 13.7 % for ERA5, and improved the ETS from 0.36 to 0.44. The best improvement was observed in the LS, where the hybrid model increased ETS by +0.18 and reduced MAE from 13.19 % to 10.71 %. The hybrid model consistently outperformed ERA5 across all defined meteorological conditions, detecting approximately 10 % more ISSRs overall.

However, the model presents limitations, especially in predicting very high RHi values (above 120 %), likely due to the very limited availability of such samples in the dataset. Although ISSR detection has improved, reanalysis products still exhibit limitations for supporting accurate contrail impact estimates, and similar challenges are expected to apply to forecast products required for real-time contrail avoidance, particularly given the absence of clearly established performance requirements. Future work could explore advanced downsampling techniques to improve collocation between IAGOS and ERA5 datasets despite their different spatial and temporal resolutions.