Tijana Janjic

The current study presents machine learning (ML)‐based schemes that independently represent model error and observation error during data assimilation. The Model Error ML scheme (MLME) uses a generative adversarial network (GAN) to produce flow‐dependent model corrections. The Observation Error ML scheme (MLOE) also uses the GAN to adaptively estimate the observation error covariance matrix. Furthermore, a generalized formulation (CorrFOE) is derived to incorporate the often‐neglected cross‐correlations between forecast and observation errors. The proposed schemes are rigorously evaluated via twin experiments with the Lorenz III model. Results show that the ML‐based schemes reduce the root‐mean‐square error (RMSE) of analyses relative to the control and, for model error, relative to the additive‐noise baseline. Additionally, the MLME scheme is particularly effective at recovering small‐scale structures. Crucially, the synergistic combination of both ML schemes with the explicit inclusion of cross‐correlation between forecast and observation errors produces the most accurate analyses. The added computational costs for MLME, MLOE and CorrFOE are moderate, confirming their operational potential.

Precipitation forecasts in the tropics are poor due to large model and initial condition errors. However, it has been hypothesized that the coupling of tropical waves and convection offers a source of predictability, suggesting that capturing these waves accurately in the model and in initial conditions could lead to improved precipitation forecasts. In this work, we investigate whether the data assimilation (DA) algorithm, ensemble Kalman filter (EnKF), is fundamentally capable of recovering tropical waves and thereby providing initial conditions that lead to skillful precipitation forecasts. To capture the essence of tropical dynamics without contamination of land–sea contrasts, sea surface temperature gradients, and influences from the extratropics, we use a tropical aquachannel configuration at 13-km resolution with the Icosahedral Nonhydrostatic (ICON) numerical model. To isolate the role of the initial conditions provided by DA, we assume a perfect model. In our setup, Kelvin waves dominate over other wave types and primarily modulate precipitation. In addition, there is a rainfall event similar to a Madden–Julian oscillation (MJO), which is a planetary-scale disturbance coupled to convection. We show that, by assimilating wind observations, we can reduce the errors in the representation of the Kelvin waves sufficiently to provide accurate precipitation forecasts up to several weeks. Even the MJO-like rainfall event, which starts after a forecast lead time of 10 days, is captured by the forecast ensemble. We find that accurate initial conditions for humidity are important to slow down error growth in the tropics. As emphasized by several other studies, we conclude that wind observations are by far the most important input to achieve skillful tropical forecasts.

Accurate representation of atmospheric dynamics at convection scale remains a major challenge for numerical models and a critical aspect in operational weather predictions. In this work, the ICOsahedral Non-hydrostatic (ICON) model is run at convection-permitting scale over the Italian domain, in combination with the Local Ensemble Transform Kalman Filter (LETKF), following the operational configuration of Arpae Emilia-Romagna and ItaliaMeteo Agency. We focus on a poorly-predicted extreme convective storm in the Marche region, Italy, highlighting the crucial role of low-level moisture convergence in convection initiation and the significant undersampling of humidity in conventional data. To address this, we investigate the added value of humidity-sensitive microwave radiances from polar satellites. Assimilation of clear-sky observations from the Microwave Humidity Sounder (MHS) leads to notable improvements in precipitation forecasts compared to the current operational setup, based on conventional and radar observations only. Infrared all-sky radiances in water vapor channels from the geostationary Meteosat Second Generation SEVIRI instrument are further integrated, providing higher spatial and temporal resolution but limited cloud penetration capability. The joint assimilation of microwave and infrared satellite channels leads to improvements in both surface and upper-level variables, supporting the future operational assimilation of satellite radiances at convective-scale in the Arpae and ItaliaMeteo system. The relative contribution of each observation type is evaluated through an updated version of the Partial Analysis Increments algorithm (Diefenbach et al., 2023), which is corrected to account for posterior covariance inflation and localization.Building on the promising results of this work, we present ongoing developments towards ensemble-based data assimilation in a Machine Learning Limited Area Model (ML-LAM). Machine learning weather prediction models have demonstrated competitive forecast skill at coarse resolution, but convective-scale ML-LAMs remain much less explored. A recent study (Adamov et al., 2025) presents the development of a high-resolution ML-LAM, trained on a convective-scale analyses dataset over Switzerland. The potential reproducibility of ML-LAM across different regions makes it appealing for application in other LAM settings. We show here the implementation of ML-LAM over the Italian domain, evaluating the skill against the physics-based model in severe convection conditions. This serves as a first step towards the assimilation of satellite microwave radiances in a operational-like setting using an LETKF scheme. Diefenbach, T., Craig, G., Keil, C., Scheck, L. and Weissmann, M., QJRMS, 149(752), 740–756, (2023). Adamov, S., Oskarsson, J., Denby, L., Landelius, T., Hintz, K., Christiansen, S., Schicker, I., Osuna, C., Lindsten, F., Fuhrer, O. and Schemm,S., arXiv, (2025).

Radar data assimilation (DA) is critical for convective-scale forecasting, as it provides real-time, high-resolution information on precipitation, wind, and convective system dynamics that is not captured by surface observations or satellite data. Polarimetric radar observations complement conventional reflectivity (Zh) and radial velocity (Vr) measurements by enabling the determination of hydrometeor types and particle size characteristics. Differential reflectivity (ZDR) is one of the key polarimetric radar variables, defined as the ratio between horizontal and vertical reflectivity, that provides direct information on hydrometeor shape and size. Despite its strong potential to better constrain storm microphysics and improve convective-scale forecasts, the assimilation of ZDR remains challenging. Challenges associated with observation operators, error characterisation, and data quality underscore the need for further research in this area.The current study investigates the direct assimilation of ZDR in an observing system simulation experiment (OSSE) of a long-lived supercell. The OSSE is conducted using the ICOsahedral Nonhydrostatic (ICON) model with a two-moment microphysics scheme and the Local Ensemble Transform Kalman Filter (LETKF), employing both hydrometeor mixing ratios and number concentrations as analysis variables. Synthetic observations are generated using the polarimetric radar forward operator EMVORADO developed at the Deutscher Wetterdienst. The synthetic ZDR observations are assimilated in addition to the non-polarimetric variables, namely Zh and Vr, while a reference experiment assimilating only non-polarimetric synthetic observations was conducted for comparison. A series of sensitivity experiments are performed to assess the impact of DA settings on assimilation performance, for varying observation error, localisation radius, and ensemble size. In addition, appropriate thresholds and no-reflectivity (clear air) equivalents for ZDR observations are examined.

Quantifying the evolution of uncertainty is critical to both probabilistic forecasting and data assimilation (DA) in numerical weather prediction (NWP). In this study, we investigate the applicability of conformal prediction (CP), a recent machine learning (ML) method, to quantify uncertainty in a controlled, idealized setting. We use a toy model, designed to mimic convective process. The CP provides a set of possible outcomes with a chosen confidence level. Here, we compare and evaluate the average empirical coverage, the average interval length and average interval score loss (AISL) for the three variants of CP i.e., a) Standard CP, b) Normalized CP and c) Conformalized Quantile Regression. We also combine DA with the CP estimates of uncertainty and quantify the significance of improvement. Our results highlight the strengths and limitations of each approach, providing insights into the effectiveness of CP to complement ensemble-based uncertainty quantification in simplified atmospheric models.

Forecasting precipitation in tropical regions is challenging because of substantial errors in both the models and the initial conditions. The interaction between tropical waves and convection suggests possible predictability. Therefore, an accurate representation of these waves in the models and initial conditions is important for increasing the accuracy of precipitation forecasts. This study intends to improve the predictive reliability of the ICON (Icosahedral Nonhydrostatic) global model for tropical weather events, such as tropical waves and the Madden-Julian Oscillation (MJO). We initially analyze the ability of data assimilation (DA) to conserve total energy, enstrophy, moist static energy, and other physical properties. Then, we implement an advanced DA technique, the Quadratic Programming Ensemble (QPEns), with a moist static energy constraint. Preliminary findings show that the moist static energy constraint, together with accurate wind and humidity data, decreases forecast errors and improves tropical wave representation. This induces more reliable long-term precipitation forecasts.

The current study utilizes the operational data assimilation system of Deutscher Wetterdienst (DWD) to investigate the impacts of improved radar forward operator. First of all, it is shown that for experiments in which both conventional and radar data are assimilated and the latent heat nudging (LHN) is applied, the one with improved operator (i.e., with improved Mie-scattering scheme and accounting for beam broadening effect and etc.) exhibits neutral impacts on short-term forecasts. However, in subsequent experiments, in which conventional data are not assimilated and the LHN is switched off, the one with improved operator not just reduces representation error during data assimilation cycles but also enhances the short-term forecast skills. In addition, it is found that the subsequent experiments result in much shorter observation error correlation length scales for radar reflectivity data, indicating that the application of the LHN or assimilation of conventional data may increase the length scales.

The accuracy of numerical weather prediction models is highly dependent on the precision of the initial conditions, especially for forecasting storms and convective-scale weather events. Radars, with their ability to capture the internal structure and important microphysical and dynamical processes within convective systems, play a crucial role in improving weather forecasts at convective scales. Unlike conventional single-polarization radar, dual-polarization radar additionally provides information on the types and sizes of hydrometeor particles. As a result, polarimetric radar data (PRD) is a valuable data source for data assimilation (DA). Despite its potential, PRD is not yet directly assimilated into operational convection-permitting numerical models. This limitation arises from several challenges, including the highly non-linear nature of observation operators for polarimetric variables and the difficulty of estimating model error at convective scales, which require further research.Our study primarily aims to directly assimilate PRD within an idealized setup. To accomplish this, Observation System Simulation Experiments (OSSEs) were conducted to simulate the evolution of a long-lived supercell using the ICOsahedral Nonhydrostatic (ICON) model with a two-moment microphysics scheme. For the assimilation of PRD data, the Kilometer-scale Ensemble Data Assimilation (KENDA) system was utilized, which incorporates the Local Ensemble Transform Kalman Filter (LETKF), along with the polarimetric radar forward operator EMVORADO-POL developed at the Deutscher Wetterdienst (DWD). In the current idealized setup, two types of DA experiments were conducted: a reference experiment that assimilated only non-polarimetric variables, such as reflectivity and radial velocity, and an experiment that assimilated differential reflectivity (ZDR) in addition to the non-polarimetric variables. The results from both experiments were compared, and appropriate thresholds and equivalents of noreflectivity data for polarimetric data were examined. Additionally, the sensitivity to DA settings, such as localization radius and the number of ensemble members, was also tested.

Accurate representation of atmospheric dynamics at convection scale still represents a major challenge for numerical models and a critical aspect in operational weather predictions. Reliable forecast initial conditions, generated by the data assimilation cycle using new observations coming from different platforms, are crucial to improve the forecast accuracy in deep convection environments. In this work, the ICOsahedral Non-hydrostatic (ICON) model is run at convection-permitting scale over the Italian domain, in combination with the Kilometre-scale Ensemble Data Assimilation (KENDA) system, to test the model performance on a poorly-predicted extreme convective storm in the Marche region, Italy, on 15 September 2022. We show here the positive impact of data assimilation at convection scale on the forecast of this event, which allows to improve the localization and the intensity of the storm although substantial underestimation of precipitation still persists. The relative impact of different observations datasets is evaluated, starting from conventional and radar data operationally assimilated for numerical weather predictions over Italy. After pointing out the importance of low-level moisture convergence in the process of convection initiation and the significant undersampling of humidity field in conventional data, the added value of humidity-sensitive microwave radiances from polar satellites is analyzed. Observations sensitive to mid-lower tropospheric humidity in clear-sky conditions are employed, taken from the Microwave Humidity Sounder instrument, still little investigated in limited-area models at many numerical weather prediction centers. In order to better exploit the information content of microwave satellite observations, the preliminary development towards all-sky assimilation is presented.

Precipitation forecasts in the tropics are poor due to large model and initial condition errors, leaving ample room for improvement. In particular, it has been hypothesized that the coupling of tropical waves and convection offers a source of predictability, suggesting that capturing these waves accurately in the model and in initial conditions could lead to improved precipitation forecasts. In this work, we investigate whether standard data assimilation (DA) algorithms like the Ensemble Kalman Filter (EnKF) are fundamentally capable of recovering tropical waves and thereby provide initial conditions that lead to skillful precipitation forecasts. To capture the essence of tropical dynamics without contamination of land-sea contrasts, sea-surface temperature gradients and influences from the extra-tropics, we use a tropical aqua channel configuration at 13km grid-spacing with the ICON numerical weather prediction model. Further, to isolate the role of the initial conditions provided by DA, we assume a perfect model. In our setup, Kelvin waves dominate over other wave types and primarily modulate precipitation. In addition, there is evidence of a Madden-Julian-Oscillation (MJO)-like feature that appears coupled to large-scale convective activity. We show that when sufficient wind observations are assimilated, the DA can reduce the errors in the representation of the Kelvin waves sufficiently to provide accurate precipitation forecasts up to several weeks. Surprisingly, even the MJO-like rainfall event, which starts after a forecast lead time of 10 days, is captured by the forecast ensemble. Further, we find that accurate initial conditions for humidity are important to slow down error growth for all model variables. Like emphasized by several other studies, we conclude that wind observations are by far the most important input to achieve skillful tropical forecasts. A secondary challenge is to improve initial conditions of humidity by developing DA algorithms to account for non-Gaussian error statistics. Investigating the role of model error in DA and the resulting forecasts is left for future work.