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Advanced Numerical Modeling Techniques in Meteorology: Exploring the Frontier of Weather Prediction and Data Assimilation

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A special issue of Atmosphere (ISSN 2073-4433). This special issue belongs to the section "Atmospheric Techniques, Instruments, and Modeling".

Deadline for manuscript submissions: closed (31 May 2026) | Viewed by 8823

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Editors

Dr. Miodrag Rancic

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Lynker at NOAA/NWS/OMD, 5830 University Research Ct, College Park, MD 20740, USA
Interests: numerical methods; modeling; data assimilation; machine learning/artificial intelligence
Special Issues, Collections and Topics in MDPI journals

Dr. Ivana Tosic

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Guest Editor

Institute of Meteorology School of Physics, University of Belgrade, Belgrade, Serbia
Interests: extreme events; precipitation; temperature; climate variability and numerical modelling
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The field of meteorology is undergoing a transformative phase, driven by revolutionary breakthroughs in the application of artificial intelligence (AI), advancements in numerical modeling techniques, and the burgeoning potential of quantum computing. This Special Issue of Atmosphere aims to provide a comprehensive overview of these cutting-edge methodologies, offering insights into their applications, challenges, and prospects.

Numerical modeling techniques have been the backbone of modern weather prediction. These models simulate atmospheric processes using mathematical and algorithmic expressions of physical law that drive the atmosphere and require significant computational resources. Recent advancements have enhanced the accuracy and efficiency of these models, incorporating finer spatial resolutions, improved boundary conditions, and novel algorithms. This Special Issue will delve into the latest developments, highlighting key improvements and their impact on weather forecasting.

Artificial intelligence (AI) has revolutionized various scientific domains, and meteorology is no exception. Yet still, an open frontier is how and whether, by integrating AI with traditional physics-based models, researchers can create hybrid systems that leverage the strengths of both approaches. AI algorithms can analyze vast amounts of data, identify patterns, and make predictions with unprecedented speed. When combined with the rigorous foundation of physics models, these hybrid techniques may offer a powerful tool for weather prediction and data assimilation even for situations in which they were not trained, such as extreme weather events that arise as a natural outcome of ongoing climate change. This Special Issue will explore the methodologies and case studies demonstrating the benefits of or denying the efficacy of AI-integrated physics models.

Quantum computing represents the next frontier of computational power, promising to solve complex problems that are beyond the reach of classical computers. In meteorology, quantum computing holds the potential to revolutionize data assimilation, improve model accuracy, and significantly reduce computation times. Although still in its nascent stages, the application of quantum computing in meteorology is an exciting area of research. This Special Issue will discuss the current applications of quantum computing in meteorology, and the challenges that need to be addressed for its widespread adoption.

The intersection of advanced numerical modeling techniques, hybridization of AI-integrated physics models, and quantum computing heralds a new era in meteorology. By embracing these innovative approaches, meteorologists can enhance the accuracy of weather predictions, improve data assimilation processes, and tackle previously insurmountable challenges. This Special Issue of Atmosphere aims to foster collaboration, stimulate discussion, and inspire further research in these groundbreaking areas. We invite contributions from researchers, practitioners, and experts to share their insights, findings, and visions for the future of meteorological science.

You may choose our Joint Special Issue in Meteorology.

Dr. Miodrag Rancic
Dr. Ivana Tosic
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Atmosphere is an international peer-reviewed open access monthly journal published by MDPI.

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Keywords

numerical modeling
data assimilation
weather forecasting
artificial intelligence (AI)
quantum computing

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Published Papers (8 papers)

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Research

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25 pages, 16743 KB

Open AccessArticle

Open Hydroclimatic Data and Iterative Machine Learning for River Discharge Forecasting in Babahoyo, Ecuador: Benchmarking, Uncertainty, and Operational Limits Without In Situ Validation

by Rolando Licapa-Redolfo, Alexander Haro-Sarango, Persi Vera-Zelada, Denis Javier Aranguri-Cayetano, Roxana Mabel Sempértegui-Rafael, Olegario Cabrera-Cabrera, Edwar Cieza-Sánchez, Martha Huamán-Tanta and Diana Carolina Castillo Martínez

Atmosphere 2026, 17(8), 808; https://doi.org/10.3390/atmos17080808 - 21 Aug 2026

Viewed by 171

Abstract

This study evaluates the potential and limitations of open/model-derived hydroclimatic data for multi-horizon river discharge forecasting in Babahoyo, Ecuador. A quantitative, applied, retrospective longitudinal design used daily data for 2017–2026. The discharge target is the GloFAS v4 seamless product—reanalysis until July 2022, archived operational forecast thereafter; meteorological predictors are ERA5/ERA5-Land/IFS reanalysis, not forecasts. The framework combined leakage-aware feature engineering, temporal validation, rolling-origin backtesting, naïve baselines, machine-learning regression, conformal prediction intervals, and high-flow classification. Performance was strongest at one day, where models reproduced the signal closely (R² = 0.909), although persistence remained highly competitive. Skill deteriorated at t + 7 and t + 14, where peak timing and magnitude became unreliable. Interval coverage was near-nominal at t + 1 but unreliable at longer horizons. The high-flow classifier identified most q90 cases, yet moderate precision and the absence of gauge validation prevent operational warning claims. Because the target is a 5 km grid simulation of a channel 100–150 m wide, the metrics quantify agreement with GloFAS, not with the physical river, and are reported to three significant digits. Overall, the study is a conservative benchmark for open hydroclimatic data in data-limited tropical floodplains: useful for exploratory monitoring and uncertainty diagnosis, but not a substitute for local hydrometric validation. Full article

(This article belongs to the Special Issue Advanced Numerical Modeling Techniques in Meteorology: Exploring the Frontier of Weather Prediction and Data Assimilation)

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16 pages, 2344 KB

Open AccessArticle

Reconstruction of Frontal Gradients Using Radial Basis Function Interpolation

by Miodrag Rancic

Atmosphere 2026, 17(8), 718; https://doi.org/10.3390/atmos17080718 - 24 Jul 2026

Viewed by 302

Abstract

The accurate representation of frontal zones—characterized by sharp scalar gradients—remains a critical challenge in regional objective analysis and data assimilation, particularly when utilizing sparse or stochastically distributed observations. This study evaluates the efficacy of Multiquadric Radial Basis Functions (RBFs) as a high-order alternative [...] Read more.

C^{\infty}

-continuous RBF approach against nearest neighbor and linear mesh interpolation schemes using both synthetic baroclinic wave profiles and an operational case study of the intense extratropical cyclone that impacted the East Coast of North America in mid-March 1993. To mitigate characteristic boundary artifacts and geometric clipping in bounded regional domains, we implement a targeted numerical stabilization framework combining localized boundary mirroring with four-corner domain anchoring. Our quantitative results demonstrate that the optimized RBF framework substantially improves gradient fidelity and reduces Root Mean Square Error across a wide range of observation densities. Furthermore, we evaluate the computational scalability of RBFs on high-performance computing architectures, demonstrating how Algebraic Multigrid solvers and Graphics Processing Unit acceleration mitigate the foundational

O (N^{3})

computational bottleneck. We conclude that RBF interpolation provides a physically consistent, analytically differentiable manifold that addresses the derivative discontinuities of traditional linear methods, offering a stable pre-processing framework for high-resolution meteorological analysis and machine learning optimization. Full article

(This article belongs to the Special Issue Advanced Numerical Modeling Techniques in Meteorology: Exploring the Frontier of Weather Prediction and Data Assimilation)

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17 pages, 1772 KB

Open AccessArticle

A Validation of Temporal Downscaling Models of Estimating Hourly Temperatures Under South African Conditions

by Phumudzo Charles Tharaga, Abraham Stephanus Steyn and Mashapha Elvis Malobane

Atmosphere 2026, 17(7), 637; https://doi.org/10.3390/atmos17070637 - 28 Jun 2026

Viewed by 388

Abstract

High-resolution weather data is essential for studies related to fruit production, building sciences and other mathematical modelling. Most of the historical weather data prior to 1980 was mainly daily. The introduction of automatic weather stations led to the introduction of hourly, minute, and second interval weather data, depending on the period during which the measurement was conducted. In order to conduct studies on climate change and generate the Climate normal, at least 30 years of data is required, and for most of the stations in South Africa, which have long-term data, their normal period was from 1961 to 1990, and the new normal was from 1981 to 2010. It becomes difficult to use daily temperatures only to do analysis for studies that require hourly temperatures, such as the calculation or estimation of chill units or chilling hours. Therefore, there is a need to find a mathematical model or stochastically generating model to derive high temporal resolution temperature data. The temporal downscaling model was used to obtain a full record of hourly temperatures for the period 1981–2010. The validation was based on all winter days within this base period for which observed data were available. A sine curve with input parameters, including daily minimum and maximum temperatures, as well as the day of the year, was more suitable. Other models were also tested, and the results were similar. All the models performed very well under normal weather conditions, while all models failed to simulate the sudden disruption in temperature due to a cold front or any storm activity. Only models for weather forecasting are able to predict sudden changes, but the historical simulators failed, as their inputs were only the daily minimum and maximum, and there was no recording of hourly temperatures available. Full article

(This article belongs to the Special Issue Advanced Numerical Modeling Techniques in Meteorology: Exploring the Frontier of Weather Prediction and Data Assimilation)

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22 pages, 5877 KB

Open AccessArticle

Optimizing WRF Spectral Nudging to Improve Heatwave Forecasts: A Case Study of the Sichuan Electricity Grid

by Shuanglong Jin, Shun Li, Bo Wang, Hao Shi and Shanhong Gao

Atmosphere 2026, 17(2), 144; https://doi.org/10.3390/atmos17020144 - 28 Jan 2026

Viewed by 1167

Abstract

Accurate forecasting of heatwaves is critical for ensuring the safe operation of electricity grids. Focusing on the complex terrain of Sichuan, China, this study investigates the optimization of spectral nudging parameters within the Weather Research and Forecasting (WRF) model to improve predictions of heatwave events. To overcome the subjectivity inherent in the traditional selection of the spectral nudging cutoff wavenumber, we propose an objective method based on power-spectrum energy diagnostics of the background field. This method determines an optimal domain-specific cutoff wavenumber. A series of sensitivity experiments were designed for a significant heatwave event that affected the Sichuan electricity grid in August 2019. These experiments evaluated the impact of different spectral nudging configurations, which considered varying domain sizes and forecast lead times, on correcting large-scale circulation drift and enhancing near-surface air temperature forecasts. The results demonstrate the following: (1) For a smaller domain or a longer forecast lead time, spectral nudging effectively compensates for circulation drift induced by weakening lateral boundary constraints, significantly improving the forecast of heatwave intensity and spatial extent, representing a compensatory effect. (2) For a larger domain that already adequately resolves large-scale circulation evolution, spectral nudging can over-constrain the model’s internal dynamical processes, thereby degrading forecast performance, an outcome termed the over-constraint effect. (3) The proposed energy-threshold method provides an objective, physics-based strategy for identifying dominant large-scale waves and optimizing the spectral nudging cutoff wavenumber. This work offers practical insights for the operational application of spectral nudging over complex terrain to advance extreme temperature forecasting. Full article

(This article belongs to the Special Issue Advanced Numerical Modeling Techniques in Meteorology: Exploring the Frontier of Weather Prediction and Data Assimilation)

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34 pages, 9217 KB

Open AccessEditor’s ChoiceArticle

Collaborative Station Learning for Rainfall Forecasting

by Bagati Sudarsan Patro and Prashant P. Bartakke

Atmosphere 2025, 16(10), 1197; https://doi.org/10.3390/atmos16101197 - 16 Oct 2025

Cited by 2 | Viewed by 2180

Abstract

Cloudbursts and other extreme rainfall events are becoming more frequent and intense, making precise forecasts and disaster preparedness more challenging. Despite advances in meteorological monitoring, current models often lack the precision needed for hyperlocal extreme rainfall forecasts. This study addresses the research gap in spatial configuration-aware modeling by proposing a novel framework that combines geometry-based weather station selection with advanced deep learning architectures. The primary goal is to utilize real-time data from well-placed Automatic Weather Stations to enhance the precision and reliability of extreme rainfall predictions. Twelve unique datasets were generated using four different geometric topologies—linear, triangular, quadrilateral, and circular—centered around the target station Chinchwad in Pune, India, a site that has recorded diverse rainfall intensities, including a cloudburst event. Using common performance criteria, six deep learning models were trained and assessed across these topologies. The proposed Bi-GRU model under linear topology achieved the highest predictive accuracy (R² = 0.9548, RMSE = 2.2120), outperforming other configurations. These findings underscore the significance of geometric topology in rainfall prediction and provide practical guidance for refining AWS network design in data-sparse regions. In contrast, the Transformer model showed poor generalization with high MAPE values. These results highlight the critical role of spatial station configuration and model architecture in improving prediction accuracy. The proposed framework enables real-time, location-specific early warning systems capable of issuing alerts 2 h before extreme rainfall events. Timely and reliable predictions support disaster risk reduction, infrastructure resilience, and community preparedness, which are essential for safeguarding lives and property in vulnerable regions. Full article

(This article belongs to the Special Issue Advanced Numerical Modeling Techniques in Meteorology: Exploring the Frontier of Weather Prediction and Data Assimilation)

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22 pages, 8353 KB

Open AccessArticle

Application of Hybrid Data Assimilation Methods for Mesoscale Eddy Simulation and Prediction in the South China Sea

by Yuewen Shan, Wentao Jia, Yan Chen and Meng Shen

Atmosphere 2025, 16(10), 1193; https://doi.org/10.3390/atmos16101193 - 16 Oct 2025

Viewed by 1123

Abstract

In this study, we compare two novel hybrid data assimilation (DA) methods: Localized Weighted Ensemble Kalman filter (LWEnKF) and Implicit Equal-Weights Variational Particle Smoother (IEWVPS). These methods integrate a particle filter (PF) with traditional DA methods. LWEnKF combines the PF with EnKF, while IEWVPS integrates the PF with the four-dimensional variational (4DVAR) method. These hybrid DA methods not only overcome the limitations of linear or Gaussian assumptions in traditional assimilation methods but also address the issue of filter degeneracy in high-dimensional models encountered by pure PFs. Using the Regional Ocean Model System (ROMS), the effects of different DA methods for mesoscale eddies in the northern South China Sea (SCS) are examined using simulation experiments. The hybrid DA methods outperform the linear deterministic variational and Kalman filter methods: compared to the control experiment (no assimilation), EnKF, LWEnKF, IS4DVar and IEWVPS reduce the sea level anomaly (SLA) root-mean-squared error (RMSE) by 55%, 65%, 65% and 80%, respectively, and reduce the sea surface temperature (SST) RMSE by 77%, 78%, 74% and 82%, respectively. In the short-term assimilation experiment, IEWVPS exhibits superior performance and greater stability compared to 4DVAR, and LWEnKF outperforms EnKF (LWEnKF’s posterior SLA RMSE is 0.03 m, lower than EnKF’s value of 0.04 m). Long-term forecasting experiments (16 days, starting on 20 July 2017) are also conducted for mesoscale eddy prediction. The variational methods (especially IEWVPS) perform better in simulating the flow field characteristics of eddies (maintaining accurate eddy structure for the first 10 days, with an average SLA RMSE of 0.05 m in the studied AE1 eddy region), while the filters are more advantageous in determining the total root-mean-squared error (RMSE), as well as the temperature under the sea surface. Overall, compared to EnKF and 4DVAR, the hybrid DA methods better predict mesoscale eddies across both short- and long-term timescales. Although the computational costs of hybrid DA are higher, they are still acceptable: specifically, IEWVPS takes approximately 907 s for a single assimilation cycle, whereas LWEnKF only takes 24 s, and its assimilation accuracy in the later stage can approach that of IEWVPS. Given the computational demands arising from increased model resolution, these hybrid DA methods have great potential for future applications. Full article

(This article belongs to the Special Issue Advanced Numerical Modeling Techniques in Meteorology: Exploring the Frontier of Weather Prediction and Data Assimilation)

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15 pages, 1849 KB

Open AccessEditor’s ChoiceArticle

Determining Wind Shear Threshold by Using Historical Sounding Data in Experimental Area

by Tingting Shu, Qinglin Zhu, Xiang Dong, Houcai Chen, Leke Lin and Xuan Liu

Atmosphere 2025, 16(9), 1064; https://doi.org/10.3390/atmos16091064 - 10 Sep 2025

Viewed by 1238

Abstract

This paper conducts a technical study on a method for determining the occurrence threshold of wind shear based on historical sounding data. After analyzing the impact of low-altitude wind shear on aircraft flight safety, a method for determining the occurrence threshold of wind shear based on historical sounding data is proposed. A statistical analysis of the sounding data from the test area over a period of 15 years from 2010 to 2024 has been conducted, which includes the occurrence events and probability statistics of 1000 m wind shear for all 12 months of the year. The simulation results validate the feasibility and effectiveness of the method for determining the occurrence threshold of wind shear based on historical sounding data in the test area, forming a method that can be extended to all altitude ranges of aircraft flight and all flight regions globally. This statistical method provides a technical foundation for the efficient detection of wind shear at local airports and enhances flight safety at these airports. Full article

(This article belongs to the Special Issue Advanced Numerical Modeling Techniques in Meteorology: Exploring the Frontier of Weather Prediction and Data Assimilation)

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Review

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29 pages, 2576 KB

Open AccessReview

A Semi-Supervised SVM-Firefly Hybrid for Rainfall Estimation from MSG Data

by Ouiza Boukendour, Mourad Lazri, Rafik Absi, Fethi Ouallouche, Karim Labadi, Youcef Attaf, Amar Belghit and Soltane Ameur

Atmosphere 2026, 17(2), 133; https://doi.org/10.3390/atmos17020133 - 26 Jan 2026

Viewed by 1169

Abstract

In this paper, two improvements in precipitation classification have been performed. Supervised machine learning has demonstrated considerable performances in classification tasks. However, supervised machine learning can only be applied to labeled data. In some cases, large amounts of unlabeled data contain valuable information for better classification. In the classification of precipitation intensities from satellite images, unlabeled data constitute the majority and remain largely unexplored. To exploit both labeled and unlabeled data, a Semi-Supervised Support Vector Machine (S3VM) is implemented as the first improvement for classification results. The labeling of the limited available data is derived from radar measurements covering a small portion of the Meteosat Second Generation Satellite observations. The results show that the S3VM model outperforms the standard SVM model, with up to a 15% improvement in classification accuracy compared to the standard SVM. To achieve the second improvement, the S3VM was combined with the Firefly Algorithm (FFA) to optimize its hyperparameters. This hybridization (S3VM-FFA) enabled an even more robust performance. A comparative study showed that the S3VM-FFA approach yielded highly satisfactory results, achieving a 17% improvement in classification compared to the SVM results. Based on these classifications, precipitation quantities at different scales are estimated. Similarly to the classification results, statistical evaluation parameters indicate that the S3VM-FFA outperforms both the standard SVM and the conventional S3VM. Full article

(This article belongs to the Special Issue Advanced Numerical Modeling Techniques in Meteorology: Exploring the Frontier of Weather Prediction and Data Assimilation)

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