The bottleneck the team attacked is one that anyone who has pushed a weather or air quality model to higher resolution knows well. Doubling the horizontal resolution of an air quality model quadruples the number of grid cells, and numerical stability then forces the model to take proportionally shorter time steps. The combined effect is punishing: previous research cited in the study estimates that increasing horizontal resolution eighteenfold inflates the computational load three hundred times. Operational forecasting systems today mostly run at horizontal resolutions of several to tens of kilometers, which is too coarse for the urban-scale, street-by-street predictions that city managers increasingly demand. Faster hardware and smarter code are therefore not luxuries but prerequisites for the next generation of forecasts.

Graphics processing units offer a way out, because their thousands of parallel processors excel at exactly the kind of repetitive grid arithmetic that atmospheric models perform. The scale of modern GPU power is striking: the El Capitan supercomputer, which topped the TOP500 list in late 2024, delivers 1.742 exaflops of double-precision performance largely through AMD Instinct MI300A accelerators, each of which alone outperforms the entire Earth-Simulator, the world’s fastest machine in 2003. Yet most atmospheric models, including EPICC-Model, were written in Fortran for CPUs, with loop structures and data flows that translate poorly to GPUs. Simply copying code across rarely works; the algorithms must be rethought for the hardware.

The EPICC-Model team had already seen this dynamic play out within their own code. In earlier work, Cao and colleagues ported the model’s gas-phase chemistry module, historically the dominant cost at more than 40 percent of simulation time, onto China’s domestically developed GPU-like accelerators using the Heterogeneous-compute Interface for Portability, or HIP, a programming framework analogous to NVIDIA’s CUDA. That port cut the chemistry module’s share of runtime from 45.7 percent to 29.9 percent, but it exposed a new culprit: the horizontal advection module, which moves pollutants across the model grid with the wind, jumped from 13.3 percent to 25.0 percent of total runtime and became the model’s leading bottleneck. The new study targets exactly that module.

The heart of the advection scheme is the piecewise parabolic method, or PPM, a high-order Godunov-type algorithm from 1984 that approximates transported quantities with parabolic functions and is prized for its precision and robustness. It is the same scheme used in the latest versions of the widely used CMAQ and CAMx models. The researchers first rewrote the Fortran HADVPPM subroutine in standard C, then extended it with HIP calls so it could run on the GPU-like accelerator, which has 3840 computing units and 16 gigabytes of device memory, at the Earth System Numerical Simulation Facility (EarthLab) in Beijing. The resulting package, GPU-HADVPPM4HIP V1.0, follows the familiar heterogeneous computing sequence: allocate device memory, copy data from CPU to accelerator, launch parallel kernels, and copy results back.

Precision was checked at every step. Comparing the original Fortran, the rewritten C, and the HIP versions on identical inputs, the team found mean relative errors on the order of 10 to the minus 7 percent under default compilation, rising only slightly to around 10 to the minus 6 percent with aggressive O3 optimization. Interestingly, most of the small error crept in during the Fortran-to-C rewrite rather than the C-to-HIP step, which makes sense because HIP is essentially an extension of standard C. In a full 28-hour coupled simulation, the GPU version reproduced the Fortran model’s fields almost exactly, with differences in ozone of about 10 to the minus 2 ppbV and in PM2.5 of about 10 to the minus 3 micrograms per cubic meter, and normalized mean biases near zero.

The performance story unfolded in stages. A naive coupling, dubbed HIP-Ori, was actually a disaster: because the model called the advection solver roughly 9.8 million times per time step, each call triggering its own CPU-to-GPU data transfers, a one-hour integration ballooned from 1015 seconds in the original Fortran code to 20,400 seconds. The first fix, HIP-Opt1, restructured the loop hierarchy and expanded one-dimensional arrays into four- and five-dimensional blocks so that entire pollutant categories could be processed in single GPU calls, cutting transfers from about 9.8 million to just 10 per time step. That single change yielded a 17-fold improvement in model-level efficiency. A second optimization, HIP-Opt2, assigned each horizontal grid cell to its own GPU thread through coordinated thread-block indexing, after decoupling iterative calculations so that no step depended on the previous one, adding another 1.5-fold gain.

The team also implemented a hybrid MPI-plus-HIP scheme across EarthLab’s heterogeneous cluster, mapping each CPU process to a dedicated GPU accelerator so that the model scales across many nodes. In the final configuration, a 28-hour simulation that took the unoptimized GPU version 149.7 hours of wall-clock time finished in just 6.0 hours, roughly a 25-fold cumulative improvement over the naive port. At the module level, the GPU advection solver including data transfer overhead ran 39.3 percent faster than the Fortran original; with transfers excluded, the kernel itself was 20.5 times faster. Offline, on an array of 100 million double-precision values, the HIP solver compiled with O3 optimization reached that headline 556.5-fold speedup over the unoptimized Fortran baseline, and still managed 128-fold when both were compiled with the same aggressive flags.

Perhaps the most instructive finding is where the remaining time goes. Profiling showed that for large inputs, memory copying between CPU and GPU consumes roughly half of total execution time, a share that keeps growing with data size. This confirms that data movement, not arithmetic, is the defining constraint of heterogeneous computing, and it explains why the coupled model gains far less than the raw kernel speedup. The authors point to remedies including pinned-memory chunked transfers, asynchronous communication, unified memory architectures, and mixed-precision computation, as well as newer PCIe interconnects whose per-lane data rates have climbed from 16 gigatransfers per second in PCIe 4.0, used at EarthLab, to a projected 128 in PCIe 7.0.

The work also carries a broader message about scientific software in the GPU era. The EPICC-Model with its new advection solver reproduced observed PM2.5 and ozone variations reasonably well across eight Chinese cities during July 2021, with mean correlation coefficients of 0.70 for PM2.5 and 0.76 for ozone, demonstrating that the accelerated code remains scientifically trustworthy on domestic hardware. As the authors note, achieving kilometer-scale pollution simulations, of the kind that recently won a Gordon Bell Prize for climate modeling using NVIDIA GH200 GPUs, will require adapting entire air quality models to heterogeneous supercomputers, where nine of the world’s ten fastest machines now reside. Porting a single module is only the beginning; the real challenge, and opportunity, lies in redesigning the whole computational workflow around the GPU’s massively parallel architecture.

Subject of Research: GPU acceleration of the advection module in the EPICC-Model air quality modeling system

Article Title: Enhancing the advection module performance in the EPICC-Model V1.6.0 via GPU-HADVPPM4HIP V1.0 coupling and GPU-optimized strategies

Article References: Cao, K., Wu, Q., Tang, X., Li, J., Chen, X., Chen, H., Wang, W., Wu, H., Kong, L., Li, J., Zhu, J., & Wang, Z. (2026). Enhancing the advection module performance in the EPICC-Model V1.6.0 via GPU-HADVPPM4HIP V1.0 coupling and GPU-optimized strategies. Geoscientific Model Development, 19(19), 9807-9829. https://doi.org/10.5194/gmd-19-9807-2026

Image Credits: AI Generated

DOI: 10.5194/gmd-19-9807-2026

Keywords: GPU computing, air quality modeling, EPICC-Model, advection, piecewise parabolic method, HIP, high-performance computing, heterogeneous computing, EPICC-Model V1.6.0, GPU-HADVPPM4HIP, EarthLab, numerical weather prediction

The central finding of the study is sobering for forecasters: none of the numerical weather prediction models available at the time could anticipate the severity of the rainfall intensity. Numerical weather prediction, or NWP, relies on physics-based simulations of the atmosphere run on supercomputers, and while these models have become remarkably skilled at forecasting synoptic-scale systems such as monsoon depressions and cyclones, they routinely struggle with localized, short-lived convective extremes. The Kolkata event fell squarely into that blind spot. The rain was not produced by a large, well-organized weather system that models could track for days in advance; instead, it emerged from intense convection confined to a small area, persisting in nearly the same location for hours and stacking up rainfall totals that overwhelmed urban drainage.

To understand the event, the authors assembled an unusually comprehensive set of observations. They drew on radiosonde and radio wind soundings, known as RSRW, which are balloon-borne instruments launched from meteorological stations that profile temperature, humidity and wind from the surface up through the depth of the troposphere. They complemented these in-situ measurements with ERA5, the fifth-generation reanalysis dataset produced by the European Centre for Medium-Range Weather Forecasts, which blends historical observations with model physics to create a physically consistent picture of the atmosphere. On top of that, the researchers examined radar and satellite observations, which captured the storm’s structure and evolution in real time. This multi-instrument approach allowed them to reconstruct both the thermodynamic environment, meaning the temperature and moisture conditions that fuelled the storm, and the dynamic behaviour of the convection itself.

What emerged from the RSRW and ERA5 analysis was a set of meteorological parameters with significantly elevated values over the affected area, and, importantly, those elevated values coincided closely with the spatial and temporal distribution of the rainfall. In other words, the atmosphere over Kolkata and its surroundings displayed a distinctive thermodynamic fingerprint before and during the deluge: extreme instability, abundant moisture through a deep column of air, and the kind of profile that strongly favours vigorous, sustained convection. The authors argue that these parameters can serve as precursors for extreme rainfall conditions of short duration, offering a way to anticipate such events even when conventional NWP rainfall forecasts fail to capture their localized, high-impact nature.

This precursor-based approach matters because thermodynamic indices have a long history in severe weather forecasting. Classic indices such as the K index, the Total Totals index and various convective available potential energy measures, developed by researchers including George, Miller, and Litynska and colleagues in the mid-twentieth century, condense complex sounding data into single numbers that indicate whether the atmosphere is primed for thunderstorms. Bondyopadhyay has previously worked on determining suitable thermodynamic indices for predicting thunderstorm events over eastern India, and the new study extends that line of thinking from ordinary thunderstorms to the extreme tail of short-period rainfall. Rather than asking simply whether storms will form, the precursor framework asks whether the environment is loaded with enough moisture and instability to produce rainfall of exceptional intensity if convection does fire.

The radar and satellite component of the analysis added a second, equally important layer of insight. The observations revealed strong convection prevailing over the Kolkata area in an almost stagnant state for several hours. This persistence is the key to understanding why the event was so destructive. Convective storms often move with the prevailing winds, spreading their rainfall across a swath of territory; when a storm instead remains anchored over the same small area, its rainfall accumulates on one spot, and the hydrological consequences multiply. The nearly stationary character of the Kolkata convection meant that a few hours of intense rain fell on a single urban basin, producing flooding that the city’s infrastructure had no capacity to absorb. The authors emphasize that this kind of near-stagnant convective signature, visible in real-time radar and satellite data, provides highly useful information for nowcasting, the short-range forecasting discipline concerned with conditions over the next few hours.

To place the Kolkata event in context and to generalize their methodology, the researchers also analysed two secondary cases in which high amounts of rainfall were reported within very short periods. This comparative strategy is essential for distinguishing a genuine precursor signal from a one-off coincidence. If the same constellation of elevated thermodynamic parameters appears across multiple short-duration extreme rainfall events, then the parameters can plausibly be used as operational warning indicators rather than merely as diagnostic curiosities examined after the fact. The study’s framing also connects to a broader scientific debate about terminology: as recent work on cloudburst disambiguation has pointed out, not every extreme short-term rainfall event constitutes a cloudburst in the strict sense, and careful case-by-case analysis of the kind performed here helps refine how meteorologists classify and communicate these hazards.

The broader climatic backdrop gives the study additional urgency. Research over the past decade has documented a striking rise in extreme precipitation across India, including a threefold increase in widespread extreme rain events over central India and a strengthening of summer monsoon precipitation extremes linked to long-term climatic and anthropogenic factors. Dense cities are particularly exposed to this trend because short-duration rainfall extremes translate almost directly into urban flooding: impervious surfaces prevent infiltration, drainage systems are designed for historical rainfall statistics, and millions of residents and assets are packed into low-lying areas. An event like the September 2025 Kolkata deluge, unprecedented in intensity for the city, illustrates how quickly the tail of the rainfall distribution can outpace the assumptions embedded in urban planning and emergency response.

It is notable that much of the existing literature on short-duration extreme rainfall in India focuses on the Himalayan region, where cloudbursts and the flash floods and debris flows they trigger have been studied extensively in places such as Kedarnath, Uttarkashi and Nainital, often using reanalysis datasets like ERA5 and the India Meteorological Department’s high-resolution reanalysis. The Kolkata event demonstrates that the same analytical toolkit, sounding-based thermodynamic diagnostics combined with reanalysis and remote sensing, applies equally to a sprawling tropical delta city far from the mountains. The authors acknowledge the India Meteorological Department for providing the data and support that made the research possible, and their institutional position inside the Regional Meteorological Centre Kolkata underscores the operational motivation behind the work: finding practical, computationally light indicators that duty forecasters can monitor alongside model guidance.

The practical takeaway is a two-track strategy for anticipating and managing short-duration rainfall extremes. Before an event, elevated values of key thermodynamic parameters derived from soundings and reanalysis can flag environments capable of producing extreme localized rainfall, compensating for the known inability of NWP models to resolve the precise intensity and placement of such convection. During an event, radar and satellite monitoring of convective motion becomes decisive: if strong convection is detected and it is nearly stationary, forecasters can warn of accumulating rainfall and escalating flood risk in real time. Neither track alone would have been sufficient for Kolkata in September 2025, but together they form a coherent nowcasting and early-warning framework. As extreme short-period rainfall grows more frequent in a warming climate, the identification of reliable meteorological precursors of the kind documented in this study may prove to be one of the most valuable tools available for protecting densely populated cities from the next unprecedented night of rain.

Subject of Research: Meteorological precursors of an extreme short-duration rainfall and flooding event over Kolkata, India

Article Title: Analysis of extreme rainfall episode in short period over Kolkata & neighbourhood, India and identification of meteorological precursors

Article References: Bondyopadhyay, S., & Biswas, H. R. (2026). Analysis of extreme rainfall episode in short period over Kolkata & neighbourhood, India and identification of meteorological precursors. Theoretical and Applied Climatology, 157(11), Article 708. https://doi.org/10.1007/s00704-026-06630-z

Image Credits: AI Generated

DOI: 10.1007/s00704-026-06630-z

Keywords: Kolkata, extreme rainfall, flash flooding, nowcasting, numerical weather prediction, ERA5 reanalysis, radiosonde, thermodynamic indices, convection, India Meteorological Department, urban flooding, monsoon extremes

The researchers turned their attention to a well-documented event from the Deep Propagating Gravity Wave Experiment, or DEEPWAVE, a field campaign conducted over New Zealand in 2014. On 12 July of that year, a research aircraft flown by the German Aerospace Center traced a rectangular path across the South Island, sampling the atmosphere at two stacked levels: one near 7.9 kilometers altitude and another near 10.9 kilometers, close to the tropopause. The meteorological setup was favorable for wave generation, with moderate northwesterly winds of roughly 10 to 15 meters per second at 5 kilometers altitude blowing perpendicular to the Southern Alps, and about 20 meters per second near the tropopause, with little change in wind direction with height. Those stacked flight legs provided rare, high-frequency in situ measurements of waves and turbulence signatures near the tropopause, exactly the kind of ground truth that model developers crave.

The simulation tool at the heart of the study is the ICON model, the ICOsahedral Nonhydrostatic modeling framework developed jointly by the German Weather Service and the Max Planck Institute for Meteorology. ICON uses an icosahedral-triangular grid built from geodesic Delaunay triangulation, a height-based vertical coordinate and C-grid staggering of its variables. Jagan and Schmidli ran ICON in numerical weather prediction mode at horizontal grid spacings of approximately 2 kilometers, 1 kilometer and 500 meters, all with 137 vertical levels and a model top at 30 kilometers. They then varied the maximum vertical grid spacing in the upper troposphere and lower stratosphere, the critical region spanning roughly 6 to 25 kilometers altitude, among 400, 200 and 100 meters. To anchor the finest end of the comparison, they added an online-nested large-eddy simulation that zoomed down to a remarkable 130 meters over the southern flight segment, using four nested domains stepping from 1 kilometer down to the 130-meter innermost nest.

The turbulence question was addressed by pitting two schemes against each other. The first is the operational turbulent kinetic energy scheme, which predicts a single TKE value and augments the classical shear-driven turbulence budget with empirical extra source terms, one for large-scale horizontal shear and one for breaking subgrid-scale mountains, both originally designed to support aviation turbulence products such as the eddy dissipation rate. The second is the newly developed two-energy scheme, which carries two prognostic turbulence energies, dynamically adjusts its mixing length, avoids prescribed minimum diffusion coefficients and employs an assumed probability density function method for buoyancy production, all intended to better handle the anisotropic, strongly stratified turbulence found aloft rather than the boundary-layer conditions for which most closures were originally tuned.

The reference simulation, run at 1 kilometer resolution with the two-energy scheme, painted a vivid picture of the event. Alternating bands of ascent and descent stretched downstream of the main ridge from the mid-troposphere into the lower stratosphere, strongest in the troposphere and weakening with height. A powerful wave with vertical velocities exceeding 3 meters per second rose above the Mount Cook region, New Zealand’s highest summit, while a weaker wave formed above the Two Thumb Range farther southeast. The simulated wave field proved quasi-stationary across the three-hour flight window, which made the comparison with the aircraft data meaningful. Against the observations, the model agreed reasonably well on the lower flight leg but underestimated wave amplitude on the upper leg, and the large-eddy simulation better captured the wavelength and phase of the waves even though the coarser NWP runs better reproduced their amplitude.

Resolution emerged as a decisive factor. At 2 kilometers, the simulated waves took on an artificially hydrostatic character, their horizontal wavelengths stretching as the model lost the ability to represent shorter scales. At 500 meters the waves became more non-hydrostatic and vertically aligned, and the number of resolved waves multiplied as shorter wavelengths entered the picture, an effect even more pronounced at 130 meters in the large-eddy simulation, where clear examples of trapped lee waves appeared in the stable layer below about 5 kilometers. Vertical resolution mattered just as much: simulations with 400-meter vertical spacing showed clear differences from the reference, particularly in the stratosphere, while 200-meter and 100-meter runs were nearly identical, indicating that near-convergence of the primary wave requires vertical grid spacing of 200 meters or finer in the upper troposphere and lower stratosphere.

The most striking finding concerned the turbulence schemes themselves. Both produced essentially the same resolved wave structures, yet the parameterized turbulent kinetic energy differed enormously between them. The operational TKE scheme generated substantially higher TKE throughout the wave field, with turbulence patches sprinkled across the troposphere and even reaching into the lower stratosphere, whereas the two-energy scheme sensibly confined turbulence to the atmospheric boundary layer and the strongest low-level wave regions. By systematically switching off the empirical source terms, the researchers traced the excess to the horizontal-shear term. This term is a two-dimensional Smagorinsky-type closure that assumes grid-scale deformation feeds an irreversible cascade into unresolved turbulence, but in the simulated mountain-wave case much of the deformation came from large, coherent, largely reversible gravity waves. Unable to tell the difference, the closure converted wave-related deformation into spurious TKE, which is why the excess energy appeared spatially correlated with the wave field rather than with genuinely turbulent regions.

Further confirmation came from bulk diagnostics averaged over a subdomain of the Southern Alps. Area-averaged vertical velocity variance at 500 meters matched the large-eddy simulation closely in the lower troposphere, while the 1 and 2 kilometer runs systematically underestimated it in the trapped-lee-wave layer. Above that layer, the 1 and 0.5 kilometer runs agreed well, signaling near-convergence for the dominant wave. Notably, the momentum flux profiles at 1 kilometer were nearly identical regardless of turbulence scheme, and the spurious horizontal-shear TKE left no corresponding signature in the wave drag, a decoupling the authors interpret as further evidence that the extra turbulence was artificial. The low-level gravity-wave momentum flux, a key target quantity for gravity-wave drag parameterizations, kept increasing as resolution improved from 1 kilometer to 500 meters, meaning the bulk momentum budget had not yet converged even at these very fine grids. Intriguingly, the comparison also showed that the large-eddy simulation is not automatically the more realistic reference: at 130 meters it resolved the shortest waves’ wavelength and phase but damped their amplitude, likely over-dissipating near-grid-scale wave energy, and it underestimated the vertical velocity fluctuations observed in the upper troposphere.

The practical implications reach well beyond academic curiosity. Turbulence in the upper troposphere and lower stratosphere is intermittent and localized, shaping stratosphere-troposphere exchange of greenhouse gases and pollutants and posing real hazards on long-haul routes that cross major mountain ranges. The study’s guidance is concrete: reliable simulation of small-scale mountain waves and turbulence at kilometer-scale resolution demands horizontal grid spacings of 1 kilometer or finer and vertical spacings of 200 meters or finer in the UTLS, while trapped lee waves and downstream wave structure remain stubbornly resolution-sensitive even then. Equally important, operational centers running kilometer-scale models over mountainous terrain should reconsider the empirical horizontal-shear and subgrid-orography terms of their TKE closures, which can inflate turbulence where none exists, or adopt alternatives like the two-energy scheme, which behaves stably in strongly stratified conditions without exhibiting the artifact. The authors caution that they do not claim the new scheme is more accurate everywhere, and genuine sub-kilometer turbulence downstream of the secondary ridge remained under-resolved in every configuration, including the large-eddy run. Future work will extend the analysis to additional DEEPWAVE cases and seek to couple the two-energy scheme with gravity-wave parameterizations, bridging the gap between explicitly resolved and parameterized wave-turbulence interactions in global and climate models, a step that could ultimately make turbulence forecasts that pilots and passengers depend on considerably more trustworthy.

Subject of Research: Simulation of mountain waves and turbulence in the upper troposphere and lower stratosphere using the ICON model at varying resolutions and turbulence schemes

Article Title: Impact of model resolution and turbulence scheme on the representation of mountain waves and turbulence

Article References: Impact of model resolution and turbulence scheme on the representation of mountain waves and turbulence. (n.d.). https://doi.org/10.5194/acp-26-13721-2026

Image Credits: AI Generated

DOI: 10.5194/acp-26-13721-2026

Keywords: mountain waves, gravity waves, turbulence, ICON model, DEEPWAVE, large-eddy simulation, turbulent kinetic energy, model resolution, upper troposphere, lower stratosphere, aviation safety, numerical weather prediction

The answer, according to Piero Serafini of the University of L’Aquila and colleagues, is: a great deal. The team compared the Weather Research and Forecasting model (WRF), developed by NCAR, NOAA and the US Air Force, with the ICON model (ICOsahedral Nonhydrostatic), created by the German Weather Service and the Max Planck Institute for Meteorology. Both were configured at roughly 2 kilometre grid spacing, the current operational standard for convection-permitting forecasts used by national weather services across Europe. The researchers matched the two models as closely as possible, aligning their domains, vertical level distributions, boundary conditions and even developing a custom Python algorithm to harmonise the 50 vertical levels, from a lowest layer just 20 metres above the surface to the upper atmosphere at 24,500 metres.

Even with this meticulous balancing, the results diverged dramatically. All seven simulations reproduced Daniel’s overall track, from its birth over the Aegean Sea on 4 September to its dissipation near Egypt on 12 September. But the storm’s intensity varied sharply from run to run. WRF consistently produced deeper central pressures and stronger winds than ICON, painting a more ferocious cyclone. The explicit WRF run generated a minimum central pressure of 982 hectopascals with winds near 36 metres per second, while the fully parameterized ICON run reached 980 hectopascals with winds of about 33 metres per second. At the other extreme, ICON’s special gray-zone configuration produced a feeble system with a central pressure of just 1001 hectopascals, essentially failing to capture the storm’s tropical transformation at all.

The stakes of these differences become clear when considering what Daniel actually did. The cyclone began as an extratropical disturbance embedded in a pronounced omega blocking pattern over Europe, with an intrusion of stratospheric potential vorticity triggering cyclogenesis near the Greek coast. On 5 and 6 September, persistent easterly winds funnelled moisture from the Aegean and Black Seas into thunderstorms with cloud tops exceeding 13 kilometres. Surface stations in the Thessaly region recorded more than 750 millimetres of rain in a single day and up to 1235 millimetres over four days. As the storm drifted south over sea surfaces approaching 28 degrees Celsius, an anomalously warm energy reservoir, it underwent a marked structural transformation, barotropically aligning into a warm-core vortex consistent with a medicane, the Mediterranean’s rare tropical-like cyclone.

To evaluate how faithfully the models captured this evolution, the team deployed an arsenal of diagnostic tools. An objective cyclone tracker, newly developed for the study, followed the storm by combining mean sea-level pressure with the geopotential structure of the lower troposphere, avoiding the trap of latching onto spurious pressure minima beneath individual thunderstorm cells. Precipitation was verified against the IMERG satellite product, using the Fractions Skill Score to measure how well each simulation captured both the amount and the spatial placement of rainfall. The storm’s tropical character was assessed with Hart’s Cyclone Phase Space, which tracks thermal asymmetry and warm-core structure, and with a novel technique the authors call the Temporal Annular Symmetric Mean, which averages equivalent potential temperature and wind in concentric rings around the storm’s core over eight consecutive time steps.

The track results revealed a nuanced picture. WRF’s explicit run achieved the best overall performance, with a mean error of 63 kilometres and a root-mean-squared error of 76 kilometres, while ICON’s runs clustered between 83 and 105 kilometres of mean error. Yet rigorous significance testing showed that this apparent WRF advantage was not statistically significant, being overshadowed by variability along the storm’s life cycle. Intriguingly, each model excelled at a different stage: WRF better reproduced the barotropic tropical-like phase, while ICON handled the early baroclinic dynamics more accurately, likely benefiting from its global-model heritage. For the critical landfall near Benghazi, the best simulation, WRF with a shallow convection scheme, placed the landfall within just 9 kilometres of the observed location, with a delay of only 5 hours.

The most striking finding concerned the shallow convection schemes, which represent small, non-precipitating cumulus clouds that remain unresolved even at 2 kilometre grid spacing. Including these schemes proved important for both models, significantly improving landfall accuracy compared with fully explicit or fully parameterized configurations. The researchers propose a physical explanation: shallow cumuli vent boundary-layer moisture into the lower free troposphere, drying the sub-cloud layer and delaying the onset of resolved deep convection, so that latent heating is released over a wider area rather than in a few grid-point updrafts. This produces a weaker but better organised cyclone, consistent with the smoother eyewall structures and improved extreme-rainfall localisation seen in the shallow runs. WRF’s shallow configuration was the only setup to achieve skill at the native grid scale for the most extreme rainfall thresholds.

The internal anatomy of the simulated storms told an equally compelling story. WRF runs generated a vertically coherent warm core extending up to about 300 hectopascals, with a distinct eyewall-like structure and winds packed tightly around the centre. ICON’s explicit run, by contrast, produced a shallow warm anomaly confined below 550 hectopascals, limiting the depth-integrated thickness anomaly and hence the surface pressure deepening. The fully parameterized runs of both models tended to over-intensify the cyclone, apparently by creating deep convection cells that rotate in phase around the storm axis, feeding an unrealistic positive feedback between latent heat release and pressure fall. And ICON’s gray-zone configuration represented a critical failure mode, over-damping convective development so severely that the storm never transitioned to a tropical-like maintenance mechanism, remaining cold-core and disorganised throughout.

The authors are careful to note the limits of their conclusions. Validation relied heavily on satellite-derived tracks and sparse surface observations, since Daniel evolved mostly over the open sea, and Libya has few weather stations near the affected area. The scatterometer measurements that were available tend to underestimate wind speeds in deep convection, and the observed minimum pressure of 996 hectopascals may itself be an overestimation given the lack of data near the storm’s peak intensity. As a single-case study, the findings may be specific to Daniel’s unusual, multi-stage evolution, which stretched model physics across heterogeneous regimes within a single integration. Differences between the full WRF and ICON configurations also reflect unmatched physics suites, such as WRF’s single-moment ice microphysics versus ICON’s fully two-moment scheme, that cannot be fully disentangled from the convection treatment itself.

Nevertheless, the practical message for forecasters is clear. At kilometre-scale resolutions, the same physical option may not behave equivalently across different models, because discretization, diffusion and vertical coordinates all shape the outcome. Scheme portability cannot be assumed, and each model requires dedicated calibration. For long-lived, high-impact systems like Daniel, no single optimal setup is robust across all phases of a storm’s life, so case-by-case sensitivity analysis remains essential. Early-warning systems, the authors argue, should not rely exclusively on nominal horizontal resolution but on demonstrated model skill for the specific class of events being targeted. As the Mediterranean warms and rare tropical-like cyclones threaten an increasingly vulnerable coastline, knowing exactly how the clouds are represented in the forecast could mean the difference between a warning issued in time and a catastrophe that no one predicted.

Subject of Research: High-resolution sensitivity of Mediterranean tropical-like cyclone Daniel simulations to convection scheme choices in the WRF and ICON weather models

Article Title: Multi-model high-resolution analysis of Tropical-Like Cyclone Daniel with WRF and ICON: peculiarities and sensitivity to convection schemes

Article References: Serafini, P., Ricchi, A., Marsigli, C., D'Amico, C., Nastasi, M., Pelosini, R., & Ferretti, R. (2026). Multi-model high-resolution analysis of Tropical-Like Cyclone Daniel with WRF and ICON: peculiarities and sensitivity to convection schemes. Weather and Climate Dynamics, 7(3), 1525-1546. https://doi.org/10.5194/wcd-7-1525-2026

Image Credits: AI Generated

DOI: 10.5194/wcd-7-1525-2026

Keywords: Medicane Daniel, Mediterranean cyclone, WRF, ICON model, convection parameterization, tropical-like cyclone, numerical weather prediction, cyclone tracking, Fractions Skill Score, shallow convection, Libya flooding, extreme precipitation

The research, conducted by Sumia Akter, Jayeef Rahman Muaz, and Rabiul Awal, set out to answer a question that has been simmering in the weather prediction community for years: for short-term forecasting, known in the trade as nowcasting, can data-driven deep learning models match or beat traditional numerical weather prediction? The stakes are particularly high in Bangladesh, a delta nation crisscrossed by rivers and battered each year by extreme rainfall events. Conventional numerical weather prediction models, which simulate the physics of the atmosphere on supercomputers, remain computationally intensive and have historically shown limited skill in this region, where complex monsoon dynamics and local topography challenge global simulation frameworks.

The team compared four deep learning architectures against the Weather Research and Forecasting model, or WRF, one of the most widely used physics-based forecasting systems in the world. The four contenders were a Simple Long Short-Term Memory network, a Stacked LSTM, a Bidirectional LSTM, and a Gated Recurrent Unit, commonly abbreviated as GRU. These models belong to a class of neural networks known as recurrent architectures, which are specifically designed to process sequences of data over time. Rather than solving equations of atmospheric motion, they learn statistical patterns from historical records, in this case hourly rainfall data drawn from the ERA5 reanalysis dataset, a globally consistent reconstruction of past weather produced by assimilating observations into a numerical model.

The experimental design was deliberately rigorous. Each model was trained independently for each of six stations spread across Bangladesh’s climatologically diverse landscape, using hourly ERA5 reanalysis data spanning 2018 through 2024. This per-station approach allowed the networks to internalize the local rainfall rhythms of each city rather than forcing a single national model to average across wildly different climates. The evaluation went beyond simple error measurements: the researchers assessed performance using both regression metrics, which quantify how closely predictions track the actual amount of rain, and binary detection metrics, which measure whether the models correctly flag whether rain will occur at all.

The results were striking. Across the full test period, the Simple LSTM achieved the strongest overall performance, explaining approximately 88 percent of the rainfall variance in the ERA5 reference data while producing the lowest prediction errors of any model tested. The GRU delivered nearly comparable results, suggesting that the simpler recurrent designs, despite their relative architectural minimalism, capture the temporal structure of rainfall sequences remarkably well. In practical terms, this means that a model trained on seven years of hourly data could account for the vast majority of the variability in what the atmosphere would do in the next hour, a level of skill that could translate directly into actionable early warnings for urban flood management.

Geography mattered, however. The study found consistently stronger performance at wetter stations such as Chittagong and Sylhet, both located in regions that receive some of the highest rainfall totals in the subcontinent, than at the drier northwestern stations of Rajshahi and Rangpur. The explanation lies in a well-known pitfall of machine learning applied to rare events: class imbalance and rainfall intermittency. In dry regions, most hours contain no rain at all, so the statistical signal the networks must learn is sparse and noisy. When genuine rain events are rare exceptions buried in a sea of zeros, models struggle to distinguish meaningful precursors from random fluctuations, and their skill degrades accordingly. This finding carries an important lesson for anyone deploying AI weather models in arid or seasonally dry climates.

To probe how the models behaved under different rainfall regimes, the researchers conducted an event-category analysis across ten WRF simulation events spanning extreme, moderate, and weak rainfall conditions. The deep learning models showed their closest agreement with the ERA5 reference values during extreme events, precisely the situations in which accurate forecasts matter most for protecting lives and infrastructure. During weak events, however, skill declined notably, a consequence of near-zero rainfall conditions in which tiny absolute errors loom large relative to the minuscule amounts of rain being predicted. The pattern suggests that these networks excel at recognizing the signatures of heavy, organized rainfall but find light drizzle far harder to pin down.

The physics-based WRF model, by contrast, fared poorly across the board. The study documented systematic overestimation of rainfall, temporal displacement of peak rainfall timing, and strongly negative R-squared values across all event categories and stations. A negative R-squared means the model’s predictions were worse than simply guessing the long-term average, a sobering result for a system that demands substantial computational resources. The temporal displacement issue is particularly consequential for nowcasting: if a model correctly predicts that a deluge is coming but places it an hour or two off, the warning it provides may arrive too early to be trusted or too late to be useful. For a country where flash floods can develop with terrifying speed, timing errors of that magnitude can undermine public confidence in forecasts.

To ensure the differences among the deep learning architectures were not statistical flukes, the researchers applied a Friedman test, a non-parametric method for comparing the ranks of multiple models across repeated trials. The test confirmed statistically significant differences in root-mean-square error ranks among the four architectures, with a chi-squared statistic of 10.60 and a p-value of 0.014. A Nemenyi post-hoc test then pinpointed the source of the difference: the Simple LSTM significantly outperformed the Stacked LSTM, with a p-value of 0.0095. The implication is counterintuitive but increasingly common in applied machine learning: adding layers and complexity does not automatically improve performance, and with limited training data, a leaner architecture can generalize better than a deeper one.

The broader significance of this work extends well beyond the borders of Bangladesh. As climate change intensifies the hydrological cycle, extreme rainfall events are becoming more frequent and more severe across South Asia and much of the developing world, yet the regions at greatest risk often lack the supercomputing infrastructure required to run high-resolution numerical models in real time. Deep learning nowcasting offers a compelling alternative: once trained, these models can generate predictions in seconds on modest hardware, using freely available reanalysis and satellite data as inputs. The caveat, as this study makes clear, is that data-driven models inherit the limitations of their training data and falter where events are rare or conditions drift outside the historical envelope. The most promising path forward, many researchers believe, is a hybrid approach in which physics-based simulations and learned statistical patterns complement one another. For now, the message from Dhaka’s flood-prone horizon is clear: for the crucial first hour of warning, a simple neural network trained on seven years of data can see the coming rain better than a supercomputer solving the equations of the atmosphere.

Subject of Research: Comparison of deep learning and numerical weather prediction models for one-hour-ahead rainfall nowcasting in Bangladesh

Article Title: Comparison of data-driven and numerical weather prediction models for rainfall nowcasting in major cities of Bangladesh

Article References: Akter, S., Muaz, J. R., & Awal, R. (2026). Comparison of data-driven and numerical weather prediction models for rainfall nowcasting in major cities of Bangladesh. PLOS Climate, 5(10), e0001088. https://doi.org/10.1371/journal.pclm.0001088

Image Credits: AI Generated

DOI: 10.1371/journal.pclm.0001088

Keywords: rainfall nowcasting, deep learning, LSTM, GRU, numerical weather prediction, WRF model, Bangladesh, ERA5 reanalysis, flood forecasting, PLOS Climate, monsoon, machine learning

The core problem the researchers tackled is one of scale and cost. Numerical weather prediction models simulate the atmosphere by solving equations of fluid dynamics and thermodynamics on a grid, and the finer that grid becomes, the more computationally punishing the exercise. Increasing spatial resolution leads to a quadratic or even cubic growth in the number of grid points, translating into orders-of-magnitude more floating-point operations. Even the European Centre for Medium-Range Weather Forecasts, in a landmark experiment, needed a substantial fraction of the Summit supercomputer at Oak Ridge National Laboratory to run a global 1 kilometer simulation at a pace of roughly one simulated week per day. Operational forecasting centers simply cannot afford to run kilometer-scale global models within the time windows that forecasts demand.

The practical workaround has long been downscaling: taking the output of a coarser global model and deriving finer regional detail from it. Dynamical downscaling embeds a high-resolution regional model within the global one, but inherits the same computational burden. Statistical downscaling, by contrast, learns the mapping between low-resolution and high-resolution meteorological fields from historical data, offering simpler implementation, lower cost, and often higher accuracy. Deep learning has supercharged this approach by borrowing techniques from computer vision, where super-resolution models routinely turn blurry images into sharp ones. The catch, as the authors note, is that meteorological downscaling must guarantee accuracy and physical consistency, not merely visual plausibility.

CorrDiff, originally developed by NVIDIA researchers, takes a two-step approach that elegantly sidesteps a fundamental obstacle in generative downscaling. Because low-resolution and high-resolution atmospheric data occupy very different statistical distributions, training a diffusion model directly on the translation between them is difficult. CorrDiff therefore first trains a deterministic regression model, a UNet neural network, to predict the conditional mean of the high-resolution field. A second network, an Elucidated Diffusion Model, is then trained to correct the regression output. During inference, random noise is fed through the denoising process conditioned on the low-resolution input, and the result is added back to the regression prediction. By sampling multiple random noises, the model produces an ensemble of plausible high-resolution fields, yielding a probabilistic forecast rather than a single deterministic answer.

The Chinese team pushed this framework far beyond its original scope. Where the original CorrDiff work covered Taiwan at 2 kilometer resolution on a 448 by 448 grid, the new model covers nearly all of China on a 1600 by 2400 grid at 3 kilometers, roughly twenty times larger. The researchers extended the target variables beyond surface quantities to include upper-air fields across six pressure levels, added high-resolution orography as an input, and introduced a global residual connection: instead of predicting the full high-resolution field, the networks learn the residual between it and a bilinear interpolation of the coarse input, a strategy that accelerated convergence and improved accuracy. Training relied on 25 kilometer ERA5 reanalysis data from ECMWF as inputs and 3 kilometer reanalysis from the China Meteorological Administration Regional Reanalysis Atmospheric System as ground truth, using 11,688 samples spanning 2019 to 2022.

The experimental design was meticulous. Five regression models and their CorrDiff counterparts were trained with different combinations of input and output variables, probing how dependencies between variables affect downscaling quality. On a validation set drawn from January, April, July, and October 2023, all models consistently beat simple interpolation of the coarse data. Notably, the team found that combining radar reflectivity prediction with general downscaling in a single model compromised accuracy for other variables, while adding orography improved surface pressure predictions. A smaller network failed to match the accuracy of its larger sibling, confirming that model capacity matters at this scale. All models were trained on eight NVIDIA H20 GPUs, with training times per epoch ranging from roughly one to four hours.

When the trained models were applied to real global forecasts, the results were striking. The researchers downscaled 25 kilometer forecasts from two sources: the conventional CMA Global Forecast System and Sphere Fusion Forecast, a deep learning weather model built on Spherical Fourier Neural Operators. Against the operational CMA Mesoscale Model, a 3 kilometer regional numerical prediction system, as a baseline, the downscaled forecasts achieved lower Mean Absolute Error for almost all target variables. Power spectral analysis added nuance: the diffusion model generated richer high-frequency detail than the regression model, and for many near-surface variables its spectra agreed more closely with the reanalysis ground truth than CMA-MESO did, though the authors caution it may also introduce some non-physical high-frequency components.

Perhaps the most compelling evidence came from tropical cyclones. In case studies of Typhoons Khanun and Haikui, the regression-based downscaling produced overly smooth wind fields, a consequence of the over-smoothing tendency of deterministic models, and dramatically underestimated the probability of radar reflectivity exceeding 50 dBZ. CorrDiff, by contrast, reproduced realistic small-scale convective structures and matched the reflectivity distribution of the reanalysis data far more closely, outperforming CMA-MESO in Fractions Skill Scores between 12 and 36 hours of forecast lead time. The team also showed that the ensemble variance of CorrDiff predictions correlates with actual error: grid points with low variance tend to be more accurate, offering a practical tool for identifying where a forecast can be trusted.

The authors are candid about limitations. CorrDiff’s Mean Absolute Error is consistently higher than the regression model’s, an expected consequence of diffusion models optimizing a different objective, and the iterative denoising process makes inference several times slower, a cost that grows further when generating ensembles. Analysis of the correction fields revealed that the diffusion model learns spatially organized adjustments concentrated over meteorologically active regions such as the Qinghai-Tibet Plateau, but also over-corrects in some smooth areas, suggesting that region-aware or variable-dependent correction strategies could improve future versions. The uncertainty estimates, while empirically useful, do not yet correspond to physically grounded measures of atmospheric predictability.

Even so, the implications are profound. A data-driven pipeline that ingests coarse global forecasts, whether from traditional numerical models or from rapidly emerging AI weather systems, and emits 3 kilometer regional forecasts that rival or beat an operational mesoscale model could reshape how national weather services deliver local predictions for agriculture, energy, transportation, and disaster risk. With the model code and sample data released on Zenodo, and with promising directions including fine-tuning on operational data, physically grounded uncertainty quantification, and interpretable deep learning, the study signals that generative AI is no longer just painting pretty pictures of the atmosphere. It is learning to fill in the fine print of the weather itself, one denoising step at a time.

Subject of Research: Diffusion-based statistical downscaling of weather forecasts to 3 km resolution over China

Article Title: China regional 3 km downscaling based on residual Corrective Diffusion model

Article References: China regional 3 km downscaling based on residual Corrective Diffusion model. (n.d.). https://doi.org/10.5194/gmd-19-9235-2026

Image Credits: AI Generated

DOI: 10.5194/gmd-19-9235-2026

Keywords: downscaling, diffusion models, CorrDiff, weather forecasting, deep learning, numerical weather prediction, China, radar reflectivity, typhoons, ERA5, uncertainty quantification, Geoscientific Model Development

The WBGT is the workhorse of heat stress assessment worldwide. Unlike a simple thermometer reading, it is an ISO-standardised index that integrates four environmental factors at once: air temperature, humidity, wind speed, and radiation, covering both shortwave radiation from the sun and longwave radiation emitted by surrounding surfaces. Because it blends these variables into a single number, WBGT is widely used to trigger heat management plans at sporting events, military training exercises and industrial sites. When the index crosses agreed thresholds, organisers can activate shade stations, adjust pacing requirements, or postpone starts. The problem, until now, has been that WBGT is usually measured at a handful of fixed weather stations, which tells organisers almost nothing about what a walker experiences deep in a sun-baked forest clearing or on a shaded stretch of canal path two hours into the course.

That gap matters because heat stress at the human scale is intensely local. A runner moving through alternating sun and shade, over asphalt and through woodland, encounters rapidly shifting microclimates that a regional weather model simply cannot resolve. To capture this variability, the research team—Kobe Vandelanotte, Bram Du Moulin, Siebe Puynen, Thomas Vergauwen, Sara Top and Steven Caluwaerts—deployed a mobile measurement campaign during the 2024 Dodentocht. Instruments were carried along the route to collect spatio-temporal WBGT data as the event unfolded, producing a moving picture of heat stress conditions that matched the actual experience of participants rather than the conditions at a distant airport weather station.

These field observations served a second, crucial purpose: they allowed the team to evaluate a modelling system designed to simulate heat stress at metre-scale resolution. The system couples a numerical weather prediction model, which handles the broader atmospheric state, with a micro-scale radiation model that resolves how buildings, trees and terrain shape the radiation environment street by street and field by field. When the modelled WBGT values were compared against the mobile measurements along the 100-kilometre route, the system delivered what the authors describe as a reasonable approximation of observed conditions. Importantly, it was able to capture some local shade-induced cooling effects—the dips in heat stress that occur when a route passes under tree cover—demonstrating that the micro-scale radiation component was doing real work rather than smoothing over the fine-grained detail.

With the model validated, the researchers turned it from a diagnostic instrument into a decision-making tool. They simulated a series of alternative event-management scenarios for the 2024 Dodentocht, asking a question that every endurance organiser now confronts: what could we have done differently? The scenarios included shifting the start time, rerouting the course, and adjusting assumed walking speeds, each of which changes when and where participants encounter the hottest part of the day and how much heat they accumulate over the event.

The headline finding is striking. For the 2024 edition, starting the event three hours earlier—at 18:00 local time instead of the official 21:00 start—would have reduced cumulative heat-stress exposure by 35 percent, measured as degree hours above a WBGT threshold of 20 degrees Celsius. That single scheduling decision, achievable with no change to the route and no additional infrastructure, would have removed roughly a third of the dangerous heat load carried by participants. In practical terms, an earlier start shifts more of the course into the cooler evening and overnight hours, so that walkers reach the most punishing midday stretch further along, or in some cases past, the peak of the day’s heat.

Route choice proved equally consequential. Under identical meteorological conditions and the official 21:00 start time, the 2023 route accumulated 16.5 percent more degree hours above 20 degrees Celsius WBGT than the 2024 route. The difference illustrates how sensitive endurance events are to seemingly small course design choices: the amount of shade, the exposure of open stretches, and the timing with which the route delivers participants into sun-exposed sections all feed directly into cumulative exposure. A course that is a few kilometres longer but better shaded, or one that reorders its segments so that open terrain is crossed at night, can meaningfully lower the health risk for every participant on the field.

The metric the team uses—degree hours above a WBGT threshold—deserves attention because it captures what a single snapshot cannot: the accumulation of heat stress over time. Physiologically, heat illness risk depends not just on how hot it is, but on how long the body is working hard while hot, and whether it gets a chance to recover. A walker crossing a hot, sunlit section at kilometre 60 after twenty hours of exertion faces a very different risk profile from one crossing the same section fresh. Cumulative exposure metrics of this kind therefore align better with the way heat accumulates in the human body than peak-temperature warnings alone, and they give organisers a quantifiable target to optimise against rather than a binary go/no-go decision.

The broader context makes tools like this increasingly urgent. Climate change is driving more frequent and more intense extreme heat episodes across Europe and beyond, and participants in outdoor endurance events are among the most exposed populations, combining prolonged outdoor duration with high metabolic heat production from sustained physical exertion. Mass-participation events—from marathons and ultramarathons to long-distance walking events and cycling sportives—have already seen cancellations, medical surges and, in tragic cases, fatalities linked to heat. Organisers traditionally rely on historical averages and fixed station data to plan, but a warming climate is eroding the reliability of the past as a guide. High-resolution heat stress modelling offers a way to plan for the conditions that will actually occur, and to stress-test contingency plans before race day rather than improvising during a medical emergency.

What this study demonstrates, ultimately, is a workflow: measure, validate, simulate, decide. Mobile observations ground-truth the model; the validated model becomes a virtual laboratory in which organisers can compare start times, routes and pacing scenarios; and the resulting exposure estimates feed directly into heat management plans, from shade and hydration placement to medical staffing and cancellation thresholds. The authors present the system as a reliable and actionable tool for developing and implementing effective heat management strategies for outdoor endurance events, and the Dodentocht results show that the payoff can be large—an earlier start alone cutting exposure by more than a third. As summers grow hotter, the events that adapt fastest will be those that treat heat stress not as an act of nature to be endured, but as a design variable to be engineered, modelled and minimised long before the first participant takes a step.

Subject of Research: High-resolution wet bulb globe temperature modelling to assess and reduce heat stress exposure in ultra-endurance events

Article Title: Too hot to race? Demonstrating heat stress modelling as an adaptation tool for endurance events

Article References: Too hot to race? Demonstrating heat stress modelling as an adaptation tool for endurance events. (n.d.). https://doi.org/10.1371/journal.pclm.0001058

Image Credits: AI Generated

DOI: 10.1371/journal.pclm.0001058

Keywords: heat stress, wet bulb globe temperature, endurance events, numerical weather prediction, micro-scale radiation modelling, climate change adaptation, ultra-endurance, Dodentocht, heat management, WBGT, event planning, Belgium

The work, led by Marc Bocquet of CEREA, ENPC, EDF R&D and Institut Polytechnique de Paris, together with Tobias Sebastian Finn and Sibo Cheng of the same laboratory and Alban Farchi of the European Centre for Medium-Range Weather Forecasts, builds on the concept of data assimilation networks, or DANs. Data assimilation is the process by which observations of the real world are continually folded into a numerical model to keep its trajectory anchored to reality. In chaotic systems, where tiny errors amplify exponentially, this correction must happen frequently and intelligently. Classical methods such as the ensemble Kalman filter, or EnKF, rely on an ensemble of forecasts to represent the flow-dependent error statistics that tell the analysis step which parts of the state are most uncertain.

What makes the DAN approach conceptually radical is what the network is trained to do. In earlier machine learning applications to data assimilation, neural networks were trained to imitate the outputs of an existing scheme, essentially learning to copy a Kalman filter or a variational method. A DAN, by contrast, is embedded directly in the forecast–analysis cycle and trained against only two things: the true trajectory of the system and the noisy, sparse observations of it. The network must discover, from scratch, how to combine a forecast state with incoming observations to produce a stable and accurate sequential estimator. It is not taught how a good assimilation algorithm works; it must invent one.

The surprise, first reported by the group in 2024, was that a DAN trained this way could match a well-tuned EnKF even when its architecture was reduced to process a single forecast state rather than an ensemble. That result flew in the face of long-standing practice. Operational weather centres such as ECMWF run ensembles of variational analyses precisely because single-state methods like 3D-Var and 4D-Var, which use static background error covariances, systematically underperform ensemble methods on chaotic dynamics. In the Lorenz-96 model, a standard benchmark representing a mid-latitude atmospheric circle, a well-tuned EnKF achieves a time-averaged analysis error of roughly 0.18 to 0.20, while classical single-state methods stall near 0.40. The DAN, with no ensemble at all, reached the EnKF level.

The new paper dissects the mechanism behind this performance. The key insight is that the learned analysis operator implicitly reconstructs an effective analysis error covariance matrix from the forecast state alone. When the researchers linearised the network’s response to the projected innovation, the difference between the observations and what the forecast predicts, the resulting Jacobian behaved like a flow-dependent covariance matrix remarkably close to that of a well-tuned EnKF, particularly in its dominant eigenvectors, which carry most of the uncertainty. In other words, the network had learned, without ever being told, to estimate the errors of the day from a single state, something that was thought to require an ensemble.

The theoretical underpinning, the authors argue, lies in a generalised form of the multiplicative ergodic theorem, originally due to Oseledec. For an ergodic chaotic system, the unstable subspaces along which errors grow are measurable functions of the state itself. Viewing the entire sequential assimilation process as its own random dynamical system, there exists a mapping from the forecast state to the dominant error-growth directions, and hence to an effective forecast error covariance. Recent work by Sacco and colleagues and by Sakov has shown that such a state-to-covariance map can be exploited explicitly to build competitive filters from a single trajectory. The DAN, it turns out, learns this map implicitly.

Crucially, the network does not memorise global configurations of the state. The researchers showed through scaling experiments that the learned operator extracts local patterns with a limited spatial range, a property made natural by its residual convolutional architecture. When they trained a DAN on the standard 40-variable Lorenz-96 model and applied it unchanged to a doubled, 80-variable version, it performed on par with an EnKF tuned for the larger system. In the limit of large state dimensions, a fixed-size network could not possibly memorise ever more numerous global patterns, so it must be identifying a small set of local structures. The team made these patterns visible by computing a mean marginal gain tensor, a three-index sensitivity of the analysis to perturbations of the forecast state and the innovation, averaged over the invariant distribution of the dynamics. Exploiting the translational symmetry of Lorenz-96, they showed this tensor must be circulant, and its dominant entries indeed form a compact local pattern that persists across model sizes and across sparse and randomised observation configurations.

The second major advance is a stress test in stronger nonlinearity. By lengthening the interval between observation updates, the team pushed the system well beyond the mildly nonlinear regime, past the Lyapunov time of the model, equivalent to about three days of a real weather forecast, and up to twice that horizon. The EnKF degrades steadily under these conditions and becomes uninformative beyond a certain point. The hardest baseline, the iterative ensemble Kalman filter, which combines an ensemble-derived prior with a nonlinear Gauss-Newton optimisation, remains the most accurate scalable method in such regimes. Remarkably, a computationally boosted DAN matched the IEnKF’s accuracy across this extended range, and could even be trained where the IEnKF became difficult to stabilise, all without an ensemble and without any iterative minimisation at inference time.

The explanation for this second capability is subtle. A DAN restricted to a purely linear response to the innovation, which explicitly encodes the state-to-covariance map, matches the EnKF in the mild regime but degrades faster than the EnKF as nonlinearity increases, exactly as its implicit Gaussian prior would predict. The full DAN, however, learns an effective nonlinear analysis response consistent with a non-Gaussian prior inferred from the forecast state. A scaling diagnostic of the network’s response to amplified innovations shows that, in more nonlinear regimes, the impact of large innovations is systematically stronger than a linear analysis would produce. Both ingredients, the flow-dependent covariance information and the learned non-Gaussian response, are necessary; together they parallel the two pillars of the IEnKF, its ensemble and its iterative solver, compressed into a single deterministic network.

The implications reach beyond benchmark models. The authors point to newly developed end-to-end atmospheric processors, systems that ingest raw observations and predict future observations without any explicit background state, and argue that such systems must be implicitly learning analysis operators in their latent spaces, complete with internal representations analogous to error covariances. This reframes a seeming paradox in recent diagnostic studies of observation-driven processors. At the same time, the authors are careful about limits: ensembles remain essential for probabilistic forecasting, uncertainty quantification and strongly multi-modal posteriors, and the multiplicative ergodic theorem guarantees only that the state-to-covariance map exists, not that it is continuous, local or learnable in every setting. But for point estimation in chaotic geophysical flows, the message is striking. The ensemble, long considered indispensable, may be a computational shortcut rather than a fundamental requirement, and a neural network that has never seen a Kalman gain can rediscover the physics of error growth on its own.

Subject of Research: Learned data assimilation neural networks for chaotic dynamical systems

Article Title: Elucidating the performance of data assimilation neural networks for chaotic dynamics

Article References: Bocquet, M., Finn, T. S., Cheng, S., & Farchi, A. (2026). Elucidating the performance of data assimilation neural networks for chaotic dynamics. Nonlinear Processes in Geophysics, 33(3), 401-424. https://doi.org/10.5194/npg-33-401-2026

Image Credits: AI Generated

DOI: 10.5194/npg-33-401-2026

Keywords: data assimilation, neural networks, chaotic dynamics, ensemble Kalman filter, Lorenz-96, deep learning, error covariance, multiplicative ergodic theorem, nonlinear filtering, numerical weather prediction, machine learning, geophysics

The contest pits two fundamentally different approaches against each other. Physics-based forecasts come from numerical weather prediction models, the traditional workhorses of meteorology, which solve equations describing atmospheric dynamics, radiation, and ocean and land-surface processes on a discretised grid. Data-driven forecasts, by contrast, are built by artificial intelligence systems trained on vast archives of historical weather data, typically reanalysis datasets such as ERA5, which blend observations with model output to create a consistent record of past atmospheric states. In just a few years, data-driven models have achieved improvements in forecast skill that took physics-based approaches decades, and they now rival or beat numerical models on standard metrics, including for some extreme events. Yet important weaknesses remain: AI models can struggle with extremes, and their training loss functions tend to prioritise performance near the centre of the climatological distribution rather than in the tails, where the stakes are highest.

That tail behaviour matters enormously here, because the relationship between temperature and mortality is strongly non-linear. Deaths rise disproportionately once temperatures climb past a location-specific threshold known as the minimum mortality temperature, so a forecast with a small average temperature error can still produce a badly wrong estimate of health impacts if that error is concentrated on the hottest days. The researchers exploited this non-linearity deliberately, using an epidemiological transformation as an explicitly impact-oriented error metric. Rather than comparing forecast temperatures against observations, they converted both forecasts and reanalysis data into estimates of the attributable fraction of mortality, the proportion of deaths statistically attributable to non-optimal temperatures, and compared those impact estimates instead.

The epidemiological machinery behind this conversion is well established. The study drew on exposure-response functions fitted for 854 European cities across 30 countries by a large health impact assessment published in The Lancet Planetary Health in 2023. Those fits were built with distributed lag non-linear models, a two-stage framework in which a quasi-Poisson regression first captures the over-dispersed relationship between temperature and all-cause mortality, including its complex lagged structure through a cross-basis function, and a multivariate meta-regression then pools the city-level estimates while accounting for differences in vulnerability between cities. The relative risk of dying at a given temperature is expressed as a ratio against the risk at the minimum mortality temperature, and the attributable fraction follows directly from that ratio.

For the meteorological side, the authors used the two flagship forecast systems of the European Centre for Medium-Range Weather Forecasts, widely considered among the best in the world. The physics-based contender was the Integrated Forecasting System high-resolution model, cycle 48r1, while the data-driven contender was the Artificial Intelligence Forecasting System, single v1. Both were evaluated deterministically at lead times of one, three, five, seven and ten days over the boreal summer of 2024, from 1 June to 31 August, with ERA5 reanalysis serving as the ground truth. The summer of 2024 was chosen both because it offered the most recent model versions and because it was the hottest summer on record globally and for Europe, making it a realistic test bed for the conditions under which health-impact forecasts would actually be used operationally.

The results begin with a telling case study of Rome, selected because Italy reported Europe’s highest heat-related death toll in 2024. In Rome, the data-driven forecasts actually achieved lower mean absolute errors for temperature than the physics-based forecasts, yet their bias in the attributable fraction was larger in magnitude at every lead time examined. This divergence between temperature skill and impact skill is the study’s central lesson: the two quantities tell qualitatively different stories. A modest warm bias in temperature can translate into a substantial overestimate of mortality risk, while a cool bias on a scorching day can lull health authorities into underestimating a lethal event. The non-linear transformation amplifies errors precisely where impacts are greatest.

Scaled up to the continental level using population-weighted averages across all 854 cities, the picture sharpened. Both forecast types systematically underestimated temperature-related mortality, but the underestimation was more pronounced for the data-driven forecasts, particularly at hot temperatures where the forecasts would matter most for warning systems. Quantile-quantile analysis showed both models falling systematically below the zero-error line for attributable fraction, and Kolmogorov-Smirnov tests confirmed that the error distributions of the two models were statistically distinct at lead times of three, five and seven days. Scatter plots of forecast bias against temperature revealed negative correlations: the hotter the day, the more the forecasts underpredicted the health burden. For the physics-based model this underestimation emerged only at exceptionally hot temperatures, consistent with known difficulties in representing land-atmosphere coupling, soil moisture deficits and urban effects during European heatwaves.

The lead-time behaviour added a further twist. Temperature forecast errors grew with lead time as expected, but the errors in attributable fraction did not show a comparably clean growth pattern, a finding the authors attribute to the non-linear propagation of temperature errors through the epidemiological transformation, combined with the limited sample of a single summer. The data-driven model showed its largest systematic underestimation of mortality near the end of the first forecast week, close to the predictability limit for these impact metrics. Interestingly, the mean absolute error of the impact forecasts was nearly identical between the two models up to five days ahead, suggesting that for practical warning purposes on short timescales, the AI model is already competitive.

What makes these findings compelling is their practical upside. Data-driven forecasts are dramatically cheaper to run than numerical models, which demand supercomputing resources that many national weather services and health agencies lack. If the systematic underestimation of heat mortality in AI forecasts can be corrected, bespoke impact forecasts could be produced at low cost in resource-limited settings, extending life-saving early warning capability to places that currently have none. The authors propose two concrete remedies: a temperature-dependent bias correction applied after the forecast, and a modification of the training loss function to give greater weight to hot temperatures, so the model learns that errors in the heat matter more than errors elsewhere in the distribution.

The study’s limitations are acknowledged candidly: a single summer cannot establish generalisability, only two global deterministic models were tested rather than regional systems or ensembles, and applying epidemiological fits to temperatures outside their calibration range introduces uncertainty at the very hottest extremes. Extending the comparison to ensemble forecasts, to recent probabilistic AI models trained to represent full distributions rather than single values, and to other regions and health outcomes are flagged as the natural next steps. Even so, the verdict is cautiously optimistic. Temperature-related mortality forecasts built on data-driven weather models performed approximately as well as those built on physics-based models, and with targeted improvements to how hot temperatures are represented, they could become a promising foundation for the next generation of heat-health early warning systems, at a moment when Europe can ill afford to miss another deadly summer.

Subject of Research: Comparison of data-driven and physics-based weather forecasts for predicting temperature-related mortality in Europe during summer 2024

Article Title: Forecasting European temperature-related mortality in Summer 2024: data-driven vs. physics-based forecast approaches

Article References: Holmberg, E., & Olivetti, L. (2026). Forecasting European temperature-related mortality in Summer 2024: data-driven vs. physics-based forecast approaches. Natural Hazards and Earth System Sciences, 26(10), 4825-4842. https://doi.org/10.5194/nhess-26-4825-2026

Image Credits: AI Generated

DOI: 10.5194/nhess-26-4825-2026

Keywords: heat-related mortality, data-driven weather forecasting, numerical weather prediction, early warning systems, Europe, summer 2024, attributable fraction, ECMWF, AIFS, extreme heat, epidemiological forecasting, machine learning

The core idea behind the work is post-processing. Rather than replacing numerical weather prediction altogether, the researchers treat the model output as a starting point that can be refined by a neural network trained on observations. This approach acknowledges a practical reality: numerical models encode decades of atmospheric science and remain the backbone of operational forecasting, but their raw precipitation fields often need correction before they reach emergency managers, hydrologists and the public. Previous deep learning post-processing efforts have shown promise, but the authors identify two persistent weaknesses. First, many networks fail to capture meteorological features that operate across multiple spatial scales, from broad synoptic rain bands down to localized convective cells. Second, and perhaps more fundamentally, extreme precipitation is vanishingly rare in training data, creating a severe class imbalance that causes standard networks to systematically underpredict the very events that matter most for disaster preparedness.

Rain-PostEFNet addresses these weaknesses through a carefully assembled architecture that borrows proven components from computer vision research. For feature extraction, the framework employs EfficientNet, a convolutional neural network family renowned for its efficient scaling of network depth, width and input resolution. On top of that sits ECA-Net, an efficient channel attention mechanism that adaptively reweights the importance of different feature channels, allowing the model to emphasize the meteorological signals most relevant to rainfall at each location and scale. The third pillar is FPN-Swin-Unet, which combines a feature pyramid network with a Swin transformer-based U-Net to refine features across multiple resolutions. The U-Net lineage traces back to biomedical image segmentation, where encoder-decoder structures proved adept at recovering fine spatial detail, and the Swin transformer adds hierarchical, window-based attention that captures long-range dependencies without prohibitive computational cost.

What distinguishes the framework from many predecessors, however, is its multi-task learning strategy. Instead of treating precipitation forecasting as a single regression problem, Rain-PostEFNet jointly optimizes two related tasks: classifying whether rain will fall in a given category, and regressing the actual precipitation amounts. The classification branch is trained with a weighted focal loss, a function specifically designed for imbalanced datasets. Focal loss down-weights the easy, abundant examples of light or no rain and focuses the network’s learning capacity on the rare, hard examples of intense precipitation. The regression branch uses the familiar mean squared error loss to sharpen the quantitative accuracy of predicted rainfall amounts. By training both objectives simultaneously, the network learns representations that serve detection and estimation at once, which the authors argue is key to improving predictive skill for rare heavy rain events.

Evaluating a precipitation forecasting model fairly requires standardized benchmarks, and the team turned to PostRainBench, a comprehensive benchmark dataset for post-processing numerical weather prediction that spans three climatologically distinct regions: China, Germany and Korea. This diversity matters, because rainfall regimes differ dramatically across these countries, from the monsoon-driven deluges of East Asia to the more moderate frontal systems of Central Europe. Performance was measured with three established verification metrics: the Critical Success Index, which captures the ratio of correct rain detections to all predicted and observed events; the Heidke Skill Score, which measures improvement over random chance; and overall accuracy. Together these metrics reward models that find the balance between detecting real rain and avoiding false alarms, a trade-off that has long challenged forecast verification.

The results are remarkable, especially for the Chinese dataset. For moderate rainfall, Rain-PostEFNet achieved relative improvements in Critical Success Index of 63.94 percent in China, 4.28 percent in Germany and 2.1 percent in Korea compared with state-of-the-art baseline methods. For heavy rainfall, the gains were even larger in China, reaching 78.34 percent, alongside 9.09 percent in Germany and 7.68 percent in Korea. The Heidke Skill Score told a similar story, rising by 52.18 percent in China and 2.95 percent in Germany for moderate rain, and by 52.4 percent in China and 6.78 percent in Germany for heavy rain. The outsized Chinese improvements likely reflect both the challenging nature of that region’s precipitation and the severity of the baseline errors there, but the consistent direction of improvement across all three countries suggests the framework captures something genuinely general about how to correct numerical forecasts.

To verify that the performance gains truly stem from the proposed design rather than sheer model size, the authors conducted an ablation study, systematically removing components and measuring the impact. The analysis confirmed that both the multi-task learning framework and the attention mechanisms contribute meaningfully to refining the numerical predictions. In other words, the joint classification-regression objective and the adaptive channel attention are not decorative additions; each plays a measurable role in the network’s ability to detect and quantify rainfall. This kind of component-level validation is increasingly expected in machine learning research, where headline numbers can sometimes mask architectures whose benefits are poorly understood.

The practical implications extend well beyond the leaderboard. Accurate precipitation forecasting underpins disaster preparedness, water resource management and climate modeling, and the events that current systems handle worst, extreme rainfall episodes, are precisely those with the highest human and economic stakes. A post-processing layer like Rain-PostEFNet could be deployed alongside existing operational numerical models, sharpening the rainfall fields that feed flood warning systems, reservoir operations and agricultural planning. Because the approach refines rather than replaces numerical forecasts, it complements the substantial investments meteorological agencies have already made in physical modeling, and it can be retrained as those models evolve. The authors also note the broader context of artificial intelligence entering earth system science, from neural global forecasting models to data-driven process understanding, positioning their work as part of a quiet revolution in how weather prediction is built.

Transparency was a priority for the team. The PostRainBench dataset is publicly available on GitHub, and the Rain-PostEFNet code has been released as well, allowing other researchers to reproduce the experiments, apply the framework to new regions and build on the architecture. The research was supported by the National Key R&D Program of China, the Joint Laboratory for Artificial Intelligence and Digital Meteorological Applications Research, the Yibin Science and Technology Program and the Sichuan Science and Technology Program, reflecting institutional commitment to integrating artificial intelligence into meteorological applications. The work was conducted by researchers at the University of Electronic Science and Technology of China, the Sichuan Artificial Intelligence Research Institute, the Institute of Plateau Meteorology of the China Meteorological Administration and the joint laboratory in Beijing.

Challenges remain before such systems become routine in operational forecasting. The severe class imbalance that motivates the focal loss never fully disappears, and performance gains in Germany and Korea, while consistent, are far more modest than in China, hinting that regional climate characteristics, dataset size and baseline quality all shape how much post-processing can deliver. Extreme events, by definition, offer few training examples, and no amount of architectural ingenuity fully substitutes for observations of rare phenomena. Still, the study demonstrates that multi-scale feature refinement and imbalance-aware training can extract substantially more skill from existing numerical forecasts, particularly for the heavy rainfall that matters most. As climate change intensifies the hydrological cycle and pushes precipitation extremes beyond the historical distributions on which both physical models and neural networks were trained, tools that squeeze additional accuracy from every forecast will only grow in value. Rain-PostEFNet offers a template for how computer vision and meteorology can converge on that task, one corrected rain map at a time.

Subject of Research: Deep learning post-processing of numerical weather prediction precipitation forecasts

Article Title: Enhancing NWP precipitation forecasting with Rain-PostEFNet: A multi-scale deep learning approach

Article References: Naz, F., She, L., Sui, X., Zhang, C., & Shao, J. (2026). Enhancing NWP precipitation forecasting with Rain-PostEFNet: A multi-scale deep learning approach. Applied Intelligence, 56(14), Article 408. https://doi.org/10.1007/s10489-026-07457-x

Image Credits: AI Generated

DOI: 10.1007/s10489-026-07457-x

Keywords: precipitation forecasting, numerical weather prediction, deep learning, post-processing, extreme rainfall, multi-task learning, channel attention, EfficientNet, Swin transformer, PostRainBench, focal loss, flood preparedness