The theoretical foundation of the approach is Takens’ delay embedding theorem, a landmark result from 1981 showing that the phase-space structure of a deterministic chaotic system can be reconstructed from time-delayed coordinates of a single observed variable. In other words, even if most of a system’s state variables are hidden, the shadow they cast on the ones you can see may be enough to reconstruct the underlying dynamics. The DSDL framework operationalizes this idea by building two mathematical objects: a non-delayed attractor constructed from multivariate time series, and a delayed attractor for the target variable to be predicted. A nonlinear mapping between the two, learned from data and extended with higher-order monomial terms, then maps the current state of the system to its future state.

To test whether this works when parts of the system are simply missing, the team subjected DSDL to a punishing gauntlet of five canonical nonlinear systems: the classic three-variable Lorenz’ 63 model, a seven-dimensional hyperchaotic circuit system, the Lorenz’ 96 model with eight variables, a multiscale coupled version of Lorenz’ 96 that explicitly represents interactions among slow, intermediate and fast components, and the Kuramoto–Sivashinsky equation with 64 spatial variables, a benchmark of spatiotemporal chaos. In each case, only a subset of state variables was retained as observable, while the rest were treated as unobserved. The multiscale coupled Lorenz’ 96 system is particularly important because it mimics key features of the real atmosphere, where slowly evolving large-scale variables interact with rapidly varying small-scale processes.

The results were compared against a battery of representative data-driven forecasting methods, including artificial neural networks, echo state network reservoir computing, long short-term memory networks, next-generation reservoir computing, and SINDy, a sparse-regression method for discovering governing equations. Performance was quantified with two metrics: the Effective Prediction Time, which measures how long a forecast stays within one standard deviation of the reference trajectory, and the Coefficient of Variation, which measures how consistent that performance is across repeated experiments. All results were averaged over 100 independent trials. Across every system and every missing-variable configuration tested, DSDL achieved the longest effective prediction horizons and the lowest variability, indicating that its advantage is not an artifact of any particular dynamical regime.

Some of the individual results are striking. In the multiscale coupled Lorenz’ 96 system, DSDL maintained the most persistent predictability precisely when the small-scale variables were unobserved, the hardest configuration. In the Kuramoto–Sivashinsky equation, the framework retained a prediction horizon approaching 40 dynamical time units even after 12 of its 64 spatial variables were removed, substantially outperforming the alternatives. SINDy could not even be evaluated for that system, because estimating the high-order spatial derivatives it requires from incomplete observations is hopelessly unstable without prior knowledge of the governing equations. The authors also extended DSDL to handle temporal gaps between training and prediction periods, showing meaningful skill in experiments up to ten steps ahead, a capability that matters for seasonal forecasting where predictors and targets are separated in time.

The real test, of course, is the actual climate system. The team applied DSDL to one-month-lead hindcasts of summer precipitation over China for the period 2000 to 2022, using the CN05.1 gridded precipitation dataset built from 2,416 stations, supplemented with GPCC data over Taiwan, and drawing predictors from sea surface temperature in the NOAA ERSST v6 analysis and 500-hPa geopotential height from the ECMWF ERA5 reanalysis. The globe was partitioned into 36 regions of 30 by 60 degrees, and sea surface temperature and circulation variables from each region, along with their time-lagged terms and second-order nonlinear combinations, were assembled into a large candidate predictor pool. A cross-validated stepwise regression procedure then automatically identified the key precursor variables for each precipitation grid point, keeping the selection transparent and traceable rather than hand-tuned.

The hindcast skill was concentrated exactly where theory says it should be. Over eastern China’s monsoon region, where seasonal precipitation is strongly modulated by large-scale circulation and slowly varying air–sea coupling, DSDL reproduced the dominant drought–flood anomaly patterns with positive anomaly spatial correlations in most years and operational Ps scores that remained stable around 70 to 80 across the 23-year period. Anomaly temporal correlations were highest over the Yangtze River basin, North China and the Northeast, and weakest over parts of the Northwest and Southeast, where precipitation is dominated by localized topographic and convective processes that sparse large-scale predictors cannot capture.

The framework’s performance in extreme years is likely to draw the most attention. In July 2020, persistent Meiyu rainfall produced severe flooding along the middle and lower reaches of the Yangtze River, with drier conditions over parts of southern China. DSDL reproduced both the major wet anomaly center and the north–south contrast between the Yangtze basin and southern China, earning positive spatial correlation scores and high Ps values. Two years later, during the severe 2022 summer drought over the Yangtze basin, the model recovered the widespread dry anomaly structure across southern China and captured the drought conditions over the Southwest, alongside wetter anomalies to the north. Capturing the sign and spatial organization of such high-impact seasonal anomalies at a one-month lead is exactly the kind of skill that operational forecasters prize.

The deeper message of the study is conceptual as much as technical. Conventional data-driven forecasting architectures are typically built on the implicit assumption of relatively complete observations and continuous trajectories, and they tend to treat missing variables as truncated boundary conditions or noise, suffering catastrophic skill loss when the state space is incomplete. DSDL instead exploits the fact that large-scale low-frequency climate variability is dynamically coupled to the observable variables through teleconnections and air–sea interactions, so that sparse local observations retain recoverable information about the global attractor. In this view, climate predictability does not depend solely on fully observed state-space information; it can be partially preserved within limited observations through nonlinear dynamical coherence.

The authors are careful to spell out the limitations. The climate application covers only one-month-lead summer precipitation over China, and whether the recoverable predictability persists at one-season or multi-season leads remains open. The study also did not compare DSDL against operational dynamical seasonal prediction systems or hybrid statistical–dynamical models, and the physical mechanisms linking the automatically identified precursor regions to Chinese rainfall, including possible connections to ENSO, Indo-Pacific air–sea interaction and the western Pacific subtropical high, still require dynamical diagnosis. Skill is weaker over topographically complex and arid inland regions, and the model smooths some local extreme anomalies. Scenarios involving temporal discontinuities and irregular observations remain untested. Even so, the demonstration that a dynamics-informed framework grounded in nonlinear embedding theory can extract seasonal predictability from deliberately incomplete information points toward a new generation of hybrid forecasting methods, one in which the mathematics of chaos and the machinery of deep learning work together rather than in competition.

Subject of Research: Recovering climate predictability from sparse observations using dynamical system deep learning based on nonlinear embedding theory

Article Title: Recovering climate predictability from sparse observations via dynamical system deep learning

Article References: Li, H., Li, J., Wu, Z., Wang, M., Liu, G., Wang, N., Song, H., & Zhen, S. (2026). Recovering climate predictability from sparse observations via dynamical system deep learning. Climate Dynamics, 64(11), Article 460. https://doi.org/10.1007/s00382-026-08413-8

Image Credits: AI Generated

DOI: 10.1007/s00382-026-08413-8

Keywords: climate predictability, dynamical system deep learning, Takens embedding theorem, sparse observations, chaos theory, seasonal prediction, East Asian summer monsoon, precipitation hindcasts, machine learning, air-sea interactions, Lorenz systems, Kuramoto-Sivashinsky

Reanalyses occupy a special place in climate science. They are essentially the most honest simulations a modelling system can produce: a numerical model runs forward in time while a data assimilation scheme continuously nudges it back toward reality using observations. The result is a physically consistent, gap-free record of the past. Global products such as ERA5 for the atmosphere or GLORYS12 for the ocean do this superbly at planetary scales, but their horizontal resolution is too coarse to capture the Mediterranean’s notoriously complex geography, where steep mountains, narrow straits, and intense land-sea contrasts generate mesoscale processes that global grids simply blur out. Regional reanalyses exist for the Mediterranean, but until now they have been either ocean-only or atmosphere-only, never both at once.

MESMAR-R closes that gap by coupling three model components through the OASIS3-MCT coupler at half-hourly intervals. The atmospheric core is the Weather Research and Forecasting model running on a grid of roughly 15 kilometres with 41 vertical levels, while the ocean component uses the NEMO model at approximately 7 kilometres with 72 vertical levels spanning the entire basin from the Atlantic box to the Dardanelles. A hydrological discharge model routes surface and subsurface runoff collected by the atmospheric model directly into coastal ocean points, meaning rivers genuinely interact with the sea rather than being prescribed from climatology. Air-sea fluxes of momentum, heat, and freshwater are computed within the atmospheric model to guarantee consistency with its boundary-layer physics, then passed conservatively to the ocean, while sea surface temperature and currents flow back the other way.

The assimilation strategy is deliberately asymmetric. The ocean receives a full three-dimensional variational analysis every three days, ingesting temperature and salinity profiles from Argo floats, gliders, moorings, and expendable bathythermographs, along with along-track satellite altimetry, weak surface relaxations, and a large-scale bias correction for the deep layers. The atmosphere, by contrast, is constrained through spectral nudging toward ERA5: only spatial scales longer than roughly 850 kilometres are relaxed, with timescales of about an hour for winds and temperature and a day for humidity. This leaves the regional model free to develop its own mesoscale weather, including Mediterranean tropical-like cyclones, while remaining anchored to the large-scale circulation of the global reanalysis. The authors describe the system as weakly coupled, since observations in one medium do not instantly correct the other, but information propagates between components dynamically through the exchanged fluxes during each model integration.

The evaluation against observations is where the new product earns its credentials. Over the common comparison period of 2000 to 2020, MESMAR-R delivers the lowest root-mean-square error of any tested product for sea surface height, with typical errors below four centimetres basin-wide, and it more than halves the sea surface salinity error relative to the global GLORYS12 reanalysis. For sea surface temperature it is essentially indistinguishable from the dedicated regional ocean reanalysis MEDREA24, and both substantially outperform the global product. In the upper ocean, the layer that matters most for air-sea interaction, MESMAR-R shows the lowest temperature errors in the 20 to 60 metre range and leads or ties for best salinity performance in the top 210 metres. Bias profiles reveal only a small fresh bias near the surface and near-zero thermal drift below 200 metres, indicating that the system stays honest at depth.

The atmospheric component, handicapped by its simplified nudging-based assimilation, naturally trails the dedicated ERA5 and CERRA reanalyses in area-averaged skill. Root-mean-square errors for two-metre temperature, relative humidity, wind speed, and pressure are moderately higher, and the gap is largest for precipitation over land. But the comparison maps tell a subtler story: MESMAR-R achieves localized improvements near complex coastlines and orography, precisely where the 15-kilometre model resolves gradients that coarser reference datasets smooth away. Crucially, the atmospheric fields remain internally consistent with the ocean beneath them, which is the entire point of a coupled product. For studying compound events, where a marine heatwave coincides with an atmospheric heat dome, that consistency matters more than shaving a few hundredths of a degree off an error metric.

Sensitivity experiments disentangle the contributions of coupling and data assimilation, and they deliver one of the study’s most instructive findings: coupling alone does not improve a reanalysis. A fully coupled simulation with no data assimilation showed the largest error growth, particularly in the subsurface ocean, while an uncoupled ocean reanalysis forced by ERA5 slightly outperformed the full coupled system for most parameters. Yet coupling measurably improved sea surface salinity, especially in the Aegean Sea, where the interactive exchange of freshwater fluxes enhances realistic evaporation and cools and salinifies the surface in ways prescribed forcing cannot replicate. Ocean data assimilation, meanwhile, proved to be the dominant control on basin-scale heat content, with the reanalysis reproducing the observed warming rate of roughly 1.3 watts per square metre in the upper 700 metres, against an observational estimate of about 1.4 watts per square metre, and correlations with observed heat content reaching 0.93 to 0.94.

The long-term climate trends extracted from the reconstruction read like a diagnosis of a basin under stress. Total Mediterranean sea level rose at approximately 3.06 millimetres per year over 1993 to 2024, in excellent agreement with independent estimates, and a striking 94 percent of that rise is mass-driven, reflecting the basin’s response to Atlantic sea-level rise through the Strait of Gibraltar rather than local thermal expansion. Beneath that total, a powerful thermo-halo compensation plays out: the halosteric component of sea level falls at nearly 3.9 millimetres per year basin-wide as the sea salinifies, almost exactly cancelling the thermosteric rise from warming. The eastern basin warms fastest in heat content, consistent with the documented abrupt warming and salinification of Levantine Intermediate Water since the early 2000s, while the western basin shows the strongest salinity-driven density increase, a hotspot centred on the Alboran Sea and the western gyre.

The atmospheric trends confirm the region’s reputation as a climate change amplifier. Winter warming averages about 0.040 degrees Celsius per year across the Mediterranean domain, accelerating to roughly 0.047 degrees per year in summer, with the strongest signals over southern Europe. Precipitable water increases almost everywhere, by about 0.023 percent per year in winter and a remarkable 0.100 percent per year in summer, yet relative humidity near the surface declines across large parts of Europe and mean precipitation does not follow the moisture upward. The picture is a warming, drying regime in which the atmosphere holds more water but delivers it in fewer, more intense bursts, favouring longer dry spells punctuated by extreme events. Winter wind trends even leave fingerprints in the ocean, with localized strengthening over the Gulf of Lion deepening the mixed layer while the southeastern basin shoals as buoyancy loss weakens.

The authors are candid about limitations. Observational coverage is not homogeneous across the 32 years, and because the atmospheric component is nudged toward ERA5, it partly inherits the time-varying information content of the global observing system, so decadal trends should be interpreted with that caveat in mind. Mid-depth temperature skill trails MEDREA24, and localized degradations near the northern Adriatic and the Dardanelles point to riverine and boundary-condition challenges. Future versions may adopt observation-space atmospheric assimilation and fully balanced air-sea corrections. Even so, MESMAR-R stands as one of the first regional coupled reanalyses ever produced, and its balanced, physically coherent reconstruction of the Mediterranean’s recent past arrives at a moment when the region needs it most, offering researchers, forecasters, and even machine-learning emulators a single dataset in which the sea and the sky finally tell the same story.

Subject of Research: A coupled regional atmosphere-ocean-hydrology reanalysis of the Mediterranean Sea covering 1993-2024, evaluated against observations and used to quantify regional climate trends

Article Title: Evaluation of a coupled regional reanalysis for the Mediterranean region covering the period 1993–2024

Article References: Storto, A., de Toma, V., & Yang, C. (2026). Evaluation of a coupled regional reanalysis for the Mediterranean region covering the period 1993–2024. Ocean Science, 22(5), 2809-2834. https://doi.org/10.5194/os-22-2809-2026

Image Credits: AI Generated

DOI: 10.5194/os-22-2809-2026

Keywords: Mediterranean Sea, reanalysis, data assimilation, coupled modelling, climate change, sea level rise, ocean heat content, salinification, air-sea interactions, NEMO, WRF, marine heatwaves

The IOD has long been defined by the difference in sea surface temperature anomalies between the western and eastern tropical Indian Ocean. When the western side is warmer than the east during its positive phase, convection shifts westward, altering winds, moisture transport, and rainfall patterns over a vast area. Because the index used to monitor the dipole captures this west-east temperature contrast, generations of studies have treated all positive and negative IOD events as variations of a single mode. Yet whether genuinely distinct spatial types of the IOD exist, and whether those types arise through different physical mechanisms and produce different climate impacts, remained unresolved questions in the literature.

To probe that diversity, the research team began with a deceptively simple step: they analyzed typical IOD events identified by the traditional IOD index and examined the spatial structure of sea surface temperature anomalies in each one. According to Professor Wang, the corresponding author of the study, the team initially expected the IOD to display a single dominant sea surface temperature anomaly pattern, exactly as it has traditionally been described. Instead, the analysis exposed two clearly separable spatial types hiding within the conventional definition. By combining multiple analytical approaches, including empirical orthogonal function combinations, the researchers identified and formally defined the two varieties of the dipole.

The first variety, which the team calls the west-east type IOD, matches the classical textbook picture: sea surface temperature anomalies of opposite sign occupy the western and eastern tropical Indian Ocean, producing a dipole that stretches across the full width of the basin. The second variety, the central-east type IOD, is subtly but importantly different. In this type, the opposing temperature anomalies are situated between the central and eastern Indian Ocean, leaving the far western basin largely outside the dipole structure. That shift in the anchor point of the western anomaly may sound like a minor detail, but the study demonstrates that it changes nearly everything about how the event develops and what it does to the climate system.

The two types, the researchers found, are built by different air-sea coupling processes. The west-east type IOD is strongly influenced by the wind-thermocline-SST feedback, a well-known amplification loop in the tropical ocean. In this feedback, surface winds alter the depth of the thermocline, the boundary between warm surface water and cooler water below, and the resulting changes in upper-ocean heat content reinforce the sea surface temperature gradient that drove the winds in the first place. Enhanced easterly winds and thermocline changes work together to strengthen the east-west temperature contrast, allowing the west-east type IOD to grow through the monsoon season and typically reach its peak in autumn.

The central-east type IOD follows a different script. It develops earlier in the seasonal cycle and exhibits weaker air-sea coupling and weaker thermocline responses than its west-east counterpart. Because the ocean’s subsurface dynamics contribute less to its growth, the central-east type evolves along a distinct seasonal trajectory, with its anomalies establishing themselves sooner but intensifying less dramatically. This difference in development timing and coupling strength means that the two types are not interchangeable expressions of the same phenomenon; they are physically distinct modes whose separation matters for anyone trying to predict or interpret Indian Ocean variability.

Those physical differences translate directly into different climate impacts. The west-east type IOD shows a stronger connection with East African autumn rainfall, because its anomaly structure and convection response position rainfall-bearing circulation changes over the region. The central-east type IOD, by contrast, has a weaker influence on East African rainfall because its convection response is centered over the central Indian Ocean, farther from the circulation patterns that deliver rain to East Africa. Dr. Jiayu Zheng, first author of the study, explained the practical consequence of this distinction. Traditional IOD events, she noted, contain signals from both types, which may contribute to uncertainty in the relationship between the IOD index and regional climate responses. Separating the two types, she said, reveals a more consistent relationship between the west-east type IOD and East African rainfall variability.

That last point carries weight well beyond academic taxonomy. Scientists have long known that the IOD index correlates imperfectly with regional climate outcomes, and part of that scatter has often been attributed to noise, to the influence of other modes such as the El Niño-Southern Oscillation, or to internal atmospheric variability. The new findings suggest that some of the apparent inconsistency is structural: when a single index blends two physically different modes, the resulting correlations with any particular region will inevitably be diluted. By sorting events into their proper types, forecasters and researchers may be able to sharpen the link between Indian Ocean conditions and the rainfall anomalies that millions of people experience on the ground.

The study also documents a trend that raises the stakes of this improved understanding. The researchers found that positive west-east type IOD events have become more frequent in recent decades, and that these events can trigger extreme rainfall episodes leading to flooding over East Africa. East Africa’s vulnerability to flooding is well documented, with intense seasonal rains repeatedly overwhelming infrastructure, displacing communities, and damaging agriculture across the region. If the flavor of IOD event that most strongly drives such extremes is becoming more common, then distinguishing it from the weaker-impact central-east type becomes not just a matter of scientific precision but a component of seasonal preparedness and risk assessment for flood-prone regions.

Taken together, the results reframe the Indian Ocean Dipole as a family of related but distinct climate modes rather than a single oscillation. The work advances the understanding of IOD diversity by demonstrating that the two types differ in their spatial structures, their air-sea coupling processes, their seasonal evolution, and their regional climate footprints, and it offers a new perspective for interpreting IOD variability and assessing its effects. For the research community, the immediate implication is methodological: analyses and forecasts that rely on the traditional IOD index may benefit from explicitly separating the west-east and central-east types before drawing conclusions about teleconnections, predictability, or long-term change. For the people of East Africa and other regions whose climates feel the pulse of the Indian Ocean, the study is a reminder that the ocean’s most influential dipole speaks in two voices, and that learning to tell them apart is an urgent step toward anticipating the floods and droughts each one can bring.

Subject of Research: Two distinct types of the Indian Ocean Dipole climate mode and their differing air-sea coupling processes and regional climate impacts

Article Title: Researchers uncover that the Indian Ocean Dipole has two distinct types

Article References: Researchers uncover that the Indian Ocean Dipole has two distinct types. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: Indian Ocean Dipole, climate variability, sea surface temperature, air-sea coupling, thermocline, East Africa rainfall, monsoon, National Science Review, climate modes, flooding, Indian Ocean, seasonal forecasting