This study aims to quantify the relationship between the duration and occurrence frequency of droughts in China, particularly focusing on different drought intensities. By analyzing daily meteorological drought composite index (MCI) data from 1897 meteorological stations across China spanning from 1961 to 2020, the study reveals a significant double-logarithmic relationship between drought duration and occurrence frequency. The results show that shorter drought durations are associated with higher occurrence frequencies, while longer durations correspond to lower frequencies. This relationship is characterized by parameter kb. Spatially, the values of the parameter exhibit a gradient from northwest to southeast, with higher values in arid and semi-arid regions and lower values in humid and semi-humid regions. Notably, the parameter k
It is widely acknowledged that the joint inversion of magnetotelluric and seismological datasets enhances the quality of the crustal structure solution, even when the physical correlation between electrical resistivity and seismic velocity is weak or indirect. The structurally coupled joint inversion approach has received considerable attention over the past two decades for its ability to estimate such parameters by penalizing their cross-gradient vectors at similar spatial positions. Despite this interest, various structural couplings and different physical directions (incremental or decremental) have been partially overlooked. We hereby propose an approach for the joint inversion of magnetotelluric (MT) and Rayleigh wave dispersion (RWD) data to estimate uncorrelated parameters by integrating particle swarm optimization (PSO) and the Pareto optimality approach. We used the optimality framework of these methods to overcome the difficulties associated with traditional joint inversion algorithms and to obtain optimal solutions that account for both similar and contrasting physical sensitivities. The significant correlation between the inverted and synthetic models under both noise-free and noisy datasets, together with the consistent results obtained from comparison with a traditional derivative-based joint inversion algorithm, further strengthened our confidence in applying the proposed modeling approach to the field data from the southeastern Biga Peninsula, western Anatolia. The models inverted from the field data corroborate the efficacy of the presented method. A notable characteristic of the proposed methodology is its capacity to estimate uncorrelated physical parameters, such as electrical resistivity and seismic velocity, without the imposition of penalties. Therefore, the presented method not only offers advantages in joint inversion but also allows modelers to observe and analyze model parameters having different sensitivities that may indicate different physical directions.
rare event samplingensemble boosting: lightly perturbing simulated moderate events into more extreme ones. We formulate a new, flexible sampling strategy and characterizes a critical parameter – the
advance split time, dictating when to perturb – in a simple atmospheric turbulence model, with generalizable entropy-based criteria.
Climate science needs more efficient ways to study high-impact, low-probability extreme events, which are rare by definition and costly to simulate in large numbers. Rare event sampling (RES), including ensemble boosting, offers a novel strategy to extract more information from those occasional simulated events, by applying small perturbations to turn a moderate event into a severe one which otherwise might not come for many more simulation-years. But how severe the events can become, and their estimated probabilities, depend sensitively on the details of the perturbation. In particular, for sudden and transient events like precipitation, performance of boosting depends sensitively on the choice of advance split time (AST) of the perturbation. Heuristically, the perturbation must come early enough before the event to let the ensemble of simulations diversify, but not so early that they forget the special initial conditions that led to the extreme. In pursuit of guidelines for choosing the AST, we study the effect of AST in the task of sampling extreme fluctuations of a passive tracer in a quasigeostrophic turbulent channel flow. This model system is idealized, but captures key elements of midlatitude storm track dynamics while exposing similar algorithmic challenges. We formulate AST selection as a concrete optimization problem for statistical accuracy against a ground truth. Given that such a ground truth would not generally be available, we propose a proxy objective function to optimize in practice: thresholded entropy, which rewards ensembles with both a high mean and a large spread. We show that ensemble boosting, when given a well-chosen AST and equipped with methods to estimate probabilities, can accurately sample extremes at long return periods. We furthermore find evidence that thresholded entropy successfully identifies an optimal AST, which is roughly 1–3  ddy turnover timescales in the quasigeostrophic system. Moreover, this proxy captures the variation
Sandy shoreline–sandbar systems exhibit complex variability arising from the interplay between hydrodynamic forcing and intrinsic morphological feedbacks. Using long-term satellite-derived shoreline and sandbar observations, we applied global polynomial modeling to reconstruct low-dimensional deterministic dynamics for 4 contrasting coastal sites. The resulting autonomous models reproduce key morphodynamic features, including self-sustained shoreline oscillations, shoreline–sandbar coupling, and intermittent transitions between quasi-stable configurations. Nonlinear stability analyses reveal that these systems behave as chaotic oscillators, characterized by locally divergent yet globally bounded trajectories. Energetic episodes correspond to rapid shoreline–sandbar exchanges, whereas long low-energy states reflect stable attractor confinement. Together, these results demonstrate that sandy coasts are governed by deterministic but chaotic dynamics, in which internal coupling and self-organization control both variability and finite predictability. The proposed framework offers a physically consistent and data-driven approach to characterize and compare coastal morphodynamics within a unified nonlinear dynamical perspective.
Seismic inversion for estimating elastic properties is a key technique for reservoir characterization after drilling. The choice of inversion method strongly influences the accuracy, efficiency, and reliability of results. Bayesian inference based on Markov Chain Monte Carlo (MCMC) algorithms provides a robust framework for incorporating data uncertainty and prior geological knowledge. In this study, we compare the performance of four inversion methods – Metropolis-Hastings (MH), Hamiltonian Monte Carlo (HMC), the Metropolis-Adjusted Langevin Algorithm (MALA), and its variant Lip-MALA – in prestack seismic inversion using both synthetic models and real data from an eastern Venezuelan hydrocarbon reservoir. Results indicate that gradient-based methods (HMC, MALA, Lip-MALA) outperform MH in velocity estimation, while density inversion remains more challenging. MH and MALA achieve shorter execution times, whereas HMC and Lip-MALA improve accuracy at higher computational cost. This analysis evaluates mean values and standard deviation (SD) estimates for P-wave velocity, S-wave velocity, and density, with quality assessed through correlation metrics, objective function behavior, seismic traces, and Root Mean Square Error (RMSE). A two-dimensional inversion with real data further demonstrates algorithms performance under complex geological conditions. The findings highlight trade-offs between accuracy and efficiency, providing practical guidelines for selecting inversion method in seismic reservoir characterization.
This study examines whether the predictability of precipitation dynamics in Serbia has been influenced by climate change. We apply Generalized Weighted Permutation Entropy (GWPE) to evaluate the temporal structure of daily precipitation series using the parameter q, which filters subsets of small (q<0) and large (q>0) fluctuations. The analysis covers data from 14 weather stations between 1961 and 2020. Entropy values for q=0q=2, corresponding to Permutation Entropy and Weighted Permutation Entropy respectively, remained stable spatially and temporally. In contrast, GWPE values for
Accurate forecasting of aftershock distributions is vital for effective post-earthquake emergency response, early warning systems, and long-term seismic hazard mitigation. This study introduces a novel nonlinear, multiscale framework for modeling the evolution of Coulomb stress following a major earthquake. The proposed approach integrates rate-and-state friction laws, a KPP-type reaction–diffusion equation, and the Banach fixed-point theorem to simulate the dynamic redistribution of stress in space and time. Central to the model are two time-dependent parameters – α(t), which governs the decay of stress memory consistent with Omori's law, and β(t), which modulates the nonlinear diffusion and reaction dynamics. Applied to the 2018 Hualien earthquake in Taiwan, the framework resolves stress changes and their gradients at depths of 6–25 km. Results indicate that stress gradients are more predictive of aftershock occurrences within the first 50 d and at depths shallower than 12 km, while stress changes play a dominant role at greater depths and later times. Validation using AUC and Molchan error metrics demonstrates the model's strong spatial forecasting capability. The framework's adaptive convergence and modular structure support real-time seismic hazard assessment and integration into PSHA workflows, offering a promising tool for aftershock modeling and disaster resilience planning.
Regime dependencies and Granger causal relationships between tropical and extratropical teleconnections are inferred using Bayesian structure learning. Using ERA5 data, an examination of the differences between the learned graphical structures during particular phases of the Interdecadal Pacific Oscillation (IPO) are used to infer the role of the background state on interactions between the major climate teleconnections. These relationships present a clear regime dependency on the phase of IPO. In the positive phase, IPO autocorrelations are weak whereas Indian Ocean Dipole (IOD) and El Niño Southern Oscillation (ENSO) autocorrelations and the influence of the Madden Julian Oscillation (MJO) are indicative of an enhanced Walker circulation. In contrast, during the negative phase, IPO autocorrelations are strongest with evidence of an enhanced role for extratropical teleconnections on the tropics. Exclusion of MJO removes important tropical-extratropical influences while increasing posterior edge weights between ENSO, the IPO and IOD. Our analysis reveals the dependence of the ENSO autocorrelation on the phase of the background IPO state, and the role of the MJO as being key to link the extratropical tropospheric modes Pacific North American and North Atlantic Oscillation (PNA, NAO) and equatorial surface ocean temperatures (IOD, ENSO) and as a consequence convection.
Regional Climate Model (RCM) emulators enable rapid and computationally efficient RCM projections given Global Climate Model (GCM) inputs, complementing dynamical downscaling by approximating physical representations with statistical models. However, while existing RCM emulators perform well in deterministic emulations, they do not sample internal RCM variability and remain computationally expensive. Here, we present MESMER-RCM, a probabilistic RCM emulator designed for spatially resolved annual 2 m temperature. MESMER-RCM is a generative model that enables both data-efficient learning and interpretability. It can generate large ensembles of synthetic, yet physically plausible, RCM realizations, capturing the internal RCM variability at a fraction of the computational cost. This work offers a fast and reliable RCM emulation framework, supporting finer-scale what-if analyses of regional climate responses and informing local adaptation and mitigation strategies.
Most data-driven methods, among them Dynamic Mode Decomposition (DMD), focus on analysing and reconstructing the average behaviour of a system. However, the primary interest often lies in the anomalous behaviour, known as extreme events. This is especially the case in climate research, where extreme events have significant economic and societal costs. Therefore, we extend a DMD method to account for extreme events by adding a penalisation term. This extension allows us to not only better reconstruct the extreme events, but also extract the spatiotemporal structures related to those extreme events. DMD was originally developed by Schmid and Sesterhenn (Schmid and Sesterhenn, 2008)modes) from high-dimensional data. In its essence DMD uses most relevant modes to filter the noise and reconstruct the original signal. We ask “Is the noise really noise”! Or can we attribute some of these dynamic modes, that result from the DMD, to extreme events? We applied this new method to the climate system, well known for its high-dimensionality. As a proof of concept, we applied the method to two well-studied European heatwaves: those of 2003 and 2010. Across both cases, our extreme%–0.85 %
We examine the local stable and unstable manifolds of chaotic attractors and their associated growth rates for the quantification of (non-)hyperbolicity in low dimensional nonlinear autonomous dissipative models. This is motivated by a desire for a deeper understanding of transversality and hyperbolicity to inform key challenges to prediction in spatially extended chaotic systems in geophysical flows. In particular, we apply local measures of chaos to quantify the relationship between transversality, dimension, and hyperbolicity on the subspaces of the attractors' invariant manifolds. We consider unstable directions and growth rates determined over finite time intervals, specifically those predicated on information over the past evolution i.e., finite time backwards Lyapunov vectors, and those that include information from both the past and future i.e., finite time covariant Lyapunov vectors. Our study reveals general properties across a diverse set of chaotic attractors at short, intermediate and extended forecast horizons associated with the emergence of distinct locally evolving regions of instability.
This work extends the Mapping Particle Filter to account for local dependencies. Two localization methods are tested: a global particle flow with local kernels, and iterative local mappings based on correlation radius. Using a two-scale Lorenz-96 truth and a one-scale forecast model, experiments with full/partial and linear/nonlinear observations show Root Mean Square Error reductions using localized Gaussian mixture priors, achieving competitive performance against Gaussian filters.
Data assimilation involves sequential inference in geophysical systems with nonlinear dynamics and observational operators. Non-parametric filters are a promising approach for data assimilation because they are able to represent non-Gaussian densities. The mapping particle filter is an iterative ensemble method that incorporates the Stein Variational Gradient Descent (SVGD) to produce a particle flow transforming state vectors from prior to posterior densities. At every pseudo-time step, the Kullback-Leibler divergence between the intermediate density and the target posterior is evaluated and minimized. However, for applications in geophysical systems, challenges persist in high dimensions, where sample covariance underestimation leads to filter divergence. This work proposes two localization methods, one in which a local kernel function is defined and the particle flow is global. The second method, given a localization radius, physically partitions the state vector and performs local mappings at each grid point. The performance of the proposed Local Mapping Particle Filters (LMPFs) is assessed in synthetic experiments. Observations are produced with a two-scale Lorenz system, while a one-scale Lorenz model is used as surrogate, introducing model error in the inference. The methods are evaluated with both full and partial observations, as well as with different linear and non-linear observational operators. The LMPFs with Gaussian mixtures in the prior density perform similarly to Gaussian filters such as the Ensemble Transform Kalman Filter (ETKF) and the Local Ensemble Transform Kalman Filter (LETKF) in most cases, and in some scenarios, they provide competitive performance in terms of analysis accuracy.
The urban heat island (UHI), where urban areas experience higher near-surface temperatures than surrounding rural areas, has long been recognized as a serious issue in urban climatology due to global warming and rapid urbanization. This study investigates the key mechanisms of the UHI through a simple theoretical thermodynamic model. Using a simple day-night model based on the surface energy balance (SEB), we demonstrate that the UHI primarily results from two mechanisms: reduced diurnal temperature range (DTR) due to larger heat capacity of urban materials and increased mean temperature due to lower urban albedo. These mechanisms explain why the UHI intensity is stronger at night than during the day. The UHI intensity obtained from the theoretical model shows a qualitatively similar diurnal variation to that found in observations, supporting the applicability of the theoretical model for understanding the UHI. An analysis of temporal dynamics of UHIs in a megacity (Seoul) and a major city (Suwon) in South Korea shows that the long-term changes in the UHI in both cities are significantly correlated with those in the urban-rural difference in DTR, highlighting the role of urban heat storage in the UHI. In particular, this study emphasizes that well-known UHI mechanisms can be explained in a simple and intuitive manner through a time-integrated theoretical framework, underscoring the academic value of simplified models in interpreting complex urban climate processes. Moreover, this approach demonstrates broader applicability beyond UHI research, suggesting that such models can serve as practical tools in diverse climatic and environmental contexts.
This study investigates the impact of very high frequency data assimilation on analysis and forecast accuracy with the local ensemble transform Kalman filter for idealized deep convection. Previous studies showed that assimilating every 30 s data from Phased Array Weather Radar (PAWR) alleviates the problem of strongly non-Gaussian error probability distribution due to rapid nonlinear evolution of deep convection in real-world cases. This study performs perfect model observing system simulation experiments to understand better the impact of assimilating radar reflectivity every 30 s focusing on non-Gaussianity. The idealized experimental settings have unique advantage in verifications for unobserved variables since it was unclear in the previous studies with real-world data. The results show that every 30 s data assimilation contributes to a significant improvement of the analysis accuracy, particularly for vertical velocity associated with strong convection, although the impact on the forecast accuracy is limited. We also find a significant reduction in the non-Gaussianity of first guess ensemble. The impact of assimilation frequency on reducing non-Gaussianity is enhanced when the uncertainty in background wind or stability is included in the initial ensemble perturbation.
Seismic rotational motions recorded in near-field and strong-motion observations show discrepancies with theoretical predictions derived from linear elastodynamic theory. To investigate potential nonlinear contributions, this study incorporates geometric nonlinear effects into wave propagation theory using the Green–Lagrange strain tensor. A staggered-grid finite-difference method is used to simulate six-component (translational and rotational) wavefields generated by three basic moment-tensor source types: isotropic (ISO), double-couple (DC), and compensated linear vector dipole (CLVD). The results demonstrate that nonlinear effects, as a secondary source, have a universal intensity pattern adhering to the physics of wave motion. However, the efficiency of exciting these effects and the modulation of wavefield attributes (such as P-wave polarization) depend strongly on source type. Simulations show that rotational components exhibit higher sensitivity to nonlinear effects driven by S-waves. Reference simulations of two moderate-to-strong earthquakes suggest that surface waves are the primary carriers of nonlinear features.
This paper addresses a major challenge in assimilating 3D radar reflectivity data with a localized ensemble transform Kalman filter (LETKF). In the case of observations with significant reflectivity and small or zero corresponding simulated reflectivities for all ensemble members, i.e., when the ensemble spread is vanishing, the filter ignores the observations based on its low-variance estimate for the background uncertainty. For such low-variance cases, the LETKF is insensitive to observations and their contribution to the analysis increment is effectively zero. Targeted covariance inflation (TCI) has been suggested to deal with the ensemble spread deficiency (Yokota et al., 2018; Dowell and Wicker, 2009; Vobig et al., 2021). To actually make TCI work in a fully cycled convective-scale data assimilation framework, here we will introduce a process-oriented approachconditional approachcriteriaThe process-oriented conditionalWe will describe the theoretical basis of the new TCI approach. Furthermore, we will present numerical results of a case study in an operational framework, for which the TCI is applied to radar observations at each hourly assimilation step throughout a data assimilation cycle. We are able to demonstrate that the TCI is able to clearly improve the assimilation of radar reflectivities, making the system dynamically generate reflectivity that would otherwise be missing. Related to this, we are able to show that the fractional skill score of radar reflectivity forecasts over lead times of up to 6 h is significantly improved by up to 10 %. All of the results are based on the German radar network and the ICON-D2 model covering central Europe.
Prediction and mitigation of extreme weather events are important scientific and societal challenges. Recently, Miyoshi and Sun (2022) proposed a control simulation experiment framework that assesses the controllability of chaotic systems under observational uncertainty, and within this framework, Sun et al. (2023) developed a method to prevent extreme events in the Lorenz 96 model. However, since their method is primarily designed to apply control inputs to all grid variables, the success rate decreases to approximately 60 % when applied to a single site, at least in a specific setting. Herein, we propose an approach that mitigates extreme events by updating local interventions based on multi-scenario ensemble forecasts. Our method achieves a high success rate, reaching 94 % even when applying interventions at one site per step, albeit with a moderate increase in the intervention cost. Furthermore, the success rate increases to 99.4 % for interventions at two sites. Unlike control-theoretic approaches adopting a top–down strategy, which determine inputs by optimizing cost functions, our bottom–up approach mitigates extreme events by effectively utilizing limited intervention options.
Identifying the optimal strategy for initializing coupled climate prediction systems is challenging due to the spatio-temporal scale separation and disparities in the observational network. We aim to clarify when strongly coupled data assimilation (SCDA) is preferable to weakly coupled data assimilation (WCDA). We use a two-components coupled Lorenz-63 system, mimicking the atmosphere and the ocean, and the Ensemble Kalman Filter (EnKF) to compare WCDA and SCDA for diverse spatio-temporal scale separations and observational networks – only in the atmosphere, the ocean, or both components. In the fully observed scenario, SCDA and WCDA yield similar performances. However, little differences are present, and we conjecture these are due to the SCDA being more sensitive to the approximations at the basis of the EnKF present in the cross-update – linear analysis update and sampling error, and how they impact the cross-update between ocean and atmosphere. This sensitivity increases as the temporal scale separation increases and is stronger on the slow and large-scale components. When observations are only in one of the components, the spatio-temporal scale separation influences SCDA's performance. In this scenario, the largest improvements are found when the observed component has a smaller spatial scale. The fast-to-slow update has a larger benefit with a larger temporal scale separation. Meanwhile, with the slow-to-fast update, the improvement is limited to instances when the temporal scale separation is less than one-half. This suggests that SCDA of fast atmospheric observations can potentially improve the large and slow ocean component. Conversely, observations of the fine ocean can improve the large atmosphere at a comparable temporal scale. However, when both components are highly chaotic, and the observed component's spatial scale is the largest, SCDA does not improve over WCDA. In such a case, the cross-updates may become too sensitive to data assimilation approximations. We further validated that WCDA systematically outperforms uncoupled data assimilation (UCDA) in both components, legitimizing the transition toward WCDA.
Ensemble Lagrangian simulations aim to capture the full range of possible outcomes for particle dispersal. However, single-member Lagrangian simulations are most commonly available and only provide a subset of the possible particle dispersal outcomes. This study explores how to generate the variability inherent in Lagrangian ensemble simulations by creating variability in a single-member simulation. To obtain a reference for comparison, we performed ensemble Lagrangian simulations by advecting the particles from the surface of the Gulf Stream, around 35.61° N, 73.61° W, in each member to obtain trajectories capturing the variability of the full 50-member ensemble. Subsequently, we performed single-member simulations with spatially and temporally varying release strategies to generate comparable trajectory variability and dispersal and also with adding Brownian motion diffusion to the advection. We studied how these strategies affected the number of surface particles connecting the Gulf Stream with the eastern side of the subtropical gyre. We used an information theory approach to define and compare the variability in the ensemble with the single-member strategies. We defined the variability as the marginal entropy or average information content of the probability distributions of the position of the particles. We calculated the relative entropy to quantify the uncertainty of representing the full-ensemble variability with single-member simulations. We found that release periods of 12 to 20 weeks most effectively captured the full ensemble variability, while spatial releases with a 2.0° radius resulted in the closest match at timescales shorter than 10 d. We found that adding relatively high amounts of Brownian motion diffusion (Kh=1000 m2 s−1) captures the entropy aspects of the full ensemble variability well but leads to an overestimation of connectivity. Our findings provide insights to improve the representation of variability in particle trajectories and define a framework for uncertainty quantification in Lagrangian ocean analysis.
Systematic errors in dynamical climate models remain a significant challenge to accurate climate predictions, particularly when modeling the nonlinear coupling between the atmosphere and ocean. Despite notable advances in dynamical climate modeling that have improved our understanding of climate variability, these systematic errors can still degrade prediction skills. In this study, we adopt a twin experiment framework with a reduced-order coupled atmosphere-ocean model to explore the utility of machine learning in mitigating these errors. Specifically, we train a data-driven model on data assimilation increments to learn and emulate the underlying dynamical climate model error, which is then integrated with the dynamical climate model to form a hybrid model. Comparison experiments show that the hybrid model consistently outperforms the standalone dynamical climate model in predicting atmospheric and oceanic variables. Further investigation using hybrid models that correct only atmospheric or only oceanic errors reveals that atmospheric corrections are essential for improving short-term predictions, while concurrently addressing both atmospheric and oceanic errors yields superior performance in long-term climate prediction.