Explore the vast range of titles available.

Statistical postprocessing techniques are nowadays key components of the forecasting suites in many national meteorological services (NMS), with, for most of them, the objective of correcting the impact of different types of errors on the forecasts. The final aim is to provide optimal, automated, seamless forecasts for end users. Many techniques are now flourishing in the statistical, meteorological, climatological, hydrological, and engineering communities. The methods range in complexity from simple bias corrections to very sophisticated distribution-adjusting techniques that incorporate correlations among the prognostic variables. The paper is an attempt to summarize the main activities going on in this area from theoretical developments to operational applications, with a focus on the current challenges and potential avenues in the field. Among these challenges is the shift in NMS toward running ensemble numerical weather prediction (NWP) systems at the kilometer scale that produce very large datasets and require high-density high-quality observations, the necessity to preserve space-time correlation of high-dimensional corrected fields, the need to reduce the impact of model changes affecting the parameters of the corrections, the necessity for techniques to merge different types of forecasts and ensembles with different behaviors, and finally the ability to transfer research on statistical postprocessing to operations. Potential new avenues are also discussed.

The impact of the El Niño‐Southern Oscillation (ENSO) on the extratropics is investigated in an idealized, reduced‐order model that has a tropical and an extratropical module. Unidirectional ENSO forcing is used to mimick the atmospheric bridge between the tropics and the extratropics. The variability of the coupled ocean‐atmosphere extratropical module is then investigated through the analysis of its pullback attractors (PBAs). This analysis focuses on two types of ENSO forcing generated by the tropical module, one periodic and the other aperiodic. For a substantial range of the ENSO forcing, two chaotic PBAs are found to coexist for the same set of parameter values. Different types of extratropical low‐frequency variability (LFV) are associated with either PBA over the parameter ranges explored. For periodic ENSO forcing, the coexisting PBAs exhibit only weak nonlinear instability. For chaotic forcing, though, they are quite unstable and certain extratropical perturbations induce transitions between the two PBAs. These distinct stability properties may have profound consequences for extratropical climate predictions: in particular, ensemble averaging may no longer help isolate the LFV signal. Plain Language Summary The authors have investigated the variability of a simplified coupled ocean‐atmosphere model for the Earth's midlatitudes, subject to the influence of the El Niño‐Southern Oscillation (ENSO). This study reveals that multiple climates may coexist, each of which is characterized by distinct types of low‐frequency variability (LFV) and predictability properties. When the ENSO forcing is periodic, these climates are fairly robust against perturbations, but when it is chaotic, small perturbations induce transitions between the different climates. These properties could have profound consequences for extratropical climate predictions, since ensemble averaging may no longer be a valid approach to ascertain the LFV signal. Key Points Two pullback attractors (PBAs) coexist in the model's midlatitudes for both periodic and chaotic El Niño‐Southern Oscillation (ENSO) forcing These local PBAs are nonlinearly unstable, with some trajectories that visit both of them The ENSO forcing synchronizes the midlatitude behavior in unexpected ways

The stability properties of intermediate-order climate models are investigated by computing their Lyapunov exponents (LEs). The two models considered are PUMA (Portable University Model of the Atmosphere), a primitive-equation simple general circulation model, and MAOOAM (Modular Arbitrary-Order Ocean-Atmosphere Model), a quasi-geostrophic coupled ocean–atmosphere model on a β-plane. We wish to investigate the effect of the different levels of filtering on the instabilities and dynamics of the atmospheric flows. Moreover, we assess the impact of the oceanic coupling, the dissipation scheme, and the resolution on the spectra of LEs. The PUMA Lyapunov spectrum is computed for two different values of the meridional temperature gradient defining the Newtonian forcing to the temperature field. The increase in the gradient gives rise to a higher baroclinicity and stronger instabilities, corresponding to a larger dimension of the unstable manifold and a larger first LE. The Kaplan–Yorke dimension of the attractor increases as well. The convergence rate of the rate function for the large deviation law of the finite-time Lyapunov exponents (FTLEs) is fast for all exponents, which can be interpreted as resulting from the absence of a clear-cut atmospheric timescale separation in such a model. The MAOOAM spectra show that the dominant atmospheric instability is correctly represented even at low resolutions. However, the dynamics of the central manifold, which is mostly associated with the ocean dynamics, is not fully resolved because of its associated long timescales, even at intermediate orders. As expected, increasing the mechanical atmosphere–ocean coupling coefficient or introducing a turbulent diffusion parametrisation reduces the Kaplan–Yorke dimension and Kolmogorov–Sinai entropy. In all considered configurations, we are not yet in the regime in which one can robustly define large deviation laws describing the statistics of the FTLEs. This paper highlights the need to investigate the natural variability of the atmosphere–ocean coupled dynamics by associating rate of growth and decay of perturbations with the physical modes described using the formalism of the covariant Lyapunov vectors and considering long integrations in order to disentangle the dynamical processes occurring at all timescales.

The prediction of the weather at subseasonal‐to‐seasonal (S2S) timescales is dependent on both initial and boundary conditions. An open question is how to best initialize a relatively small‐sized ensemble of numerical model integrations to produce reliable forecasts at these timescales. Reliability in this case means that the statistical properties of the ensemble forecast are consistent with the actual uncertainties about the future state of the geophysical system under investigation. In the present work, a method is introduced to construct initial conditions that produce reliable ensemble forecasts by projecting onto the eigenfunctions of the Koopman or the Perron‐Frobenius operators, which describe the time‐evolution of observables and probability distributions of the system dynamics, respectively. These eigenfunctions can be approximated from data by using the Dynamic Mode Decomposition (DMD) algorithm. The effectiveness of this approach is illustrated in the framework of a low‐order ocean‐atmosphere model exhibiting multiple characteristic timescales, and is compared to other ensemble initialization methods based on the Empirical Orthogonal Functions (EOFs) of the model trajectory and on the backward and covariant Lyapunov vectors (CLVs) of the model dynamics. Projecting initial conditions onto a subset of the Koopman or Perron‐Frobenius eigenfunctions that are characterized by time scales with fast‐decaying oscillations is found to produce highly reliable forecasts at all lead times investigated, ranging from one week to two months. Reliable forecasts are also obtained with the adjoint CLVs, which are the eigenfunctions of the Koopman operator in the tangent space. The advantages of these different methods are discussed. Plain Language Summary Weather forecasts often reach their limit of predictability at one to two weeks. In order to extend forecast skill beyond this two week limit, the weather prediction community has begun transitioning to the use of coupled models that include both atmosphere and ocean dynamics, with the slower ocean dynamics enabling an extended forecast horizon. Due to uncertainties in the accuracy of the initial conditions and the model itself, such forecasts must be probabilistic. The primary approach for probabilistic weather prediction is to generate ensemble forecasts that integrate multiple copies of the model started from slightly different initial conditions. Here we show that the method used to determine the ensemble of initial conditions has a significant impact on the probabilistic forecast skill at horizons ranging from a few weeks to a few months. We show that many of the existing techniques used for short forecasts are suboptimal for longer forecast horizons. We introduce a new perspective and corresponding techniques that permit the initialization of these ensemble forecasts using information that is intrinsic to the nature of the evolution of the coupled system dynamics, and present data‐driven methods that allow this information to be estimated directly from historical data. Key Points Several methods for initializing ensemble forecasts with long lead times are tested in the context of an ocean‐atmosphere coupled model The methods providing the most reliable ensembles are the adjoint Lyapunov vectors and the adjoint modes of the Dynamic Mode Decomposition These vectors are related to the eigenfunctions of the Koopman and Perron‐Frobenius operators of the system

Various studies identified possible drivers of extremes of Arctic sea ice reduction, such as observed in the summers of 2007 and 2012, including preconditioning, local feedback mechanisms, oceanic heat transport and the synoptic- and large-scale atmospheric circulations. However, a robust quantitative statistical analysis of extremes of sea ice reduction is hindered by the small number of events that can be sampled in observations and numerical simulations with computationally expensive climate models. Recent studies tackled the problem of sampling climate extremes by using rare event algorithms, i.e., computational techniques developed in statistical physics to reduce the computational cost required to sample rare events in numerical simulations. Here we apply a rare event algorithm to ensemble simulations with the intermediate complexity coupled climate model PlaSim-LSG to investigate extreme negative summer pan-Arctic sea ice area anomalies under pre-industrial greenhouse gas conditions. Owing to the algorithm, we estimate return times of extremes orders of magnitude larger than feasible with direct sampling, and we compute statistically significant composite maps of dynamical quantities conditional on the occurrence of these extremes. We find that extremely low sea ice summers in PlaSim-LSG are associated with preconditioning through the winter sea ice-ocean state, with enhanced downward longwave radiation due to an anomalously moist and warm spring Arctic atmosphere and with enhanced downward sensible heat fluxes during the spring-summer transition. As a consequence of these three processes, the sea ice-albedo feedback becomes active in spring and leads to an amplification of pre-existing sea ice area anomalies during summer.

In recent theory trying to explain the origin of baroclinic low-frequency atmospheric variability, the concept of eddy memory has been proposed. In this theory, the effect of synoptic-scale heat fluxes on the planetary-scale mean flow depends on the history of the mean meridional temperature gradient. Mathematically, this involves the convolution of a memory kernel with the mean meridional temperature gradient over past times. However, the precise shape of the memory kernel and its connection to baroclinic wave dynamics remains to be explained. In this study we use linear and proxy response theory to determine the shape of the memory kernel of a truncated two-layer quasigeostrophic atmospheric model. We find a memory kernel that relates the eddy heat flux to the zonal mean meridional temperature gradient on time scales greater than 2 days. Although the shape of the memory kernel is complex, we show that it may be well approximated as an exponential, particularly when reproducing baroclinic low-frequency intraseasonal modes of variability. By computing the terms in the Lorenz energy cycle, we find that the shape of the memory kernel can be linked to the finite time that growing baroclinic instabilities require to adapt their growth properties to the local zonal mean atmospheric flow stability. Regarding the explanation for observed baroclinic annular modes in the Southern Hemisphere, our results suggest that it is physical for these modes to be derived directly from the thermodynamic equation by considering an exponentially decaying memory kernel, provided accurate estimates of the necessary parameters are incorporated.

High-resolution gridded precipitation data is scarce, especially at time intervals shorter than daily. However hydrological applications for example benefit from a finer temporal resolution of rainfall information. In this context, we introduce an hourly precipitation dataset for Belgium, featuring a resolution of 1 km. An hourly high-resolution gridded precipitation product over Belgium can provide valuable insights into the dynamics of both short-term and long-term rainfall events, which can be used for wide-ranging applications such as flash flood forecasting and warning systems, studying precipitation extremes and trends, validating weather and climate models or detecting changes in precipitation patterns due to climate change. Similar products such as EURADCLIM (Europe) (Overeem et al., 2023) and RADKLIM (Germany) (Winterrath et al., 2018), both radar-based gauge-adjusted datasets, have already been created and published. Both datasets are high spatial resolution dataset (2 and 1 km, respectively). A high resolution precipitation grid of hourly precipitation data for Belgium covering the period from 1940 to 2016 using the analog technique, is created. The analogs are sampled from the period 2017–2022 for which high resolution radar data precipitation fields are available. The initial step involves identifying the criteria, i.e. atmospheric parameters such as atmospheric pressure, temperature and humidity, that can be used to determine analogous days. These atmospheric parameters are obtained from the ERA5 observational data provided by the European Centre for Medium-Range Weather Forecasts (ECMWF). In a second step, hourly precipitation data for suitable analog days are extracted from our radar database, and then used to create the high resolution grid of hourly precipitation for Belgium from 1940 to 2016. Data from rain gauges on the Belgian terrain were used for validation of the candidate precipitation analogs. The dataset for this project lists the top 25 analog days for 1940–2016 based on similarities in weather patterns. The analogs are ranked based on how closely they match to their target day. The database is relying on the Zarr archiving format and is composed of two archives. A first archive contains all target days together with the 25 best analogs. The second one provides a precipitation field for each hour of every day in the past. The Zarr format of the database allows slicing through the database. For example, it allows one to easily delimit a specific area of interest and a specific time frame for which the high resolution gridded median hourly precipitation fields are needed. The median field dataset is available on Zenodo (https://doi.org/10.5281/zenodo.14965710) (Debrie et al., 2025).

For most statistical postprocessing schemes used to correct weather forecasts, changes to the forecast model induce a considerable reforecasting effort. We present a new approach based on response theory to cope with slight model changes. In this framework, the model change is seen as a perturbation of the original forecast model. The response theory allows us then to evaluate the variation induced on the parameters involved in the statistical postprocessing, provided that the magnitude of this perturbation is not too large. This approach is studied in the context of a simple Ornstein–Uhlenbeck model and then on a more realistic, yet simple, quasi-geostrophic model. The analytical results for the former case help to pose the problem, while the application to the latter provides a proof of concept and assesses the potential performance of response theory in a chaotic system. In both cases, the parameters of the statistical postprocessing used – the Error-in-Variables Model Output Statistics (EVMOS) method – are appropriately corrected when facing a model change. The potential application in an operational environment is also discussed.

This paper describes a reduced-order quasi-geostrophic coupled ocean-atmosphere model that allows for an arbitrary number of atmospheric and oceanic modes to be retained in the spectral decomposition. The modularity of this new model allows one to easily modify the model physics. Using this new model, coined the \"Modular Arbitrary-Order Ocean-Atmosphere Model\" (MAOOAM), we analyse the dependence of the model dynamics on the truncation level of the spectral expansion, and unveil spurious behaviour that may exist at low resolution by a comparison with the higher-resolution configurations. In particular, we assess the robustness of the coupled low-frequency variability when the number of modes is increased. An \"optimal\" configuration is proposed for which the ocean resolution is sufficiently high, while the total number of modes is small enough to allow for a tractable and extensive analysis of the dynamics.

A new framework is proposed for the evaluation of stochastic subgrid-scale parameterizations in the context of the Modular Arbitrary-Order Ocean-Atmosphere Model (MAOOAM), a coupled ocean–atmosphere model of intermediate complexity. Two physically based parameterizations are investigated – the first one based on the singular perturbation of Markov operators, also known as homogenization. The second one is a recently proposed parameterization based on Ruelle's response theory. The two parameterizations are implemented in a rigorous way, assuming however that the unresolved-scale relevant statistics are Gaussian. They are extensively tested for a low-order version known to exhibit low-frequency variability (LFV), and some preliminary results are obtained for an intermediate-order version. Several different configurations of the resolved–unresolved-scale separations are then considered. Both parameterizations show remarkable performances in correcting the impact of model errors, being even able to change the modality of the probability distributions. Their respective limitations are also discussed.