Andrey Gavrilov

Projections of future climate carry large uncertainties, commonly quantified through the spread of a multi-model ensemble. The models contributing to such ensembles, however, are neither equally plausible nor independent. Weighting schemes address this by rewarding models that better reproduce the observed climate and penalizing redundant models, with both contributions computed from distances in a chosen predictor space. The performance weighting is governed by a free parameter, calibrated through a perfect-model test in which each model is treated in turn as a pseudo-reality. This parameter is set by following the philosophy of "constraining as much as possible without being overconfident'', monitoring how often the perfect models fall inside a pre-chosen confidence interval. Two problems follow: the test is not sensitive to the position of the pseudo-truth within the interval, and it assumes that some value of the performance parameter hits the target frequency, which is not guaranteed. Here, we reformulate perfect-model tests using the continuous ranked probability score (CRPS), a statistic that compares the entire weighted distribution with the pseudo-reality, and we select the performance parameter at its minimum. The use of this metric shifts the objective of weighting from constraining the projections to predicting well, with the narrowing of the ranges following as a consequence. On synthetic data, the resulting scheme constrains more than its coverage-based counterpart without suffering from overconfidence, provided that the model families are conservatively specified. We apply the two criteria to CMIP6 precipitation projections over land under SSP5-8.5, comparing predictor distances based on sea-level pressure fields and causal networks inferred from sea-level pressure time series. The CRPS-based weights narrow the very likely range by up to 32% for 2041-2060, while the end-of-century projections remain weakly constrained. Causal-network distances carry usable information and yield appreciable spread reductions, but they rest on shallower optima than a simple area-weighted RMSE, which remains the most reliable predictor distance we tested.

The problem of forced response estimation from a single realization was addressed in the recent ForceSMIP project [Wills et al. 2025], which compiles many state-of-the-art statistical methods, including both methods supervised by large Earth System Model (ESM) ensembles and methods that use only a single target climate realization. Single-realization estimation is frequently approached using various linear filtering techniques, in particular Linear Inverse Models (LIMs) and Dynamic Mode Decomposition (DMD) [Penland et al. 1995 and Schmid 2010]. Standard LIM and DMD do not explicitly account for external forcing. DMD with control (DMDc) naturally extends these methods to incorporate essential external forcing information as a control variable [Proctor et al. 2016].We investigate how these forcing inputs can be incorporated into the DMDc model to estimate forced responses. This results in three variants of DMDc for forced response estimation. One variant was already used in Tier 1 of the ForceSMIP project, while the other two have yet to be tested. We evaluate all three methods using near-surface air temperature (tas) and sea-level pressure (psl) from four Earth system models (CanESM5, MIROC6, MPI-ESM, and MPI-ESM1-2-LR) using data from MMLEA v2 [Maher et al. 2025]. Specifically, we analyze their ability to recover forced responses and characterize the DMDc variants across these Earth system models and variables.References: Maher, Nicola, et al. "The Updated Multi-Model Large Ensemble Archive and the Climate Variability Diagnostics Package: New Tools for the Study of Climate Variability and Change." Geoscientific Model Development 18.18 (2025): 6341-6365. Penland, Cécile, and Prashant D. Sardeshmukh. "The Optimal Growth of Tropical Sea Surface Temperature Anomalies." Journal of Climate 8.8 (1995): 1999-2024. Proctor, Joshua L., Steven L. Brunton, and J. Nathan Kutz. "Dynamic Mode Decomposition with Control." SIAM Journal on Applied Dynamical Systems 15.1 (2016): 142-161. Schmid, Peter J. "Dynamic Mode Decomposition of Numerical and Experimental Data." Journal of Fluid Mechanics 656 (2010): 5-28. Wills, Robert CJ, et al. "Forced Component Estimation Statistical Method Intercomparison Project (ForceSMIP)." Authorea Preprints (2025).

Cloud feedback is one of the key sources of uncertainty in the sensitivity of climate projections to anthropogenic forcing in Earth system models (ESMs). Improving its representation remains challenging because clouds sit at the intersection of radiation, dynamics, and microphysics, and small errors in any of these can strongly affect climate sensitivity.. Consequently, analysing and understanding errors in simulated cloud feedback, evaluated against observations, is essential for advancing cloud parameterizations in ESMs.In this work, we explore methodological frameworks for evaluating cloud feedback in climate models that move beyond simple model–observation comparisons toward physically interpretable insights into model properties and dynamics. We propose two advances: (1) improved cloud regime identification by extending standard k-means clustering to Wasserstein k-means, and (2) the use of explainable machine-learning methods to evaluate the extent the ESMs capture the realistic sensitivity between the cloud radiative anomalies and key cloud-controlling factors. We demonstrate these approaches by evaluating different versions of the HadGEM model in AMIP experiments against observations, illustrating their potential to support more physically grounded diagnosis of cloud-feedback behaviour in climate models.

Land-atmosphere interactions are key drivers of climate extremes, mediating the influence of soil moisture, vegetation, and surface energy exchanges on droughts, heatwaves, and compound events. Observed vegetation changes such as climate-induced tree mortality, phenological shifts, and large-scale deforestation can substantially alter these interactions by modifying surface energy and water fluxes. A critical challenge is to understand how soil water-energy feedbacks propagate through the atmosphere, which is essential for both predicting extremes and evaluating Earth System Models (ESMs).To address this, we propose a unified causal and explainable framework to disentangle soil water-energy feedbacks from observational data, creating a benchmark for ESM evaluation. First, we construct machine learning emulators to represent the dynamical responses of land and atmosphere modules to external forcings, consistent with a structural causal model (SCM). These emulators act as efficient, process-aware surrogates, enabling the reconstruction of causal pathways (e.g., soil moisture/temperature → near-surface states) in a computationally tractable way. Using do-calculus combined with explainable AI (XAI), we then estimate the causal coupling strengths of water-energy feedbacks, isolating the direct effects of soil states from confounding atmospheric influences. By comparing these causal estimates against observational constraints, we can evaluate and benchmark ESM representations, revealing structural biases, deficiencies, and uncertainties in simulated pathways.Bridging causal inference, machine learning, and observations, our framework provides a robust tool for process-level diagnosis, model benchmarking, and ultimately improving the physical fidelity of complex ESMs. It advances the mechanistic understanding of how land states drive atmospheric extremes, offering actionable insights for predicting droughts and heatwaves under current and future climates.

Anticipating and defining food crises remain primary challenges for humanitarian and governmental actors [1]. Traditional frameworks rely on predefined risk thresholds for different levels of food intake, but they neglect sudden-onset or "flash" events that abruptly alter the status quo [2]. This research proposes a data-driven methodology to identify and characterize these events, framing them as critical transitions in food security. By leveraging high-frequency, district-level data of food intake, we examine the evolution of food consumption across highly vulnerable countries and compare these findings with qualitative assessments from domain experts.Building on previous research, this work evaluates the efficacy of multiple quantitative methods, ranging from time series analysis (variance, autocorrelations), unsupervised statistical change-point detection [3], dynamical systems theory [4], and deep learning [5], for defining food crises directly from raw data streams. To validate this framework, we first present results from synthetic experiments designed to simulate the noisy, daily measurements typical of this setting. Then, we assess the capacity of these methods to discern system-wide changes to real-world events. These experiments showcase the feasibility of objectively distinguishing between noise and genuine system transitions.This study highlights the necessity of moving beyond static metrics toward a multi-method detection framework. We aim to provide humanitarian actors with a data-driven trigger for intervention, ensuring that flash deteriorations are no longer obscured by the limitations of static indicators and noisy measurements. Ultimately, this unified approach contributes to the development of more effective early warning systems and supports evidence-based decision-making for global food security.References:[1] P. Foini, M. Tizzoni, G. Martini, D. Paolotti, and E. Omodei, ‘On the forecastability of food insecurity’, Sci Rep, 2023, doi: 10.1038/s41598-023-29700-y.[2] Herteux et al., ‘Forecasting trends in food security with real time data’, Commun Earth Environ, 2024, doi: 10.1038/s43247-024-01698-9.[3] Wu, D., Gundimeda, S., Mou, S., Quinn, C. ‘Unsupervised Change Point Detection in Multivariate Time Series’, AISTATS 2024, PMLR, https://proceedings.mlr.press/v238/wu24g.html[4] Zoeter, Onno, and Tom Heskes, ‘Change point problems in linear dynamical systems’, JMLR, 2005, https://www.jmlr.org/papers/volume6/zoeter05a/zoeter05a.pdf[5] T. De Ryck, M. De Vos and A. Bertrand, ‘Change Point Detection in Time Series Data Using Autoencoders With a Time-Invariant Representation,’ IEEE Tran Signal Process, 2021, doi: 10.1109/TSP.2021.308703

The spatiotemporal coupling between soil moisture and precipitation is a fundamental pillar of the global hydrological cycle. With the escalating risk of severe droughts and pluvial extremes, a critical question arises: whether observed variations in soil moisture and precipitation coupling are the result of anthropogenic Forced Response (FR) or Internal Variability (IV). While recent benchmarks, such as the Forced Component Estimation Statistical Method Intercomparison Project, have advanced the estimation of forced components from observational data, a significant gap remains: how to leverage these diagnostic tools to elucidate the non-stationary and non-linear interactions across the full moisture spectrum.This study introduces a statistical attribution framework that reconciles stationary and non-stationary coupling regimes, allowing for a more robust characterization of shifting climate dynamics. We extend the analysis of direct impacts—where FR and IV drivers linearly alter coupled variables—to the assessment of indirect impacts, where drivers exert non-linear influence on mediating variables, which modulate the dynamic sensitivity and strength of the coupling mechanisms. By decoupling these pathways, we move beyond the simple attribution of trends in moisture states; instead, we identify how anthropogenic forcing and internal variability are fundamentally restructuring the feedback mechanisms of the hydrological cycle.

A significant fraction of multidecadal fluctuations in the reanalysis-based gridded estimates of the observed climate variability over the past century and a half lie outside of the envelope generated by ensembles of climate-model historical simulations. Several pattern-recognition methods have been previously used to map out a truly global reach of the observed vs. simulated climate-data differences; in our own work we dubbed these global discrepancies the stadium wave to highlight their most striking spatiotemporal characteristic. Here we used a novel combination of such methods in conjunction with a large multi-model ensemble and two popular twentieth-century reanalysis products to: (i) succinctly describe the geographical evolution of the observed stadium wave in the annually sampled near-surface atmospheric temperature and mean sea-level pressure fields in terms of three basic patterns; (ii) show the robustness of this identification with respect to methodological details, including the demonstration of the truly global character of the stadium wave; and (iii) provide essential clues to its dynamical origin. All input time series were first decomposed into the forced signal and the residual internal variability; multi-model forced-signal estimates were also decomposed into their common-evolution part and the individual-model residuals. Analysis of the latter residuals suggests a contribution to the stadium-wave dynamics from a delayed climate response to variable external forcing despite the observed stadium-wave patterns’ exhibiting the magnitudes and the level of global teleconnectivity unmatched by the forced-signal residuals.

Earth system model (ESM) intercomparison is essential for assessing model performance and identifying future challenges in climate modeling. The Taylor diagram [1] is one of the most widely used tools for this purpose, as it provides an intuitive summary of standard evaluation metrics — such as correlation, root-mean-square error, and standard deviation — by comparing multiple simulated datasets against a reference, typically observations or a ground truth, within a single plot.However, in several relevant applications, including the development of new ESM parameterizations, the comparison of conceptual models, or the evaluation of simulated statistical distributions, classic linear correlation and RMSE metrics may be insufficient. Here, we propose a set of extensions to the Taylor diagram based on a generalization of cross-covariance using kernels, allowing both nonlinear relationships and distributional aspects of similarity to be taken into account. Nonlinear similarity is characterized through a kernel-space analogue of rotational alignment, while distributional similarity can be quantified using metrics such as maximum mean discrepancy, as originally introduced in [2], as well as alternative kernel-based measures. Using controlled synthetic experiments, we show that the proposed kernel Taylor diagrams can resolve differences in model skill that remain indistinguishable under the classical Taylor diagram. These results indicate that the kernel-based extensions provide complementary diagnostic information to standard metrics and can support more informative Earth system model evaluation and development.[1] Taylor, K. E. (2001), Summarizing multiple aspects of model performance in a single diagram, J. Geophys. Res., 106(D7), 7183–7192, doi:10.1029/2000JD900719.[2] Wickstrøm, K., Johnson, J. E., Løkse, S., Camps-Valls, G., Mikalsen, K. Ø., Kampffmeyer, M., & Jenssen, R. (2022). The Kernelized Taylor Diagram. doi:10.48550/arXiv.2205.08864

Complex multiscale dynamics of the atmosphere in extratropical latitudes includes various persistent atmospheric regimes with the residence time up to several weeks. Identification, simulation and prediction of such dynamics remains one of the challenging problems. In this work we use a stochastic recurrent neural network (RNN) with specific architecture to address this problem, appealing to RNN’s ability to handle memory effects well. The proposed RNN connects two types of variables: (i) a low-dimensional representation of the physical variables via Principal Component Analysis (PCA), and (ii) Kernel PCA variables which serve to better represent the target atmospheric regimes [1]. The stochastic component of the RNN has a simple form which allows us to analytically write Bayesian log-posterior and log-likelihood functions to train and cross-validate the model given the particular dataset.Using the observed and climate-model-generated winter geopotential height data in the Northern Hemisphere, we show that the proposed stochastic model is able to reproduce/predict various dynamical properties and distributions of the target regimes in the kernel space, as well as to reconstruct kernel variables from a low-dimensional representation of the original spatio-temporal field.References1. Mukhin et al. (2022). Revealing recurrent regimes of mid-latitude atmospheric variability using novel machine learning method. Chaos: An Interdisciplinary Journal of Nonlinear Science, 32(11).