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Future disruptions to fire activity will threaten ecosystems and human well-being throughout the world, yet there are few fire projections at global scales and almost none from a broad range of global climate models (GCMs). Here we integrate global fire datasets and environmental covariates to build spatial statistical models of fire probability at a 0.5° resolution and examine environmental controls on fire activity. Fire models are driven by climate norms from 16 GCMs (A2 emissions scenario) to assess the magnitude and direction of change over two time periods, 2010-2039 and 2070-2099. From the ensemble results, we identify areas of consensus for increases or decreases in fire activity, as well as areas where GCMs disagree. Although certain biomes are sensitive to constraints on biomass productivity and others to atmospheric conditions promoting combustion, substantial and rapid shifts are projected for future fire activity across vast portions of the globe. In the near term, the most consistent increases in fire activity occur in biomes with already somewhat warm climates; decreases are less pronounced and concentrated primarily in a few tropical and subtropical biomes. However, models do not agree on the direction of near-term changes across more than 50% of terrestrial lands, highlighting major uncertainties in the next few decades. By the end of the century, the magnitude and the agreement in direction of change are projected to increase substantially. Most far-term model agreement on increasing fire probabilities (∼62%) occurs at mid- to high-latitudes, while agreement on decreasing probabilities (∼20%) is mainly in the tropics. Although our global models demonstrate that long-term environmental norms are very successful at capturing chronic fire probability patterns, future work is necessary to assess how much more explanatory power would be added through interannual variation in climate variables. This study provides a first examination of global disruptions to fire activity using an empirically based statistical framework and a multi-model ensemble of GCM projections, an important step toward assessing fire-related vulnerabilities to humans and the ecosystems upon which they depend.

While weighted multi-model approaches are widely used to improve predictive capability, hydrological models (HMs) and their weighted combinations that perform well under past conditions may not guarantee robustness under future climate scenarios. Furthermore, the extent to which weighting schemes influence the propagation of runoff projection uncertainty remains insufficiently explored. Therefore, this study evaluates the capacity of strategies that weight monthly scale HMs to narrow runoff projection uncertainty. Since standard approaches rely only on historical simulation skill and offer static weighting, this study introduces a refined framework, the Uncertainty Optimizing Multi-Model Ensemble (UO-MME), which dynamically considers the trade-offs between calibration performance and projection uncertainty. In performing the uncertainty decomposition, a total of 140 ensemble runoff projections, generated through a modelling chain comprising five GCMs, two emission scenarios, two downscaling methods, and seven HMs, were analyzed for Beydag and Tahtali watersheds in Türkiye. Results indicate that standard techniques, such as Bayesian model averaging, ordered weighted averaging, and Granger–Ramanathan averaging, led to either marginal reductions or noticeable increases in projection uncertainty, depending on the case and projection period. Conversely, the UO-MME achieved average reductions in projection uncertainty of around 30% across the two watersheds by balancing the influences of climate signals produced by GCMs that are reflected in the projections through HMs while maintaining high simulation accuracy, as indicated by Nash–Sutcliffe efficiency values exceeding 0.75. Although not designed to eliminate inherently irreducible uncertainty, the UO-MME framework helps temper the inflation of noisy GCM signals in runoff responses, providing more balanced hydrological projections for water resources planning.

Background Ensemble modeling aims to boost the forecasting performance by systematically integrating the predictive accuracy across individual models. Here we introduce a simple-yet-powerful ensemble methodology for forecasting the trajectory of dynamic growth processes that are defined by a system of non-linear differential equations with applications to infectious disease spread. Methods We propose and assess the performance of two ensemble modeling schemes with different parametric bootstrapping procedures for trajectory forecasting and uncertainty quantification. Specifically, we conduct sequential probabilistic forecasts to evaluate their forecasting performance using simple dynamical growth models with good track records including the Richards model, the generalized-logistic growth model, and the Gompertz model. We first test and verify the functionality of the method using simulated data from phenomenological models and a mechanistic transmission model. Next, the performance of the method is demonstrated using a diversity of epidemic datasets including scenario outbreak data of the Ebola Forecasting Challenge and real-world epidemic data outbreaks of including influenza, plague, Zika, and COVID-19. Results We found that the ensemble method that randomly selects a model from the set of individual models for each time point of the trajectory of the epidemic frequently outcompeted the individual models as well as an alternative ensemble method based on the weighted combination of the individual models and yields broader and more realistic uncertainty bounds for the trajectory envelope, achieving not only better coverage rate of the 95% prediction interval but also improved mean interval scores across a diversity of epidemic datasets. Conclusion Our new methodology for ensemble forecasting outcompete component models and an alternative ensemble model that differ in how the variance is evaluated for the generation of the prediction intervals of the forecasts.

This chapter contains sections titled: Introduction Formulation and Solution of the Inverse Problem EnKF History Matching Workflow Field Case Conclusion References

Here we present the first multi-model ensemble of regional climate simulations at kilometer-scale horizontal grid spacing over a decade long period. A total of 23 simulations run with a horizontal grid spacing of ∼ 3 km, driven by ERA-Interim reanalysis, and performed by 22 European research groups are analysed. Six different regional climate models (RCMs) are represented in the ensemble. The simulations are compared against available high-resolution precipitation observations and coarse resolution ( ∼ 12 km) RCMs with parameterized convection. The model simulations and observations are compared with respect to mean precipitation, precipitation intensity and frequency, and heavy precipitation on daily and hourly timescales in different seasons. The results show that kilometer-scale models produce a more realistic representation of precipitation than the coarse resolution RCMs. The most significant improvements are found for heavy precipitation and precipitation frequency on both daily and hourly time scales in the summer season. In general, kilometer-scale models tend to produce more intense precipitation and reduced wet-hour frequency compared to coarse resolution models. On average, the multi-model mean shows a reduction of bias from ∼  −40% at 12 km to ∼  −3% at 3 km for heavy hourly precipitation in summer. Furthermore, the uncertainty ranges i.e. the variability between the models for wet hour frequency is reduced by half with the use of kilometer-scale models. Although differences between the model simulations at the kilometer-scale and observations still exist, it is evident that these simulations are superior to the coarse-resolution RCM simulations in the representing precipitation in the present-day climate, and thus offer a promising way forward for investigations of climate and climate change at local to regional scales.

The impact of climate change on Sahel precipitation suffers from large uncertainties and is strongly model-dependent. In this study, we analyse sources of inter-model spread in Sahel precipitation change by decomposing precipitation into its dynamic and thermodynamic terms, using a large set of climate model simulations. Results highlight that model uncertainty is mostly related to the response of the atmospheric circulation to climate change (dynamic changes), while thermodynamic changes are less uncertain among climate models. Uncertainties arise mainly because the models simulate different shifts in atmospheric circulation over West Africa in a warmer climate. We linked the changes in atmospheric circulation to the changes in Sea Surface Temperature, emphasising that the Northern hemispheric temperature gradient is primary to explain uncertainties in Sahel precipitation change. Sources of Sahel precipitation uncertainties are shown to be the same in the new generation of climate models (CMIP6) as in the previous generation of models (CMIP5).

In spite of the chaotic nature of the atmosphere and involvement of complex nonlinear dynamics, forecasting climate fluctuations over different timescales is feasible due to the interaction between the atmosphere and the slowly varying underlying surfaces. This review provides insights into climate predictions across subseasonal to decadal timescales and into making projections of future climate change. Different sources of uncertainty in climate predictions are discussed, including internal variability uncertainty, which is large for short-term predictions of up to a decade or two, model uncertainty for predictions at all timescales, and scenario uncertainty for climate change projections at the end of this century. Climate models have been significantly improved in recent decades, mostly through improved parameterization of unresolved processes and enhancement of the spatial resolution, while ensemble forecasting has also been developed to capture strong predictable signals. Future research should aim to reduce uncertainty in climate predictions, for example, through the application of high-resolution climate models. However, sub-grid-scale features would still be parameterized, underlining the need for further improvements in physical parameterizations to account for sub-grid-scale processes. There is also a need for improvement and extension of the current observing system, which will greatly advance understanding of the key processes and features in the climate system. The advanced observing system in the future will also be beneficial for more accurate representation of the initial state of the components of the climate system in order to obtain more accurate climate predictions. In spite of progress in model development, the spread of projected precipitation by different models under a specific radiative forcing of greenhouse gases is still large at the regional scale. Improving future projections of regional precipitation requires better accounting for internal variability and model uncertainty, which can be partly achieved by improvement and extension of the observing system.

In ecology, the true causal structure for a given problem is often not known, and several plausible models and thus model predictions exist. It has been claimed that using weighted averages of these models can reduce prediction error, as well as better reflect model selection uncertainty. These claims, however, are often demonstrated by isolated examples. Analysts must better understand under which conditions model averaging can improve predictions and their uncertainty estimates. Moreover, a large range of different model averaging methods exists, raising the question of how they differ in their behaviour and performance. Here, we review the mathematical foundations of model averaging along with the diversity of approaches available. We explain that the error in model‐averaged predictions depends on each model's predictive bias and variance, as well as the covariance in predictions between models, and uncertainty about model weights. We show that model averaging is particularly useful if the predictive error of contributing model predictions is dominated by variance, and if the covariance between models is low. For noisy data, which predominate in ecology, these conditions will often be met. Many different methods to derive averaging weights exist, from Bayesian over information‐theoretical to cross‐validation optimized and resampling approaches. A general recommendation is difficult, because the performance of methods is often context dependent. Importantly, estimating weights creates some additional uncertainty. As a result, estimated model weights may not always outperform arbitrary fixed weights, such as equal weights for all models. When averaging a set of models with many inadequate models, however, estimating model weights will typically be superior to equal weights. We also investigate the quality of the confidence intervals calculated for model‐averaged predictions, showing that they differ greatly in behaviour and seldom manage to achieve nominal coverage. Our overall recommendations stress the importance of non‐parametric methods such as cross‐validation for a reliable uncertainty quantification of model‐averaged predictions.

The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with standard probability and probabilistic predictions. Yet, due to the steadily increasing relevance of machine learning for practical applications and related issues such as safety requirements, new problems and challenges have recently been identified by machine learning scholars, and these problems may call for new methodological developments. In particular, this includes the importance of distinguishing between (at least) two different types of uncertainty, often referred to as aleatoric and epistemic. In this paper, we provide an introduction to the topic of uncertainty in machine learning as well as an overview of attempts so far at handling uncertainty in general and formalizing this distinction in particular.

Climate projection uncertainty can be partitioned into model uncertainty, scenario uncertainty and internal variability. Here, we investigate the different sources of uncertainty in the projected frequencies of daily maximum temperature and precipitation extremes, which are defined as events that exceed the 99.97th percentile. This is done globally using large initial-condition ensembles. For maximum temperature extremes, internal variability that generates deviations about the ensemble average, dominates in the next 2 decades. Around the middle of the twenty-first century model and scenario uncertainty become the dominant contribution in the tropics but internal variability remains dominant in the extra-tropics. Towards the end of the century, model and scenario uncertainty increase to near equal contributions of ∼ 40% each globally with large regional fluctuations. For precipitation extremes, internal variability dominates throughout the twenty-first century, except for some tropical regions, for example, West Africa. In regions where internal variability constitutes the major source of uncertainty, the potential impact of reducing model uncertainty on the signal-to-noise ratio of the climate projection is estimated to be small. We discuss the caveats of the methodology used and impact of our findings for the design of future climate models. The importance of internal variability found here emphasizes that large ensembles are a vital tool for understanding climate projections.