We review the field of data assimilation (DA) from a Bayesian perspective and show that, in addition to its by now common application to state estimation, DA may be used for model selection. An important special case of the latter is the discrimination between a factual model–which corresponds, to the best of the modeller's knowledge, to the situation in the actual world in which a sequence of events has occurred–and a counterfactual model, in which a particular forcing or process might be absent or just quantitatively different from the actual world. Three different ensemble-DA methods are reviewed for this purpose: the ensemble Kalman filter (EnKF), the ensemble four-dimensional variational smoother (En-4D-Var), and the iterative ensemble Kalman smoother (IEnKS). An original contextual formulation of model evidence (CME) is introduced. It is shown how to apply these three methods to compute CME, using the approximated time-dependent probability distribution functions (pdfs) each of them provide in the process of state estimation. The theoretical formulae so derived are applied to two simplified nonlinear and chaotic models: (i) the Lorenz three-variable convection model (L63), and (ii) the Lorenz 40-variable midlatitude atmospheric dynamics model (L95). The numerical results of these three DA-based methods and those of an integration based on importance sampling are compared. It is found that better CME estimates are obtained by using DA, and the IEnKS method appears to be best among the DA methods. Differences among the performance of the three DA-based methods are discussed as a function of model properties. Finally, the methodology is implemented for parameter estimation and for event attribution.

How will our estimates of climate uncertainty evolve in the coming years, as new learning is acquired and climate research makes further progress? As a tentative contribution to this question, we argue here that the future path of climate uncertainty may itself be quite uncertain, and that our uncertainty is actually prone to increase even though we learn more about the climate system. We term disconcerting learning this somewhat counter-intuitive process in which improved knowledge generates higher uncertainty. After recalling some definitions, this concept is connected with the related concept of negative learning that was introduced earlier by Oppenheimer et al. (Clim Change 89:155–172, 2008). We illustrate disconcerting learning on several real-life examples and characterize mathematically certain general conditions for its occurrence. We show next that these conditions are met in the current state of our knowledge on climate sensitivity, and illustrate this situation based on an energy balance model of climate. We finally discuss the implications of these results on the development of adaptation and mitigation policy. Copyright Springer Science+Business Media Dordrecht 2013

Causal counterfactual theory provides clear semantics and sound logic for causal reasoning and may help foster research on, and clarify dissemination of, weather and climate-related event attribution. The current event attribution framework obeys the spirit of counterfactual logics. The author has proposed a methodology, which relies on in silico experimentation to derive both the factual and counterfactual probabilities. The attributable proportion are also used to name the same quantity. The FAR, as well as these similar terms, is used to communicate the idea, particularly relevant in epidemiology from which it originates, that the exposition to a given risk factor X translates into an increase of, say, the frequency of a given disease Y. In causal theory, the probability of necessary causation PN formally embeds the notion of causal attribution in its definition. Finally, at a more practical level, attribution studies applying causal theory require the availability of counterfactual model simulations.

We describe a new approach that allows for systematic causal attribution of weather and climate-related events, in near-real time. The method is designed so as to facilitate its implementation at meteorological centers by relying on data and methods that are routinely available when numerically forecasting the weather. We thus show that causal attribution can be obtained as a by-product of data assimilation procedures run on a daily basis to update numerical weather prediction (NWP) models with new atmospheric observations; hence, the proposed methodology can take advantage of the powerful computational and observational capacity of weather forecasting centers. We explain the theoretical rationale of this approach and sketch the most prominent features of a “data assimilation–based detection and attribution” (DADA) procedure. The proposal is illustrated in the context of the classical three-variable Lorenz model with additional forcing. The paper concludes by raising several theoretical and practical questions that need to be addressed to make the proposal operational within NWP centers.