Estimating model evidence using data assimilation

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

Cosmic Rays and Large Extra Dimensions

We have proposed that the cosmic ray spectrum "knee", the steepening of the cosmic ray spectrum at energy E \gsim 10^{15.5} eV, is due to "new physics", namely new interactions at TeV cm energies which produce particles undetected by the experimental apparatus. In this letter we examine specifically the possibility that this interaction is low scale gravity. We consider that the graviton propagates, besides the usual four dimensions, into an additional $\delta$, compactified, large dimensions and we estimate the graviton production in $p p$ collisions in the high energy approximation where graviton emission is factorized. We find that the cross section for graviton production rises as fast as $(\sqrt{s}/M_f)^{2+\delta}$, where $M_f$ is the fundamental scale of gravity in $4+\delta$ dimensions, and that the distribution of radiating a fraction $y$ of the initial particle's energy into gravitational energy (which goes undetected) behaves as $\delta y^{\delta -1}$. The missing energy leads to an underestimate of the true energy and generates a break in the {\sl inferred} cosmic ray spectrum (the "kne"). By fitting the cosmic ray spectrum data we deduce that the favorite values for the parameters of the theory are $M_f \sim 8$ TeV and $\delta =4$.Comment: 8 pages, 1 figur

DADA: data assimilation for the detection and attribution of weather and climate-related events

A new nudging method for data assimilation, delay‐coordinate nudging, is presented. Delay‐coordinate nudging makes explicit use of present and past observations in the formulation of the forcing driving the model evolution at each time step. Numerical experiments with a low‐order chaotic system show that the new method systematically outperforms standard nudging in different model and observational scenarios, also when using an unoptimized formulation of the delay‐nudging coefficients. A connection between the optimal delay and the dominant Lyapunov exponent of the dynamics is found based on heuristic arguments and is confirmed by the numerical results, providing a guideline for the practical implementation of the algorithm. Delay‐coordinate nudging preserves the easiness of implementation, the intuitive functioning and the reduced computational cost of the standard nudging, making it a potential alternative especially in the field of seasonal‐to‐decadal predictions with large Earth system models that limit the use of more sophisticated data assimilation procedures

Slowdown of the greening trend in natural vegetation with further rise in atmospheric CO2_{2}

Satellite data reveal widespread changes in Earth\u27s vegetation cover. Regions intensively attended to by humans are mostly greening due to land management. Natural vegetation, on the other hand, is exhibiting patterns of both greening and browning in all continents. Factors linked to anthropogenic carbon emissions, such as CO$_{2}$ fertilization, climate change, and consequent disturbances such as fires and droughts, are hypothesized to be key drivers of changes in natural vegetation. A rigorous regional attribution at the biome level that can be scaled to a global picture of what is behind the observed changes is currently lacking. Here we analyze different datasets of decades-long satellite observations of global leaf area index (LAI, 1981–2017) as well as other proxies for vegetation changes and identify several clusters of significant long-term changes. Using process-based model simulations (Earth system and land surface models), we disentangle the effects of anthropogenic carbon emissions on LAI in a probabilistic setting applying causal counterfactual theory. The analysis prominently indicates the effects of climate change on many biomes – warming in northern ecosystems (greening) and rainfall anomalies in tropical biomes (browning). The probabilistic attribution method clearly identifies the CO$_{2}$ fertilization effect as the dominant driver in only two biomes, the temperate forests and cool grasslands, challenging the view of a dominant global-scale effect. Altogether, our analysis reveals a slowing down of greening and strengthening of browning trends, particularly in the last 2 decades. Most models substantially underestimate the emerging vegetation browning, especially in the tropical rainforests. Leaf area loss in these productive ecosystems could be an early indicator of a slowdown in the terrestrial carbon sink. Models need to account for this effect to realize plausible climate projections of the 21st century

Slowdown of the greening trend in natural vegetation with further rise in atmospheric CO2

This is the final version. Available on open access from the European Geosciences Union via the DOI in this recordCode and data availability: All data used in this study are available from public databases or the literature, which can be found with the references provided in the respective “Materials and methods” subsection. Processed data and analysis scripts are available from the corresponding author upon request, and the repository was published under https://zenodo.org/record/5348210 together with this article. Correspondence and requests for materials should be addressed to Alexander J. Winkler ([email protected] or [email protected]).Satellite data reveal widespread changes in Earth's vegetation cover. Regions intensively attended to by humans are mostly greening due to land management. Natural vegetation, on the other hand, is exhibiting patterns of both greening and browning in all continents. Factors linked to anthropogenic carbon emissions, such as CO2 fertilization, climate change, and consequent disturbances such as fires and droughts, are hypothesized to be key drivers of changes in natural vegetation. A rigorous regional attribution at the biome level that can be scaled to a global picture of what is behind the observed changes is currently lacking. Here we analyze different datasets of decades-long satellite observations of global leaf area index (LAI, 1981-2017) as well as other proxies for vegetation changes and identify several clusters of significant long-term changes. Using process-based model simulations (Earth system and land surface models), we disentangle the effects of anthropogenic carbon emissions on LAI in a probabilistic setting applying causal counterfactual theory. The analysis prominently indicates the effects of climate change on many biomes-warming in northern ecosystems (greening) and rainfall anomalies in tropical biomes (browning). The probabilistic attribution method clearly identifies the CO2 fertilization effect as the dominant driver in only two biomes, the temperate forests and cool grasslands, challenging the view of a dominant global-scale effect. Altogether, our analysis reveals a slowing down of greening and strengthening of browning trends, particularly in the last 2 decades. Most models substantially underestimate the emerging vegetation browning, especially in the tropical rainforests. Leaf area loss in these productive ecosystems could be an early indicator of a slowdown in the terrestrial carbon sink. Models need to account for this effect to realize plausible climate projections of the 21st century.Deutsche Forschungsgemeinschaft (DFG)NASAAlexander von Humboldt Foundatio

A common framework for approaches to extreme event attribution

The extent to which a given extreme weather or climate event is attributable to anthropogenic climate change is a question of considerable public interest. From a scientific perspective, the question can be framed in various ways, and the answer depends very much on the framing. One such framing is a risk-based approach, which answers the question probabilistically, in terms of a change in likelihood of a class of event similar to the one in question, and natural variability is treated as noise. A rather different framing is a storyline approach, which examines the role of the various factors contributing to the event as it unfolded, including the anomalous aspects of natural variability, and answers the question deterministically. It is argued that these two apparently irreconcilable approaches can be viewed within a common framework, where the most useful level of conditioning will depend on the question being asked and the uncertainties involved

Predicting climate change using response theory: global averages and spatial patterns

The provision of accurate methods for predicting the climate response to anthropogenic and natural forcings is a key contemporary scientific challenge. Using a simplified and efficient open-source general circulation model of the atmosphere featuring O(105105) degrees of freedom, we show how it is possible to approach such a problem using nonequilibrium statistical mechanics. Response theory allows one to practically compute the time-dependent measure supported on the pullback attractor of the climate system, whose dynamics is non-autonomous as a result of time-dependent forcings. We propose a simple yet efficient method for predicting—at any lead time and in an ensemble sense—the change in climate properties resulting from increase in the concentration of CO22 using test perturbation model runs. We assess strengths and limitations of the response theory in predicting the changes in the globally averaged values of surface temperature and of the yearly total precipitation, as well as in their spatial patterns. The quality of the predictions obtained for the surface temperature fields is rather good, while in the case of precipitation a good skill is observed only for the global average. We also show how it is possible to define accurately concepts like the inertia of the climate system or to predict when climate change is detectable given a scenario of forcing. Our analysis can be extended for dealing with more complex portfolios of forcings and can be adapted to treat, in principle, any climate observable. Our conclusion is that climate change is indeed a problem that can be effectively seen through a statistical mechanical lens, and that there is great potential for optimizing the current coordinated modelling exercises run for the preparation of the subsequent reports of the Intergovernmental Panel for Climate Change

Attribution: how is it relevant for loss and damage policy and practice?

Attribution has become a recurring issue in discussions about Loss and Damage (L&D). In this highly-politicised context, attribution is often associated with responsibility and blame; and linked to debates about liability and compensation. The aim of attribution science, however, is not to establish responsibility, but to further scientific understanding of causal links between elements of the Earth System and society. This research into causality could inform the management of climate-related risks through improved understanding of drivers of relevant hazards, or, more widely, vulnerability and exposure; with potential benefits regardless of political positions on L&D. Experience shows that it is nevertheless difficult to have open discussions about the science in the policy sphere. This is not only a missed opportunity, but also problematic in that it could inhibit understanding of scientific results and uncertainties, potentially leading to policy planning which does not have sufficient scientific evidence to support it. In this chapter, we first explore this dilemma for science-policy dialogue, summarising several years of research into stakeholder perspectives of attribution in the context of L&D. We then aim to provide clarity about the scientific research available, through an overview of research which might contribute evidence about the causal connections between anthropogenic climate change and losses and damages, including climate science, but also other fields which examine other drivers of hazard, exposure, and vulnerability. Finally, we explore potential applications of attribution research, suggesting that an integrated and nuanced approach has potential to inform planning to avert, minimise and address losses and damages. The key messages are In the political context of climate negotiations, questions about whether losses and damages can be attributed to anthropogenic climate change are often linked to issues of responsibility, blame, and liability. Attribution science does not aim to establish responsibility or blame, but rather to investigate drivers of change. Attribution science is advancing rapidly, and has potential to increase understanding of how climate variability and change is influencing slow onset and extreme weather events, and how this interacts with other drivers of risk, including socio-economic drivers, to influence losses and damages. Over time, some uncertainties in the science will be reduced, as the anthropogenic climate change signal becomes stronger, and understanding of climate variability and change develops. However, some uncertainties will not be eliminated. Uncertainty is common in science, and does not prevent useful applications in policy, but might determine which applications are appropriate. It is important to highlight that in attribution studies, the strength of evidence varies substantially between different kinds of slow onset and extreme weather events, and between regions. Policy-makers should not expect the later emergence of conclusive evidence about the influence of climate variability and change on specific incidences of losses and damages; and, in particular, should not expect the strength of evidence to be equal between events, and between countries. Rather than waiting for further confidence in attribution studies, there is potential to start working now to integrate science into policy and practice, to help understand and tackle drivers of losses and damages, informing prevention, recovery, rehabilitation, and transformation

Inferring causation from time series in Earth system sciences

The heart of the scientific enterprise is a rational effort to understand the causes behind the phenomena we observe. In large-scale complex dynamical systems such as the Earth system, real experiments are rarely feasible. However, a rapidly increasing amount of observational and simulated data opens up the use of novel data-driven causal methods beyond the commonly adopted correlation techniques. Here, we give an overview of causal inference frameworks and identify promising generic application cases common in Earth system sciences and beyond. We discuss challenges and initiate the benchmark platform causeme.net to close the gap between method users and developers

Beyond equilibrium climate sensitivity

ISSN:1752-0908ISSN:1752-089