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Structural vector autoregressive (SVAR) processes are commonly used time series models to identify and quantify causal interactions between dynamically interacting processes from observational data. The causal relationships between these processes can be effectively represented by a finite directed process graph - a graph that connects two processes whenever there is a direct delayed or simultaneous effect between them. Recent research has introduced a framework for quantifying frequency domain causal effects along paths on the process graph. This framework allows to identify how the spectral density of one process is contributing to the spectral density of another. In the current work, we characterise the asymptotic distribution of causal effect and spectral contribution estimators in terms of algebraic relations dictated by the process graph. Based on the asymptotic distribution we construct approximate confidence intervals and Wald type hypothesis tests for the estimated effects and spectral contributions. Under the assumption of causal sufficiency, we consider the class of differentiable estimators for frequency domain causal quantities, and within this class we identify the asymptotically optimal estimator. We illustrate the frequency domain Wald tests and uncertainty approximation on synthetic data, and apply them to analyse the impact of the 10 to 11 year solar cycle on the North Atlantic Oscillation (NAO). Our results confirm a significant effect of the solar cycle on the NAO at the 10 to 11 year time scale., Comment: 32 pages. Comments welcome!

In this study we consider the problem of detecting and quantifying changes in the distribution of the annual maximum daily maximum temperature (TXx) in a large gridded data set of European daily temperature during the years 1950-2018. Several statistical models are considered, each of which models TXx using a generalized extreme value (GEV) distribution with the GEV parameters varying smoothly over space. In contrast to several previous studies which fit independent GEV models at the grid box level, our models pull information from neighbouring grid boxes for more efficient parameter estimation. The GEV location and scale parameters are allowed to vary in time using the log of atmospheric CO2 as a covariate. Changes are detected most strongly in the GEV location parameter with the TXx distributions generally shifting towards hotter temperatures. Averaged across our spatial domain, the 100-year return level of TXx based on the 2018 climate is approximately 2{\deg}C hotter than that based on the 1950 climate. Moreover, also averaging across our spatial domain, the 100-year return level of TXx based on the 1950 climate corresponds approximately to a 6-year return level in the 2018 climate.

Self-organizing maps (SOMs) are a technique that has been used with high-dimensional data vectors to develop an archetypal set of states (nodes) that span, in some sense, the high-dimensional space. Noteworthy applications include weather states as described by weather variables over a region and speech patterns as characterized by frequencies in time. The SOM approach is essentially a neural network model that implements a nonlinear projection from a high-dimensional input space to a low-dimensional array of neurons. In the process, it also becomes a clustering technique, assigning to any vector in the high-dimensional data space the node (neuron) to which it is closest (using, say, Euclidean distance) in the data space. The number of nodes is thus equal to the number of clusters. However, the primary use for the SOM is as a representation technique, that is, finding a set of nodes which representatively span the high-dimensional space. These nodes are typically displayed using maps to enable visualization of the continuum of the data space. The technique does not appear to have been discussed in the statistics literature so it is our intent here to bring it to the attention of the community. The technique is implemented algorithmically through a training set of vectors. However, through the introduction of stochasticity in the form of a space--time process model, we seek to illuminate and interpret its performance in the context of application to daily data collection. That is, the observed daily state vectors are viewed as a time series of multivariate process realizations which we try to understand under the dimension reduction achieved by the SOM procedure., Comment: Published in at http://dx.doi.org/10.1214/08-AOAS174 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

The observed warming in the atmosphere and ocean can be used to estimate the climate sensitivity linked to present-day feedbacks, which is referred to as the effective climate sensitivity (Shist). However, such an estimate is affected by uncertainty in the radiative forcing, particularly aerosols, over the historical period. Here, we make use of detection and attribution techniques to derive the surface air temperature and ocean warming that can be attributed directly to greenhouse gas increases. These serve as inputs to a simple energy budget to infer the likelihood of Shist in response to observed greenhouse gases increases over two time periods (1862–2012 and 1955–2012). The benefit of using greenhouse gas attributable quantities is that they are not subject to uncertainties in the aerosol forcing (other than uncertainty in the attribution to greenhouse gas versus aerosol forcing not captured by the multi-model aerosol response pattern). The resulting effective climate sensitivity estimate, Shist, ranges from 1.3 °Cto 3.1 °C(5%–95% range) over the full instrumental period (1862–2012) for our best estimate, and gets slightly wider when considering further uncertainties. This estimate increases to 1.7 °C–4.6 °C if using the shorter period (1955–2012).We also evaluate the climate model simulated surface air temperature and ocean heat content increase in response to greenhouse gas forcing over the same periods, and compare them with the observationally-constrained values.We find that that the ocean warming simulated in greenhouse gas only simulations in models considered here is consistent with that attributed to greenhouse gas increases from observations, while one model simulates more greenhouse gas-induced surface air warming than observed. However, other models with sensitivity outside our range show greenhouse gas warming that is consistent with that attributed in observations, emphasising that feedbacks during the historical period may differ from the feedbacks at CO2 doubling and from those at true equilibrium.

The enhancement of the stratospheric aerosol layer by volcanic eruptions induces a complex set of responses causing global and regional climate effects on a broad range of timescales. Uncertainties exist regarding the climatic response to strong volcanic forcing identified in coupled climate simulations that contributed to the fifth phase of the Coupled Model Intercomparison Project (CMIP5). In order to better understand the sources of these model diversities, the Model Intercomparison Project on the climatic response to Volcanic forcing (VolMIP) has defined a coordinated set of idealized volcanic perturbation experiments to be carried out in alignment with the CMIP6 protocol. VolMIP provides a common stratospheric aerosol data set for each experiment to minimize differences in the applied volcanic forcing. It defines a set of initial conditions to assess how internal climate variability contributes to determining the response. VolMIP will assess to what extent volcanically forced responses of the coupled ocean-atmosphere system are robustly simulated by state-of-the-art coupled climate models and identify the causes that limit robust simulated behavior, especially differences in the treatment of physical processes. This paper illustrates the design of the idealized volcanic perturbation experiments in the VolMIP protocol and describes the common aerosol forcing input data sets to be used.