Abstract. End users studying impacts and risks caused by human-induced climate change are often presented with large multi-model ensembles of climate projections whose composition and size are arbitrarily determined. An efficient and versatile method that finds a subset which maintains certain key properties from the full ensemble is needed, but very little work has been done in this area. Therefore, users typically make their own somewhat subjective subset choices and commonly use the equally weighted model mean as a best estimate. However, different climate model simulations cannot necessarily be regarded as independent estimates due to the presence of duplicated code and shared development history.Here, we present an efficient and flexible tool that makes better use of the ensemble as a whole by finding a subset with improved mean performance compared to the multi-model mean while at the same time maintaining the spread and addressing the problem of model interdependence. Out-of-sample skill and reliability are demonstrated using model-as-truth experiments. This approach is illustrated with one set of optimisation criteria but we also highlight the flexibility of cost functions, depending on the focus of different users. The technique is useful for a range of applications that, for example, minimise present-day bias to obtain an accurate ensemble mean, reduce dependence in ensemble spread, maximise future spread, ensure good performance of individual models in an ensemble, reduce the ensemble size while maintaining important ensemble characteristics, or optimise several of these at the same time. As in any calibration exercise, the final ensemble is sensitive to the metric, observational product, and pre-processing steps used.

Recent years have witnessed significant interest in convex relaxations of the power flows, with several papers showing that the second-order cone relaxation is tight for tree networks under various conditions on loads or voltages. This paper shows that ac-feasibility, i.e., to find whether some generator dispatch can satisfy a given demand, is NP-hard for tree networks.

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Climate models serve as indispensable tools to investigate the effect of anthropogenic emissions on current and future climate, including extremes. However, as low‐dimensional approximations of the climate system, they will always exhibit biases. Several attempts have been made to correct for biases as they affect extremes prediction, predominantly focused on correcting model‐simulated distribution shapes. In this study, the effectiveness of a recently published quantile‐based bias correction scheme, as well as a new subset selection method introduced here, are tested out‐of‐sample using model‐as‐truth experiments. Results show that biases in the shape of distributions tend to persist through time, and therefore, correcting for shape bias is useful for past and future statements characterizing the probability of extremes. However, for statements characterized by a ratio of the probabilities of extremes between two periods, we find that correcting for shape bias often provides no skill improvement due to the dominating effect of bias in the long‐term trend. Using a toy model experiment, we examine the relative importance of the shape of the distribution versus its position in response to long‐term changes in radiative forcing. It confirms that the relative position of the two distributions, based on the trend, is at least as important as the shape. We encourage the community to consider all model biases relevant to their metric of interest when using a bias correction procedure and to construct out‐of‐sample tests that mirror the intended application.