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.

Abstract. The rationale for using multi-model ensembles in climate change projections and impacts research is often based on the expectation that different models constitute independent estimates; therefore, a range of models allows a better characterisation of the uncertainties in the representation of the climate system than a single model. However, it is known that research groups share literature, ideas for representations of processes, parameterisations, evaluation data sets and even sections of model code. Thus, nominally different models might have similar biases because of similarities in the way they represent a subset of processes, or even be near-duplicates of others, weakening the assumption that they constitute independent estimates. If there are near-replicates of some models, then treating all models equally is likely to bias the inferences made using these ensembles. The challenge is to establish the degree to which this might be true for any given application. While this issue is recognised by many in the community, quantifying and accounting for model dependence in anything other than an ad-hoc way is challenging. Here we present a synthesis of the range of disparate attempts to define, quantify and address model dependence in multi-model climate ensembles in a common conceptual framework, and provide guidance on how users can test the efficacy of approaches that move beyond the equally weighted ensemble. In the upcoming Coupled Model Intercomparison Project phase 6 (CMIP6), several new models that are closely related to existing models are anticipated, as well as large ensembles from some models. We argue that quantitatively accounting for dependence in addition to model performance, and thoroughly testing the effectiveness of the approach used will be key to a sound interpretation of the CMIP ensembles in future scientific studies.

Uncertainties in climate projections exist due to natural variability, scenario uncertainty, and model uncertainty. It has been argued that model uncertainty can be decreased by giving more weight to those models in multimodel ensembles that are more skillful and realistic for a specific process or application. In addition, some models in multimodel ensembles are not independent. We use a weighting approach proposed recently that takes into account both model performance and interdependence and apply it to investigate projections of summer maximum temperature climatology over North America in two regions of different sizes. We quantify the influence of predicting diagnostics included in the method, look at ways how to choose them, and assess the influence of the observational data set used. The trend in shortwave radiation, mean precipitation, sea surface temperature variability, and variability and trend in maximum temperature itself are the most promising constraints on projections of summer maximum temperature over North America. The influence of the observational data sets is large for summer temperature climatology, since the observational and reanalysis products used for absolute maximum temperatures disagree. Including multiple predicting diagnostics leads to more similar results for different data sets. We find that the weighted multimodel mean reduces the change in summer daily temperature maxima compared to the nonweighted mean slightly (0.05–0.45 °C) over the central United States. We show that it is essential to have reliable observations for key variables to be able to constrain multimodel ensembles of future projections.