<i>De praeceptis ferendis</i>: good practice in multi-model ensembles

Ensembles of air quality models have been formally and empirically shown to outperform single models in many cases. Evidence suggests that ensemble error is reduced when the members form a diverse and accurate ensemble. Diversity and accuracy are hence two factors that should be taken care of while designing ensembles in order for them to provide better predictions. There exists a trade-off between diversity and accuracy for which one cannot be gained without expenses of the other. Theoretical aspects like the bias-variance-covariance decomposition and the accuracy-diversity decomposition are linked together and support the importance of creating ensemble that incorporates both the elements. Hence, the common practice of unconditional averaging of models without prior manipulation limits the advantages of ensemble averaging. We demonstrate the importance of ensemble accuracy and diversity through an inter-comparison of ensemble products for which a sound mathematical framework exists, and provide specific recommendations for model selection and weighting for multi model ensembles. To this end we have devised statistical tools that can be used for diagnostic evaluation of ensemble modelling products, complementing existing operational methods.