On weighted ensembles: do the weights derived with different methods make sense?

Weighted combinations of multiple estimates of the same property is a commonplace technique in hydrology and earth sciences in general. These collections of estimates – ensembles – commonly consist of different realisations of model structures, parametrisations, input data and/or perturbed initial conditions. The use of weighted ensembles is often motivated by their capability to quantify and reduce error and uncertainty. Just how should we derive the weights is not necessarily clear: the literature knows a large number of methods for weighting, ranging from a simple average (the ensemble mean or median) to complex machine learning algorithms, each with various constraints, properties or assumptions. But do the weights derived by different methods make sense? Can we associate the derived weights to the performance of the ensemble members? Are they related to hydrological signatures (hydrological processes)? Do descriptive catchment attributes predict weights associated to certain ensemble members? Understanding these associations is required for appropriate solutions to the major challenge of regionalisation of ensemble weights.  

We performed a large sample study of 482 catchments and more than 116 000 simulations of conceptual hydrological model (HBV) and explore how different model averaging methods and constraints to the weights influence the associations and performance of a weighted ensemble. The results show that constraining the weights to strictly positive values is advantageous because the output is less sensitive to the composition and size of the ensemble (i.e. the weights are more stable). Constrained weights do not risk negative streamflow predictions, which can often occur when members are assigned negative weights. Furthermore, constrained weights are more reliable in reproducing flow quantiles (particularly low flows) and flow variation, and their overall performance in the testing period is similar, or better, than predictions derived with weights without constraints. Nevertheless, allowing flexibility of free weights produces outputs with better daily and weekly streamflow dynamics. Based on our explorations on the associations and performance, we present our recommendations for selecting an appropriate model averaging methods in hydrology.