Marko Kallio

It has become more and more common in hydrology to consider multiple estimates of hydrological variables – ensembles – over single model runs. Ensemble members represent different realisations of various model structures, input data, and/or parametrisations. Improved predictions can be made using weighted ensembles with wide variety of model averaging methods found in the literature, but only a few explicitly discuss constraints to the weights. Here I perform a large sample study of 482 catchments and approximately 440 000 small and large weighted ensembles of streamflow and focus on comparing how constraints to the weights influence overall performance of the weighted ensemble, and their ability to reproduce select hydrological signatures. The results show that constraining the weights is clearly advantageous for they are less sensitive to the composition of the ensemble, they are less sensitive to the size of the ensemble, do not risk negative streamflow predictions, are more reliable in reproducing flow quantiles and variation (but not in daily and weekly dynamics), and their overall performance in terms of KGE is not worse when the weights have no constraints. From the results it is also clear that bias correction should be conducted separately and explicitly, prior to deriving weights for the ensemble. This is necessary for methods which require the weights to sum to 1, but is also advantageous for methods with implicit bias correction where the sum of weights is free, for it limits the magnitude of weights. I recommend that 1) bias correction be applied explicitly prior to deriving the weights, 2) use constrained weights and do not allow an intercept in the weighted ensemble, and 3) choose the method and potential pre-processing technique considering the specific hydrological signatures you wish to target. I also note that the ensemble mean is inferior in reproducing the hydrological signatures compared to weighted ensembles, and that the ensemble mean is best applied for ensembles without transformations. This research is useful for choosing the weighting method particularly when careful testing of alternatives is not possible, for whatever reason.