Do probabilistic medium-range temperature forecasts need to allow for non-normality?

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The gaussian spread regression model for the calibration of site specific ensemble temperature forecasts depends on the apparently restrictive assumption that the uncertainty around temperature forecasts is normally distributed. We generalise the model using the kernel density to allow for much more flexible distribution shapes. However, we do not find any meaningful improvement in the resulting probabilistic forecast when evaluated using likelihood based scores. We conclude that the distribution of uncertainty is either very close to normal, or if it is not close to normal, then the non-normality is not being predicted by the ensemble forecast that we test.