situations in the past when a 60% probability was forecast, on 60% of those occasions did the rainfall actually exceed 1 cm. In practice, the probabilities generated from operational weather ensemble forecasts are not highly reliable, though with a set of past forecasts (reforecasts or hindcasts) and observations, the probability estimates from the ensemble can be adjusted to ensure greater reliability. Another desirable property of ensemble forecasts is resolution. This is an indication of how much the forecast deviates from the climatological event frequency – provided that the ensemble is reliable, increasing this deviation will increase the usefulness of the forecast. This forecast quality can also be considered in terms of sharpness, or how small the spread of the forecast is. The key aim of a forecaster should be to maximise sharpness, while maintaining reliability. Forecasts at long leads will inevitably not be particularly sharp (have particularly high resolution), for the inevitable (albeit usually small) errors in the initial condition will grow with increasing forecast lead until the expected difference between two model states is as large as the difference between two random states from the forecast model's climatology. Calibration of ensemble forecasts If ensemble forecasts are to be used for predicting probabilities of observed weather variables they typically need calibration in order to create unbiased and reliable forecasts. For forecasts of temperature one simple and effective method of calibration is linear regression, often known in this context as Model output statistics. The linear regression model takes the ensemble mean as a predictor for the real temperature, ignores the distribution of ensemble members around the mean, and predicts probabilities using the distribution of residuals from the regression. In this calibration setup the value of the ensemble in improving the forecast is then that the ensemble mean typically gives a better forecast than any single ensemble member would, and not because of any information contained in the width or shape of the distribution of the members in the ensemble around the mean. However, in 2004, a generalisation of linear regression (now known as Nonhomogeneous Gaussian regression) was introduced that uses a linear transformation of the ensemble spread to give the width of the predictive distribution, and it was shown that this can lead to forecasts with higher skill than those based on linear regression alone. This proved for the first time that information in the shape of the distribution of the