forecasting". This type of a forecast significantly reduces errors in model output. When models of different physical processes are combined, such as combinations of atmospheric, ocean and wave models, the multi-model ensemble is called hyper-ensemble. Probability assessment The ensemble forecast is usually evaluated by comparing the ensemble average of the individual forecasts for one forecast variable to the observed value of that variable (the "error"). This is combined with consideration of the degree of agreement between various forecasts within the ensemble system, as represented by their overall standard deviation or "spread". Ensemble spread can be visualised through tools such as spaghetti diagrams, which show the dispersion of one quantity on prognostic charts for specific time steps in the future. Another tool where ensemble spread is used is a meteogram, which shows the dispersion in the forecast of one quantity for one specific location. It is common for the ensemble spread to be too small, such that the observed atmospheric state falls outside of the ensemble forecast. This can lead the forecaster to be overconfident in their forecast. This problem becomes particularly severe for forecasts of the weather about 10 days in advance, particularly if model uncertainty is not accounted for in the forecast. Reliability and resolution (calibration and sharpness) The spread of the ensemble forecast indicates how confident the forecaster can be in his or her prediction. When ensemble spread is small and the forecast solutions are consistent within multiple model runs, forecasters perceive more confidence in the forecast in general. When the spread is large, this indicates more uncertainty in the prediction. Ideally, a spread-skill relationship should exist, whereby the spread of the ensemble is a good predictor of the expected error in the ensemble mean. If the forecast is reliable, the observed state will behave as if it is drawn from the forecast probability distribution. Reliability (or calibration) can be evaluated by comparing the standard deviation of the error in the ensemble mean with the forecast spread: for a reliable forecast, the two should match, both at different forecast lead times and for different locations. The reliability of forecasts of a specific weather event can also be assessed. For example, if 30 of 50 members indicated greater than 1 cm rainfall during the next 24 h, the probability of exceeding 1 cm could be estimated to be 60%. The forecast would be considered reliable if, considering all the