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The Anomaly Correlation Coefficient (ACC) is one of the most widely used measures in the verification of spatial fields.   It is the spatial correlation between a forecast anomaly relative to climatology, and a verifying analysis anomaly relative to climatology.  ACC represents a measure of how well the forecast anomalies have represented the observed anomalies and shows how well the predicted values from a forecast model "fit" with the real-life data.  When ACC is calculated for a sequence of forecasts, say at a series of forecast lead-times, it is a measure of how well trends in the predicted anomalies follow trends in actual anomalies.

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• For medium range forecasts the anomaly correlation coefficient is evaluated between:
  
  • the mean of the anomaly of the forecast product relative to the medium range model climate (M-climate) and
  • the mean of the anomaly of the verifying CTRL analysis relative to the medium range model climate (M-climate).
• For extended range products the correlation is evaluated between:
  • the mean of the anomaly of the forecast product measured relative to the extended range model climate (ER-M-climate) and
  • the mean of the anomaly of the verifying the CTRL analysis relative to the extended range model climate (ER-M-climate).
• For seasonal products the correlation is evaluated between:
  • the mean of the anomaly of the forecast product relative to the a model climatology based on the ERA-interim re-analysis (based on the period 1993-2016) and
  • the mean of the anomaly of the verifying observations or reanalysis relative to the seasonal model climate (S-M-Climate). 

The medium range model climate (M-climate) and extended range model climate (ER-M-climate) are based on re-forecasts spanning the last 20 years, which used the ERA5 reanalysis for their initialisation

The seasonal model climate (S-M-climate) is based on re-forecasts spanning the last 20 years, which used the ERA-interim re-analysis for their initialisation

 In the analysis below (Fig6.4.1 and Fig6.4.2), forecasts by all IFS models progressively correlate less well with observed values as forecast lead-time increases.  In these graphs HRES has 9Km resolution, the medium range ensemble has 18Km resolution.  The unperturbed ensemble control (CTRL) performs better than any individual perturbed member of ensemble (PF in the diagrams).  The ensemble mean smooths out many smaller scale features and performs best against the verifying analysis.  This supports preferential use of the ensemble mean in practical forecasting.  Typically ACC falls to 0.6 at around day8 or day9 for ensemble control (CTRL), and at around day10 for the ensemble mean (EM).

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