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- Compute the year-to-year variance of the observed (ERA5) index for the hindcast period (1993-2016 for all systems, except NCEP where 1999-2016 is used):
ovar. - Compute the year-to-year variance for each ensemble member of the hindcast for the same period, and average across members to obtain the hindcast variance:
hvar. Note this is done independently for each start date and leadtime - Estimate the scaling factor (to be applied to the real time forecasts):
- Compute:
scaling_factor = sqrt(ovar)/sqrt(hvar) - Apply a cap to
scaling_factorso it is limited to1.4(equivalent to approximately a doubling of the variance) - Apply a correction to reduce the inflation (
scaling_factor > 1.0) when applied to large anomalies or short hindcast periods (shorter than 20 years):
norm_anom = realtime_fcst_anom / sqrt(hvar)
hclength_factor = 2.0 * min(1.0, sqrt(hclength/20))
corrected_scaling_factor = (1.0+(scaling_factor-1.0)*exp(-norm_anom*norm_anom/(2*hclenghthclength_factor*hclength_factor)))
- Compute:
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