C3S seasonal forecast product descriptions: additional details

Graphical products

SST indices - single and multi-model

Variance correction

In order to create a meaningful multi-system combination of the SST indices, all their anomalies from each individual forecast system have been adjusted so their variance resembles that of the real world. 

The description of the SST indices plots states the following:

A form of variance adjustment, similar to the weighting in the multi-model anomalies, is applied. In this case, for each system, a (capped) multiplication factor is applied to the index time series, which matches the model and observed variance of anomalies. This variance adjustment is based on the common hindcast period (1993-2016, with the exception of NCEP, where 1999-2016 is used for NINO regions). The single-system ensemble member charts show the adjusted anomaly time series for each member, and the multi-system chart simply overlays the members from each system.

The following steps describe the way this variance adjustment is performed:

1. 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 .
2. 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
3. Estimate the scaling factor (to be applied to the real time forecasts):
   1. Compute: scaling_factor = sqrt(ovar)/sqrt(hvar) 
   2. Apply a cap to scaling_factor  so it is limited to 1.4  (equivalent to approximately a doubling of the variance)
   3. 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*hclength_factor*hclength_factor)))

Note that steps 3b and 3c are not applied to IOD indices and step 3c is not applied to the ENSO relative indices.

Relative Niño indices

From June 2026 ECMWF has introduced an additional measure of El Niño strength, alongside the more traditional Niño 3.4 SST anomalies, the relative Niño indices. These indices compare each one of the classical monitoring Niño regions (e.g. Niño3.4) with the rest of the tropics at the same time, offering a perspective that is less sensitive to long-term warming. This relative index was first proposed in the paper "Defining El Niño indices in a warming climate" (Geert Jan van Oldenborgh et al., 2021, Environ. Res. Lett. 16 044003; DOI 10.1088/1748-9326/abe9ed) and further explored in the follow-up paper "A Relative Sea Surface Temperature Index for Classifying ENSO Events in a Changing Climate" (Michelle L. L’Heureux et al., 2024, J. Climate, 37; DOI 10.1175/JCLI-D-23-0406.1.). Its implementation at ECMWF has been described in an ECMWF Science blog post by Tim Stockdale "Measuring the strength of El Niño – introducing Relative Niño indices" (DOI 10.21957/d05ccfe150).

The details of the scaling factors (s in the following equation) used at ECMWF to produce these relative indices are shown below, and some additional details of how they were computed are available in the blog post linked above.

       Niño3.4  Niño3  Niño4  Niño1+2
month                                
1        1.233  1.239  1.300    1.208
2        1.262  1.291  1.264    1.154
3        1.303  1.297  1.246    1.067
4        1.306  1.213  1.243    1.049
5        1.219  1.138  1.275    1.070
6        1.152  1.112  1.294    1.073
7        1.079  1.080  1.150    1.055
8        1.092  1.110  1.107    1.074
9        1.155  1.150  1.184    1.114
10       1.185  1.189  1.233    1.158
11       1.194  1.199  1.256    1.197
12       1.212  1.213  1.296    1.222

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