Lagged ensemble vs burst sampling strategy for initializing sub-seasonal forecasts

The WWRP/WCRP Sub-seasonal to Seasonal Prediction (S2S) database contains real-time and re-forecasts from 11 operational centres. Several S2S models are initialized frequently with a small ensemble size (e.g. 4 ensemble members every day). In order to inflate the ensemble size, real-time forecasts are produced by combining all the forecasts produced over a window of several days to produce a “lagged ensemble” in which ensemble members have different lead times. The other S2S models are initialized less frequently (e.g. once or twice a week) but with a large ensemble size (e.g. 51 members). This initialization strategy is referred to as “burst sampling”. Both strategies have advantages and inconvenience and it is not clear which strategy is optimal for sub-seasonal prediction. 
The ECMWF sub-seasonal forecasts are produced using the burst-sampling strategy: a 51-member ensemble is run twice a week (every Monday and Thursday). A large set of re-forecasts, run on a daily basis, have been produced to assess the potential benefit of replacing this current ensemble configuration by a lagged-ensemble approach. We are interested in answering the following two questions, if the current 51-member ensemble run twice a week is replaced by a sub-seasonal ensemble run every day with an ensemble size Ne:

• What is the minimum value of Ne so that there is a lagged ensemble forecast (Nd forecast days combined) which is at least as skilful as the current system on Mondays and Thursdays?

• For a given value of Ne, what is the optimal number Nd of forecast days to combine? Greater values of Nd produce larger lagged ensemble size, but also reduce the accuracy of the forecasts by adding ensemble members with older start dates. 

Results indicate that:

1. A lagged ensemble is more beneficial in the Tropics than in the Northern Extratropics particularly for shorter lead times (weeks 1 and 2).  

2. The minimum daily ensemble size to produce sub-seasonal forecasts (beyond week 1) at least as skilful as the current ECMWF forecasts on Mondays and Thursdays is Ne=20 with an optimal number of lag days Nd=3. The values of Ne (Nd) decrease (increase) with increased lead time. 

These results suggest that a lagged-ensemble could be a viable alternative to the current ensemble extended-range forecasting system at ECMWF.