A New Method for Determining the Optimal Lagged Ensemble

We propose a general methodology for determining the optimal lagged ensemble in subseasonal forecasting. The mean square error of a lagged ensemble is shown to depend only on the time-lagged error covariance matrix of the forecast, which can be estimated from a relatively short data set and parameterized in terms of analytic functions of time. The resulting parameterization allows the skill of forecasts to be evaluated for an arbitrary ensemble size and initialization frequency, without the need of additional hindcast experiments. For instance, the skill of a lagged ensemble initialized four times daily can be estimated from an hindcast data set that contains only one forecast per day. This methodology is applied to forecasts of the Madden Julian Oscillation (MJO) from version 2 of the Climate Forecast System (CFSv2). For leads greater than a week, the most skillful forecasts of the MJO are obtained using a lagged ensemble stretching over 5 days and an initialization frequency of 4 times per day. No significant improvement in MJO forecast skill was found for larger ensembles or for more frequent initializations. While the methodology developed here was applied to CFSv2, the technique is general and can be applied to any forecast system.