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 depends only on a quantity called the cross-lead error covariance matrix, which can be estimated from a short hindcast dataset 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. On this page, we provide the relevant numerical codes related to this methodology and then apply it to forecasts of the Madden Julian Oscillation (MJO) from version 2 of the Climate Forecast System (CFSv2).

If you use these algorithms and find bugs or improvements, then please let us know.

Main references

A New Method for Determining the Optimal Lagged Ensemble

L. Trenary, T. DelSole, M. K. Tippett, and K. Pegion, 2016

Software

1. R Codes

   1. Lagged Error Covariance Matrix

   2. Empirical Lagged Error Covariance Matrix

   3. Extrapolate Empirical Lagged Error Covariance Matrix

   4. Mean Square Error

   5. Weighted Mean Square Error

   6. Plot NMSE

   7. tar file: all codes + example data (Madden Julian Oscillation)

2. Matlab Codes (requires version 2013a or higher)

   1. Lagged Error Covariance Matrix

   2. Empirical Lagged Error Covariance Matrix

   3. Extrapolate Empirical Lagged Error Covariance Matrix

   4. Mean Square Error

   5. Weighted Mean Square Error

   6. Plot NMSE

   7. tar file: all codes + example data (Madden Julian Oscillation)