A new method for determining the optimal lagged ensemble.

Area of Science:

• Atmospheric Science
• Climate Modeling
• Data Assimilation

Background:

• Lagged ensemble forecasting is crucial for improving weather and climate predictions.
• Accurate estimation of forecast errors is essential for ensemble optimization.
• The Madden-Julian Oscillation (MJO) presents a significant challenge for subseasonal to seasonal prediction.

Purpose of the Study:

• To develop a general methodology for determining optimal lagged ensemble configurations.
• To minimize the mean square forecast error (MSE) for ensemble forecasts.
• To apply and validate this methodology using the Climate Forecast System version 2 (CFSv2) for MJO prediction.

Main Methods:

• Developed a method based on the cross-lead error covariance matrix to determine optimal ensemble size and initialization frequency.
• Estimated the cross-lead error covariance matrix from hindcast data and parameterized it using analytic functions.
• Applied the methodology to CFSv2 MJO forecasts and analyzed forecast skill for various ensemble parameters.
• Investigated the impact of initialization frequency on capturing error covariance structures.
• Demonstrated optimal weighting of ensemble members to reduce forecast error.

Main Results:

• The MSE of a lagged ensemble depends solely on the cross-lead error covariance matrix.
• Forecast skill for MJO improves little with ensemble sizes larger than 5 days or initializations more frequent than 4 times per day for leads > 1 week.
• Infrequent initializations can lead to the loss of critical error covariance matrix structures.
• Optimal weighting of lagged ensemble members can significantly reduce forecast error at longer lead times (≥10 days).

Conclusions:

• The proposed methodology provides a general framework for optimizing lagged ensemble forecasts.
• The findings offer practical guidance for configuring ensemble forecasts for systems like CFSv2, particularly for MJO prediction.
• The technique is adaptable to other numerical weather prediction and climate forecast systems.