Time-correlated model error in the (ensemble) Kalman smoother.

Area of Science:

• Data assimilation
• Numerical modeling
• Geosciences

Background:

• Data assimilation often assumes perfect models, neglecting model equation errors.
• Current methods for incorporating model errors use ad-hoc approximations with limited understanding of their impact.
• Approximations in model errors can interact with finite-ensemble-size effects.

Purpose of the Study:

• To systematically evaluate the influence of model error approximations in weak-constraint ensemble smoothers.
• To analyze the effects of incorrect temporal correlations in model errors within Kalman and ensemble Kalman smoothers.
• To understand the interaction between model error approximations and finite-ensemble-size effects.

Main Methods:

• Investigated incorrect temporal correlations in additive model errors for Kalman smoothers.
• Analyzed ensemble Kalman smoothers, considering time-correlation errors and finite ensemble effects.
• Disentangled contributions from different approximations assuming small errors.

Main Results:

• Incorrect correlation time-scales in Kalman smoothers negatively affect solutions; overestimation is worse than underestimation.
• Ensemble Kalman smoother gain is affected by time-correlation and finite ensemble errors.
• Analysis mean is impacted by time-correlation and unexpected finite-ensemble effects.
• Analysis covariance is influenced by time-correlation errors and an in-breeding term.

Conclusions:

• This study provides the first thorough analysis of time-correlation and finite-ensemble-size errors in weak-constraint ensemble smoothers.
• Findings will aid in developing more robust data assimilation methods for applications like numerical weather prediction.