The importance of data assimilation components for initial conditions and subsequent error growth

Despite a specific data assimilation method, data assimilation (DA) in general can be decomposed into components of the prior information, observation forward operator that is given by the observation type, observation error covariances, and background error covariances. In a classic Lorenz model, the influences of the DA components on the initial conditions (ICs) and subsequent forecasts are systematically investigated, which could provide a theoretical basis for the design of DA for different scales of interests. The forecast errors undergo three typical stages: a slow growth stage from 0 h to 5 d, a fast growth stage from 5 d to around 15 d with significantly different error growth rates for ensemble and deterministic forecasts, and a saturation stage after 15 d. Assimilation strategies that provide more accurate ICs can improve the predictability. Cycling assimilation is superior to offline assimilation, and a flow-dependent background error covariance matrix (P^f) provides better analyses than a static background error covariance matrix (B) for instantaneous observations and frequent time-averaged observations; but the opposite is true for infrequent time-averaged observations, since cycling simulation cannot construct informative priors when the model lacks predictive skills and the flow-dependent P^f cannot effectively extract information from low-informative observations as the static B. Instantaneous observations contain more information than time-averaged observations, thus the former is preferred, especially for infrequent observing systems. Moreover, ensemble forecasts have advantages over deterministic forecasts, and the advantages are enlarged with less informative observations and lower predictive-skill model priors.