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Alison Fowler

Data assimilation for the coupled atmosphere and ocean.

The initialisation of coupled atmosphere-ocean models for long-term forecasting is currently an area of active research. In order to provide accurate initial conditions in which the atmosphere and ocean are consistent with one another it is necessary to take into account the coupling within the assimilation algorithm. Various approaches have been proposed based on incremental 4D-Var with varying degrees of coupling; ranging from 'strongly coupled' 4D-Var to 'uncoupled' 4D-Var which is only coupled in the sense that the background is generated from a coupled model. We have shown that the benefits of a strongly coupled DA system include the reduced chance of an initialisation shock caused by an analysis in which the atmosphere and ocean are out of balance and the improved use of near surface observations s(Smith et al. 2015) .

Long window 4D-Var and model error.

An outstanding issue is choosing a window length which is optimal for both the atmosphere and ocean. Ideally a long window length (approximately 2 days) would be used to allow for sufficient information from observations in the ocean to constrain the initial conditions, however the presence of model error in the coupled system prohibits this. This is demonstrated using an idealised single column model of the atmosphere and ocean. We find that the absolute errors in the analysis of atmospheric temperature increase as we increase the window length (figure 1), however the absolute errors in the analysis of oceanic temperature decrease in some regions as we increase the window length (figure 2). This is because large biases in the atmospheric model, which develop after 12 hours, mean that the assimilation of observations after 12 hours leads to a biased analysis. However, in the ocean, negligible model error up to 2 days means that the analysis error reduces as more observations are assimilated.

To allow for a 2 day assimilation window in coupled 4D-Var it is therefore necessary to take into account the model error in the atmosphere which develops after 12 hours. Weak constraint 4D-Var methods allow for this by not only estimating the state at the initial time but also estimating the model error.

Figure 1: The effect of increasing window length on the absolute analysis error of atmospheric temperature.
Figure 2: The effect of increasing window length on the absolute analysis error of oceanic temperature.

More information.

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