Simulation and diagnosis of observation, model and background error contributions in data assimilation cycling

Data assimilation is usually cycled in time, through a temporal succession of analysis and forecast steps. This implies that forecast errors arise from contributions of observation, model and background errors, which are introduced during successive steps of the cycling. A linearized expansion of forecast errors is here considered, in order to derive expressions and estimates of respective accumulated contributions of these different errors with varying ages. Experiments are conducted in the context of the Météo‐France global numerical weather prediction system ARPEGE. Formal and experimental results indicate that old background errors, which contain all error components arising from corresponding previous cycles, are dampened by successive steps of the cycling, so that they become negligible after a 4‐day period. It is then shown that the variance contribution of recent observation errors tends to converge in time like a power series, within 4 days. This leads the observation error contribution variance to be globally stable in time, which can be interpreted as an approximate compensation between damping of old observation errors and accumulation of recent observation errors. Ensemble experiments and innovation‐based diagnostics are also used to estimate and compare model error contributions with observation error contributions. Such model error diagnostics are likely to be useful e.g. for calibrating model error parametrization schemes in ensemble systems.