Spectral analysis of forecast error investigated with an observing system simulation experiment

The spectra of analysis and forecast error are examined using the observing system simulation experiment framework developed at the National Aeronautics and Space Administration Global Modeling and Assimilation Office. A global numerical weather prediction model, the Global Earth Observing System version 5 with Gridpoint Statistical Interpolation data assimilation, is cycled for 2 months with once-daily forecasts to 336 hours to generate a Control case. Verification of forecast errors using the nature run (NR) as truth is compared with verification of forecast errors using self-analysis; significant underestimation of forecast errors is seen using self-analysis verification for up to 48 hours. Likewise, self-analysis verification significantly overestimates the error growth rates of the early forecast, as well as mis-characterising the spatial scales at which the strongest growth occurs. The NR-verified error variances exhibit a complicated progression of growth, particularly for low wavenumber errors. In a second experiment, cycling of the model and data assimilation over the same period is repeated, but using synthetic observations with different explicitly added observation errors having the same error variances as the control experiment, thus creating a different realisation of the control. The forecast errors of the two experiments become more correlated during the early forecast period, with correlations increasing for up to 72 hours before beginning to decrease.