Prior and Posterior Inflation for Ensemble Filters: A Comparative Study using the Community Atmosphere Model

The quality and accuracy of ensemble prediction systems is highly dependent on factors such as the ensemble size and model errors. Various techniques such as inflation are traditionally used to mitigate for sampling errors when a small ensemble size is used. Here, a spatially and temporally adaptive posterior inflation algorithm is developed using analysis innovations and Bayes formulation. The proposed algorithm features an observation-impact removal strategy as an efficient way to sequentially compute the posterior inflation distribution. The usefulness of posterior inflation is investigated and compared to prior inflation with an 80-member ensemble in the Community Atmosphere Model (CAM). 6-hour forecasts of the atmospheric state, in the Troposphere and lower Stratosphere, are generated over the month of September 2010. GPS Radio Occultation (GPS-RO) refractivity observations in addition to wind and temperature data from aircraft, ACARS and satellites are assimilated. The following questions are addressed: What inflation scheme is more effective at handling sampling errors? When model bias dominates other error sources, which inflation strategy yields a better fit to the observations? Does inflating both the prior and the posterior ensemble perturbations help mitigate for different error sources? The evaluation of the inflation algorithms is assessed using observation space diagnostics including root-mean-squared errors, model biases, ensemble spread and consistency. Further, the inflation patterns are studied and correlations to observation network densities are carefully examined.