Using Initial State and Forecast Temporal Variability to Evaluate Model Behavior

The statistics of model temporal variability ought to be the same as those of the filtered version of reality that the model is designed to represent. Here, we introduce simple diagnostics to quantify temporal variability on different time scales and apply them to the NCEP and CMC global forecasting systems. These diagnostics enable comparison of temporal variability in forecasts with the initial states from which the forecasts are produced and therefore serve as a complement to other diagnostics that examine, e.g., time-mean biases. Differences between 1-day temporal variability and variability on longer time scales is consistent with previous studies that highlight regions of strong synoptic-scale variability in the storm tracks, with variability on longer time scales highlighting preferred areas for blocking. The diagnostics indicate strong similarities between the NCEP and CMC systems in the representation of temporal variability in geopotential height, and larger differences in the representation of temporal variability in specific humidity. Because the analysis error differs between analyses separated by 1 day, we argue that the mean square differences between analyses separated by 1 day should be larger than differences between forecast states separated by 1-day in the forecast integration. We find this expectation is not always met and discuss possible causes. The NCEP forecast 1-day temporal variability steadily decreases as forecast time increases for most forecast variables, indicating a systematic reduction in temporal variability in the forecast model. The CMC perturbed forecast temporal variability increases during the first half of the period considered, and decreases during the second half, reflecting the impact of a CMC ensemble system upgrade designed to reduce spurious episodic tropical precipitation.