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## Variable separation in ensemble simulations
Consider a time series of one prognostic variable at one point
Here, the overbar-trem is the overall mean value for all realizations, the hat-term is the deviation of the time series of ensemble means from the overall mean, and the tilde-term is the deviation of the time series of a particular realization from the time series of ensemble means.
For simplicity, assume that the ensemble consists of two realizations
only. In the figure below, the time series for the chosen variable at
a specific point in space is displayed by the red line (realization
no. 1) and a blue line (realization no. 2). The full black line is the
time series of the ensemble mean, and the dashed line is the overall
mean value from the combined set time series (
We interpret the deviation that corresponds to the hat-term (black dashed line with arrows) as a representation of the deterministic variability. Then, the variability corresponding to the tilde-term (red and blue solid lines with arrows) represents the non-deterministic variability. A mathematical expression relating these quantities to the variance of the time series is presented here. |