# The Relative Measure of Predictability (RMOP)

How can we obtain information from ensembles about the predictability of a a particular flow regime, or take into account the variability in predictability at different times of year? The RMOP is a tool that attempts to quantify this information, by using the last 30 days of ensemble forecasts to estimate the value of the current ensemble forecast.

## Theory

Consider the graphic below, which illustrates a low and high uncertainty ensemble run at a model grid point. The vertical lines near the base of the graphic indicate 10 equally likely climatological "bins" of of 500-hPa heights for the grid point. The horizontal line marks the climatological probability (10%) of an ensemble member being in a bin, while the red (lightly cross-hatched) and blue (heavily cross-hatched) bars indicate the percentage of ensemble members from the low and high-uncertainty ensembles, respectively, falling into each climatological bin.

It has been shown that when a many ensemble members fall into the same climatological bin, the atmosphere is inherently more predictable than when they are spread out among many bins. We can use this fact to quantify the "relative predictability" of the atmosphere at each grid-point in the ensemble forecast, by comparing the current ensemble run distribution of a forecast variable, like 500-hPa height, with those over a past period. In the NCEP ensemble forecast system, the last 30 days of ensemble forecasts are used, and the the number of ensemble members falling in the same climatological bin as the ensemble mean forecast is use to measure the predictability.

## Application of theory

To illustrate the use of RMOP, consider the graphic of RMOP from the ensemble run of 00 UTC 11 October 2001 valid 00 UTC 17 October 2001 (a 144-hr forecast), found below:

The shading indicates the RMOP of the ensemble mean 500-hPa height at each grid point, compared to ensemble forecasts of 500-hPa height over the previous 30 days. These are in 10% increments as indicated by the color bar at the bottom of the graphic. Shading at 90% indicates that at least 9 of 10 ensemble forecasts in the past 30 days had fewer ensemble members in the same "bin" as the ensemble mean than the present forecast. In this case, the trough in the eastern US is 90% predictable relative to ensemble forecasts in the past 30 days.

The blue numbers over each box represents the percentage of time that a forecast with the given degree of predictability has verified over the past 30 days. Here, over the 90% predictability box we see that only 55% of the forecasts with 90% relative predictability at 144 hours have verified in the same climatological bin as the observed 500-hPa height at 144 hours over the past 30 days. Note that in general, the values are generally lower than the RMOP numbers below the bar. This is because:

• The underlying forecast model is imperfect,
• The initial conditions are imprecise, and
• The atmosphere behaves chaotically.

We can expect verification percentages to decrease with