Climatological Probabilities

A new feature has been added to the standardized anomaly maps. The color filled regions on the maps are the

The climatological probabilities are derived using the

σ = standard deviation

k = standardized anomaly

μ = mean

X = random variable (height, temperature or other meteorological parameter)

In other words, no more than 1/

Example:

If the GFS suggests a 120 hour forecast of 500 hPa Heights at -6.0 standard deviations, we can compute this climatological probability using a "poor man's" PDF. This is done by taking 1 over the anomaly value, squaring it, multiplying the squared value by 2 (to account for both sides of the median), than converting to a percent. So 1/

In other words, the probability that the 500 hPa heights will differ from the climatological mean by more than 6 standard deviations is <= to 1.4%. Likewise the probability that the 500 hPa height will lie within 6 standard deviations of the mean is >= 98.6% . Please be mindful that we are using model forecast data and the various problems and biases of each model.

Since meteorological data does not typical fall in line with a Gaussian distribution, the ideal frame of reference for the standardized anomalies is a PDF for a given meteorological parameter on the grid. But since we can not easily compute a PDF for all of the points we forecast for, we opt for computing these climatological probabilities using this method. This accounts for the climatological variance and provides a more reasonable climatological probability than extracting sigma values from a standard Bell Curve.