The rank histogram is not a verification method per se, but rather a diagnostic tool to evaluate the spread of an ensemble. The underlying assumption is that the ensemble member forecasts are distributed so as to delineate ranges or "bins" of the predicted variable such that the probability of occurrence of the observation within each bin is equal. For each specific forecast, the bins are determined by ranking the ensemble member forecasts from lowest to highest. The interval between each pair of ranked values forms a bin. If there are N ensemble members, then there will be N+1 bins. The outer bins, lowest and highest – valued, are open-ended.

Rank histograms are prepared by determining which of the ranked bins the observation falls into for each case, and plotting a histogram of the total occurrences in each bin, for the full verification sample. It is desirable to use a large sample of cases so that there is likely to be some occurrences in each of the bins. The example on the left below shows a single case where the observation (temperature) falls in the third bin. An example of a finished rank histogram for a 20 member ensemble (21 bins) is shown on the right.

To check your understanding of the interpretation of the rank histogram, please complete the following exercise. As you do the exercise, it is useful to keep in mind the assumption underlying the rank histogram, that the probability that the observation will fall in each bin is equal. If this is true, then over a large enough sample, the histogram should be flat or roughly so. Then one can conclude that on the average, the ensemble spread correctly represents the uncertainty in the forecast.

Drag and drop exercise: Suppose you are faced with rank histograms as shown below. There are 5 of them, let’s say from different ensemble forecasts of surface temperature. All the ensembles have 10 members, hence the rank histogram consists of 11 bins. Drag each of the ensemble characteristics tags on the right to the rank histogram which displays that characteristic.

Correct. This ensemble shows a nearly "flat" rank histogram, indicating that on average the spread is correct. Small variations about the "expected frequency value" (about 0.09 for 11 bins) are normal sampling variation.

Correct. For this ensemble, the observation too frequently occurs in the warmest (highest-valued) bins. Therefore, the ensemble tends to underforecast the temperature (cold bias).

Correct. For this ensemble, the observation too often occurs in the colder-valued bins, which means there is a tendency to overforecast the temperature (a warm bias).

Correct. This is the most common form of the rank histogram for operational ensembles –they tend to be underdispersive.

Correct. For this ensemble, the observation tends to occur too often toward the center of the distribution, and not frequently enough toward the extremes. This is an overdispersed ensemble on average – too large a spread. In practice, this doesn’t frequently occur.

Incorrect. Try again.

Please drag the component text labels to their correct position on surface chart.

You have completed the exercise