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Rank Histogram / Talagrand Diagram

Statistics Definitions > Rank Histogram

What is a Rank Histogram?

rank histogramRank histograms (sometimes called verification rank histograms or Talagrand diagrams) are a way to show how reliable an ensemble forecast is compared to a set of newly observed data. In other words, they show the bias for the model. If an ensemble forecast is accurate, the rank histogram — a graph of observed data — will be flat (represented by the red line in the image to the left). Deviations from a uniform distribution(i.e. histogram blocks that are above or below the red line) mean that the model isn’t completely accurate. These types of diagrams are not commonly used outside of ensemble forecasting.

How Talagrand Diagrams are Constructed

The Talagrand is basically a histogram. Usually, you would use observed data to make the histogram, using the actual data points to define the bins(class intervals). The difference with this type of histogram is that you use the forecast data to create the bins, and then you use observed (new) data to fill those bins. Metereologist Peter Houtekamer suggests the following steps for creating a rank histogram:

Step 1: Place forecasts in order. For this example, let’s say the forecast values are: {0.25, 0.7, 1.49, 2.17, 4.2}.

Step 2: Define bins based on the list of forecast values from Step 1. There are 6 bins for this list of data:

  1. Values below 0.25 (the lowest value),
  2. Values between 0.25 and 0.7,
  3. Values between 0.7 and 1.49,
  4. Values between 1.49 and 2.17,
  5. Values between 2.17 and 4.2,
  6. Values above 4.2 (the highest value).

Step 3: Place observations in the appropriate bin. Ideally, a large number of observations should be taken over multiple days from different locations.

Step 4: Make a histogram using the new data. Houtekamer states that this histogram should be a uniform distribution, since each bin should represent an equally likely scenarios.

Houtekamer,P. (n.d.). Ensemble forecasts. Retrieved 1/14/2017 from:


If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.

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Rank Histogram / Talagrand Diagram was last modified: October 12th, 2017 by Stephanie

One thought on “Rank Histogram / Talagrand Diagram

  1. sagar

    I am in need to plot the talagrand diagram or rank histogram. I am very thankful to you for providing the information. I have a doubt in the above said 4 steps. especially in third step. I have let us say 20 ensemble numbers. I need to plot talgrand diagram for the average rainfall. Now let us say for 1june I have one average value. Then 20 ensemble numbers for a model. Now i will do the bins. Based on the small value to higer value, i will get 21 bins. Now i have to plcae my observation.
    these are my ensemble values. now my observation value is 49.3025
    Now tell me how can i plot talgrand diagram. I am getting confuse on number of observations. How can i get multi observations. right now i have only one observation.