Using the Hydrologic Ensemble Forecast Service (HEFS)

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### 3.0 Developing Products from Hydrologic Ensembles » 3.2 Box Plots

A box and whiskers plot, sometimes called simply “box plots,” helps us visualize how we get probability guidance from an ensemble of single-valued forecasts. Consider this simplified example of an ensemble with seven members, each shown with a different color and line style.

We will develop a box plot for a specific time that shows the following: 1) median member, 2) middle three members, 3) middle five members, and 4) two outliers.

#### Box Plot Activity - Time 1

#### Box Plot Activity - Time 2

Click on the rectangle for Time 1. In the pop-up window, move the lines for the ensemble members on the left so their positions match their order in the line graph on the right. For example, the median ensemble member should be in the middle of the box. Note that the box part of the box plot represents the middle three ensemble members, including the median. The whiskers capture the middle five members, and the high and low outliers account for all seven members.

Now do the same thing for Time 2. Click the rectangle, then arrange the lines for the ensemble members (right) so they match their order in the line graph in the box plot (left). You'll be matching the median and middle three members, the second highest and lowest members, and the high and low outliers.

#### Question

Is the ensemble member that was the median in time 1 the same as the median ensemble member in time 2? (Choose the best response.)

a) Yes
b) No

The correct answer is b.

The median member changes from time 1 to time 2.

Please make a selection.

#### Question

Is the size of the box plot (the range of values it represents) different in time 2 than in time 1? (Choose the best response.)

a) Yes
b) No

The correct answer is a.

The size of the box plot, and thus the spread of the ensemble members is larger in time 2 than in time 1.

The box plots capture the distribution of ensemble members at a specific time. They help us visualize the value range represented by the ensemble members and the size of the “ensemble spread”. The placement or rank of an ensemble member at one time can be different at another time. Multiple box plots over a time period allow us to evaluate the change in the spread and thus the change in the uncertainty represented by the ensemble forecast. The larger the box and whiskers, the more spread there is in the ensemble forecast.

Please make a selection.

For the remainder of this lesson, we will use examples from the HEFS with a large number of ensemble members. As shown above, the box in the box plots represents the middle 50%, and the middle 90% falls within the whiskers.

The lowest whisker is at the 95% exceedance probability, meaning that fewer than 5% of the members are at or below this level. The highest whisker is at the 5% exceedance probability, which means that only 5% of members have values above this level. The bottom and top of the box are the 75% and 25% exceedance probabilities. The line near the middle, the median, is the 50% exceedance probability.