Ensemble spread as a multiboxplot¶

When a weather forecast is run as an ensemble — dozens of slightly different model runs that each evolve differently — the key question is not just “what is the most likely value?” but “how uncertain is the forecast, and how does that uncertainty change over time?”

A multiboxplot (also called a letter-value plot) answers that question in a single chart. For every time step it draws a stack of nested boxes:

Part	What it shows
Thin whisker line	Full range (0th–100th percentile)
Widest box	10th–90th percentile spread
Middle box	25th–75th interquartile range
Horizontal bar	Median (50th percentile)

The boxes get wider as they approach the median and darker toward the edges, making it easy to read the centre of the distribution at a glance while still seeing the tails.

This notebook walks through the chart step-by-step, from loading ensemble data through to overlaying the ensemble mean as a reference line.

Imports¶

We need three packages:

``earthkit.data`` to fetch sample data
``earthkit.plots`` for the chart
``xarray`` — we call xr.set_options(keep_attrs=True) so that unit and variable-name metadata survive arithmetic operations like .mean() (without this, the attributes are silently dropped and earthkit-plots cannot auto-label axes or convert units)

[1]:

import earthkit.data as ekd
import earthkit.plots as ekp
import xarray as xr

xr.set_options(keep_attrs=True)

[1]:

<xarray.core.options.set_options at 0x1140efd90>

Selecting the variable¶

The dataset contains several variables. We pick "2t" (2-metre temperature). After squeeze() the result has shape (number=50, t=145) — 50 ensemble members at 145 time steps.

This is exactly the shape multiboxplot expects: one dimension to reduce over (the ensemble number dimension) and one to use as the x axis (the time t dimension).

[3]:

t2m = ds["2t"]
print(t2m.dims, t2m.shape)

('latitude', 'longitude', 'levelist', 'number', 'datetime', 't') (1, 1, 1, 50, 1, 145)

The minimal chart¶

ekp.timeseries.multiboxplot is the one-liner shortcut. It:

Creates a TimeSeries subplot for you automatically
Auto-detects the time dimension (t) as the x axis
Computes quantiles along the remaining dimension (number) at each time step
Draws the nested box structure

The units="celsius" argument converts the raw Kelvin values to °C before computing the quantiles, so all box positions, tick labels, and axis labels are already in the requested units.

[4]:

ekp.timeseries.multiboxplot(t2m, units="celsius").show()

../../../_images/examples_examples_time-series_timeseries-multibox_8_0.png

Resampling to a coarser time resolution¶

With 145 time steps at 6-hourly intervals, the boxes are very narrow and tightly packed. The resample argument groups the data into wider windows before quantile computation, producing fewer but more legible boxes.

resample="12h" computes 12-hour block means across all ensemble members before computing quantiles. The result has roughly half as many columns, so each box is twice as wide and easier to read.

[5]:

ekp.timeseries.multiboxplot(t2m, units="celsius", resample="12h").show()

../../../_images/examples_examples_time-series_timeseries-multibox_10_0.png

Overlaying the ensemble mean¶

The multiboxplot shows the spread, but it is useful to also show the ensemble mean as a single reference line so readers can trace the central forecast trajectory without having to estimate the midpoint of each box visually.

ekp.timeseries.multiboxplot returns the TimeSeries chart object, so you can chain .line() on it to add any further layers. The units="celsius" and resample="12h" arguments must be repeated so the mean line is computed in the same units and at the same time resolution as the boxes.

zorder=10 places the line on top of all the box patches, which are drawn at zorder 3–5.

[6]:

(
    ekp.timeseries.multiboxplot(t2m, units="celsius", resample="12h")
    .line(t2m.mean(dim="number"), units="celsius", resample="12h", zorder=10)
    .show()
)

../../../_images/examples_examples_time-series_timeseries-multibox_12_0.png

Decorating the chart¶

earthkit-plots uses format strings for titles and labels. Placeholders like {variable_name} and {units} are filled in from the data’s metadata at render time, so the same template works across different variables and unit choices.

xticks accepts the same frequency / format arguments as pandas date formatters. "D" produces one tick per day; "%d %b" formats as “13 Nov”.

[7]:

(
    ekp.timeseries.multiboxplot(t2m, units="celsius", resample="12h")
    .line(t2m.mean(dim="number"), units="celsius", resample="12h", zorder=10)
    .xticks(frequency="D", format="%d %b")
    .ylabel("{variable_name} ({units})")
    .title("ECMWF ensemble 2-metre temperature forecast")
    .show()
)

../../../_images/examples_examples_time-series_timeseries-multibox_14_0.png

Adding a quantile legend¶

The nested boxes are self-explanatory once you know the convention, but for a publication or presentation you can attach a small diagram that labels each quantile tier. multiboxplot_legend() creates a miniature replica of the box structure beside the main axes and annotates it with the quantile percentages.

This method is available on the TimeSeries object returned by the shortcut; it does not need to be called in the chain — you can call it after assigning the chart to a variable.

[8]:

chart = (
    ekp.timeseries.multiboxplot(t2m, units="celsius", resample="12h")
    .line(t2m.mean(dim="number"), units="celsius", resample="12h", zorder=10)
    .xticks(frequency="D", format="%d %b")
    .ylabel("{variable_name} ({units})")
    .title("ECMWF ensemble 2-metre temperature forecast")
)

chart.multiboxplot_legend()
chart.show()

../../../_images/examples_examples_time-series_timeseries-multibox_16_0.png