Draft

Ensembles and probabilities

Many slightly different runs instead of one: how to read plumes and spaghetti plots.

Why run a model many times?

We never know the exact state of the atmosphere, and that small uncertainty grows with time. A single forecast shows one possible future and looks more certain than it is. An ensemble starts many runs from starting states that differ within the uncertainty of the observations, and sometimes also changes the model’s physics slightly. If the atmosphere is in a stable pattern the runs stay together; if a small difference can tip the outcome, they separate.

Reading a plume

010203040012345678910days aheadwind speed (kn)your limit: 25 knday 7

On day 7, 5 of 20 members are above 25 kn: a 25% chance, which is how an ensemble turns into a probability. The thick line is the ensemble mean.

Illustrative ensemble: 20 made-up forecasts of wind speed. Real plumes, from services such as ECMWF’s or NOAA’s ensembles, look like this.
  1. Look at the spread. Lines close together mean a confident forecast. A fan means that tomorrow’s forecast is firm but next week’s is not.
  2. Find your limit. Mark the wind or wave height you do not want to sail in and count how many members exceed it at the time you care about. That fraction is the probability.
  3. Compare the mean and a single run. The ensemble mean smooths out disagreement, so it is more accurate on average but hides storms; a single member is one possible outcome, not the likely one.
  4. Watch for two groups. If members split into two clusters, there are two plausible outcomes (for example the low passes north or south) and an average of them describes neither.

Spaghetti plots and storm tracks

A spaghetti plot draws the same feature, such as the 1000 hPa isobar or a storm’s track, for every member on one map. Tight bundles mean agreement; a wide tangle means uncertainty. For tropical cyclones it is the standard way to show where the centre could go: Tropical cyclone models.

How big are ensembles?

  • The ECMWF ensemble has 51 members (one control run and 50 perturbed ones); NOAA’s GEFS has 31.
  • Because an ensemble needs many runs, each member usually has a coarser grid than the same centre’s main forecast.
  • Some national weather services also run high-resolution ensembles for a smaller area, giving probabilities for the next day or two.

Limits

  • Ensembles are often slightly over-confident near the surface: the spread is a little narrower than the real uncertainty, so treat a 10% chance as a real possibility, not a negligible one.
  • A probability is about a place and time as seen by the model grid. Local effects the grid cannot show, like a gust off a headland, are not in it (Wind: mean, gusts and coasts).
  • “70% chance of more than 25 kn” does not mean the wind will be 70% of 25 kn. It means 7 out of 10 members exceeded it.