Forecast Tools: Ensemble Forecast Systems

In the early 1960s a famous meteorologist at MIT, Ed Lorenz, discovered that if he started his computer model with slightly different initial values it produced results that were drastically different.  A small difference in the initial conditions grew to a much larger difference during the forecast period.  Lorenz puzzled over these results for quite a while, but eventually published a paper entitled Deterministic Nonperiodic Flow, one of the most important papers ever in the atmospheric sciences.  Lorenz then  contributed to the development of a new field in mathematics that examines the behavior of chaotic systems, which are systems that are sensitive to their initial conditions.

Lorenz passed away in 2008, but I was fortunate to meet him when I was a young professor and swap stories about exploring Utah.  He was an avid hiker, climber, and cross-country skier who would have fit in well with the Wasatch Weather Weenies.  

Ed Lorenz.  Source: Realclimate.org.

Lorenz showed that atmosphere is a chaotic system.  It cannot be predicted like the phases of the moon or the tides.  Small differences in the initial state of the atmosphere can yield dramatically different forecasts.  This places a limit on forecast accuracy as we project farther into the future.  However, how predictable the atmosphere is varies somewhat from day-to-day and region-to-region.  Some patterns are more predictable than others.  The idea behind an ensemble forecast system is to produce lots of forecasts with somewhat different initial analyses (or in some cases model configurations) to get a handle on forecast confidence and the range of possibilities during the forecast period.  

The National Centers for Environmental Prediction Global Ensemble Forecast System (GEFS) provides global ensemble forecasts out to 16 days in the future.  The GEFS consists of 21 forecast members, one being the Global Forecast System (GFS) model forecast, the other 20 additional forecasts produced with slightly different initial conditions.  One way that meteorologists visualize the output from all of these models is using spaghetti diagrams that include a couple of selected contours from all the ensemble members on a single plot.  For example, we can plot the 5280 and 5700 m geopotential height contours at 500-mb from this morning's model analyses.

Source: NCEP

The upper-level flow roughly parallels these contours.  Because they lie nearly on top of one another, the initial analyses in these forecasts are quite similar.  The weak northward bulge in the 5700 m contour over the Intermountain West reflects the weak upper-level ridge that sat over us this morning.

As we go forwards in time, the forecasts begin to diverge, just as chaos theory suggests.

    

Add: NCEP

This is a 5-day forecast based on the analyses above and is valid at 0500 MST Wednesday 4 January.  Although there is clear divergence of the forecasts, it varies geographically.  There is good correspondence between the ensemble members over the western United States.  They all produce a ridge of comparable amplitude.  This is one reason why we have high confidence that a ridge will build over Utah following the cold front passage tonight.  Over the northeast United States and eastern Canadian Provinces, however, there is a mess of contours indicating great uncertainty in the timing and amplitude of the upper-level trough.  This is an area where forecast confidence is lower, especially with regards to the timing and amount of any precipitation that might accompany the upper level trough.

Now, lets go way out in the future and examine the 10 and 16 day forecasts.

Source: NCEP

Chaos in action.  There's a mess of spaghetti, although some might argue that there's also some "signal in the noise."  For example, in the 10-day forecast (top), many of the ensemble members suggest a trough over the eastern United States.

If you were forecasting in that area, you might have a closer look by examining postage stamps from the ensembles.  Those below from the Penn State e-Wall provide a glimpse of a subset of 12 of the ensemble members.  Many show a long-wave trough over the eastern United States and a ridge over the west, but there are variations in amplitude in position and a couple favoring a trough that is shifted a bit to the west.

Source: Penn State e-Wall

Ensemble forecast systems are useful because they help us assess forecast confidence, examine the full range of possibilities during the forecast period, and better quantify the likelihood of specific weather events.  They aren't a panacea, however.  For example, what actually occurs can lie outside the envelope of possibilities forecast by the ensemble.  There are a number of reasons for this, including biases in the model and an inability of the ensemble to produce solutions that diverge fast enough (sometimes called underdispersion).  Ensemble modeling systems are, however, an area of active research that should yield substantially better medium and long range forecasts in the coming years.