Ensembles

Edward Lorenz (1963) noted that small difference in the initial state could lead to huge differences in the resultant forecast.  Atmospheric processes are non-linear so small differences in the initial conditions can lead to significant differences in the end solution.  Unfortunately,  there will always be significant uncertainty in the initial conditions.  Data assimilation requires large amounts of data to be ingested into a numerical model with  various types of data having different error characteristics.  Quality control needs to be applied to this data in such a way as too minimize errors.  However, the quality control if too stringent may sometimes smooth data points or if it is not applied sufficiently may introduce spurious waves.  Ensemble forecasting attempts to account for some of the uncertainty in the initial conditions allowing a forecaster to look at the impact that slight differences in initial conditions may have on a forecast. 

 

A number of atmospheric processes also occur at a scale below the scale that the operational models can resolve so these processes are parameterized.  When you parameterize a physical process you essentially are approximating the effects of the physical process on the atmosphere which introduces small errors that can grow with time.  Therefore,  ensemble forecasts systems need to also vary the physics or parameterization schemes between the various members. 

 

Finally,  even the mathematics used in the model may introduce small differences.  For example,  the mathematics in a spectral model are different than those in a one that used finite differencing.  UCAR offers a matrix of the ways that the MREF (now GEFS) and SREF are perturbed (see http://meted.ucar.edu/nwp/pcu2/ens_matrix/).  Essentially, the GEFS ensembles initial conditions are perturbed but not the physics or mathematics as all the models use the same parameterization schemes for convection, radiation, etc., and all members are also spectral models.  Essentially, the GEFS members have the same physics and mathematics as the GFS.  By contrast,  the SREF members have both the initial conditions, physics and mathematics perturbed.  Therefore,  the SREF members should have more diversity among its members than the GEFS.  However,  even SREF at times will not have sufficient diversity or spread. 

 

Two UCAR sites offer training of ensemble forecast systems.  The first training site is an introduction to ensemble forecasting that explains the strengths and weaknesses of using spaghetti diagrams and ensemble mean products (http://meted.ucar.edu/nwp/pcu1/ensemble_webcast/).  One important point the training package makes is that when using ensemble guidance to assess the probability of an event,  be sure to take into account any biases that the model may have.  For example,  the tendency for the GFS  and RSM members have to be too far north with their precipitation maxima during convection with strong systems.  The second site offers a little more advanced training packet on the use of ensembles (http://meted.ucar.edu/nwp/pcu1/ensemble/print.htm).  These UCAR modules should be completed as the use of ensemble forecasting techniques will increase as the NWS transitions to probabilistic forecasts. 

 

 

 

 

 

 

 

Another important thing to remember is that the various ensemble members have a significantly lower resolution of the terrain than the operational models especially the NAM.  Therefore,  near the mountains the qpf from the individual members will also lack resolution and will often underpredict precipitation along the windward slopes of the mountains and may also overpredict precipitation to the lee of the mountains.  The GEFS members have the most degraded terrain representation of the ensemble members.  Note in the graphic below how it fails to depict the coastal mountains in California and also does not depict the Sacramento Valley.  The various WRF members and RSM members of the SREF have slightly different representations of terrain but all have a resolution of either 40– or 45-km.  The figure at top right shows their approximate resolution.  The eta members of the SREF have a 32 km resolution (below left).  Note that all the Sref members have much lower resolution than the 12-km NAM (below right).  Note how much smoother the terrain of all the ensemble members compared to the 12-km NAM.  If you expect a precipitation maximum associated with a terrain or land-sea interactions like the sea-breeze, use the higher resolution models.  The PQPF for higher thresholds associated with these smaller scale features,  the ensemble members will underforecast the probabilities. 

GEFS members terrain

Approximate resolution of terrain in RSM and WRF SREF members

Eta SREF members terrain

12 km NAM terrain

USWRP has recognized the need for methods to assess the predictability of warm-season convective events (Fritsch and Carbone, 2004) and cool-season storms (Ralph et al., 2005).  Both articles stressed the important role that ensemble methods would have in helping determine the probability of event occurring.  Each also note the need for probabilistic forecasts.  Undoubtedly,  ensemble methods will be provide one of the backbones for producing these forecasts. Ensemble methods are already being used by the HPC Winter-Weather Desk to help assess the probability of heavy snow and icing. 

Next Page

In later sections,  exercises will be presented on using ensemble guidance in the forecast process to help identify the potential for extreme rainfall events.  However,  the next two sections will provide an overview of the performance of the GFS and NAM at predicting QPF.