Singular Vectors - SV

The Singular Vector (SV) technique seeks perturbations for wind, temperature and pressure that will maximize their impact on a 48 hour forecast as measured by the total energy over the hemisphere outside the tropics.  This maximization does not mean that SVs only intensify weather systems; just as often they weaken or displace them.

A special version of the SV is used in the tropics to deal with uncertainties in the moisture processes typical of low latitudes, in particular in tropical cyclones.  These tropical SVs may also influence forecasts of extra-tropical developments, (e.g. when tropical cyclones enter mid-latitudes some days into the forecast and interact with the baroclinic developments in the westerlies).

The advantages of Singular Vectors are:

• they deliver rearward sloping baroclinic structures, which should generally be more realistic. 
  
• the spread of outcomes grows realistically.
• the code is fairly inexpensive to run (it has a low 320km resolution).  There is no evidence yet that higher resolution SVs would improve ensemble skill.
  

 The disadvantages of the Singular Vectors are:

• they don’t directly take into account analysis uncertainty, observation coverage or accuracy.
• they produce rather localized variability (in the very short range).
• they under-develop variability in tropical regions. Tropical singular vectors are used to try to offset this problem.

Points to note:

• Average SV total energy charts can be used to identify unstable regions. 
• SV perturbations tend to be localized in areas of strong barotropic and baroclinic instability.
• SV growth tends to be characterized during the model run by:
  • an upscale energy transfer.
  • an upward energy transfer (most rapid for smaller scales).
  • initial potential energy being converted into kinetic energy.
• Information for the final-time synoptic-scale structure is contained in the sub-synoptic scale SVs.  At initial time:
  
  • SVs with sub-synoptic scale wave numbers may grow very rapidly to reach synoptic scales.
    
  • SVs with large scale wave numbers grow much more slowly than unconstrained, smaller-scale perturbations.  The presence or absence of large scales has little effect on SV growth. 
• The atmospheric flow structure in winter tends to be more baroclinically unstable than in summer.  During winter the flow over Pacific and Atlantic sectors is on average more unstable than in other regions.

Additional Sources of Information

(Note: In older material there may be references to issues that have subsequently been addressed)

• Read more about quantifying forecast uncertainty.
• Read more on singular vectors.
• Read more on tropical singular vectors.