• Introduction
  
• Data Assimilation
  
• SSI
  
• Harmonics
• Variables
  
• Example
• Sources

How does 3D-VAR work?

SSI is a particular version of a 3 dimensional variational method (3D-var).  This method defines a function out of the forecast data, the observations, and the ideal solution.  Finding the minimum of this function gives the answer.  The function is called "J", or the "objective function".  The variables in that function (in matrix form) are:

• the solution to the problem (after bringing the forecast to match the observations): x
• the observations: y
  
• the error in the observations: O
• the error in the forecast: B
• the error in the scale (representativeness) of the observations versus the model: F
• the operator that moves the variable from the forecast location to the observation location: L
  

The objective function    is the sum of two things: the solution, (x) and the  difference between the solution and the observations (Lx-y).  Both of these are multiplied by their respective errors.  The minimum of this function can be found using calculus, and from that we can figure out the ideal data; this ideal data, once found, is what goes on record as the reanalysis data.  The minimum is found by iteration: the computer comes up with an approximate answer, then does the calculation again to get a closer answer, and again more than 100 times until it is close enough.

What's different about SSI?

SSI gets its name from the coordinates it uses: instead of using a grid over the globe to represent a location, it uses spherical harmonic equations.  This goes very well with a model that uses spherical harmonic functions, because the variables used in the data assimilation can be the same, or similar to, the variables used in the model.  This means the only translating between coordinates is on the observations, and since there are far fewer observations than analysis data, this speeds up the program considerably.