Ross Bannister, Data Assimilation Research Centre
Read-in the initial guess,
¯
Set-up the background state, 
(
for first run, from last forecast for later runs)
¯
Set-up the linearization state 
¯
Work out perturbation of the background from the linearization state, 
¯
Do a forecast to the end of the current cycle, starting from 
¯
Calculate the gradient of 
w.r.t. model observations 
¯
Linearize the forward model, 
¯
Calculate the Hessian in model space, 
¯
Diagonalize the Hessian, eigenvectors 
, eigenvalues 
¯
Calculate the components of the 
-transform, 
(this makes the Hessian in transformed space identity, 
)
¯
Calculate the gradient of 
w.r.t. the transformed variables, 
(the analysis increment in transformed space is 
)
¯
Calculate the analysis increment in model space, 
¯
Calculate a new linearization state, 
¯
¬ If 
, go to 
, otherwise 
is the analysis: perform an integration from 
and go to 