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Home > Research > Ifsdocs > ENSEMBLE >  
   

IFS documentation front page


Table of contents

Chapter 1. Theory

Chapter 2. Computational details

REFERENCES


 
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2.1 The singular vector code




The singular vector computation is called from CUN3 in CNT0 or from CUN2 in CUN1, depending on whether the Hessian of the objective function is used or not. General routines related to the singular vector computation can be found in the directory `sinvect'. The technical routines needed for the Lanczos or Jacobi-Davidson algorithm are contained in the directory `lanczos' of IFSAUX.


2.1.1 Set-up routines




Details of the set-up routines are given in Table 2.1.


Table 2.1 Constants in namelist NAMLCZ controlling the singular vector computation.
NAME
TYPE
PURPOSE
DEFAULT
LANCZOS
LOGICAL
Activates singular vector computation with Lanczos algorithm (NCONF=601)
TRUE
LJACDAV
LOGICAL
Activates singular vector computations with Jacobi-Davidson algorithm (NCONF=131)
FALSE
LOCNORM
LOGICAL
Switch to localize norm computation in grid space
TRUE
ALAT1
REAL
NW corner of local area (defined by point 1)
30
ALON1
REAL
359.5
ALAT3
REAL
SE corner of local area (defined by point 3)
90
ALON3
REAL
0
NLEVMIN
INTEGER
Minimum level of local area
1
NLEVMAX
INTEGER
Maximum level of local area
NLEVG
LSPTRLC0
LOGICAL
Switch to truncate in spectral space at initial (0) time
FALSE
LSPTRLC1
LOGICAL
Switch to truncate in spectral space at final (1) time
FALSE
NWTRMIN0(1)
INTEGER
Spectral coefficients with total wavenumber outside window are set to zero
0
NWTRMAX0(1)
INTEGER
NXMAX
LNEWNORMT0
LOGICAL
Switch to re-define the norm at initial time
FALSE
NEWNORMT0
INTEGER
Re-defines initial norm
1: total energy
2: kinetic energy
3: vorticity squared
4: stream function squared
5: rotational kinetic energy
1
NITERL
INTEGER
Maximum number of Lanczos or Jacob-Davidson inner iterations
70
NINNER
INTEGER
Number of Jacobi-Davidson inner iterations
2
NJDSTOP
INTEGER
Value of NSTOP when LJACDAV=TRUE
144
LEVOLC
LOGICAL
Switch to evolve singular vectors
TRUE
NEIGEVO
INTEGER
Number of singular vectors to evolve
35
NLANTYPE
INTEGER
Determines type of singular vectors
1: energy type norms are used
2 and 3: obsolete
4: same as 1 but now NCONF = 131
5: Hessian is used at initial time
6: for computing eigensystem of the Hessian
1


The routine SULCZ defines the constants as listed in Table 2.1 and determines the configuration of the singular vector computation.






2.1.2 Main routines




The defining equation (1.2) for the singular vectors takes the form

 
(2.1)


The routine OPM is the identity in case a simple energy norm is used at initial time, or it is equal to the Hessian of the 3D-Var objective function. In the routine OPK, the propagators of the tangent and adjoint model are evaluated. Depending on the setting of the constants in NAMLCZ, additional operators may be active, such as SPTRLCZTL when LSPTRLC0=TRUE. It truncates the state vector in spectral space by setting all harmonic coefficients with total wavenumber smaller than NWTRMIN0, or larger than NWTRMAX0, to zero at initial time.


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