94
a)
analdiCdec94_nh N=42
FAC=O.10E+02
2~------------------~
>(!}
ffi 1
z w
o~~~~~~~~~~~
b)
o 5 10 15 20 25 30 35 40
N WAVE NUMBER
analdiCdec94_nh N=42
FAC= O.40E+12
> 2 ~-------------~
:I:
a..
o a: ......
(J)
Z
w O~~~~~~~~~~~
o 5 1 0 15 20 25 30 35 40
N WAVE NUMBER
c)
analdif_dec94_nh N=42
FAC= O.40E-l 0
r' 2 ... - ..... - - - - - - - - - - - ,
. .
z
:::>
LL.
:::::E
1
w
a:
~O-J.,..,.,..,..,..,..,.,..,.,..,.........,.,~.,..,....,.,.......,..,......,..;:;;:;:;~
o 5 10 15 20 25 30 35 40
N WAVE NUMBER
Figure 4: The mean 2D total wavenumber spectrum of analysis difference fields in terms
of a) energy, b) ens trophy, c) streamfunction variance. This mean has been calculated
over 42 analysis difference fields, based on experimental operational analysis code and
the operational suites at ECMWF. The experimental suites involve both different model
formulations and different analysis technique (R. Gelaro, personal communication).
matrix
(2.14)
are independent of initial conditions as n -+ 00, and hence are invariants
of the dynamical system. The logarithms of these eigenvalues are the
Lyapunov exponents Ii.
lt is straightforward to see that the singular values O"i of the propagator