107
The accumulation of initial energy towards the truncation limit suggests
that a significantly more accurate estimation of singular vector growth
should be obtainable using a higher resolution model. In fact studies using a T42 resolution tangent model confirm this (Hartmann et aI, 1995;
Buizza et aI, 1996). With this resolution, a significant fraction of perturbation energy is located at subsynoptic scales at initial time, cascading
to synoptic scales at optimisation time (see also section 3.2). One practical consequence of this result is that the predictability of synoptic scale
weather may be determined more by uncertainties in the initial state on
scales much smaller than the disturbance itself, and less by uncertainties
on the scale of the disturbance. In particular, the notion that the predictability of synoptic scale weather is determined by the e-folding time of
a characteristic eigenmode is incorrect (confirming earlier results of Farrell,
1990).
As mentioned, although the structures of these baroclinic singular vectors are not modal, their geographical locations are more prevalent in regions of strong haroclinity. Fig 7a for example, shows the 'Eady index'
f du
aE = 0.31 N dz
(3.1)
based on the a winter mean static stability and wind shear (from ECMWF
data; for details see Buizza and Palmer, 1995). (Of course the functional
relationship between the wind shear, Coriolis parameter and static stability in 3.1 are not particular to the Eady model). Fig 7b shows the location
of the dominant singular vectors at initial time (based on their vorticity
maxima) from daily calculations over a whole winter. It can be seen that
the singular vectors tend to be positioned in regions of strong Eady index, over the east Asian/west Pacific region, the northeast American/west
Atlantic region, and the northern subtropical African region. The tropics
and southern hemisphere extratropics also appear in these northern winter
statistics, though to a lesser extent.
3.2 Pseudo-inverse analysis
In terms of the singular vectors, we can decompose the forward tangent
propagator Las,
L=U~V*
(3.2)
The accumulation of initial energy towards the truncation limit suggests
that a significantly more accurate estimation of singular vector growth
should be obtainable using a higher resolution model. In fact studies using a T42 resolution tangent model confirm this (Hartmann et aI, 1995;
Buizza et aI, 1996). With this resolution, a significant fraction of perturbation energy is located at subsynoptic scales at initial time, cascading
to synoptic scales at optimisation time (see also section 3.2). One practical consequence of this result is that the predictability of synoptic scale
weather may be determined more by uncertainties in the initial state on
scales much smaller than the disturbance itself, and less by uncertainties
on the scale of the disturbance. In particular, the notion that the predictability of synoptic scale weather is determined by the e-folding time of
a characteristic eigenmode is incorrect (confirming earlier results of Farrell,
1990).
As mentioned, although the structures of these baroclinic singular vectors are not modal, their geographical locations are more prevalent in regions of strong haroclinity. Fig 7a for example, shows the 'Eady index'
f du
aE = 0.31 N dz
(3.1)
based on the a winter mean static stability and wind shear (from ECMWF
data; for details see Buizza and Palmer, 1995). (Of course the functional
relationship between the wind shear, Coriolis parameter and static stability in 3.1 are not particular to the Eady model). Fig 7b shows the location
of the dominant singular vectors at initial time (based on their vorticity
maxima) from daily calculations over a whole winter. It can be seen that
the singular vectors tend to be positioned in regions of strong Eady index, over the east Asian/west Pacific region, the northeast American/west
Atlantic region, and the northern subtropical African region. The tropics
and southern hemisphere extratropics also appear in these northern winter
statistics, though to a lesser extent.
3.2 Pseudo-inverse analysis
In terms of the singular vectors, we can decompose the forward tangent
propagator Las,
L=U~V*
(3.2)