109
Some examples of this pseudo-inverse field are shown in Buizza et al (1996)
based on a 30 singular vector truncation, and a 36-hour forecast error. By
adding this estimate to the initial analysis, a much superior forecast can be
obtained, not only at 36 hours, but throughout the entire medium-range.
It should be noted that the pseudo-inverse component of initial error may
be small compared with the total error. Indeed, associated with the noninvertibility of the full operator L, the forecast error will be insensitive to
estimates of initial error in strongly decaying directions.
This technique is closely related (but not identical) to the sensitivity
analysis technique (see section 3.5) in which the forecast error is integrated
(backwards) using the adjoint model itself (see Rabier et al, 1996; Buizza
et al, 1996).
3.3 Comparison of tropical and extratropical singular vector
growth: a paradigm for tropical predictability.
It is clear from numerous studies that the large-scale tropical circulations
are much more strongly coupled to the underlying SST than are largescale extratropical circulations. As such, the prospects for extended-range
prediction in the tropics are greater than for the extratropics. Charney and
Shukla (1981) were one of the first to rationalise this disparity in behaviour
between the tropics and extratropics. These authors argued that, from a
dynamical point of view, the principal relevant difference between the largescale tropical and extratropical flows lay in their instability properties.
The absence of generic large-scale exponentially growing eigenmodes in
the tropics makes more reproducible the effects of slowly-varying lower
boundary conditions associated, for example, with SST anomalies.
Whilst these considerations are clearly important and relevant, they
cannot be considered complete. For example, the tropical flow is convectively unstable, and these in turn contribute to the growth of synoptic-scale
disturbances, eg associated with tropical cyclones. However, it is known
that inevitable errors in the initial conditions for atmospheric seasonal integrations associated with tropical synoptic and subsynoptic flow, do not
infect the planetary scale circulations in the same ubiquitous way that is
found in the extratropics.
It is manifestly impossible to describe this difference in upscale energy
cascade using modal instability theory. On the other hand, as we have
seen in the last section, singular vector analysis is able to describe, within
Some examples of this pseudo-inverse field are shown in Buizza et al (1996)
based on a 30 singular vector truncation, and a 36-hour forecast error. By
adding this estimate to the initial analysis, a much superior forecast can be
obtained, not only at 36 hours, but throughout the entire medium-range.
It should be noted that the pseudo-inverse component of initial error may
be small compared with the total error. Indeed, associated with the noninvertibility of the full operator L, the forecast error will be insensitive to
estimates of initial error in strongly decaying directions.
This technique is closely related (but not identical) to the sensitivity
analysis technique (see section 3.5) in which the forecast error is integrated
(backwards) using the adjoint model itself (see Rabier et al, 1996; Buizza
et al, 1996).
3.3 Comparison of tropical and extratropical singular vector
growth: a paradigm for tropical predictability.
It is clear from numerous studies that the large-scale tropical circulations
are much more strongly coupled to the underlying SST than are largescale extratropical circulations. As such, the prospects for extended-range
prediction in the tropics are greater than for the extratropics. Charney and
Shukla (1981) were one of the first to rationalise this disparity in behaviour
between the tropics and extratropics. These authors argued that, from a
dynamical point of view, the principal relevant difference between the largescale tropical and extratropical flows lay in their instability properties.
The absence of generic large-scale exponentially growing eigenmodes in
the tropics makes more reproducible the effects of slowly-varying lower
boundary conditions associated, for example, with SST anomalies.
Whilst these considerations are clearly important and relevant, they
cannot be considered complete. For example, the tropical flow is convectively unstable, and these in turn contribute to the growth of synoptic-scale
disturbances, eg associated with tropical cyclones. However, it is known
that inevitable errors in the initial conditions for atmospheric seasonal integrations associated with tropical synoptic and subsynoptic flow, do not
infect the planetary scale circulations in the same ubiquitous way that is
found in the extratropics.
It is manifestly impossible to describe this difference in upscale energy
cascade using modal instability theory. On the other hand, as we have
seen in the last section, singular vector analysis is able to describe, within