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model) is therefore related to perfect predictability'. Sarachik then notes
that ' .. This paradigm of EN SO predictability is radically different from our
classical concepts of mid-latitude predictability'. However, Sarachik does
not explain why there should be two paradigms: one for the tropics, the
other for the extratropics. A possible explanation could be given in terms of
the modality of the associated singular vectors. In contrast with tropical
singular vectors, the extratropical singular vectors are profoundly nonmodal and perturbation growth is therefore susceptible to the 'butterfly
effect' (cf above). As discussed above, this non-modality and associated
upscale cascade can cause extratropical weather forecasts to fail before the
timescale set by any characteristic e-folding rate.
3.4 Singular vectors for ensemble forecasting
Singular vectors are used as the basis of initial perturbations for mediumrange ensemble forecasting. The basic rationale for this is that we cannot
sample explicitly, analysis uncertainties in all the phase space directions,
the dimension of a numerical weather prediction model (at least 0(10 6 )) is
too large. Hence we sample explicitly directions in which analysis error is
likely to occur and can lead to significant departures from the unperturbed
forecast. In the linear regime these are given by the dominant singular
vector directions. Hartmann et al (1995) have shown that up to about
day 7, perturbations using singular vectors have significantly larger spread
than unstable synoptic-scale perturbations. This would suggest that the
'weakly nonlinear' timescale (cf section 2.1) lasts until about day 7.
Other directions (for example associated with decaying perturbations)
can in principle be taken implicitly into account in an ensemble forecast
by giving the unperturbed forecast a higher than average a priori weight
compared with other members of the ensemble.
Fig 10 shows two examples of ensemble forecasts made from initial conditions one week apart. The thin lines show the spread of the members of
the ensemble forecast relative to the unperturbed control forecast (using a
correlation measure of spread). The thick line shows the skill of the control
forecast (using a correlation measure of skill). The examples illustrate the
desirable occurrence of low spread indicating high skill, and high spread
indicating relatively poor skill.
Obviously one cannot make any definitive conclusions based on just two
results. The interested reader is directed to a more complete description
and validation of the ECMWF ensemble prediction system in Molteni et
al (1996).
model) is therefore related to perfect predictability'. Sarachik then notes
that ' .. This paradigm of EN SO predictability is radically different from our
classical concepts of mid-latitude predictability'. However, Sarachik does
not explain why there should be two paradigms: one for the tropics, the
other for the extratropics. A possible explanation could be given in terms of
the modality of the associated singular vectors. In contrast with tropical
singular vectors, the extratropical singular vectors are profoundly nonmodal and perturbation growth is therefore susceptible to the 'butterfly
effect' (cf above). As discussed above, this non-modality and associated
upscale cascade can cause extratropical weather forecasts to fail before the
timescale set by any characteristic e-folding rate.
3.4 Singular vectors for ensemble forecasting
Singular vectors are used as the basis of initial perturbations for mediumrange ensemble forecasting. The basic rationale for this is that we cannot
sample explicitly, analysis uncertainties in all the phase space directions,
the dimension of a numerical weather prediction model (at least 0(10 6 )) is
too large. Hence we sample explicitly directions in which analysis error is
likely to occur and can lead to significant departures from the unperturbed
forecast. In the linear regime these are given by the dominant singular
vector directions. Hartmann et al (1995) have shown that up to about
day 7, perturbations using singular vectors have significantly larger spread
than unstable synoptic-scale perturbations. This would suggest that the
'weakly nonlinear' timescale (cf section 2.1) lasts until about day 7.
Other directions (for example associated with decaying perturbations)
can in principle be taken implicitly into account in an ensemble forecast
by giving the unperturbed forecast a higher than average a priori weight
compared with other members of the ensemble.
Fig 10 shows two examples of ensemble forecasts made from initial conditions one week apart. The thin lines show the spread of the members of
the ensemble forecast relative to the unperturbed control forecast (using a
correlation measure of spread). The thick line shows the skill of the control
forecast (using a correlation measure of skill). The examples illustrate the
desirable occurrence of low spread indicating high skill, and high spread
indicating relatively poor skill.
Obviously one cannot make any definitive conclusions based on just two
results. The interested reader is directed to a more complete description
and validation of the ECMWF ensemble prediction system in Molteni et
al (1996).