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3.6 Singular vectors from a coupled tropical ocean-atmosphere
model
ENSO appears to be predictable up to a year or so in advance using relatively simple coupled models of the atmosphere and ocean (Zebiak and
Cane, 1987). According to Miinnich et al (1991), long-term variability of
ENSO is intrinsically chaotic (independent of the chaotic nature of weather
itself). The skill of ENSO forecasts made with coupled ocean-atmosphere
models is seasonally dependent (Cane et al, 1986; Webster, 1995). Typically, seasonal forecasts beginning in spring tend to be less skilful than
forecasts beginning, for example, in autumn. This is sometimes referred to
as the 'spring barrier' effect.
Blumenthal (1991) has analysed the behaviour of the eigenfunctions
of a linear Markov model approximation to a nonlinear coupled oceanatmosphere model. He fipds that in summer, the eigenfunction best describing ENSO has larger eigenvalues than at other times of year. In spring
this ENSO eigenfunction is least orthogonal to other modes, ie is associated with large projectibility (see section 2). Both types of error growth
(modal and non-modal) are implicit in singular vector analysis which has
been performed on this Markov model by Xue et al (1994).
We show some results of a singular vector analysis applied to the coupled ocean- atmosphere model of Battisti (1988). Preliminary results were
described by Palmer et al (1994), more extensive results are given in Chen
et al (1996). A similar study has been performed independently by Moore
and Kleeman (1996). The ocean component of the model used here is a
single vertical mode tropical Pacific basin anomaly model, governed by linear shallow water wave dynamics. The nonlinear thermodynamics are only
active in a surface mixed layer. The atmospheric component is a thermally
-forced steady linear model with single vertical mode (Gill, 1980). Air-sea
interactions are nonlinear: given by surface wind stress, heat flux, and sea
surface temperature, SST. The number of independent degrees of freedom
in the coupled model is reduced to 420 by considering only the equatorial
oceanic Kelvin mode, and first 3 symmetric Rossby modes. With such a
reduction, singular vectors can be computed using conventional matrix algorithms. For these calculations, the inner product is based on the spatial
variance of the SST anomaly.
The first results have been made using a climatological basic state flow.
Perturbation growth is strongly dependent on the annual cycle in the Pa-
3.6 Singular vectors from a coupled tropical ocean-atmosphere
model
ENSO appears to be predictable up to a year or so in advance using relatively simple coupled models of the atmosphere and ocean (Zebiak and
Cane, 1987). According to Miinnich et al (1991), long-term variability of
ENSO is intrinsically chaotic (independent of the chaotic nature of weather
itself). The skill of ENSO forecasts made with coupled ocean-atmosphere
models is seasonally dependent (Cane et al, 1986; Webster, 1995). Typically, seasonal forecasts beginning in spring tend to be less skilful than
forecasts beginning, for example, in autumn. This is sometimes referred to
as the 'spring barrier' effect.
Blumenthal (1991) has analysed the behaviour of the eigenfunctions
of a linear Markov model approximation to a nonlinear coupled oceanatmosphere model. He fipds that in summer, the eigenfunction best describing ENSO has larger eigenvalues than at other times of year. In spring
this ENSO eigenfunction is least orthogonal to other modes, ie is associated with large projectibility (see section 2). Both types of error growth
(modal and non-modal) are implicit in singular vector analysis which has
been performed on this Markov model by Xue et al (1994).
We show some results of a singular vector analysis applied to the coupled ocean- atmosphere model of Battisti (1988). Preliminary results were
described by Palmer et al (1994), more extensive results are given in Chen
et al (1996). A similar study has been performed independently by Moore
and Kleeman (1996). The ocean component of the model used here is a
single vertical mode tropical Pacific basin anomaly model, governed by linear shallow water wave dynamics. The nonlinear thermodynamics are only
active in a surface mixed layer. The atmospheric component is a thermally
-forced steady linear model with single vertical mode (Gill, 1980). Air-sea
interactions are nonlinear: given by surface wind stress, heat flux, and sea
surface temperature, SST. The number of independent degrees of freedom
in the coupled model is reduced to 420 by considering only the equatorial
oceanic Kelvin mode, and first 3 symmetric Rossby modes. With such a
reduction, singular vectors can be computed using conventional matrix algorithms. For these calculations, the inner product is based on the spatial
variance of the SST anomaly.
The first results have been made using a climatological basic state flow.
Perturbation growth is strongly dependent on the annual cycle in the Pa-