Principal Interaction Patterns in Baroclinic Wave Life Cycles

Achatz, Ulrich; Schmitz, Guy; Greisiger, K. M.

doi:10.1175/1520-0469(1995)052<3201:pipibw>2.0.co;2

Cited by 26 publications

(16 citation statements)

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“…Among numerous examples an interesting work is that of Schnur et al (1993), where POPs have been identified in atmospheric data resembling baroclinic waves in their respective growth and decay phases. First successful nonlinear PIP analyses of atmospheric models have been performed by Achatz et al (1995) and Kwasniok (1996). A further development of the technique using adjoint methods has recently been published by Kwasniok (1997).…”

Section: Introductionmentioning

confidence: 99%

On the Closure Problem in the Reduction of Complex Atmospheric Models by PIPs and EOFs: A Comparison for the Case of a Two-Layer Model with Zonally Symmetric Forcing

Achatz¹,

Schmitz²

1997

J. Atmos. Sci.

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The reduction of complex systems to their essential degrees of freedom (e.g., patterns spanning that part of state space that the system's trajectory passes in time) and development of reduced models based on these might be one tool for improving basic understanding of simulation results obtained from current, increasingly more complex, meteorological circulation models. Some successful work on the reduction of complex systems by principal interaction patterns (PIPs) or empirical orthogonal functions (EOFs) has already been done. However, the parameterization of the influence of unresolved modes onto the selected patterns, called closure in this context, is still an outstanding problem. Nonlinear closure schemes, although greatly improving prediction on shorter timescales, have so far been observed to lead to absolute instability of the reduced model, that is, explosive unbounded energy growth after some integration time. In this work a method is outlined for circumventing this problem. Energy conservation constraints are formulated that can be used in the extraction of a useful empirical closure from synthetic model data by minimizing the error between tendencies in the full and the reduced model with the closure parameters as variables. In the present context the computational size of the associated minimization calculations could be reduced by utilizing the zonal symmetry in the full model's forcing and boundary conditions. So it could be shown that each EOF or PIP must be an element of the subspace of a single zonal wavenumber. Coupling conditions for the closure coefficients are derived that further decrease the dimensionality of the problem. The method is tested by reducing multiple baroclinic wave life cycles in a quasigeostrophic two-layer model on the basis of both EOFs and PIPs. It is shown that the aforementioned stability problems connected with the nonlinearity of a closure are indeed avoided by the method. Furthermore, the closure greatly improves the simulation capabilities of the reduced model both on short and long timescales. In contrast to previous results on linear closure schemes, the authors find that in nonlinear closure schemes also the linear terms have to be handled carefully in order to ensure realistic behavior of the reduced model on longer timescales. In a comparison between reductions based on EOFs and PIPs substantial superiority of the latter in effectively extracting the essential degrees of freedom is demonstrated.

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Section: Introductionmentioning

confidence: 99%

On the Closure Problem in the Reduction of Complex Atmospheric Models by PIPs and EOFs: A Comparison for the Case of a Two-Layer Model with Zonally Symmetric Forcing

Achatz¹,

Schmitz²

1997

J. Atmos. Sci.

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“…This concept is general and difficult to implement. Examples are provided by Achatz et al (1995), Achatz and Schmitz (1997), Kwasniok (1996) and Selten (1995). An important aspect of this approach is that it provides a means for estimating (an upper limit of) the number of degrees of freedom of the dynamical phenomenon and to characterize the system's attractor (in the sense of a manifold within which the system may be considered approximately closed) by specifying suitable coordinates.…”

Section: Constructing Knowledge About the Dynamics Of Climatementioning

confidence: 99%

On the role of statistics in climate research

Zwiers¹,

Storch²

2004

Intl Journal of Climatology

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We review the role of statistical analysis in the climate sciences. Special emphasis is given to attempts to construct dynamical knowledge from limited observational evidence, and to the ongoing task of drawing detailed and reliable information on the state, and change, of climate that is needed, for example, for short-term and seasonal forecasting. We conclude with recommendations of how to improve the practice of statistical analysis in the climate sciences by drawing more efficiently on relevant developments in statistical mathematics.

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“…Realistic models in the atmospheric sciences are quite complex systems of nonlinear equations and this complexity has slowed the implementation of PIPs. However, Achatz et al (1995) have used PIPs in the examination of baroclinic wave life cycles. To the best of my knowledge, no one has tried a completely empirical approach t o PIPs in which they let the data define the structure of the F(-) function.…”

Section: Application Of Pipsmentioning

confidence: 99%

Spatio-temporal statistical models with applications to atmospheric processes

Wikle

1996

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Principal Interaction Patterns in Baroclinic Wave Life Cycles

Cited by 26 publications

References 0 publications

On the Closure Problem in the Reduction of Complex Atmospheric Models by PIPs and EOFs: A Comparison for the Case of a Two-Layer Model with Zonally Symmetric Forcing

On the Closure Problem in the Reduction of Complex Atmospheric Models by PIPs and EOFs: A Comparison for the Case of a Two-Layer Model with Zonally Symmetric Forcing

On the role of statistics in climate research

Spatio-temporal statistical models with applications to atmospheric processes

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