# AMIP II Diagnostic Subproject No. 29:

Diagnosis of Nonlinear Circulation Regimes

**Project coordinators:**

**A. Hannachi**

^{ 1}**F. Molteni**

^{2}**T.N.Palmer**

^{3}^{1}University of Oxford
^{2}CINECA
^{3}European Centre for Medium-Range Weather Forecasts

**Contents:**

Background

Objectives

Methodology

Data Requirements

References

Background

Many of the techniques used to diagnose climatic variability (empirical orthogonal functions, teleconnections, regression analysis, singular value decomposition etc.) are formulated using methods taken from linear analysis. Whilst these techniques can be legitimately applied to the nonlinear climate system, by virtue of their linear formulation, it is difficult to use them to analyze the nonlinear structure of the climate attractor.

There are indications that it may be important to understand the nonlinear structure of the climate attractor in order to understand recent climate change. For example, there is evidence that changes in northern-hemisphere climate in recent decades can be explained in terms of changes in the frequency of occurrence of preferred nonlinear naturally-occurring atmospheric circulation regimes (Palmer, 1998; Corti et al., 1998).

If this is so, then it is essential that global climate models (GCMs) be able to simulate accurately the observed atmospheric circulation regimes, even though the dominant intraseasonal timescale of regime fluctuations is much shorter than the decadal timescale of the climate change signal itself. More generally, GCMs should be able to simulate the non-gaussian structure of the climate attractor. As yet, only a few tests have been performed on GCMs to assess this component of their behavior (e.g. Molteni and Tibaldi, 1990; Haines and Hannachi, 1995; Hannachi, 1997, Tett et al., 1997).

In this proposal we introduce a diagnostic package which we hope will become a standard tool for the assessment of circulation regimes and associated nonlinear structure, both from GCM simulations, and from (re)analysis datasets. We propose to apply this package to the set of AMIP-II integrations.

The objectives of the intended research is to investigate:

a) Whether the climate attractors (expressed as probability density functions -PDFs) of global circulation models have statistically significant non-gaussian structure, and well defined circulation regimes in particular. Attention will be focussed on the northern hemisphere winter circulation. The regime analyses will be performed over the whole hemisphere, and over the Atlantic and Pacific sectors. The vertical (and hence thermal) structure of the PDF maxima will also be estimated. Analyses from different models, and with reanalysis data will be compared

b) The extent to which time-mean differences between models can be explained in terms of the difference in PDFs associated with dominant regimes will be explored.

c) The existence of intermittent synchronization between regimes in the Atlantic and Pacific will be explored. The existence of such intermittent synchronization may help explain why there appear to be coherent regimes on the hemispheric scale.

d) To study the differences between regimes defined by quasi-stationarity
on the one hand, and defined by PDF maxima on the other.

Two different techniques are proposed to study nonlinear low frequency variability (LFV) from both the AMIP-II and from re-analyses.

The first (dynamical) method is based on minimizing the streamfunction tendency using for example the barotropic vorticity equation (Haines and Hannachi, 1995) within the phase space spanned by the dominant low frequency Empirical Orthogonal Functions (EOFs) of the GCMs. It is believed that this technique ought to be more realistic and computationally cheaper compared to other approaches (Branstator and Opseegh, 1989, and Anderson, 1992), since there are fewer degrees of freedom involved and also because the whole of the chosen phase space, defined by the retained EOFs, can be explored. Therefore, the method converges towards a few realistic minima within the model attractor in contrast to the previously mentioned approaches which always seek a single fixed point state close to some given observed flow. We also propose at a later stage to diagnose three-dimensional (3D) flow regimes by extending the previous technique to include the vertical structure of the model variability as in Hannachi (1997). This is of particular interest if we want to relate the vertical structure of the regimes to satellite radiance observations (Christy and McNider, 1994, Hurrel and Trenberth, 1996, and Corti et al. 1998).

Local and also global analyses will be performed. Specifically, we propose to perform analyses over the North Atlantic and North Pacific sectors as well as over the whole northern hemisphere. This will enable us in particular to link local regimes to `planetary' regimes and to study the `intermittent' synchronisation mentioned earlier.

Next, the model attractors will be investigated to assess how well models do represent the non-Gaussian behaviour. Each GCM model trajectory obtained as (filtered) timeseries of the principal components (PCs) of the retained (LFV) EOFs will be analysed using a mixture analysis (Haines and Hannachi, 1995, Hannachi, 1997) in which the probability distribution of the data is expressed as a weighted sum (mixture) of Gaussians. Each Gaussian represents the probability distribution of one regime identified by its centre and its covariance matrix. The mixture model (Everitt and Hand, 1981) is very convenient for regime studies and clusters identification (Wolfe, 1970), especially given the existence of efficient iterative approaches such as the expectation-maximization algorithm (Dempster et al., 1977). This analysis will also enable us to test whether the model attractor supports non-Gaussian behaviour.

As before, the analysis will be performed locally over the North Atlantic and North Pacific sectors and also over the whole northern hemisphere. Extension to the 3D analyses will be performed at a later stage. Once the regimes and their probability distributions are identified then we will be able to do a composite analysis to analyse for the temperature field pattern corresponding to each regime flow.

We will require in the first instance the timeseries of the NDJFM daily winter time geopotential height fields at 500 mb. At a later stage we will require geopotential and temperature fields at a number of levels in the upper and lower troposphere.

**Anderson, J.L.,**1992: Barotropic stationary states and persistent anomalies in the atmosphere.

*J. Atmos. Sci*.,

**49**, 1709-1722.

**Branstator, G.**and J.D. Opsteegh, 1989: Free solutions of the barotropic vorticity equation.

*J. Atmos. Sci.*,

**46**, 1799-1814.

**Corti, S.,** F. Molteni, and T. N. Palmer, 1998: Signature of climate
change in atmospheric circulation regime frequencies. *Nature*. Submitted.

**Christy, J.R.,** and R.T. McNider, 1994: Satellite greenhouse warming.
*Nature*, **378**, 145-149.

**Dempster, A.P.,** N.M. Laird, and D.B. Rubin, 1977: Maximum likelihood
from incomplete data via the EM algorithm . *J. Roy. Stat. Soc.
B*, **39**, 1-38 (1977).

**Everitt, B.S.,** and D.J. Hand, 1981: *Finite Mixture Distributions*.
Chapmann and Hall, London.

**Haines, K.** and A. Hannachi, 1995: Weather regimes in the Pacific
from a GCM. *J. Atmos. Sci.*, **52**, 2444-2462.

**Hannachi, A.,** 1997: Low-frequency variability in a GCM: three-dimensional
flow regimes and their dynamics. *J. Climate*, **10**, 1357-1379.

**Hurrel, J.W.,** and K.E. Trenberth, 1996: Satellite versus surface
estimates of air temperature since 1979. *J. Climate*, **9**, 2222-2232.

**Molteni, F.** and S. Tibaldi, 1990: Regimes in the wintertime circulation
over northern extratropics. II: Consequences for dynamical predictability.
*Quart.
J. Roy. Meteor. Soc.*, **116**, 1263-1288.

**Palmer, T. N.,** 1998: A nonlinear dynamical perspective on climate
prediction. *J. Climate*. In Press.

**Tett, S. F. B.**, T. C. Johns, and J. Mitchell, 1997: Global and
regional variability in a coupled AOGCM. *Climate Dynamics*,
**13**, 303-323.

**Wolfe, J.H.,** 1970: Pattern clustering by multivariate mixture
analysis. *Multiv. Behav. Res.,* **5**, 329-50 (1970).

For further information, contact the AMIP Project Office (amip@pcmdi.llnl.gov).

June 14, 1999