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Gregory S. Duane
and
Joseph J. Tribbia
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Gregory S. Duane
and
Mao-Lin Shen

Abstract

“Supermodeling” climate by allowing different models to assimilate data from one another in run time has been shown to give results superior to those of any one model and superior to any weighted average of model outputs. The only free parameters, connection strengths between corresponding variables in each pair of models, are determined using some form of machine learning. It is demonstrated that supermodeling succeeds because near critical states, inter-scale interactions are important but unresolved processes cannot be effectively represented diagnostically in any single parameterization scheme. In two examples, a pair of toy quasigeostrophic (QG) channel models of the mid-latidtudes and a pair of ECHAM5 models of the Tropical Pacific atmosphere with a common ocean, supermodels dynamically combine parameterization schemes so as to capture criticality, associated critical structures, and the supporting scale interactions. The QG supermodeling scheme extends a previous configuration in which two such models synchronize with inter-model connections only between medium-scale components of the flow; here the connections are trained against a third “real” model. Intermittent blocking patterns characterize the critical behavior thus obtained, even where such patterns are missing in the constituent models. In the ECHAM-based climate supermodel, the corresponding critical structure is the single ITCZ pattern, a pattern that occurs in neither of the constituent models. For supermodels of both types, power spectra indicate enhanced inter-scale interactions in frequency or energy ranges of physical interest, in agreement with observed data, and supporting a generalized form of the self-organized criticality hypothesis.

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Gregory S. Duane
and
Joseph J. Tribbia

Abstract

The relationship between blocking events in the Atlantic and Pacific sectors of the Northern Hemisphere midlatitudes is investigated in a Vautard–Legras two-layer quasigeostrophic channel model with two sectors, each sector forced by a separate baroclinic jet. It is found that the exchange of medium-scale eddies tends to cause anticorrelation between blocking events in the two sectors, while the large-scale flow components tend to cause positive correlation. The net correlation in blocking is more positive when the jets are skewed latitudinally, a result that is confirmed in the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis data and separately in a long run of a global circulation model (GCM).

The anticorrelating effect of the eddy exchange follows from the tendency of two distinct, coextensive, chaotically vacillating channel flows to synchronize when their corresponding medium-scale eddy components are coupled (a physically unrealizable configuration), regardless of differences in initial conditions. In the Vautard–Legras model, blocking in one sector weakly inhibits blocking in the opposite sector. Generalized synchronization between two channels with forcing in different sectors implies that the two inhibition effects combine coherently, giving anticorrelation in blocking activity. The anticorrelation effect is small because of the physical distance between the sectors and the resulting long advective time scales. That the smallest-scale eddies need not be coupled to affect synchronization would follow from the existence of an inertial manifold that slaves the smallest scales to the larger scales in each channel. The paradigm of low-order chaos synchronization may be relevant to climate dynamics in a variety of situations where such inertial manifolds exist.

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Gregory S. Duane
,
Peter J. Webster
, and
Jeffrey B. Weiss

Abstract

Teleconnections between the midlatitudes of the Northern and Southern Hemispheres are diagnosed in National Centers for Environmental Prediction–National Center for Atmospheric Research reanalysis data and separately in European Centre for Medium-Range Weather Forecasts reanalysis data. The teleconnections are manifested as a small but significant tendency for blocking to occur simultaneously in the two hemispheres, though at different longitudes and different relative latitudes, during boreal winters over the period 1979–94 in both datasets.

One way to explain the correlations between blocking events is as an instance of synchronized chaos, the tendency of some coupled chaotic systems to synchronize, permanently or intermittently, regardless of initial conditions. As the coupling is weakened, the systems no longer synchronize completely, but small correlations between the states of the coupled systems are observed instead. In previous work, such behavior was observed in an idealized coupled-hemisphere model constructed from a midlatitude model due to de Swart, which extended the earlier Charney–DeVore spectral truncation of the barotropic vorticity equation by including a few extra modes. The direct coupling of the two midlatitude systems in the coupled-hemisphere model represented the exchange of Rossby waves through the upper-tropospheric “westerly ducts” in the Tropics.

Significant correlations are found between blocking events, which are chaotically timed in each hemisphere considered singly, even without several of the idealizations used in the previous study. In a model modified to include an extended tropical region, the correlations are little affected by attenuation and phase shift of the Rossby waves that couple the two midlatitude systems. Variations in the relative longitudes of topographic features in the two hemispheres leave significant correlations or anticorrelations. The annual cycle, which imposes directionality on the coupling, since the Northern Hemisphere is more strongly forced than the Southern Hemisphere at the times when the hemispheres are coupled, increases the correlations slightly. A two-hemisphere model constructed from a higher-order (wavenumber 3) truncation of the barotropic vorticity equation exhibits regime transitions between blocked and zonal flow at a more realistic rate in each hemisphere but still exhibits interhemispheric correlations.

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Brad E. Beechler
,
Jeffrey B. Weiss
,
Gregory S. Duane
, and
Joseph Tribbia

Abstract

Because of position errors traditional methods of data assimilation can broaden and weaken jets or other flow structures leading to reduced forecast skill. Here a technique to assimilate properties of coherent structures is developed and tested. Focusing on jets, the technique identifies jets in both the modeled and observed fields and warps the model grid so that the jet positions are better aligned prior to further assimilation of observations. The technique is tested using optimal interpolation on the flow in a two-layer quasigeostrophic channel. The results show that a simple and fast jet position correction algorithm can significantly improve the skill of a 12-h forecast. Furthermore, the results indicate that this method of position correction maintains its utility when observations become sparse.

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Shu-Chih Yang
,
Debra Baker
,
Hong Li
,
Katy Cordes
,
Morgan Huff
,
Geetika Nagpal
,
Ena Okereke
,
Josue Villafañe
,
Eugenia Kalnay
, and
Gregory S. Duane

Abstract

The potential use of chaos synchronization techniques in data assimilation for numerical weather prediction models is explored by coupling a Lorenz three-variable system that represents “truth” to another that represents “the model.” By adding realistic “noise” to observations of the master system, an optimal value of the coupling strength was clearly identifiable. Coupling only the y variable yielded the best results for a wide range of higher coupling strengths. Coupling along dynamically chosen directions identified by either singular or bred vectors could improve upon simpler chaos synchronization schemes. Generalized synchronization (with the parameter r of the slave system different from that of the master) could be easily achieved, as indicated by the synchronization of two identical slave systems coupled to the same master, but the slaves only provided partial information about regime changes in the master. A comparison with a standard data assimilation technique, three-dimensional variational analysis (3DVAR), demonstrated that this scheme is slightly more effective in producing an accurate analysis than the simpler synchronization scheme. Higher growth rates of bred vectors from both the master and the slave anticipated the location and size of error spikes in both 3DVAR and synchronization. With less frequent observations, synchronization using time-interpolated observational increments was competitive with 3DVAR. Adaptive synchronization, with a coupling parameter proportional to the bred vector growth rate, was successful in reducing episodes of large error growth. These results suggest that a hybrid chaos synchronization–data assimilation approach may provide an avenue to improve and extend the period for accurate weather prediction.

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