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Climate Dynamics and Predictability

Project: Predictability and Prediction Studies of Weather and Climate Variations

The studies described below are highlights of the research in CDP devoted to the prediction and predictability of climate variations and extreme events. These studies are integral to our section goals of extending and defining the spatio-temporal domain over which scientifically and societally useful forecasts can be made. CDP scientists have continued their interest in the inherent predictability of atmospheric phenomena and have utilized their expertise gained in ensemble prediction techniques to address the prediction of extreme events.

Just as the weather and seasonal forecast communities use concepts and methodologies developed by the climate dynamics community to diagnose, interpret and further develop its prediction capabilities, there is the potential for climate change researchers to apply these same concepts and techniques to climate change scenarios. Conversely, climate change scenarios provide a fertile testing ground for ideas developed by the climate dynamics community. Branstator has continued his effort to understand how the circulation patterns of interannual variability can be modified by global change. Previously, working in collaboration with Dutch colleagues, he had found that in a 62 member ensemble of business-as-usual climate change integrations that were performed with NCAR's coupled climate model known as CCSM 1.4 the secular circulation trend induced by enhanced greenhouse gases took the form of the Circumglobal Waveguide Pattern. Recently he discovered that this change in the mean state is accompanied by a change in the structure of the states that predominate in the model's interannual variability. This change in the structure of interannual variability was quantified by considering probability density functions of the leading EOFs of interannual variability in the upper troposphere. As with many climate change experiments the shift in the mean circulation in the ensemble has the signature of a linear response, but the change in the structure of the patterns of variability has a nonlinear signature - it corresponds to a phase space shift in variance with the second leading EOF become relatively more important and the first leading EOF becoming less important. Using stochastic modeling techniques Branstator has been able to pinpoint the dynamical cause for this change in the distribution of interannual states. He found that the leading CCSM circulation EOFs correspond well to the leading patterns of the stochastically driven atmospheric governing equations linearized about the CCSM climatological mean state. As the mean climate changes so do the dominant stochastically driven states. These findings have more than theoretical interest. It turns out that in this model the midlatitude response to El Nino is largely controlled by the leading patterns of interannual variability. And as these patterns change in reaction to the trend in the mean circulation, the structure of the midlatitude response to El Nino also changes.

In traditional prediction studies, Tribbia has been developing and analyzing the ENSO predictive skill of the NCAR CCSM. Over the past year, he has produced a number of experimental hindcasts demonstrating the skill of CCSM3. This suite of hindcasts is being used as a testbed for the further development of CAM3 and CCSM3. The remediation of the errors in the climatology of the simulated interannual variability is still a high priority for CCSM. Forecast studies can point to root causes of errors in ways which elucidate processes that are hidden in long term simulations.

Project: Diagnostic and Theoretical Studies of Variability and Validation

Within CDP the purpose of diagnostic analyses is twofold, diagnosis is used to test theoretical ideas concerning the mechanisms responsible for climate variations and their relative import and also test (i.e. validate) the behavior of comprehensive climate models like the NCAR CCSM against that of the observed climate system. Naturally, prediction studies can also be viewed in this latter context. Additionally, several particularly insightful examples of past CDP studies exemplifying these two types of diagnoses are detailed below.

Theoretical ideas from other fields of physics, most often statistical physics, are occasionally beneficial in the study of climate. Working in conjunction with A. Gritsun of the Russian Academy of Science's Institute for Numerical Mathematics, Branstator has succeeded in constructing a climate response operator based on the approach suggested by the Fluctuation-Dissipation Theorem. Application of this theorem to climate science was suggested thirty years ago by Leith, but this is the first demonstration of the full power of the approach. The technique makes it possible to generate a linear operator that estimates how a system will respond to an external stimulus. From a physical point of view, the interesting point is that one does not need to know the governing equations of the system to construct the operator. Rather it is sufficient to observe the system for a long time and gather covariance and lag-covariance statistics regarding the natural fluctuations of the system. From a practical standpoint, the salient result is that when applied to output from an atmospheric general circulation model, Branstator and Gritsun found that the resulting response operator was able to very accurately estimate how the AGCM would respond to an imposed heat source. This has made it possible to answer questions concerning optimum excitation of any specified response. For example a Green's function that shows how effective a point heat source at each point on the globe is at exciting the Northern Annular Mode has been generated. Further details can be found in (GB).

Using the direct approach of testing the response to external forcing, Branstator also examined the sensitivity of the atmospheric response to tropical Pacific warm events to the exact position of the tropical heating that accompanies those events. In three different AGCMs (two produced at NCAR and one at NASA), he has found there is a bifurcation point near the dateline; the character of the midlatitude response to heating west of the dateline is very different from the response to heating situated east of the dateline. Interestingly, it is the westward positioned events that have the more global response. Ongoing research is addressing the mechanisms that produce this distinction. Experiments with linearized versions of the AGCMs indicate that simple interactions between the climatological mean waves and heating induced perturbations are a major contributor but nonlinear interactions involving the synoptic eddies may also need to be taken into account. Beyond being relevant for understanding why there is a great deal of case to case variability in the effects of El Nino and La Nina events on midlatitudes, this work also may turn out to be helpful for interpreting climate change experiments. Often in these experiments climate change is associated with a large change in precipitation rate in the tropics near the dateline.

Project: Nonlinear Dynamical and Numerical Model Development Studies

In data assimilation work funded through the NSF Collaboration between Mathematics and Geophysics (CMG) program, Greg Duane (CDP visitor), Jeff Weiss (CU) and Tribbia have been examining the relationship between synchronization and assimilation. In a a recent paper they showed that the synchronization approach is equivalent to standard approaches based on least-squares optimization, including Kalman filtering, except in highly non-linear regions of state space where observational noise links regimes with qualitatively different dynamics. In such narrow regions, the synchronization approach is expected to give an improvement to Kalman filtering that will apply in any situation where a computational model is intended to track a physical process. The synchronization approach is used to calculate covariance inflation factors from parameters describing the bimodality of a one-dimensional system. See (DTW) for more details.

In addition to advances in the dynamical, the next generation of atmospheric model dynamical cores will in all likelihood span a range of scales which will include those for which the hydrostatic approximation is questionable. This will require new understanding of global non-hydrostatic effects. In search of a more refined formulation of the dynamical models for global weather prediction and climate projection, Kasahara continues his research to understand the basic dynamics of a deep nonhydrostatic atmospheric model which is more general than the primitive-equation model for weather and climate. Specifically, he has been interested in the physics behind the traditional approximation adopted in many global circulation models including ours. The traditional approximation refers to the neglect of the dynamical terms associated with the horizontal component of the angular rotation of the earth. The elimination of this approximation, therefore, is considered to be a good candidate of improvement in atmospheric modeling. Unfortunately, this improvement in modeling requires substantial resources in funding. Therefore, it is necessary to find out whether it is worthwhile to spend additional investment.

The significance of the non-traditional effect can be judged in the following way. The atmospheric motions are classified into two classes. One is the slow or rotational mode which consists of slow timescale motions of the quasi-geostrophic character. The other is the fast or irrotational mode which consists of fast timescale motions dominated by inertio-gravity motions. The large-scale atmospheric motions are dominated by the slow mode and the contribution of the fast mode is approximately, say 10 %. The non-traditional effect does not virtually affect to the slow mode, but is concerned with the fast mode. The contribution of the non- traditional effect is roughly 20-50 % of that of the fast mode. Thus, the impact of the non-traditional effect to real weather is therefore only 2-5 %. This order of magnitude of improvement can easily be absorbed by uncertainties in physical parameterizations of forecasting models. Hence, it never be easy to detect the non-traditional effect in testing under real weather situations. Since the community is concerned with the secular effect of small increases in greenhouse gases in the atmosphere, the long- term effect of the traditional approximation may or may not be ignorable.

Tribbia has also been investigating the limitations of the hydrostatic balance approximation in a different context, that of limited area modeling. With Roger Temam (Indiana University) and Antoine Rousseau (Universit'e Paris-Sud), he has been continuing the examination of approximate equations which break the strong constraint of hydrostatic balance. The reason for their interest is the well-known deficiency of the hydrostatic primitive equations, ill-posedness as an initial-boundary value problem. The ill-posedness of the system imposes severe restrictions on the applicability of the system for limited area regional climate modeling and the use of adaptive mesh methods. In the recent work they have studied a linear differential system consisting of two coupled scalar evolution equations in one space dimension which was derived from a modal analysis of the Primitive Equations of the ocean. They have shown numerically that, by adjunction of a small viscosity, the system converges to an unusual, unexpected limit system thus producing boundary layers and reflections of waves at the boundary. They proposed an alternate set of boundary conditions of transparent type for the viscous systems and, in this case, the viscous system does not produce boundary layers nor reflections of waves at the boundary. This work is described fully in (RTT).

In a study for which the RTT research noted above should have application, Tribbia is also involved in a project that examines the efficiency ofnumerical modeling on parallel machines. The collaborative effort with Aime' Fournier (IMAGe), and Ferd Baer and Houjun Wang (UMd), has developed a spectral element based, locally refined resolution version of CAM. The work is described in (BWTF).

References

Gritsun, A. and G. Branstator, 2006: Climate Response Using a Three-Dimensional Operator Based on the Fluctuation-Dissipation Theorem. accepted J. Atmos. Sci.

Rousseau, A., R. Temam, and J. Tribbia, 2005: Boundary conditions for the 2D linearized PEs of the ocean in the absence of viscosity. Discrete and Continuous Dynamical Systems - Series A, Volume 13, 5, 1257--1276.

Baer, F., H. Wang, J.J. Tribbia, and A. Fournier, 2006: Climate Modeling with Spectral Elements, accepted Mon. Wea. Rev.

Duane, G.S., J.J. Tribbia, and J.B. Weiss, 2006: Synchronicity in Predictive Modelling: A New View of Data Assimilation. To appear Nonlin. Processes in Geophys.